CIRIA 123 Soil Reinforcement Using Geosynthetics
Short Description
CIRIA guidance report for the use of Geosynthetics in the design of reinforced earth...
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This document
1
j contains3 page1)
1996
Soil reinforcement with geotextiles R.A. Jewell MA PhD CEng
CONSTRUCTION INDUSTRY RESEARCH AND INFORMATION ASSOCIATION 6 Storey's Gate London SW1PSAU
Email switchboard©ciria.org.uk Tel: (0171) 222 8891
Fax: (0171) 222 1708
A
CIRIA and the author are grateful for the help given to this projectby the funders, by the members of the Steering Group, and by the many individuals who were consulted. The author particularly acknowledges the encouragement he received from the late Professor Peter Wroth and the helpful criticism on the technical content ofparticular chapters from Dr M.D. Bolton, Mr D.I. Bush, Dr JP. Giroud, Dr J.H. Greenwood, Professor C.J.F.P. Jones, Professor A. McGown, Dr G.W.E. Milligan and Dr R.T. Murray. Soil reinforcement with geotextiles Construction IndustryResearch and Information Association CIRIA Special Publication 123, 1996
Keywords Geotextiles, soil reinforcement.
Reader Interest Geotechnical and structural engineers, local authorities, public utility engineers. All rights reserved. No partof this publication may be reproduced or transmitted in any form or by any means, including photocopying and recording, without the written permission of the copyright holder, application for which should be addressed to the publisher. Such written permission must also be obtained before any part of this publication is stored in a retrieval system of any nature.
CLASSIFICATION AVAILABILITY
Unrestricted
CONTENT
Subject area review
STATUS
Committee guided
USER
Structural and
© CIRIA 1996 ISBN 0860174255 Thomas Telford ISBN 0 7277 2502 5
geotechnical engineers
Published by CIRIA, 6 Storey's Gate, Westminster, London SW1P 3AU and Thomas Telford
Foreword This reportpresentsthe results ofa research projectcarried out for CIRIA by Dr R A Jewell, initially ofthe University ofOxford and latterly with GeoSyntee Consultants ofBrussels. Following CIRIA's usual practice, the research was guided by a steering group which comprised:
Mr N A Trenter (Chairman) Mr R G V Green
Sir William Halcrow and Partners MRM Partnership (now Rust Consulting
Dr J H Greenwood Lt Col L J Kennedy
ERA Technology Limited
Limited)
RARDE (Christchurch) and later ofRMCS Slirivenham
Professor A McGown Thelate Mr E B MacKay
Mr G R A Watts
University of Strathclyde Tarmac Construction Limited Transport Research Laboratory
CJRIA's research manager for this project was Mr F M Jardine. CIRIA gratefully acknowledgesthese organisations who provided finding for the project: Department ofthe Environment Ministry ofDefence Scottish DevelopmentAgency Transport Research Laboratory BSP Limited Don and Low Limited Du Pont de Nernours SA Godfreys of Dundee Limited IC! Fibres Geotextile Group MMG Civil EngineeringSystems Netlon Limited RhonePoulene(UK) Limited
Coverpie/uiccourtesyof? Civil Engineering Division, Netton Limited
Contents List of Tables List of Figures 1
Engineering with geotextiles 1.1 What are geotextiles? 1.2 Concepts for geotextile applications 1.3 Examples of the use of geotextiles 1.4 Construction with geotextiles 1.5 Geotextile capabilities 1.6 Geotextiles as separators 1.7 Geotextiles as soil reinforcement 1.8 Geotextile compared with other solutions 1.9 Synopsis of Chapter 1
2 Polymer and geotextile properties 2.1 Polymer types 2.2 Polymer properties 2.2.1 Index properties 2.2.2 Creep properties 2.3 Strength and stiffness of geotextiles 2.3.1 Strength properties 2.3.2 Stiffness properties 2.3.3 Extrapolation for longterm properties 2.3.4 Aged life of geotextiles 2.4 Measurement of reference properties 2.5 Damage and durability of geotextiles 2.5.1 Mechanical damage 2.5.2 Chemical and biological durability 2.5.3 Material properties in the ground 2.6 Synopsis of Chapter 2
3 Geotextile products 3.1 Woven geotextiles 3.2 Geogrids 3.2.1 Geogridlike products 3.2.2 Geomeshes Special Publication123 © CIRIA
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22 23 25 25
26 29 29 31 33 35 36 36
Contents
3.3
Other geotextile products 3.3.! Nonwoven geotextiles
3.3.2 Knitted geotextiles 3.3.3 Sheathed materials 3.4 Comparing reinforcement materials 3.4.1 Example cases 3.4.2 Data on specific strength and stiffness 3.4.3 Properties for woven geotextiles 3.4.4 Properties for geogrid reinforcement
37 37 38 38 38 39 39
40 41
3.5 Synopsis of Chapter 3
42
4 Reinforced soil behaviour
43 43 45 46 48 50 50 54
4.!
How reinforcement strengthens soil
Reinforcement orientation and stiffness Strain compatibility Interaction between soil and reinforcement Coefficient of direct sliding 4.6 Coefficient of bond 4.7 Example interaction coefficients 4.7.! Wovengeotextile 4.7.2 Geogrid 4.8 Synopsis of Chapter 4
4.2 4.3 4.4 4.5
54 55 56
5 Soil strength and bearing capacity 5.! Angles of friction 5.1.! Peak shearing resistance
59
5.2 Strength of compact soils 5.2.1 Basic concepts 5.2.2 Granular soils 5.2.3 Testing granular soils
61 61 63
5.2.4 Compact clay soils 5.2.5 Testing clay soils 5.3 Soft clay foundations
71
5.3.1 Consolidation history 5.3.2 Lower limit to undrained shear strength 5.3.3 Expected undrained shear strength 5.3.4 Testing soft clay foundations 5.4 Drained bearing capacity 5.4.1 Influence of inclined loading 5.4.2 Allowable bearing pressure
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Contents
5.5 Undrained bearing capacity
82 83 83
6 Design values and safety margins
87 87 87 88 88
5.5.1 Influence of inclined loading 5.6 Synopsis of Chapter 5
6.1 Basis of calculations 6.1.1 Design situations 6.1.2 Design values of parameters 6.1.3 Required and available forces 6.2 Loadings 6.2.1 Selfweight loading 6.2.2 Surcharge loading 6.2.3 Waterpressures 6.3 Soil properties 6.3.1 Representative values of soil strength 6.3.2 Design values of soil strength 6.3.3 Drained analysis 6.3.4 Undrained analysis 6.4 Reinforcement properties 6.4.1 Reinforcement properties for serviceability 6.5 Interaction properties 6.6 Summary of design values 6.7 Synopsis of Chapter 6
7 Limit states 7.1 Design equilibrium 7.2 Ultimate limit states: design situations 7.2.1 Internal and overall equilibrium 7.2.2 External equilibrium 7.2.3 Construction over soft soil 7.3 Serviceability limit states 7.3.1 Bounds to likely deflection 7.4 Synopsis of Chapter 7
8 Steep reinforced slopes 8.1 Internal equilibrium: idealised case
8.1.1 Idealised equilibrium 8.1.2 Analysis for required stress 8.1.3 Limit equilibrium analysis 8.2 Overall equilibrium Special Publication123 © CIRIA
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89 90 90 90 90 91 91 93
94 94 94 97 97
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99 100 100 101 101 103
105 105 107 108 109 110
Ill
Contents
8.2.1 Allowance for bond
8.2.2 Allowance for loadshedding 8.3 Internal equilibrium: practical corrections 8.3.1 Allowance for bond 8.3.2 Allowance for compaction stresses 8.4 External equilibrium 8.4.1 Direct sliding 8.4.2 Bearing capacity 8.4.3 External stability 8.5 Design charts for steep reinforced slopes 8.6 Steps for using the design charts 8.7 Design example 8.7.1 Project data and design values 8.7.2 Design steps 8.8 General methods of stability analysis 8.8.1 Comment on the method of slices 8.9 Synopsis of Chapter 8
9 Reinforcement of shallow slips in clay embankments 9.1 Factors causing instability 9.1.1 Porewater pressures 9.1.2 Shearing resistance at low effective stress 9.2 Analysisfor shallow slips 9.2.1 Assumed porewater pressure 9.2.2 Slip surface geometry 9.3 Results for shallow slips 9.3.1 Unreinforced case 9.3.2 Reinforced case: slip repair 9.4 Design charts for sideslope reinforcement 9.4.1 Contrast with steep slopes 9.5 Selection of reinforcement 9.5.1 Reinforcement types and materials 9.5.2 Reinforcement layout 9.5.3 Reinforcement bond 9.6 Construction expedients 9.7 Design example 9.8 Synopsis of Chapter 9 10 Retaining walls 10.1 Summary of design steps
iv
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Contents
11
10.2 Internal equilibrium: idealised case 10.3 Overall equilibrium 10.3.1 Overall failure mechanisms
150
10.3.2 Allowance for bond and loadshedding 10.3.3 Equations for overall equilibrium 10.3.4 Line of thrust in the reinforced zone 10.3.5 Minimum requiredlength for overall equilibrium 10.4 Internal equilibrium: practical corrections 10.5 External equilibrium 10.5.1 Direct sliding 10.5.2 Excessive eccentricity 10.5.3 Bearing capacity 10.5.4 External stability 10.6 Deformation of walls 10.6.1 Deformation of the reinforced fill 10.6.2 Deformation caused by foundation movement 10.7 Practicalaspects influencing design 10.7.1 Thrust from the backfill 10.7.2 Connections 10.7.3 Fullheight facing 10.8 Design example for a retaining wall 10.8.1 Data and design values 10.8.2 Design steps (ultimate limit state) 10.8.3 Check on serviceability 10.8.4 Design crosssection 10.9 Point loads 10.9.1 Internal equilibrium 10.9.2 Allowance for bond 10.9.3 Overall and foundation equilibrium 10.10 Sloping fill 10.11 'Loopanchor'walls 10.12 Synopsis of Chapter 10
152 154
Embankments on soft soil 11.1 Stress and force equilibrium 11.1.1 Summary of mechanics 11.2 Slip mechanisms and deformation 11.2.1 Internal stability 11.2.2 Overall stability 11.3 Construction rate and drainage
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182 183
184 185
20! V
Contents Construction period 11.3.2 Drained and undrained shear 11.3.3 Design strategies 11.3.4 Significance of foundation stability 11.4 Concepts from plasticity analysis I I .4. 1 Plasticity solutions 11.4.2 Application of plastic theory 11.5 Limit equilibrium analysis 11.5.1 General considerations 11.5.2 Rotational stability: slip circle analysis 11.5.3 Foundation and overall stability 11.5.4 Limitations of slip circle analysis 11.5.5 Translational stability: wedge analysis 11.5.6 Methods of slices 11.6 Analytical solutions 11.6.1 Foundation of uniform strength and limited depth 11.6.2 Foundation with strength increasing with depth 11.6.3 Reinforcement stiffness 11.7 Parameters for design 11.7.1 Limit states 11.7.2 Ultimate limit sales 11.7.3 Analysis for serviceability 11.7.4 Reinforcement mattress design 11.8 Design example 11.8.1 Embankment details 11.8.2 Ultimate limit state 11.8.3 Serviceability limit state 11.8.4 Conclusions for the design example 11.9 Case histories 11.10 Synopsis of Chapter 11 11.3.1
12 Working platforms and unpaved roads 12.1 Mechanics of reinforcement action 12.2 Analysis for working platforms 12.2.1 Subgrade bearing capacity 12.2.2 Stresses within the fill 12.2.3 Unreinforced design 12.2.4 Reinforced design 12.2.5 Fill bearing capacity 12.2.6 Serviceability for known reinforcement properties Vi
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202 204 204 204 205 206 207 208 208 210 211
212 213 214 215 216 217 218 218 219 223 225
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Contents
12.2.7 Serviceability for a known applied loading 12.3 Procedure for working platform design 12.3.1 Ultimate limit state analysis 12.3.2 Serviceability limit state analysis 12.4 Design example: working platform 12.4.1 Stability 12.4.2 Serviceability 12.4.3 Reinforcement properties 12.4.4 Comparative designs 12.5 Static analysis for unpaved roads 12.5.1 Subgrade bearing capacity 12.5.2 Stresses within the fill 12.5.3 Unreinforced design 12.5.4 Reinforced design 12.5.5 Fill bearing capacity 12.5.6 Serviceability 12.5.7 Design charts 12.6 Design example: static wheel loading 12.7 Allowance for traffic 12.7.1 Definition of failure 12.7.2 Rate effects 12.7.3 Fatigue relation 12.7.4 Permanent road thickness 12.7.5 Practical wheel loading 12.7.6 Allowance for mixed traffic 12.8 Procedure for unpaved road design 12.8.! Unreinforced design 12.8.2 Reinforced design 12.9 Comparisons and backanalysis 12.9.1 Unreinforced unpaved road design (llammitt, 1970) 12.9.2 Reinforced unpaved road design (Giroud and Noiray, 1981) 12.9.3 Backanalysis reinforced trafficking trials 12.10 Discussion 12.11 Synopsis of Chapter 12
13 From design to specification 13.1 Future developments
13.2 Designing reinforced soil structures 13.2.1 Concept 13.2.2 Compatibility Special Publication123 © CIRIA
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252 253 253
254 255 255 257 258 258 260 263 265 266 268 268 269 270 271 271
273 275 276 280 282 287 288 291 291
292 292
293 vii
Contents
Timing and structural life 13.2.4 Foundation and fill materials 13.2.5 Facings and slope protection Construction specification and quality assurance 13.3.1 Reinforcement materials 13.3.2 Site preparation and construction control Topics of special concern 13.4.1 Limit state design 13.4.2 Geotechnical properties 13.4.3 Geotextile properties 13.4.4 Environmental considerations 13.4.5 Interaction properties 13.4.6 Combined applications 13.4.7 Unpaved roads Concluding remarks Synopsis of Chapter 13 13.2.3
13.3
13.4
13.5
13.6
294 296 296 297 297 297 298 298 299 300 300 300 300 302 302 303
References
305
Index
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Special Publication123 © CIRIA
List of Tables 2.1 Factors
to allow for mechanical damage for some geogrid reinforcements
made from drawn HDPE
27
2.2 Factors to allow for mechanical damage for some woven geotextiles and geogrids made from polyester 3.1 Typical reference properties for yarn at 20°C and 65% relative humidity 3.2 Geometric component of extension caused by the weave in woven geotextiles 3.3 Comparison of index strength of threewoven geotextiles of weight lOOg/m2 in the longitudinal direction and 20g1m2 in thetransverse direction 3.4 Comparison of index elongation of three woven geotextiles of weight 100 Wm2 in the longitudinal direction and 20 gIm2 in the transverse direction 3.5 Typical geogrid reference properties of 20°C and 65% relative humidity 4.1 Bearing stress ratio for soil reinforcement 4.2 Bond coefficients for grid reinforcement 5.1 Typical peak angles of friction for compacted granular fills in routine applications 5.2 Peak strength and relative density index corresponding with FS = 1.3 5.3 Bearing capacityfactors 6.1 Material factors (f,) as a function ofthe required extrapolation of dataat the design temperature (Td) 6.2 Summary of design values and partial factors for the main parameters in ultimate limit state calculations (drained analysis) 8.1 Characteristic strength of the reinforcement grids in kN/m 8.2 Comparison of costs for reinforcement layouts 9.1 Gross required reinforcement force (kN/m slope) toprovidea factorof safety
FS =
1.2 and 1.3
9.2 Required reinforcement length to provide
40 41 41
42 52 53 66 68 81 93
95 122 125 138
a factor of safety FS =
1.3 10.1 Characteristic strengths for the reinforcement grids in kN/m
1.2
and
10.2 Characteristic stiffnesses of the reinforcement grids in kN/m 10.3 Available stress from reinforcement, 0AV in kN/m2, and in the maximum permissible depth for each reinforcement below the crest, 7max in m 10.4 Summary of displacement calculations for the design example 11.1 Equations from simplified analysis for an embankment on a foundation of uniform undrained strength, Slid, and limited depth, D Special Publication 123 © CIRIA
27 40
138 171
172 173 177
200 ix
List
of Tables
Recommended soil properties for ultimate limit state analysis 11.3 Recommended reinforcement properties for ultimate limit state analysis 11.4 Two available woven polyester geotextiles 11.5 Ultimate limit state results to achieve FS = 1.3 on the clay strength 11.6 Ultimate limit state results to achieve FSç = 1.1 on the clay strength 1.7 Serviceability limit state to achieve FS = 1.1 2.1 Ratioof loadcarrying capacity for reinforced and unreinforced designs (twodimensional loading case) 12.2 Variation of bearing capacity factor with outward shear stress for planestrain (2D) and axisymmetric (3D) loading 12.3 Limiting bearing stress for a circular load, R = 0.17m 12.4 Trafficking trials on a crushed stone fill over clay subgrade, reinforced by a strong woven nylon membrane Tl0 11.2
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Special Publication 123 © CIRIA
List of Figures Figure 1.1 Geotextilefunctions: (a) separation and (h) reinforcement Figure 1.2 Illustration of reinforcement action in direct shear: (a) tensile and
compressive strains in soil, and (h) resultant reinforcementforces load by membrane action: (a) rutted unpavedroad, (b) above a sinkhole and (c) in a piled embankment foundation Figure 1.4 Combined use of reinforcement to st(ffrn the foundation beneath a reinforced soil wall Figure 1.5 Local tensile cracking at the base of a loaded granular layer: (a) unreinforced case, and (b) reinforced case Figure 1.3 Reinforcement supporting
Figure 1.6 Example applications ofgeotextile separators Figure 1.7 Example applications ofgeotextiles as soil reinforcement Figure 1.8 Variation of required reinforcementforce with time: (a) steep slopes
and walls, (b) embankments on soft soil, and (c) unpaved roads Figure 2.1 DWerent types of creep behaviour in materials: (a) in a metal at high temperature, and (b) in a polymerat ambienttemperature
Figure 2.2 Sustainedload creep tests on a polyestergeotextile Figure 2.3 Sustainedload creep tests causingfailure in a polyesteryarn Figure 2.4 Yield and rupturepoints: (a) at a constantrate ofelongation, and (h) under sustainedload 2.5 Figure Strength propertiesfor a uniaxialpolyethylene geogrid Figure 2.6 Loadelongation relations foundfrom creep test data Figure 2.7 Time to chemical breakdown as a function of temperature for a spunbonded polypropylene geotextile Figure 2.8 Typical loadelongation responsefrom index tests: (a) linearbehaviour and (b) nonlinearbehaviour Figure 2.9 Creeprupture propertiesfor a geotextile material Figure 2.10 Idealisationof mechanical damage reducing strength by a constant factor irrespective of time Figure 2.11 Progressive influence with time ofthe soil environment on strength Figure 3.1 Requirementsfor reinforcement: (a) axial loadcarrying capacityand, for geogrids, (b) an adequatetransverse member arrangement Figure 3.2 Significant reinforcement in two perpendicular directions is best achievedby two separate layers Special Publication 123 © CIRIA
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List of Figures Figure 3.3 Reinforcementofembankmentson soft soil: (a) temporary force in the
Figure 3.4 Figure 3.5
Figure 3.6
direction offihling,(b)jointed layers ofreinforcementand(c) a cellular mattress Geometric components ofdeformation causedby straightening ofloadcarrying elements in a woven geotextile Uniaxial geogrid reinforcement formed by a patented process of punching holes in a sheetfollowedby drawing Geogridlike products: (a) connected sheathed strips and (b) interwoven bundledyarns with a protective coating Counterrotating die for manufacturing geomesh materials
Figure 3.7 Figure 4.1 Effects ofreinforcementon equilibrium: (a) unreinforced slope and(b) allowing for the reinforcementforce Figure 4.2 Improvement in shearing resistanceas afunctionofthe reinforcement orientation Figure 4.3 Optimum directions for reinforcement in soil: (a) to maximise bond, and(b) to maximise tensile strain Figure 4.4 Relations for strain compatibility: (a) mohilised soil shearing resistance, and(b) mobilised reinforcementforce Figure 4.5 The compatibility curve for determining the equilibrium in reinforced soil 4.6 Interactionsbetween soil and reinforcement Figure Figure 4.7 Definition ofdimensionsfor reinforcement Figure 4.8 Bond between reinforcement and soil: (a) mechanisms and (b) definitions for analysis Figure 4.9 Bearing stresses on reinforcement Figure4.10 Influence ofparticle size on soil bearing stress Figure 5.! Equilibrium stresses in frictional soil Figure 5.2 Relation between Kc, and peak angle of friction for normally consolidated granular soils Figure 5.3 Trend of increasing peakfrictional resistance with distance from the critical state line: (a) critical state line, and peak strength versus (b) initial specific volume, and (c) initial overcompression 5.4 Figure Approximations to a curved strength envelope 5.5 Variation ofpeak angle offriction with mean stress in granular soil Figure Figure 5.6 Triaxial strength datafor sands collected by Bolton (1986) Figure 5.7 Peak angle offrictionfor sand in triaxial compression Figure 5.8 Definitions for the direct shear test Figure 5.9 Typical results from a direct shear test on compact granular soil xii
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49
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Special Publication 123 © CIRIA
List of Figures Figure5.10 Normalised peak strength data from triaxial compression tests on London clay Figure5.11 Peak angle offrictionfor London clay (datafrom Figure 5.10) Figure5.12 Residualangle offriction versus granular specific volume Figure5.13 Two causes of overconsolidation in a soft clay foundation (a) reduction in ground level and (b) previous lowering of groundwater 5.14 Values of the shear strength ratio s0/o, for normally consolidated Figure clays Figure 5.15 Example of a foundation overconsolidated by previously lowered groundwater (a) effective vertical stresses, (b) overconsolidation ratio and (c) undrainedshear strength 5.16 Figure Interpretation of the relation between shearing resistance and vane correction factor Rfor normally consolidated clays Figure 5.17 Relation between undrainedshearing resistance andplasticityindex from the backanalysis ofembankmentfailures Figure 5.18 Definitions for the drained analysis of bearing capacity Figure 5.19 Reduction in bearing capacity due to load inclination Figure5.20 Drainedbearing capacityunder combined loading Figure5.21 Definitionsfor the analysisof undrainedbearing capacity Figure5.22 Undrained bearing capacityunder combined loading Figure6.1 Reinforcement strength properties Figure7.1 Equilibrium in a steep reinforced slope expressed in terms ofrequired and available stresses Figure 7.2 Equilibrium (foundation stability) for an embankment on soft soil expressed in terms ofrequiredandavailableforces Figure 7.3 Internal equilibrium for a steep reinforced slope Figure 7.4 Overall equilibriumfor a steep slope and wall Figure 7.5 Externalequilibrium checkon foundation capacity: (a) direct sliding, (b) bearingcapacity,and (c) eccentricity Figure 7.6 External equilibrium check on deepseatedfailure mechanisms Figure 7.7 Limits to the expected equilibrium shown on a compatibility curve: (a) soil behaviour, (b) reinforcement behaviour, and (c) the expected equilibrium Figure 8.1 Three types of reinforced slope Figure 8.2 Steep slope definitions Figure 8.3 Three zones in a steep reinforced slope: zone I, boundedbyAB, zone 2, to endofreinforcement, andzone 3, the unreinforced backfill 8.4 Idealised equilibrium with uniform reinforcement force in zone I Figure decreasingto zero at the back ofzone 2 Special Publication123 © CIRIA
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xiii
List of Figures
required stress in the soil exceeded everywhere by the available stress from reinforcement arranged at two spacings Figure 8.6 Stress characteristics illustrating balanced equilibrium in zone / Figure 8.7 (a) Twopart wedge mechanism and (h) boundary forces Figure 8.8 (a) Logarithmic spiral mechanism and (h) boundary forces Figure 8.9 Overall equilibrium check on the requiredreinforcement length Figure 8.10 Maximum available reinforcement force, R' to maintain overall Figure 8.5 Maximum
equilibrium Figure 8.11 Required bond length andloss ofavailable force Figure 8.12 Additional reinfoirement. Kd> KReq. to mitigate lossofavailableforce due to bond Figure 8.13 Additional reinforcement. 0mj' to allowfor bond near the crest ofa steep slope Figure 8.14 Twopart wedge analysisfor direct sliding Figure 8.15 Choice ofporepressure ratio to allow for a phreatic surface Figure 8.16 (a) Envelope ofmaximum requiredstress, and (h) locus ofmaximum available stress in a steep reinforced slope Figure 8.17 Envelope of maximum requiredstress for the design example Figure 8.18 Provision ofavailable stress for the design example Figure 8.19 Crosssection for the design example using all three reinforcement
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108 109 109 110
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118 123
124
grids 8.20 Illustrationofthe method ofslices applied to reinforced soil Figure Figure 8.21 Design chart I for steep reinforced slopes, = 0 Figure 8.22 Design chart 2 for steep reinforced slopes, r11 = 015 Figure 8.23 Design chart 3forsteep reinforced slopes, r11 = 0.50 Figure 9.1 Shallow slope failures in clay slopes: (a) slip sutface, (b) nearsurface porewater pressures, and (c) reduced shearing resistance at low
125 126 127 128 129
effective stress 9.2 Measured Figure shearingresistancefor London Clay at low effective stress Figure 9.3 (a) Maximum porewater pressure distribution in clay embankment sideslopes and (b) the idealisation for analysis Figure 9.4 Slip mechanismfor analysis Figure 9.5 Variation of the mobilised friction angle with depth to maintain equilibrium in a clay sideslope Figure 9.6 Required shearing resistance for equilihirium compared with the peak andcritical state shearingresistance ofLondon Clay Figure 9.7 Gross requiredreinforcementforce for combinations of slope height anddesign angle offriction
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List of Figures Figure 9.8 Required reinforcement length for combinations
of slope height and design angle offriction Figure 9.9 Typical reinforcement arrangementin a clay embankment sideslope Figure9.10 Envelopes ofrequiredandavailable force in reinforcementlayers for a 1:2 sideslope Figure9.11 Reinforcement layout for the design example Figure 10.1 Two examples of reinforced soil wall systems Figure 10.2 Definitions for reinforced soil walls Figure 10.3 Summary ofsteps in the design ofreinforced soil walls Figure 10.4 Analysis of internal equilibrium in a reinforced soil wall Figure 10.5 Distribution ofavailable stressfor balanced internal equilihiium Figure 10.6 Analysisfor overall equilibrium in a reinforced soil wall Figure 10.7 Maximum available force in a reinforcement layer Figure 10.8 Forces acting on the reinforced zonefor overall equilibrium Figure 10.9 Eccentricity of the resultant force on the t,ial wedge 0G. at an angleO Figure 10.10 Results to illustratethe line ofthrust in a reinforced soil wall. (case = 35° and no surcharge) with Figure 10.11 Minimumreinforcement length for balancedequilibrium (case: 4bd = trd'Yb = Yr. level backfill, and A1 = I/Ab) Figure 10.12 Minimumreinforcement lengthfor balancedequilibrium (case: thd = trd 5°, Yb = Yr. level backfill, and A1 = //Ab) Figure 10.13 Directsliding atfoundation level Figure 10.14 Possible directsliding mechanisms when LdS > L Figure 10.15 Equivalent foundationfor the analysis ofbearing capacity Figure 10.16 Check onfoundationstability: (a) bearing capacity analysis, and(h) analysisofexternalslip mechanisms 10.17 Chartfor maximum horizontal movement in reinforced soil walls Figure Figure 10.18 Resultant wall displacements following consolidation Figure 10.19 Connections at the face Figure 10.20 Forces transmitted through fullheightfacing Figure 10.21 Design example: wall details and required stresses for internal equilibrium Figure 10.22 Design example: trial reinforcement layout to provide the required stresses (a) one reinforcement material (h) use of stronger grid at base Figure 10.23 Design example: finalcrosssection Figure 10.24 inclined load on a reinforced soil wall Figure 10.25 Additional requiredstress due to a horizontal point load
td
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List
of Figures
Figure 10.26 Additional required stress due to a vertical point load Figure 10.27 Requiredstressfor internalequilibrium with point loading Figure 10.28 Wedge analysis to check internal equilibrium Figure 10.29 Wall with sloping fill Figure 10.30 Active earth pressurecoefficientsfor sloping fills Figure 10.31 Approximationfor backfill stresses due to a broken slope Figure 10.32 Detailsfor loopanchor walls Figure 11.1 Reinforcement improving stability during construction andfoundation consolidation Figure 11.2 Disturbingforces in an unreinforced embankment,with reinforcement supporting outwardshear stress Figure 11.3 The influence ofoutwardshear stress on bearing capacity Figure 11.4 Reinforcementproviding lateral restraint on thefoundationsurface Figure 11.5 improvement in bearing capacity due to lateral restraint on the foundation suiface 11.6 Figure Summary ofmechanics in a reinforced embankment on soft soil Figure 11.7 internal stability: direct slidingfailure in thefill Figure 11.8 Overall stability: slippage across thefoundationsurface Figure 11.9 Foundation stability: (a) applied stresses, (b) and (c) shear on horizontal planes, and (d) resulting shear displacement,for the case
c=O
Figure 11.10 Overallstability: envisaged rigid body failure mechanism Figure 11.11 Foundationstability: limiting embankment crosssections and prefailure' lateral deflections in thefoundationfor the cases, = +1,
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197 199
200
0,—! Figure 11.12 Relation between the maximum requiredreinforcementforce andthe rate ofconstruction 11.13 The response of soft clay to rapid stage 2 loading beneath an Figure embankment Figure 11.14 Beating capacity expressed in terms of the allowable vertical loading versus distance from the edge of loading, relevant to embankment design Figure 11.15 Plasticity solutions for strength increasing with depth Figure 11.16 Solutions for a foundation of uniform strength and limited depth above a rough stratum Figure 11.17 Practical embankment crosssections derived from plasticitysolutions
Figure 11.18 Components ofslip circle analysis in the fill and the foundation xvi
180
201 203
205 206 206 207 209
Special Publication123 © CIRIA
List of Figures Figure 11.19 Slip circle analysis for reinforced embankments: (a) foundation stability, with (b) available and (c) requiredforces; (d) overall stability, requiredforces 11.20 Figure Comparison of slip circle analysis with plasticity solutions: (a) strength increasingwith depth, and (b)foundationof limited depth 11.21 Figure Wedge analysisfor reinforced embankments: (a) exploded view of limiting stresses, (b) check onfoundationstability, and (c) check on overall stability Figure 11.22 Assumed equilibrium for analytical solutions: (a) foundation of limited depth, and (b) foundation with strength increasing with depth Figure 11.23 Influence of reinforcement stiffness on the maximum values of embankmentdisplacement andreinforcement elongation Figure 11.24 Possible embankment crosssections fbr the design example Figure 12.1 Typical arrangementfor an unpaved road Figure 12.2 General definitions for the twodimensional loading on a working platform Figure 12.3 Combined loading on the subgrade in the unreinJbrced case Figure 12.4 Action of the reinforcement to relieve subgrade of outward shear stress Figure 12.5 Envelope of available subgrade resistance (ABCE) and the stress applied by suiface load (GCH) Figure 12.6 Elemental block offill beneath the surfacepressure Figure 12.7 Horizontalforces considered in the equilibrium analysis Figure 12.8 Outward shear stress supportedby the reinforcement Figure 12.9 Interaction diagram showing the unreinforced andfully reinforced equilibrium 12.10 Limit imposed by the bearing capacityof thefill (N = pyB/sB') Figure Figure 12.11 Limit imposed by the allowable reinforcementforce (aji = taijB') Figure 12.12 Required and available stressesfor working platform example Figure 12.13 Design chartfor working platform example Figure 12.14 General definitionsfor the threedimensional loading onan unpaved road 12.15 Shear Figure loading under axisymmetric conditions: (a) shear stresses, (b)force in the reinforcement, and (c) average biaxial conditions 12.16 Figure Design chart for unreinforced and reinforcedstability under axisymmetric loading: (a) requiredfill thickness, and (b) required reinforcementforce Special Publication 123 © CIRIA
210 212
213
214 224 228 235 236 237 238 239 240 241
242 243 244 245
249 250 253 256
259 xvii
List of Figures
chartsfor (s,IyR = 10) illustratingthe influence of loadspread angle: (a) and (b) with I = 25', (c) and (d) with I = 45° 261 Figure 12.18 Design chartsfor ([3 = 35°)illustrating the influence ofthefill: (a) and (b) with sn/yR = 5, (c) and (d) with s0/1R = 20 262 Figure 12.19 Comparison between static andrepeatedload tests on unreinforced Figure 12.17 Design
unpaved roads Figure 12.20 Definition offailure in an unpaved road under static and repeated loading 12.21 Failure in unreinforced and reinforced unpaved roads subject to Figure traffic 12.22 Vane correction factors to allow for the influence of strain rate on Figure undrainedshear strength 12.23 Derivation Figure of road capacityafter N load repetitions in terms of an equivalent static load 12.24 Figure Design chartfor unreinforced unpaved roads; applicableto specific values, se/yR, and, [3 Figure 12.25 Master design chartfor reinforced unpaved roads Figure 12.26 Determination of the required reinforcement force allowing for traffic 12.27 Correlationfor unreinforced unpaved roads proposedby Hammitt Figure (1970) 12.28 Fit to the data achieved by the equation proposed by Hammitt Figure (1970) Figure 12.29 The data of Hammitt (1970) plotted as an equivalent static load Figure 12.30 Comparison between the new analysis, the relation proposed by Hammitt (1970) andthe datafor unreinforced unpaved roads Figure 12.31 Comparison ofthe new analysis with Giroud andNoiray (1981). Figure 12.32 Resultsfor the hackanalysis ofthe unreinforced unpavedroad tested by Webster and Watkins (1977) 12.33 Illustration Figure ofthe increasingequivalent load due tofatigue andthe limiting capacity caused by insufficient reinforcement modulus 13.1 Possible Figure effect of sequence of operations at a softclay site: (a) proposedlight bridgeformed on Hpiles, (b)fill placementdeforms preinstalledpiles, (c) piles installedalter construction ofapproach embankment
264 265 266 267 272 273
274 275
276 277 278 279 281
285 287
294
Figure 13.2 Possible effects ofsequence of operations when installing a culvert 295 through a basally reinforced embankment on soft clay
xviii
Special Publication 123 © CIRIA
Notation ab
A1 B
B /3 Dmax
e e e efield Cmax Cmin
fd fenv
fm F1
F2 FS FSa
G,
H H'
i,,
l,
J
of grid width available for bearing fraction of reinforcement plan area that is solid bond allowance loadshedding (or sharing) allowance fraction
width of a transverse member of a grid taking bearing effective width of loaded area effective cohesion depth of footing below ground level mean particle size maximum particle size load eccentricity on a footing eccentricity of foundation reaction from centre of reinforced block void ratio field void ratio of compacted fill void ratio at loosest condition void ratio at densest condition partial factor for mechanical damage partial factor for chemical and biological environment overall materialfactor scaleeffect factor for bearing stress ratio shapeeffect factor for bearing stress ratio factorof safety factorof safety in a 'lumpedfactor' design specific gravity depth where critical wedge intersects width face height of phreatic surface above base of a slope slope (or wall) height effective slope (or wall) height (allowing for vertical surcharge) angle of backfill above a slope crest reduction factorfor bearing capacity under inclined loading reduction factor for bearing capacity under inclined loading relative density plasticity index relative density index secant stiffness of reinforcement for relevant time period
Special Publication123 © CIRIA
xix
Notation reference stiffness at end of construction
Jd k K0 Kar Kab
Kad Kd KReq
L
L
Lr LR in n Nq
OCR
P Av AvaiIable "hase
bf "darn
env Pro "field
xx
reference stiffness at end of design life specific stiffness of a polymer empirical constantin relationbetweenrelative density and angle of friction coefficient of earth pressure at rest active earth pressure coefficient corresponding to design angle of friction for reinforced fill active earth pressurecoefficient corresponding to design angle of friction for backfill design active earth pressure coefficient design value of earth pressure coefficient required value of earth pressure coefficient width of footing or block of reinforced soil effectivewidth of footing for inclined loading bond length bond length for reinforcement layer at base of wall required reinforced length to prevent direct sliding length of reinforcement length of inclined trial wedge powerto which OCR is raised in relating (s/o') for normally and overconsolidated states slope definition in 1 vertical to n horizontal bearing capacity factor bearing capacity factor bearing capacity factor overconsolidation ratio equivalent effective pressure with respect to normal consolidation line tensile load in reinforcement available force allowing for bond available reinforcement force gross reinforcement force modified reinforcementforce at base of wall thrust from backfill on reinforced block design strength of reinforcement reinforcement strength allowing for mechanical damage reinforcement strength allowing for chemical and biological environment reinforcement force at equilibrium lateral thrustfrom the fill strength of reinforcement in the field Special Publication123 © CIRIA
Notation
(fieId)td,Td
ref (fXd. Td "Req required
RL RU T1rupture
yieId
(R)l,2, etc. qb
Q Q Qh
Q R R R121221 etc. Rh
R Sh
su Sud
(Su)m
strength of reinforcement in the field at design life, td, and design temperature, Td mobilised force in reinforcement effective normal force tensile force in reinforcement gross maximum force required for equilibrium gross available force reference strength of reinforcement reference strength of reinforcement at design time, td and temperature, Td required tensile reinforcement force required reinforcement force gross reinforcement force, likely lower value gross reinforcement force, likely upper value tensile force at which reinforcement ruptures shear force serviceability strength of reinforcement (i.e. at max. allowable elongation vertical load tensile load at which reinforcement yields horizontal resultant forces on wedges in stability analysis surcharge pressure above backfill surcharge pressure above reinforced zone applied vertical surcharge empirical constant for determining relative density index, 'R maximum compaction force per unit width of roller horizontal component of applied point load verticalcomponentof applied point load radius of slip circle pore pressure ratio design value of pore pressure ratio reaction on a foundation resultant thrust reactions between wedges in stability analysis horizontal component of load on footing vertical component of load on footing mean effective stress (= (°' + o'3)/2) horizontal spacing of reinforcement elements undrained shear strength undrained shear strength of foundation design undrained shear strength mobilisedundrainedshearstrength
Special Publication123 © CIRIA
Xxi
Notation
S S
T U
Umax
U12C. Vg
W etc.
W X
x (dx) y (dy) z
b
ds y Yeff
yf Ymax Yr Yrd '1w
Xxii
vertical spacingof reinforcement layers specific strength (of a polymer) spacing between transverse members taking bearing maximum shear stress (=(°'i — 635/2) time in creep test design life aged life temperature design temperature porewater pressure maximum pore pressure in a slope water upthrusts normal to sliding face of wedges granular specific volume specific volume at start of shearing specific volume at critical state (constant volume) weight of reinforced soil block weight of wedge width of reinforcement distance of point load edge of crest. shear displacement vertical displacement depth below ground surface effectivedepth in slope of effective height H' depth below slope surface of clay embankment depth below slope crest of change in reinforcement critical depth where bond length equals reinforcement length depth to groundwater level load inclination (= r/s1) coefficientof bond coefficientof direct sliding slope angle from horizontal unit weight of soil design value of unit weight of soil effectiveunit weight of foundation soil allowing for buoyancy unit weight of foundation soil submerged weight of foundation soil maximum dry density unit weight of reinforced soil design unit weight of reinforced soil unit weight of water Special Publication123 © CIRIA
Notation o of 0rnax Op
AL'S
Aqr 83
EEQ
8max
8RL
8sL
8su Cyjeld
o
05
a' Go
aS
0Av
(oJ)
angleof skin friction, soil on planar reinforcement surface design angle of friction between soil and reinforcement inclination of inclined loading as footing (= tan Rh/RV) maximum horizontal displacement peak friction angle between soil and reinforcement maximum settlement at crest of wall wall roughness improvement in shearing resistance increment of vertical surcharge maximum tensile strain in soil elongation of polymerat time t' in creep test tensile elongation at force equilibrium maximum tensile strain tensile elongation of reinforcement elongation of reinforcement at rupture tensile elongation of reinforcement at force equilibrium tensile elongation of reinforcement, likely lower value tensile elongation of reinforcement, likely upper value tensile strain in soil at force equilibrium tensile strain in soil, likely lower value tensile strain in soil, likely upper value elongation of reinforcement at yield inclination of reinforcement to vertical angle to horizontal of trial wedge optimum reinforcement orientation for bond optimum orientation of reinforcement optimum orientation of reinforcement in direction of maximum soil tensile strain vane strength correction factor normal effectivestress equivalent vertical stress acting at level of footing base maximum residual stress from compaction major principal effective stress minorprincipal effective stress available stress effective bearing stress on reinforcement bearing stress ratio bearing capacity of foundation soil maximum effective bearing stress beneath rough footing of effective width
I
SpecialPublication123 © CIRIA
xxiii
Notation
0comp
Of
of Oax 0min 0mob
0Req
tf
maximum horizontal stress caused by compaction
highesteffectivestress experienced by the soil design normal effectivestress applied vertical stress acting on effective footing width
I
vertical stress applied across reinforced soil foundation effective vertical stress below footing maximum normal effective stress on reinforcement minimum direct stress mobilisedstress normaleffectivestress preconsolidation pressure required stress
current vertical effectivestress direct stress on plane yy shear stress applied shear stress acting on effectivefooting width£ shear stress
4) 4)' 4)bd
4? 4? 4? 4¾
4)rnob
4)peak
xxiv
angle of shearing resistance angle of shearing resistance
in terms of effective stress mobilised angle of shearing resistance, atrestconditions design angle of friction for backfill critical state angle of shearing resistance constant volume (large strain) angle of shearing resistance design value of effective angle of shearing resistance angle of friction in normalised plot angle of shearing reistance of foundation soil mobilised angle of shearing resistance at failuretb design angle of shearing resistance of foundation soil peak angle of shearing resistance of foundation soil mobilised angle of friction mobilisedeffective angleof shearing resistance peak effective angle of shearing resistance, i.e. secant value constantpeak angle of friction, i.e. c, 4/linear envelope peak angle of friction in plane strain conditions peak angle of friction for reinforced fill angle of friction mobilised in reinforced soil peak angle of friction measured in triaxial compression angle of dilation
Special Publication 123 © CIRIA
SOIL REINFORCEMENT WITH GEOTEXTILES
Special Publication 123 © CIRIA
317
Soil ReinforcementWith Geotextiles accelerated testing 22 chemical durability of geotextiles 28 activeearth pressure coefficient 150, 161, 165, 236 sloping fills 183. 184 soft soil embankments 216 additives 22, 27 physical loss of 27 anchored earth construction 292 backwedge, critical angle for 182 backfill 148 design angle of friction 157 loading 183 thrust from 116, 1678 basal reinforcement layers 301 bearing capacity analysis 204, 205 circular load 258 clay foundation 23940 detrimental effect of outward shearstress 191, 19/ drained analysis of 7982 factors 81, 83, 175, 241, 2534 retaining walls 1623 steep reinforced slopes 116 theory 59, 116 bearing pressure, allowable 82 bearing stress allowable 176 bearing stress ratio 512, 53, 121, 171 and geogridlike products 36 in loopanchor walls 1845 maximum beneath rough strip footing 80 biaxial geogrids 35,41 Bjerrum's vane correction factor 78 Bolton's relations, use of 71 bond at crest, minimum required stress for 123 available bond force 142 bondallowance 11112, 11314, 119, 123, 1524, 158, 176, 1812, 184 bond coefficient(s) 504, 94, 121, 154, 171, 221 bond length 11012, 123, 1523 bond stress 45, 4950 capacity, possible degradation 182 318
critical factor with fully softened strength of clay 1423 development of 43 geogrid coefficient(s) 49, 56 grid reinforcement coefficient 54 net effecton overall equilibrium 153 pullout tests coefficients 49, 143 reinforcementsoil 35, 45, 91 retaining waIls 151, 162 and separation 31 BS 2846 Part 2 25 BS 6906: Part I 17, 23 BS 6906: PanS 18,23 California Bearing Ratio (CBR) test 257 carbon black 27 cellular products3 cellular reinforcement mattresses 33, 33, 225
central thirdcriterion 1567, 162 characteristic strength, safe 25 chemical/biological durability 268 longertenn environmental effects 15, 23, 29
mechanisms causing behavioural change 22
testing for breakdown 223, 23 circular loads, limiting bearing stress 263 clay claytogeotextile interface 221, 229 compact soil 73 design shear strength of 211 deterioration of longterm peak strength 91
foundation soils, directsliding on 162 high moisture content and planar slip surfaces 133 limiting resistance 23940 overconsolidated 132, 133 plastic deformation 238 soft soils
rapid drainage in 225
undrained strength of 59, 91 soils testing 734 susceptible to slickensiding 73 undrained bearing capacity 163 Special Publication123 © CIRIA
Index youngand aged soils, anticipated strength ratio 78 see also soft clay clay embankments ageing, wetted/saturated surface zone 133 design example, prevention of shallowslip development 1434 factors causing instability 1324 maximum porewater distribution, sideslopes 135 reinforcement of shallow slips in 13145 reinforcement of sideslopes 105, 132, 1378, 13940 cf. reinforcement of steep slopes 140 reinforcement layout 1412 coefficients of interaction 211 collapse calculation of risk of 87 collapse limit, soft soil embankments 229 combined applications 3012 combined loading, and undrained bearing capacity 84 compact soils 59 clay fills 299 compaction 175 compaction stress, allowance for 114, 123, 158, 1701 compaction theory 114 compactionrelative density link 65 drained peakangle of friction 62 granular, peakangleoffriction 230 strength of 6 174 compatibility, in reinforced soil 2, 2934 compatibility strain curves 467,47 composite reinforcement with drainage 292 connections and relative vertical displacement 168 in retaining walls 1689, 171 consolidation of foundations 225, 292 consolidation settlement 166, 167 constant shearing resistance 70 constantvolume angle of friction 5960, 678, 701 construction affecting instability 133 control of 2978 damage during 25 Special Publication123 © ClAlA
influence of 1645, 168
and use of geotextiles 78 construction period, soft soil embankments 2014 cornering force, working platforms 241 creep 16 creep deformation IS, 16 creep displacement 166 creep test data 20, 2/ creeprupture 1617 curve extrapolation 21 properties 24, 25 curve extrapolation 21 properties 18, 24 reinforcement material characteristics 12 with time under load 8 critical failure mechanisms 98 critical slip surfaces 106, 1078 critical state angleof friction 5960, 63,71 reinforced slopes 120 retaining wall fill 170 soil fill 219, 227 criticalstate shearing resistance 90, 225 shallow slips 137 critical stress concept 17 culverton soft clay 293, 295 cumulative elongation reinforcement grids 121, 122 and time under load relationship 20 curved strength envelope 63 cuttings, stabilisation of 132
damage,mechanical 15, 256, 29, 38, 92, 141, 143, 168 damage allowances 121, 227 damage factors 26 uniaxially drawn geogrid materials 27 detlections bounds to expected 1013 estimating expected 101 lateral 2312 deformation caused by foundation movement 1667 from construction 91, 164S interference with structure function 87 ofreinforced fill 1646 ofretainingwaIls 148, 1647, 172 319
Soil ReinforcementWith Geotextiles and slip mechanisms193201 soft soil embankments 225, 2278 in foundations 1989, 200 lateral 219 of soils 43 causing development of tensile or compressive forces 43 see also creep design
limit state 2989 maximumallowable load 16 reinforcement structures 292 design angle of friction 678, 82, 143, 1745, 216
in backfill
157
design charts sideslope reinforcement 13940 static wheel loading,unpaved roads 2612 steep reinforced slopes 11620 steps for use of 11718 steep slopes with level crest lOS, 12930 unpaved roads 25860 design earth pressure coefficient 11213, 113. 217 design equilibrium 978 design required stress 119 design shearing resistance73, 94, 217 design situations 878 design strength 151 derivationof 93 of reinforcement 94, lOS, 122 design temperature 91, 171 design time (polymermaterials) 912 design values 95, 121 basis of calculations 879 for input parameters 117, 126, 151. 161 interaction properties 94 loadings 89 pessimistic 98, 176 for serviceability101, 149, 181 soil properties 904 of soil shearing resistance 9, 48, 50, 55. 94 differential settlement, limited by geotextiles 6 dilation 64, 69
320
angle of 69
direct shear tests 54, 6871, 120, 221 modified489 direct sliding 43,48 direct sliding coefficient9,48, 50, 55, 94, 115, 118, 171,221,227 between geogrids and freedraining soil 2223 direct sliding resistance 50, 185, 229 between fill and reinforcement layer 195
of embankment fill over reinforcement layer 195, 222
fill over reinforcement 2434 possible mechanisms 161 preferential 98, 194 and retaining walls 1602, 175 soft soil embankments 1946, 22930 steep reinforced slopes 11516, 12830 unpaved roads 258 in unreinforced embankments 1967 unreinforced embankments 230 within granular fill 222 directionallystructured fabric (DSF) see knitted fabrics (geotextiles) displacement due to reinforcement elongation 166 and shear strain 67 drainage blockage, risk of 89 drained analysis, design values 901 drained bearing capacity 59, 7982, 175 under combined loading 82 drained frictional shearing resistance, compact granularsoils 635 drained peak angle of friction 62
draw ratio 16 drawdownconditions, most adverse
89
earth pressure coefficients 1089, 110, 112, 172
eccentricity, excessive, retaining walls 162 effective stresses 43 caused by desiccation 77 embankments on soft soil 222 governing undrained shear strength 74 retaining walls 182 elastic rebound 114 Special Publication 123 © CIRIA
Index
elongation causing deformation 164 cumulative 171 maximum acceptable 141 maximum allowable 92, 101, 117, 1489 over life of slope 122 maximum tensile 16 in nonwoven geotextiles 37 in woven geotextiles 40,41,41 see also reinforcement elongation embankments backanalysis of failures 78, 78 foundation design with simple sheartests 77 maximum shearing resistance 198 settlement of 219, 225 slips 133 stability of 189 see also clay embankments; soft soil embankments environmental considerations 300 environmental degradation 92 environmental degradation allowance 121, 141, 143, 171, 227 equilibrium on all potential failure mechanisms 126 allowable equilibrium, working platforms 2456 balanced 108, 158 effects of reinforcement on 44 expected equilibrium limits 1013 horizontal 185, 214 idealised 1078 influence of reinforcement stiffness, soft soil embankments 223 maintenance of with depth 1367 maximum gross required force for 1012 maximum required strength for 230 on potential slip mechanisms 1634 in reinforced soil 468 required shearing resistance for (clay) 137, 137 working platforms with known reinforcement 2456 see also overall equilibrium expected surcharge loading 89 expected water pressures 89 Special Publication123 © CIRIA
extemal equilibrium 99, 99 retaining walls 1604, 1756 steep reinforced slopes 11516, 124 external stability 98, 116 retaining walls 1634, 176 extrapolation, for longterm properties 212 face deflections, contributary factors 14950 facings 296 forces transmitted through 169, 169 fullheight 16970 factors of safety 545, 67, 68, 126, 170, 215 on potential slip surfaces 209ID in reinforced sideslopes 1378, 142 reinforced and unreinforced embankments 2323 soft soil embankments 215, 216 unreinforced 2301 working platforms 247 see also partial factor of safety; safety, lumped factor of failure by tearing 25 foundation failure 115 overall failure mechanisms 1512 potential, on slip surfaces 124 rapid undrained, soft clay 91 retaining walls 160 shallow slope 1 312 sliding failure 82 through clay softening 137 through imposed loading 190 unpaved roads 264, 2656 see also direct sliding failure surfaces, potential, deeperseated 110
fatigue coefficient ot lIammitt277 unreinforced unpaved roads 264 fibre reinforcement 2912 field strength, of the reinforcement, practical estimation of 923 field vane tests, measuring shearing resistance 779 fill integrity maintenance by geotextile separator 4 321
Soil ReinforcementWith Geotextiles maximumreinforcementelongation165 sloping 1834 stability of 301 to soft clay interface 222 unpaved roads bearing capacity 2578 stresses in 2545 thickness v applied surface pressure 2689, 2723 working platforms bearing capacity failure 247 design strengths 249 stresses in 2401 see also granular fill; reinforced fill filters nonwoven geotextiles 37 woven geotextiles 34 finite element methods 223 fissuring, and clay soils 133 forces allowable forces, working platforms 245 available forces 46. 47, 88, 154, 155 foundation bearing capacity, design value 176
foundation engineering, draft European
code 87 foundation soil, ability to support inclined and eccentric loading 149 foundation surface, slippage across 1967 foundations 226 bearing capacity 148, 163, 164, 193 reduced through inclined loading 802 consolidation of 225, 292 deformation in 1667, 1989 failure of 101, 115, 160, 198, 199, 208, 222 foundation equilibrium 1823 maximum reinforcement force 21516, 216 soft clay 189 soft soil embankment stability 197201, 204, 21011, 212, 213, 218 stability of 98, 157, 164, 164, 296 strength increasing with depth, analytical solutions 21617 of uniform strength and limited depth, analytical solutions 21516 322
friction angles of 5961 for granular fill 66, 66 mobilised angle of 177 at rest angle of 60 design angles 678 frictional bond, reduced in geogrids 35 ifictional direct sliding coefficient 222 frictional resistance 635 frictional shear 36, 45
Gault Clay embankments, failure rate 132 geogrid reinforcement bond coefficients for 51,52,534,54 definition ofdimensions for 49 formation of 35 mode of interaction during pullout 49 properties for 41, 42 soil interaction with 301 geogrids 2, 357 alternative products 2 characteristic stiffnesses 172, characteristic strengths 122, 171 direct sliding resistance for 48, 48 effects of construction on 25 geogridlike products 36, 36 interaction coefficients 556, 2223 material performance and 'limit strain' 20 see also cellular reinforcement mattresses; polymergrids geomeshes 2, 367 geotechnical properties 299300 geotechnical structures I geotextile reinforcement applications 67, 10 boosting resistance to externally applied load 11. 12 factors influencing selection 9 force required varies for differing applications 8 placement of in soil 46 geotextileclay interaction, soft clay foundations 222 geotextiles aged life of 223 application concepts 36 Special Publication 123 © CIRIA
Index capabilities of 89 chemical breakdown 300 conventional I damage and durability of 259 drawbacks to use of 1213 economic and technical benefits from use
of 12 effects of the chemical/biological environment 15, 23, 29 form of influences properties 16 importance of form of 9 improving embankments 189 longterm testing 300 multiaxial repeated loading 300 nonwoven 300 products 3142 reasons for growth in use of I as separators 910 in sideslopes of clay embankments 132 as soil reinforcement 46, 1012, 10 spunbonded nonwoven 2 strength and stiffness properties 1617, 1823 as tensionmembranes 238 tensioning before filling 8 use in construction 78 what are they? 23 related products see cellular products; geogrids; geomeshes; knitted fabrics; strips; webbings Giroud and Noiray allowance for traffic 2812 unpaved reinforced road design 2802 granular fill 170, 226, 236 granular soil(s) 638 compaction procedures for 114 strength and compaction 656 testing of 6871 groundwater 76 level 80 level fluctuation 76, 77 table rising, risk of 89 see also porewater pressure Hammitt, unpaved unreinforced road design 27680 Special Publication123 © CIRIA
high density polyethylene (HDPE) 15, 41, 42 hydrolysis, effects of on polyester 28 idealised equilibrium, steep reinforced slopes 1078 inclined loading, influence of 802 undrained bearing capacity 823 index loadelongation curve 24, 24 index properties 17, 234 index tests 17 instability, in clay embankments 1312, 1324 installation damage 23 interaction coefficients 199, 201, 221, 2223 interaction properties 94 intemal equilibrium 99, 99, 101, 102, 110, 180
retaining walls 1501, 15860, 1724 sloping fill 1834 steep reinforced slopes 10510, 11314 inward shear stress 192, 201, 215, 232, 237 isochronous loadelongation curves 20I,
21,46 knitted fabrics (geotextiles)
I, 3, 38
limitequilibrium analysis 10910, 20714 calculations 299 clay embankments 13 12 investigating serviceability 223 sideslope reinforcement 13940 working platforms 2412 limit state design 2989 ideas of 678 method of 87 limit states 97103 retaining walls 172 soft soil embankments, reinforced embankments 21819 steep reinforced slopes 122 limiting bearing stress, circular loads 263 limiting resistance to surface loading, working platforms 242 323
Soil ReinforcementWith Geotextiles load bearing capacity, improved by geotextile reinforcement 56 loadshedding allowance 11213, 154, 157, 176
loadspread angle, working platforms244 loadspreading 1801, 182 loading(s) 163 allowable 18, 20 backfill loading 183 critical, crest edge 21415 design values for 89 eccentric 80 guarding against sudden change in 2023 horizontal 17980
inclined /79 soft soil embankments 1901, 219 vertical 180I, 198. 208 locus of stress 118, 11920, 123 logarithmic spiral analysis 125 analysis of reinforced slopes 10910, /09 in slip circle analysis 211 London Clay peak shearing resistance at low effective stress 137 shearing resistance at low effective stress 134
sideslope reinforcement requirements 13940 slopes 132 triaxial tests on 1334 London Clay embankments failure rate 132 porewater pressures in 133 shallowslip analysis results 1369 loopanchor construction 292 walls 147, 1845, 186 'lumped factor' design 67 lumped factor of safety 68
material factor (a partial factor) 93, 143,
22! material properties 171 for design 15,38,92 mean effective stress 61, 62,64,71 membrane action, of geotextiles 56, 5 metal strip reinforcement 147
324
of characteristics, for bearing capacity factor 2534 method of slices 21314 comment 1256 mobilisedangle of friction 59 clay embankments 136 in fill 165, 166 steep reinforcedslopes 121 under at rest conditions 60 mobilisedaxial tensile force IS mobilisedeffective cohesion, clay embankments 136 method
mobilisedfrictional shearing IS mobilisedreinforcement force 45 in fill 166 mobilisedshearing resistance(s) 46, 59, 60 in fill 1656 variationwith depth 136 mobilisedtensile force 60 MohrCoulomb strength envelope 723
Mohr's circle of stress 60 moment equilibrium, retaining walls 156, 157, 158, 175
mud waves 8, 293, 294 noise barrier, design example for steep reinforced slopes 1204 nonwoven geotextiles 2, 9, 378, 51 direct sliding coefficient50
extensibilityof 37 in unpaved road reinforcement
378
notation used xixxiii oedometer tests, soft clay foundations 77 outward shear load/stress 1912, 191, 195, 200, 21617, 237, 239, 2534 overall equilibrium 99, 99 equations for 1545 retaining walls 1518, 1745, 1823 steep reinforcedslopes 11013 overall failure mechanisms 101, 1512, 1745
overall stability, soft soil embankments 196201, 210Il, 218 overconsolidation 74 causes
of 75, 75
Special Publication123 © CIRIA
Index with depth in soft clay foundation 767,
77 overconsolidation ratio (OCR) 75 overlapped joints 8
partial factor of safety 91, 227, 2345 in serviceability limit state calculations 90 on undrained shearing resistance of soft clay 21920 particle migration, prevention of by separators 10 particle size, influence on soil bearing stress
53,55 particle size effects 299 particles, closely packed, interlocking between 64 peakangle of friction 60, 61, 67,678,69 in direct shear tests 6970 in the fill, soft soil embankments 2245 increased with overconsolidation 71, 72 increasing with distance from critical state line 62, 62 for London Clay 71, 72 variationwith soil density and mean effective stress 64, 64 peakdirect sliding resistance 54 peakplane strain angle of friction 66 peak shearing resistance 60I, 6970 London Clay, at low effective stress 134,
'34
reduced by porewater in compact clay soil 73 permanent road thickness, unpaved roads 2689 permanent works, use of geotextile separators 4 physical mechanisms, causing behavioural change 21,22 plane strain loading 64 plane strain test 68 plane wedge, most critical mechanism through the toe 150 plasticity analysis, concepts from 2047 plasticity solutions 2056 Special Publication 123 © CIRIA
plasticity index 78 theory 2045, 21112 theory application 2067 upperand lower bound theorems of 823 plasticity theory 2045 point loads, retainingwalls 17883 polyaramid IS polyester 15, 34 creep tests 18, /8 effectof hydrolysis 28 grid products 36 strip reinforcement 147 polymergrids 121, 141, 143, 147, 170, 171 skin friction 50, 51, 55, 121, 171 polymermaterials 147 chemical and biological durability 268 creepbehaviour 1617, /7, 18 desirable properties 15 properties 1618 strength and stiffness of 15 types IS yield and/or rupture 1920 polymerreinforcement bonds and separators 3I concepts 91 polypropylene 15, 34,41,42 pore suction 77 porewater pressure assumed 1345 clay embankments 131, 132, 133, 143 in compact clay soil 73 constructioninduced 219 and design equilibrium 98 distribution developed with time in clay embankments 1345 embankments on soft soil 219 excess 201, 202, 222 freedraining granular fill 153 porepressure ratio 116, 117, 143 retaining walls 151 seasonal 1345 in soft clay 91 steep reinforced slopes 116, 117, 121, 299
priceperformance relation, polymers pullout 48 pullout tests 4950, 143
15
325
Soil ReinforcementWith Geotextiles quicklime 143 reference properties 15, 38, 92 geogrids 42 measurement of 23S for yams 40 reinforced fill 148 avoidance ofdirect sliding 161 deformation of 1646 mobilised angle of friction in 177 unpaved roads 2557 working platforms24952 reinforced soil behaviour of 4357 investigation of equilibrium in 468 stability analysis for 978 strength of IS reinforced soil walls 147, /47 definitions for 148, 148 effects of fullheight facings 16970 final vertical alignment 1667 reinforced zone, line of thrustin 1557 reinforcement bearing stresses on 52
cost of 232
design of structures 292 and development of tensile reinforcement force 44 limits to vertical spacing 120 optimum directions for 45 orientation and stiffness 456 retaining walls connections 168 rupture on working platform 247 selection of, clay embankments 1413 selection procedure 2512 soil interaction properties 301 strengthening soils 434 tension in for fill of unpaved roads 257 in two perpendicular directions 312,32 working platform calculation 250 see also geotextile reinforcement; soil reinforcement reinforcement bond 1423 reinforcement elongation 117, 164, 165, 166, 172, 1768 a component ofdeflection 94 and lateral deflection 2234 326
maximum allowable 251 reinforcement extensibility, influence of in overall stability 199201 reinforcement force available reinforcement force 126, 141, 142, 151 maximum available 152, 153, 21011 reinforcement layers, available forces in 91, 101, 102, 181, 209 reinforcement length 118, 12830, 154, 176, 184
and bond allowance 1534 constant 110 reinforcement materials comparison of 3842 properties 914 properties for soft soil embankments 2201 serviceability 934 reinforcement and separation functions 6 reinforcement spacing 157 and bond allowance 1534 reinforcement stiffness 93, 177, 201, 225,
2312 analytical solutions 21718 influence of on embankment performance 223
reinforcement strength properties 92 reduction of 92 for ultimate state analysis 221 reinforcement strips 38, 39 reinforcement zones, at constant spacing 119
reinforcementseparation interaction 7 relative density index 645, 66 representative critical state strength of soil 90 representative peak strength of soil 90 required earth pressure coefficients 122 required fill thickness v applied surface pressure, unpaved roads 2689 required forces 88, 97, 101 for equilibrium 467, 1078, 179 maximum, distribution of 21, 211 required reinforcement force 151 for equilibrium 141, 142, 143, 1545 gross,for factor of safety 138, 138 Special Publication123 © cIRIA
Index unpaved roads 2745, 2846 variation of over time 11, 12 required reinforcement length 11011, 118, 122, 1389, 138, 143, 157 minimum required for overall equilibrium 1578 to resistdirect sliding 161 required stress(es) 97 for equilibrium 107, 1089, 11819, 123, 1723 variation of with depth 108 working platform calculations 249 resistances, combinations of 43 retaining walls 105, 14787 deformation of 148, 1647 design example 1708 design steps summary 14850 ultimate limitstate 1726 external equilibrium 1604 internal equilibrium 1501, 15860 loopanchor' walls 147, 1845, 186 maximum horizontal displacement 165, 166
maximum settlement, at wall crest 166 modular block 170, 177 overall equilibrium 1518, 1823 point loads 17883 practical aspects influencing design 16770 reinforcement for 6, 6, 8 sloping fill 1834 sources of displacement 1645 see a/so steep reinforced slopes road embankment (design example) 22633 details 2267 serviceability, limit state 2302 ultimate limit state 22730 rotational stability 207 foundation and overall stability 210Il slip circle analysis 20810 rupture 20, 26, 208, 229 preferential, along bedding planes 67, 69 rupture point 1920, 19 rupture strength 16 rutting 237, 238 unpaved roads 263 SpecialPublication 123 © CIRIA
safety, lumped factor of 68, 87 safety margins and design values 8796 see also factors of safety sands, triaxial strength data 65, 66, 67 scaleeffects 56 of particle size 53, 55 seamedjoints 8 secantangle of friction 90 secantstiffness 165, 166 selfweight loadings 89, 1078, 163, 179 vertical 190, 208 separation, by woven geotextiles 34 separation and reinforcement functions, combined over poor ground 6 separationreinforcement interaction 7 separators geotextiles as 34,3, 910,9, 31 givingmechanical improvement 4 nonwoven textiles as 37, 38 strength requirements 8 serviceability 219 limit states 87, 89, 1013, 117, 121, 1489, 2302 reinforcement for equilibrium for 251 reinforcement properties for 934 retaining walls 1768, 1845 soft soil embankments analysis for 2235 parameters for 2245 reinforcement stiffness 218 unpaved roads 258 working platform limit state analysis 248 working platforms with known loading 246
working platforms with known reinforcement 2446 serviceability strength 101, 117, 122, 149 limited by design strength 172 settlement, unpaved roads 257 shallow slips 196 analysis for 1346 longterm, prediction difficulties 1323 slip repair 1379 construction expedients 143 slip surface geometry 1356 surface stability 22930 321
Soil ReinforcementWith Geotextiles shape factor 53, 56 shearbox tests/testing on clay soils 734, 170 direct sheartest 6871 sheardeformation 43, 44 influenced by reinforcement stiffness properties 46 strain development in 45 shear strain 67 shear strength, reinforced soils 43 shearing resistance 43 of clay 2023, 225 at low effective stress 131, 131, 1334 fullysoftened 143 soft clay foundation 230 design shearing resistance 73, 94 direct sheartest 69 improved by reinforcement force 45 sheathing protective 36, 36 sheathed materials 38 sheet reinforcement, advantages of 34 sideslope reinforcement, design charts 13940 simple shear tests 77 single wedge analysis 125 site preparation 2978 skin friction, polymergrids 50, 51, 55, 121, 171
slickensides 73 sliding, coefficient of direct 248 sliding block, critical depth of 21617 sliding failure 82 slip circle analysis 20810 limitations to 21112 slip circles, shallow 136,211 slip failure 160, 229 slip mechanisms, and deformation 193201 slippage, relative, modes of 222 slope protection 296 sloping fills 1834 soft clay, undrained shear strength 236 soft clay foundations 749 consolidation history 746 selection of appropriate design undrained shearing resistance 79 testing of 779
328
'soft ground construction', defined 189 soft soil, construction over 99100 soft soil application, stability analysis for 97, 98 soft soil embankments 189234 analysis for longterm stability 220 analytical solutions 21418 concepts from plasticity analysis 2047 construction rate and drainage 2014 critical length of 21516 design examples 22633 design parameters 21826 intemal stability 1946, 218, 22930 limit on embankment height 198 limit equilibrium analysis 20714 overall stability 196201 reinforced design strategies 204 failure in 208 settlement in 225 slip mechanisms and deformation 193201
stress and force equilibrium 1903 unreinforced 192 failure in 208 outward shear stress in 200 use of soil reinforcement 10, 10, 1/, 12,
323,33 see also clay embankments soft soil foundations 1001 softening, in clay soils 73 soil maximum expected unit weight 89 mechanical improvement of by reinforcement 46, 4, 6 selfweight loading of 89 soil behaviour, relevant to reinforced soil design 61 soil compaction, maximum horizontal stress 114
soil density 61,62 soil environment, influence of time 28, 28 soil index tests 77 soil interactions, and maximum available force 211 soil nailing 132 soil properties 90Special Publication123 © CIRIA
Index soft soil embankments 21920, 220 soil reinforcement geotextilesas 1012 for mechanical improvement of soil 46 with optimally placed tensile elements 12
soil shearing resistance 43, 98 design value of 90 soil strength design values 90 drained analysis 901 loss of 67 mobilisation of 223 representative values 90 soilreinforcement bond 504, 51 soilreinforcement interaction 4850 soils at rest conditions of 60 distinction between granular and clay 62 stressstrain response of 101 see a/socompact soils stability analysis, general methods 1246 degree of improvement in 138 drained soil analysis 90 foundations 98, 157, 164, /64, 296 foundations of limited depth 21112 internal, soft soil embankments 1946 overall stability 12830, 143, 154, 1745, 208
soft soil embankments 18990, 192, 204, 218, 226 and undrained shearing resistance 203 of walls 148, 177 working platforms calculations 24851 static fatigue 1617 static wheel loading, unpaved roads 2603 steel reinforcement 292 steep reinforced slopes 10530 behaviour 44 comparison of reinforcement layouts 124, 125 dcsign charts 11620 design example 1204 external equilibrium 11516 internal equilibrium idealised 10510 Special Publication123 © CIRIA
practical corrections 11314
with level crest, design charts 105. /2930 maximum required stress 108 envelope of 11819, /18 increasing linearly 107, 108 overall equilibrium 11013 placement of layers 8 steep slopes and walls external equilibrium 99, 99 internal and overall equilibrium 99, 99 stability analysis for 97, 97, 98 stiffness offullheight facing 170 geogrids /72 of polymer materials 92 referencestiffness properties 24 ofthereinforcement 93, 177, 201, 225,
23 12 analytical solutions 21718 influence of on embankment performance 223 specific stiffness 40 stiffness properties 1617, 18, 201, 3940 strain angle of friction 170 strain compatibility 15, 43, 468, 67 relations for 47 and stress equilibrium 103 strain rate effect, unpaved roads 2667 strainrate, and undrained shearstrength 79 strength due to dilation 70 index for retaining wall reinforcement 171
index strength properties, woven geotextiles 40, 4/ index strengths, polymergrids 121 of polymer materials 92 reduction of on compaction 66 reference for retaining wall reinforcement 171
referencestrength properties 24 specific strength 389, 39, 40 strength properties 1617, 18, 1920, 3940 reduced by mechanical damage 256 uniaxial polyethylene geogrid 20 329
Soil ReinforcementWith Geotextiles stress at retaining wall base 175 available stress 97 compressive, perpendicular to plane of reinforcement 45 due to horizontal wall loading 17980 horizontal, in soft soil embankment fill 190I
vertical, in foundation soil 1978 stress concentration at connections 168, 169 local 25 stress from reinforcement, retaining walls 173
stress locus, steep reinforced slopes 118 stress relief6 stressrupture 1617 stresses, principal 59 strip footing, undercombined loading 80 strips 2 sheathed 36 subgrade bearing capacity unpaved roads 2534 working platforms 23940 surcharge loading 89, 157, 163 minimum uniform vertical surcharge 89 surface bearing capacity, unpaved roads 263 sustainedload creeptests 18, 18, 19 temperature and limit state analysis for working platforms 247 and polymer behaviour 15, 16, /7, 22, 25 temporary works, use of geotextile separators 4 tensile axial force 43 tensile properties, cellularreinforcement mattresses 226 tensile reinforcement, at base of granular layer7 tensile reinforcement force 5, 44 tensile strain 43, 46, 47, 60 maximumtolerable9 in soil and reinforcement 102, 102 tension cracks embankment slopes 134, 135 330
soft soil embankments 208 waterfilled 195, 219 testing see accelerated testing Thamesgravel 170 thrust horizontal beneath edge of embankment crest 1946. 197 from backfill 1678 lateral 208 line of, in the reinforced zone 1557 timing and structural life 2946 traffic allowance Giroud and Noiray 2812 mixed on unpaved roads 270I unpaved roads 2637 1 traffic loading, unpaved roads 265 translational stability 207 wedge analysis 211,21213 triaxial compression tests/testing 60 granular soils 68 London Clay 71, 72 triaxial strengthdata, sands 65, 66, 67 twopart wedge analysis 125, 1512, 153 analysis of reinforced slopes 109, 109 direct sliding 115, /15 of intemal equilibrium 1789 of overall equilibrium 1789 for reinforced soil 167 ultimate limit state calculations/analysis 87, 89. 90 retaining wall 148, 170, 184 soft soil embankments 21923 steep reinforced slopes 98101, 117, 121, 122
working platform 2478 uncertainty, in extrapolation 212 undrained analysis, soil properties 91 undrained bearing capacity 59, 823, 84 with inclined loading 83 undrained shear strength differences in vane and criaxial compression tests 77 embankments 189, 222 expected 767 increasing with depth 91 SpecialPublication 123 © CIRIA
Index lower limitto 76 and mode of shearing 74 normally consolidated clay 75 relations for and nonorganic clays 79 undrained shearing resistance and plasticity index 78, 79 soft clay 219 and vane correction factor 78, 78 uniaxial geogrids 35, 35, 41 unpaved roads allowance for traffic 26371 backanalysis of reinforced trafficking trials 2827 comparison with previous design guidance 27587 design charts 25860, 2723 design life 274 failure, definition of 2656 failure mechanism 264 fatigue relation 268 fill bearing capacity 2578 over soft foundations 1001 permanent road thickness 2689 reinforced design 2557, 2735 Giroud and Noiray 2802 reinforced tests 283 required fill thickness v applied surface pressure 2689 required reinforcement force 2846 serviceability 258 static analysis 25360 static wheel loading design example 2603 strain rate effect 2667 stresses within the fill 2545 subgrade bearing capacity 2534 traffic allowance, mixed 270I trafficking trials 266, 266, 2827 unreinforced design 2713 unreinforced design by Hammitt 27680 unreinforced tests 2834 vane correction factor 267 wheel loading 26970 vane correction factor (Bjerrum) 78 unpaved roads 267, 267 SpecialPublication123 © CIRIA
variable (secant) peakangle of friction 63, 71
vegetation, protection with 296 vertical drains 293 vertical effective stress current 74, 75 increase in beneficial 91 vertical stress 80 vertical surcharge, uniform, allowance for 120, 181 void ratio 656
wall roughness value 108 walls see retaining walls water
free transmission through geotextile separators 3 see aLio porewater pressure
water content, of clays 71,
72
water pressures89 weathering,in nearsurfaceclays 133, 137 webbings 3 Websterand Watkins, unpaved road tests 2827 wedge analysis ISO, 181, 182 wheel loading, unpaved roads 26970 wick drains 2945 working platforms 23589 analysis 23946 comparative designs 2523 design example 24853 design procedure 2468 fill bearing capacity 2434 mechanics of reinforced action 2369 reinforced combined loading 2379, 238 reinforced design 242, 243 reinforcement anchorage 238 reinforcement properties for 2512 serviceability for known loading 246 serviceability for known reinforcement 2446 stability calculations 24851 stresses within the fill 240I subgrade bearing capacity 23940 two dimensional loading 236, 236 unreinforced combined loading 237, 237 unreinforced design 2412 331
Soil ReinforcementWith Geotextiles worstexpected live loading 89 woven geotextiles 2,6,334, 39, 51, 141 allowing steepening of side slopes 230 direct sliding coetticient50 index strength 229
332
interaction coefficients 545 properties of 40I, 226, 227, 227
point 1920. 19 zones, in steep reinforced
fill 1056, 106
Special Publication 123 © CIRIA
1
Engineering with geotextiles
Thetermgeotextile, as originally defined, refers to textiles(fabrics) used in geotechnical engineering. Two broad classes of geotextile have emerged namely conventional geotextiles, the typical products ofthe textile industry, including woven and nonwoven fabrics, and the more recent geotextilerelated products, such as geogrids and knitted fabrics, which are used in combination with, or in place of, conventional geotextiles (ISSMFE Technical Committee on Geotextiles, Giroud et al., 1985). The word geotextileis usedin this book as a generic term to include both geotextiles and geotextilerelated products. Individual categories of products are referred to by name only where strictly necessary. Thehistorical development ofgeotextiles is described in Giroud (1986) whereseveral reasons are identified to explain why contractors, designers and ownersso readily accept these materials. Contractors are interested in quicker, less weatherdependent construction, reduced volume of earthworks and the possibility of using poorerquality soils. Designers like the greater reliability and control which stems from the uniform properties ofgeotextiles, the ease ofplacement, and the ability ofgeotextiles to mitigate local soil defects. Owners favour cost savings in construction and maintenance budgets. More fundamental reasons for growth in the use of geotextiles are identified by Giroud:
I. The properties of granular soils are complemented by those of membranelike materials; granularsoilsmay be disrupted by erosion or settlement, but a geotextile with tensile strength can remain continuous. 2. Geotechnical structures are usually formed by layered construction, and membranelike materials easily form an interface between layers, or act as a liner or as protection at the ground surface. 3. Geotechnical structures are flexible and subjected to differential movements, and flexible membranelike materials are compatible with this behaviour. Another reason for the success of geotextiles is that an efficient use ofmaterials can be achieved by reinforcing soil with optimally placed tensile elements. Once reinforced, the soil can often be loaded to levels which would otherwise approach (or exceed) failure, although still providing a safe reinforced structure, because ofthe presence ofthe reinforcement. Detailed observations of geotextile reinforced soil structures under working conditions often reveal equilibrium with the soil mobilising close to its peak shearing resistance, while the reinforcement carries proportionately less tensile force SpecialPublication123 © cIRIA
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Engineeringwith geotextiles
1
than allowedfor in design. Thus the compatibility in soil reinforced by geotextiles often results in the soil strength being almost fully exploited so that the reserve of safety resides in the as yet underused,but still available, reinforcement strength. The systematic application of textiles did not immediately follow their first uses in civil engineering, such as cotton fabric (Beckham and Mills, 1935), but came with the availabilityof adequate products, in this case a synthetic fabric which could resist rot. Significantgrowth in applications only came once the fabrics were both adequate and inexpensive, with the introduction of spunbondednonwovens in the early 1970s. Thelarge European andNorth American manufacturersofnonwoven fabrics enjoyed great success in the 1970s because of their production capabilities. But smaller manufacturers also found success through innovation. New products such as strong woven fabrics, polymergrids and synthetic strips were developed in the late 1970s and early l980s, leading to the wide range ofgeotextiles and geotextilerelated products now used in geotechnical engineering.
1.1
What are geotextiles?
Geotextiles are made from polymer materials. The production of geotextiles may be considered as two steps. The first step consists in making linear elements such as filaments, fibres, tapes and yams from polymer materials, the most commonly used being polyester, polypropylene, polyethylene and polyamide. The second step consists of combining these linear elements to make a permeable planar material. There are two main types of conventional geotextile:
• woven geotextiles composedof two perpendicular sets of parallel linear elements interlaced to form a planar structure
• systematically nonwovengeotextilesformed from filaments or fibres randomly arranged and bonded together to form a planar structure. Bonding is normally achieved by mechanical, thermal or chemical means. Geotextilerelated products have a coarser structure than conventional geotextiles and those used for soil reinforcement include:
• geogrids manufactured by heating and stretching a perforated polymer sheet in either one or two directions geogrid products made from strips or yams combined in two perpendicular directions to achieve a grid form, but with varying degrees of mechanical connection at the joints and protective sheathing geomeshes made by extrusion to form a relatively low strength and low stiffness material (only temporary reinforcement properties) strips comprising yamslaid parallelin a stripand heldinpositionand protectedby a polymer coating
• alternative
• • 2
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Conceptsfor geotextile applications
1.2
• webbings, conceptually like a coarse woven fabric but made up from synthetic (above) • strips knitted geotextiles made by knitting yarnstogetherto form a planar structure • cellular products,either manufacturedby bonding strips of material into a cellular form, or formed on site by interconnecting grids to form a mattress.
Theabove categories arebroadlyin line with thedraftEuropean standard of terms and definitions for geotextiles and related products (CEN, 1990). Useful guides to available geotextile products and suppliers may be found in Ingoldand Miller (1988) for Europe, and Koerner (1990) for North America.
1.2 Conceptsfor geotextile applications This bookconsiders the uses of geotextiles for soil reinforcement. Geotextiles are also widely used to separate dissimilar soils, such as in Figure 1.1, but these are largely empirical applications. The use of geotextiles as separators is discussed briefly below in order to distinguish between reinforcement and separation. Separation is usually achieved with a nonwoven or woven geotextile to prevent intermixing ofpoor insitu soils with good quality granular materials subject to surface loading (Figure 1.1a.) The separator provides a barrier to migration of particles between the two dissimilar soils but allows the free transmission of water. One requirement for a separator is a sufficient tensile strength to maintain continuity and not rip, puncture or burst under the local stress concentrations caused by irregularities in the foundation or fill material. With geotettile
Without qeotexthe
(b) Reinforcement
Figure 1.1 Geotextila functions (a) separation and (b) reinforcement Special Publication123 © CIRIA
3
1
Engineeringwith geotextiles
Theseparationfunction ofa geotextile is primarily to maintain the integrity ofa good quality fill which would otherwise be reduced by the intermixing with poorer soil. A separator may also impart a degree ofmechanical improvement as atensileelement. The important applications for geotextile separators in temporary works are on poor ground, e.g. access roads and working areas, or in the initial stages of embankment construction over soft foundation soils. The main application in permanent works is to resist intermixing and deterioration caused by repeated loading, such as in paved roads or railroads. Therearefew general references about geotextile separation, although theapplication is described in Van Zanten (1986) and Koerner (1990). A set of technical notes on geotextile separation has been published in the Proceedings of the Institution of Civil Engineers, Transport, May 1992. The wil reinforcement functionof geotextiles is the mechanical improvement of soil. Reinforcement allows soil to carry greater shear loading than would otherwise be possible. When the disturbing forces are caused by the soil selfweight loading, such as in a soil slope or anembankment ona soft foundation soil, the inclusion ofreinforcement can allow a steeper slope or embankment to be built(Figure 1. Ib). Where the disturbing forcesarecaused by externalloads, suchas in an unpaved road or working platform, the inclusion of reinforcement can allow greater load to be applied. Reinforcement achieves this mechanical improvement by supporting tensile force which acts (a) to reduce the shear force that has to be carried by the soil, and (b) to enhance the available shearing resistance in the soil, by increasing the normal stress acting on potential shear surfaces. These actions are illustrated in Figure 1.2 for an element of reinforced soil in a direct shear test. Compressive and tensile strains develop when soil deforms in shear along a potential rupture surface (Figure 1.2a). Reinforcement acts efficiently when inclined in the
Shearing soil
IF
ii
/z///7//zA7/ (///MZ///////////
p
.
'V
Reinforcement
Tensile strain
Compressive
P,
P,tan
,
Ar
cos sin
P, = P. tan 4
P(sin 0 + cos 0tan
)
Figure 1.2 Illustration of reinforcement action in direct shear: (a) tensile and compressivestrains in soil, and (b) resultant reinforcement forces 4
Special Publication123 © CIRIA
Conceptsfor geotextile applications
1.2
directionin whichtensile strain develops in the deforming soil, so that shear deformation in the soil causestensile force in the reinforcement (Figure l.2b). The benefit of reinforcement stemsfrom thecomponents of the tensile reinforcement force, actingon the shear surface in the soil. The tangential component, sin 0, acts directly to resist the shear load applied to the soil (mechanism 1). The normal component, P, cos 0, increases the normal force across the shear surface thereby enabling greater frictional shearing resistance to be mobilised in the soil (mechanism 2). In this case the shearing resistance is increased from:
r
r'
= P tan 4) in theunreinforced soil, to
= P tan 4) + Pr(sin 0 + cos 0 tan 4)) in thereinforced soil. Geotextile reinforcement may also improve load canying (or bearing) capacity by another, separate, mechanism which applies after the reinforcement has deformed sufficiently to act like a membrane in tension (Figure 1.3). Some of the normal stress from the applied loading on the concave side can be carried by the tensile force in the curved geotextile membrane, thereby reducing the stresses applied to the underlying soil on the convexside of the geotextile. Membrane action requires locally applied loading and significant deformation. Examples where membrane action can be beneficial are (a) in a rutted unpaved road (Giroud and Noiray, 1981), (b) to prevent the collapse of fill into a sinkhole or cavity
Stress on clay
reducedby membraneaction
>AK:\
/
\
//
(b)
Sinkhole
Figure 1.3 Reinforcement supporting load by membrane action: (a) rutted unpaved road, (b) above a sinkhole and (c) in a piled embankment foundation Special Publication123 © CIRIA
5
1
Engineeringwith geotextiles
(Giroudci' al., 1985), and (c) to assistload transferbetween embankment fill and a piled foundation (Jones era!., 1990).
1.3 Examples of the use of geotextiles The rangeofapplications for geotextile reinforcement in fill materials includes vertical walls, steep slopes and embankment slip repairs. Reinforcement can also be used in construction over soft foundation soils to improve the shortterm stability of embankments and to allow increased live loading on thin granular layers such as unpaved roads and working platforms. The applications are sometimes combined, such as the reinforcement of the foundation soil, using freedraining granular soil strengthened by layers of geotextile or a cellular mattress for example, beneath a reinforced soil wall (Figure 1.4). Geotextiles may also be used in embankments on soft soil and in road foundations as a measure to limit differential settlement ratherthanto improve stability — although these two functions are closely related. Reinforcement can also relieve stresses, for example where trench backfill is reinforced to help support subsequent surface loading. The horizontal soil stresses that will develop against the back of a conventional gravity retaining wall can also be reduced by reinforcing the backfill. There are potential benefits in combining the separationand reinforcement functions of geotextiles in construction over poor ground. The separator can reduce intermixing between the fill and the foundation soilswhile the reinforcement enhances loadcarrying capacity. It can be efficientwhen these distinct functions can be provided by a single product, such as a woven geotextile.
Geogrid foundation mattress
Figure 1.4 Combined use of reinforcement to stiffen the foundation beneath a reinforced soil wall 6
SpecialPublication 123 © CIRIA
Constructionwith geotextiles
1.4
But there is a complex interaction between the reinforcement and sepaiation functions of geotextiles which should be noted. One mechanism of intermixing between fill and foundation soils is the opening and closing of tensile cracks at the base of a granular layer under repeated live loading, similar to the cracks on the underside ofa concrete beam (Figure 1 .Sa). This mechanism allows the poorerfoundation soil to be pumped up into the granular layer, causing the harmful intermixing of the two soil layers. Tensile reinforcement at the base of a granularlayer can reduce localised cracking (although distributed microcracking will still occur) and thereby reduce or indeed eliminate this mechanism of intermixing (Figure 1 .Sb). Thus a reinforced unpaved road over soft ground may be less susceptible to intermixing than the equivalent unreinforced road, and may even perform satisfactorily without a separator. However, the circumstances in which a separator may be omitted from a reinforced granularlayer over soft ground have yet to be clearly defined.
1.4 Construction with geotextiles is usuallycompatible with conventional procedures and equipment: seldom is extra plant needed. As discussed in moredetail later, theeffectiveness ofreinforcement depends critically on its orientation and location in the ground. In almost all applications the horizontal direction is sufficiently close to optimum for practical purposes, so that generally only one extra step, the laying ofthe geotextile, is required in the sequence of placement and compaction of the fill. There are additional requirements for construction with geotextiles which include: Construction with geotextiles
I. Careful handling and storage of geotextiles to avoid degradation. 2. Adequate labelling of the geotextiles with clear indication of the correct direction
of laying.
Granular tilt
Reinforcement clay (a)
(b)
Figure 1.5 Local tensÜe cracking at the base of a loaded granular layer: (a) unreinforced case, and (b) reinforced case Special Publication123 © CIRIA
7
1
Engineeringwith geotextiles 3. Sufficient control of filling to ensure that geotextiles are placed at the correct elevations in the structure and are not unduly damaged by the placing and compaction of the fill.
It is also good practice, where possible, to tension the geotextile lightly before filling. Placing reinforcement on a soft foundation soil is also straightforward as the geotextile is either laid directly on to the existing ground surface or on a thin initialfill layer. Preparation of the ground is generally needed only where irregularities would puncture or pierce the geotextile. Appropriate overlaps or seamed joints are required between adjacent sections of geotextile. For construction over extremely soft soils, it may be necessaryto use low groundpressureplantand to control initial filling to reduce the development of mudwaves. In steep slopes and walls the placement of reinforcement layers must be linked with the construction of a face. Soft facings formed by wrapping the geotextile around the soil layers can require temporary external support and formers. Alternatively, the reinforcement can be connected to facing panel units. In summary, construction with geotextiles is no less flexible than conventional earthworks, and often allows faster filling and reduced fill quantities. Special quality control procedures for geotextiles are easily combtned with conventional site practice.
1.5 Geotextile capabilities What can be achieved by a geotextile depends on its material properties and the form in which it is made. Both for reinforcement and for separation it is best first to determine and specify the required properties of the geotextile to achieve the desired function, and then to select a product that equals or exceeds the design requirements. For example, soil reinforcement should be able to support the required design load without excessive elongation to ensure that the deformation of the structure is acceptable. Becausegeotextiles continue to deform (or creep) with time under load, it may be necessaryto estimate the expected deformation at the end of construction and during the subsequentperiod to the end of the design life. This is particularlydesirable for retaining walls and abutments where outward movement and settlement are important design considerations. The strength requirements for a separatorare much less onerous, and serve mostly to prevent perforation, tearing and ripping of the geotextile. It should be noted that the magnitude of the force required from geotextile reinforcement can vary markedly between the different applications of reinforced soil. For example, individual reinforcement layers in a steep slope or wall might be required to support between 3 and 15 kN/m, whereas a single reinforcement layer beneath an embankment on soft soil might be required to support between 30 and 150 kN/m.
8
Special Publication 123 © CIRIA
Geotextilesas separators
1.6
Similarly, the maximum tensile strain which can be tolerated in the reinforcement so that the structure does not become unduly deformed, also depends critically on the application. Typical limits to the acceptable maximum tensile strain in geotextile reinforcement are of the order: 1 to 2% for bridge abutments, 3 to 5% for steep slopes and 4 to 8% for enibankments on soft soil. Thus thefactorinfluencing the selection ofa geotextile reinforcement maybe either (1) the strength or (2) the loadc/ongation properties of the material. Theform of the geotextile (woven, nonwoven, geogrid or strip) can also be an important factor in design. The bond between the geotextile and the soil is more important for strips rather than planar reinforcement products (such as woven geotextiles and geogrids) which have a larger area of contact with the soil. In poorerquality soils, the extra bond capacity afforded by the surface area of geotextile sheets, or by geogrids which mobilise an additional bearing component of bond, can make these planar reinforcement materials preferable. These bond mechanisms are considered in Chapter 4.
1.6 Geotextiles as separators Example applications for geotextile separators, most commonly nonwoven fabrics, are
indicated below: 1. A geotextile placed between the subgrade soil and an aggregate layer to form an unpaved road, a working platform or a storage area (Figure 1 .6a). 2. A geotextile placed beneath railway ballast(Figure 1 .ob), or beneath a paved road (Figure 1.6c). These are distinguished from the previous application by the higher quality of the foundation soil and the requirement to resist deterioration over very many load repetitions.
(b)
(c)
(d)
Figure 1.6 Examp/eapplications of geotextile separators Special Publication 123 © CIRIA
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Engineeringwith geotextiles
1
3. A geotextile placed underwater prior to reclamation filling (Figure 1.6d).
The important properties forthe geotextile separator vary considerably between these applications. Greater resistance to repeated loading is required in railroads than in temporary access roads, while greater extensibility and resistance topunctureare needed for land reclamation. In addition to having suitable filtration properties, the ability of the geotextile to prevent particle migration while allowing the free passage of water, a geotextile needs to have sufficient tensile strength to maintain theintegrity oftheseparator layer.
1.7 Geotextiles as soil reinforcement Four main applications for geotextile reinforcement are: Vertical walls and abutments (Figure 1 .7a). 2. Steep slopes (Figure l.7b). 3. Slip prevention and remedial measures (Figure l.7c). 4. Embankments on soft soil (Figure l.7d). 1.
In these applications, the reinforcement resists loading whichcomes mainly from the selfweight of the soil and the geometry of the structure. An important distinction needs to be drawn between the slope applications in Figures 1 .7a to c, and the use of reinforcement beneath an embankment on soft soil (Figure I .7d). In the first three cases, the reinforcement has to maintain stability throughout the life of the structure. In an embankment on soft soil, the reinforcement is only required to boost stability during the critical period of construction and subsequent foundation consolidation: once the foundation soil has increased in strength the reinforcement is no longer required to ensure stability. This difference is illustrated in
):!*: (a)
(c)
)b)
(d)
Figure 1.7 Example applications ofgeotextiles as soil reinforcement 10
Special Publication123 © CIRIA

1.0
FS
1.0
FS
Time
Time
Time
req
req
req
Required force
Time
Ti me
Time
road
Unpaved
Embankment on soft soil
Steep slope
with time: (a) steep slopes and walls, (b) embankments on soft soil,
Start of loading
Unreintorced
Reinforced
End of construction
I
End of construction
Figure 1.8 Variation of requiredreinforcement force and (c) unpaved roads
(c)
(b)
(a)
—
Unreinforced
Rei:forced
Factor of safety
C)
0 '
1,
CD
0
C')
(I)
0)
Engineeringwith geotextiles
1
the variation with time of the factor of safety, with and without reinforcement, and the corresponding required reinforcement force. Unpaved roads and working platforms are the main applications where geotextile reinforcement boosts the resistance to evterna/[v appliedload (Figure 1.8e). In this case the required tensile force in the reinforcement responds to the repeated loads. This variation over time of the requiredreinforcement force illustrated in Figure 1.8 is probably the most important factor governing the selection of a suitable geotextile Figure 1.8 by
product.
• Where sustained reinforcement force over long time periods is required, as in the • •
slope applications, the creep characteristics of the reinforcement material usually govern the selection. For an embankment on soft soil, the reinforcement force is required over a relatively limited period (during construction and consolidation) so that the longer term mechanical properties of the geotextile may not be so important. The repeated loading in an unpaved road makes the response of the geotextile to rapid and cyclic loading a governing factor.
1.8 Geotextile compared with other solutions Both economic
and technical benefits can be achieved by using geotextiles. But it is
largely the cost savings compared with conventional solutions that have encouraged applications, with savings up to 30% being reportedfor reinforced soil projects in both developed and developing countries. Economies can stem from: • reduced earth moving and landtake achieved by steepening soil slopes • increased construction speed where reinforcement and facings aredelivered ready for use • unrestricted site access because reinforced soil is stable throughout construction • the use of poorer fills strengthened by reinforcement. Technical benefits include: • a more efficient use of materials through combining the shearing resistance of soil with the tensile capacity of reinforcement • the inherent flexibility and tolerance to deformation of a reinforced soil structure • improved quality becailse critical components are prodilced and checked under factory conditions • entirely new solutions made possible by geotextile materials. But there can be drawbackswhich include: 12
Special Publication123 © CIRIA
Synopsis of Chapter 1
1.9
• someremaining uncertaintyconcerning thevery longterm material properties and durability of • possible damage togeotextiles during storage, handling and installation • awkward detailing atgeotextiles corners or in structures with geometries • incomplete codes and standardisation because of theirregular novelty of geotextiles. 1.9 Synopsis of Chapter 1 (1) Thetermgeotextile refers to textiles (fabrics) used in geotechnical engineering. Two broad classes are conventional geotextiles, the typical
(2)
products of the textile industry, including woven and nonwoven fabrics, and the morerecent geotextilerelated products, specially developed to be used in combination with, or in place of conventional geotextiles. In this book, the term geotextile is used to include both geotextiles and geotextilerelated products. The principal types of geotextile and geotextilerelated products are • woven, nonwoven and knitted geotextiles geogrids, strips, webbings and geomeshes. Their principal uses are for separation, reinforcement and filtration, sometimes in combined systems. The purpose of separation is to maintain the integrity of an earth fill, preventing intermixing with poorer quality soils while permitting drainage. The purpose of reinforcement is the mechanical improvement of soil. The geotextile achieves this by reducing shear forces in the soil and increasing the available shearing resistance. Applications of geotextile reinforcement include: • vertical walls, steep slopes and slip repairs embankments on soft soil unpaved roads and working areas.
•
(3) (4) (5)
(6)
• •
Key references Giroud, J.P. (1986). From geotextiles to geosynthetics: a revolution in geotechnical engineering. Proc. 3rd International Conference on Geotextiles, Vienna, Vol. I, 1—18.
Ingold, T.S. and Miller, K. (1988). Geotextiles manual. Thomas Telford, London. Koemer, R.M. (1990). Designing with geosynthetics. 2nd edition, PrenticeHall, New Jersey.
Special Publication 123 © cIRIA
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2
Polymer and geotextile properties
The polymermaterialpropertiesrelevantto reinforced soil design are described in this chapter, together with criteria for their selection and the methods of measurement. The strength of polymermaterials and their loadelongation properties (i.e. stiffness) vary with time under sustained load, and depend on the ambient temperature. Both time and temperature are important factors affecting the material properties of geotextiles. The strength of reinforced soil depends jointly on the mobilised frictional shearing resistance in the soil and the mobilised axial tensile force in the reinforcement. These are linked through strain compatibility. Thus both the reinforcement strength and stiffness properties are important. Geotextiles are used in the ground. Immediate changes to theirmaterial properties can be caused by mechanical damageand longerterm changes caused by the chemical and biological environment of the soil and groundwater. Therefore, the measured properties of exworks reinforcement materials only give a reference, and it is always necessary to assess the changes from these reference properties resulting from mechanical damage and the soil environment.
2.1 Polymer types Suitable grades of high density polyethylene (HDPE), polypropylene and polyesterare
the polymer materials currently used most often to manufacture geotextiles for reinforced soil applications. The desirable properties include sufficient loadelongation behaviour at ambient temperatures, acceptably smallcreepdeformation undersustained loads,only gradual strength reduction with time underload, and reasonable durability in the chemical and biological conditions found in typical soil environments. Suchdesirable properties canonly be achieved at some cost, and therelation between price and performance is significant in the choice of materials. For example, polypropylene is generally less costly than HDPE, but may creep more under sustained load. Polyaramid, a newerpolymertype, has a higher stiffness and generally creeps less than the polymers named above, but it is more costly than either HDPE or polyester. Clearly the cost which is acceptable depends on the envisaged use, the design requirements for the reinforcement, and the economic benefits. Currently, HDPE and polyester are the most popular materials for soil reinforcement, with polypropylene being attractive where the loading is shorter term and the deformation less critical. As new manufacturing processes and markets develop, the relative cost of different polymermaterials and geotextile products will change. Special Publication123 © CIRIA
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Polymer and geotextile properties
2
2.2 Polymer properties Thematerial properties ofa polymerare determined by many factors, and there is a wide variationofproperties forany polymer type. Important factors are the physical form and structure of the polymer, the density, molecular weight. crystallinity and any additives, and the amount by which the material has been drawn during processing. Drawing, the stretching of a polymer material under load, can have a profound influence on the properties and is commonly measured as adraw ratio, the ratioofthe length of the drawn material to the initial length of undrawn material. Only some of theabove characteristics ofa polymercan be discovered from thedirect appearance of the material and the manufacturer's data sheets. There is a need for classification of polymerreinforcement materials and types, such as already exists for steels and electrical laminates. But suchclassification is still at an earlystage, and design engineers must usually rely on manufacturer's information. The form of a geotextile product also influences theproperties. Forexample the loadcarrying elements in woven geotextiles are never perfectly aligned, and this leads to an extra component of extension as they straighten under load. It is still useful, however, to group geotextiles by their basic polymer type (such as polyester) although quite significant variations in material properties should be expected within each type. depending on the precise grade, the additives, the amount of drawing and other aspects of processing. Two general provisions in selecting design values for geotextile reinforcement are: I. An adequate factor of safety between the inaxiniuniallowable load used in design and the rupturestrengthof the reinforcement. 2. A maximum tensile elongation in the geotextile, selected to ensure that the deformations in the reinforced soil structure willremain acceptable, even whenthe geotextile has been when subjected to load over the design life of the structure. Either of these two requirements may govern the maximum force that a given geotextile reinforcement can be relied upon to provide in a serviceable structure. This focuses attention separately on the strength properties and on the stiffness (loadelongation) propertiesof geotextiles. In common with metals, the dimensions of a polymer material under sustained load will change with time — the phenomenon known as creep. While for most metals creep is only important at temperatures above about 300°C, and so is of little importance for civil engineering purposes. creep at ambient temperatures is normal in polymers and is significant for reinforced soil design (Figure 2.1). Creep deformation depends on the chemical composition and the processing of the polymer material, as well as on the ambient temperature. The progressive changes in the polymerduring creep have the effect of gradually reducing the strength of the material with time. This is known as creeprupture, stress16
Special Publication 123 © CIRIA
Index properties
2.2.1
30
 T = 600t
StressMNlm2
.250 0 225
10
o200
8
lo0° 20—
200
600
1000
Time:
(a) Austenitic steel. AfterHenderson eta! (1987)
Time: (b) HDPE geogrid. AfterGreenwood 1990)
Figure 2.1 Different types of creep behaviour in materials: (a) in a metal at high temperature, and (b) in a polymerat ambient temperature
or static fatigue. In general, a polymermaterial held under a sustained load would be expected to break, eventually. But under modest load this might only occur after a period of time considerably greater than the design life of the civil engineering works. There is a concept for a critical stress for some polymers where failure would neverbe expected when the material is subjected to a lesser stress; hut it is difficult to obtain the very longterm data needed to fully substantiate the concept (Wilding and Ward, 1981). In summary, the aim in design is to ensure that the reinforcement has adequate strength and stiffliess properties bearing in mind the conditions in the ground and the period under load, represented by the design life and the design temperature (t11, T11). rupture
2.2.1 Index properties A baseline is needed against which to compare the influences of time and temperature on the properties of polymers. Standard index rests provide a measure of index strength and stiffness properties which help in the comparison ofdifferent materials and in quality control work. Index tests are carried out at relatively high rates of elongation and can be completed quickly. The testdescribed in (British Standard) BS 6906: Part I (BS1, 1987) is recommended for measuring the index tensile properties of geotextiles and geogrids. The sample size is 200mm wide by 100mm long, and a rate of elongation in the range 10 ± 3%/mm is used. The test is carried out at a standard temperature 20 ± 2°C and relative humidity 65 ± 2%. The test reflects the predominantly uniaxial or planestrain loading experienced by geotextile reinforcement in most reinforced soil applications. It may be noted that the deformation ofgeotextiles is described generally in terms of load and elongation, rather than stress and strain. This is because the stateof stress and strain in the filaments, yarns orsections ofgeogrid material vary from place to place, and are not precisely known. Special Publication 123 © CIRIA
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Polymer and geotextile properties
2.2.2 Creep properties Indextestsload the polymermaterial to failurein amatter of seconds or minutes, and are of limited relevance to applications where thegeotextite is subject to longterm sustained loadfor periods of months or years. In such cases, sustainedload creep tests are required to determine the geotextile properties for design. Suchtests should be carriedout at ambienttemperatures relevant to the conditions in the ground, and on wide samples to reflect the confinement in soil which resists any tendency for lateral contraction in the geotextile. The test outlined (British Standard) BS 6906: Part 5 (BSI, 1991) is recommended. The period under sustained load should ideally approach to within a factor of 10 the design life for the geotextile, to reduce the amount ofextrapolation needed to estimate the properties at the design time and temperature (td, Td). Extrapolation of the data over a greater period is often required in practice, but should not exceed a factor of 100. Typical results from creep tests on a polyester geotextile are shown in Figure 2.2, plotted as elongation versus time, on a logarithmic scale. This shows the continuing, gradual increase in elongation with time underconstant load, which is typical ofpolymer materials. Failure in a creep test can occur after a period of time under load which depends on the load magnitude and the ambient temperature. Thedata in Figure2.3 are for polyester yarn. In general, the strength of a geotextile can only be discussed usefully if the corresponding time tofailure (or rate of elongation) and temperature are given.
2.3 Strength and stiffness of geotextiles The allowable load for a geotextile that is used in design should be selected after considering both the strength properties and the stiffness properties of the geotextile appropriate to the loading period and temperature in the ground. The data on these T = 20t 8—
60%
C
Load % ofindexlestbreakingstrength
______________________
0 1
10
100
1000
10000
Time: h
Terram WB 20/5. AfterGreenwood(1990)
Eigure 2.2 Sustainedloadcreep test on a polyester geotextile 18
Special Publication123 © cIRIA
:!6
2.3.1
Strength properties
12
—
T=20t
*
Rupture
6 
Load% of indextest breaking strength
4
I
0.1
1
10
100
1000
10000
Time:h Polyester yarn 110Tex
Figure 2.3 Sustainedloadcreep tests causing failure in a polyester yarn properties are derived from sustainedload creep tests. This approach is consistent with limit state design where both stability (strength) and serviceability (stiffness) are
investigated.
2.3.1 Strengthproperties
A polymer material, when highly loaded, mayyield and then rupture,or it may simply
rupture(with no perceptible prior yield). This is illustrated schematically in Figure 2.4 for a test (a) at a constantrate of elongation, and (b) under sustained load. When loaded with a constantrate of elongation, the yield load is defined as the highest one achieved in the test; yield is where the material supports a constant load at a constant rate of elongation (Figure 2.4a). Under sustained load the yieldpoint is defined where the rate of elongation reaches a minimum, thepointof inflection in Figure 2.4b. At this stage the material is once more supporting constantload at a constant rate ofelongation. Thusthe Test at constantrateofelongation PC
!ruPture
Test at constantload
PC
D0poInt Time(linearscale(
Elongation (a)
Rupture
(b)
Figure 2.4 Yield and rupture points: (a) at a constant rate of elongation and (b) under sustainedload Special Publication 123 © CIRIA
19
2
Polymer and geotextile properties
yield point is commonto the two tests. However, rupture may intervene before yield occurs.
It is common to use the yield pointto define the limit ofmaterial performance, because once it is exceeded rupture is imminent. The limiting load capacity, the strength oft/ic material at a given temperature, can then be represented by plotting the yieldor rupture loadversus the corresponding time to 'failure'. The usual axes are load on a linear scale versus time on a logarithmic scale, as shown in Figure 2.5, although the load is sometimes plotted on a logarithmic scale. For some geogrid materials, the limit of material performance has sometimes been defined in terms of a 'limit strain', ratherthan in terms of the measured yieldor rupture point(McGown et aL, 1984). Thedatacan be treated in the same wayas before with the decreasing 'strength' with time plotted as described above to allow for extrapolation to greater time, beyond the test data. 2.3.2 Stiffness properties
The allowableload for design is typically only a small proportion of the shortterm or itidex stiingrh of the geotextile. But designers must still consider the relation between cumulative elongation and time under load for geotextiles in order to estimate the elongation that can be expected in the reinforcement. With current knowledge, prescriptive or empirical limits for the maximum acceptable elongation in the reinforcement are often introduced to ensure that the reinforced soil structure does not deform unduly. Creep test data are againrequired. A plot of load versus elongation, on which a single curve represents the relation after a given time under load, indicates how the reinforcement stiffness reduces over time. The derivation of such isochronous loadelongation ('aries from creeptest data is shown in Figure 2.6. 50
 T20C
S
E40 o C J
30
—
20 _______________________________________________________ 0.1
1
10
100
1000
10,000
Time:h HDPEgeogrid (Tensar SR8O).(AfterWrigley1987)
Figure 2.5 Strength properties for a uniaxial polyethylene geogrid 20
Special Publication123 © CIRIA
Extrapolation for longterm properties
23.3
Isometriccurve
Creep curves
iu
Log(Ume) sochronouscurve P4
r Log (time
VP3
it Trne=t Elongabon
Figure2.6 Loadelongationrelations found from creep test data The isochronous curves show directly how the loadelongation behaviour of a geotextile changes with loading periods, such as the time under load up to the end of construction, or between the end of construction and the end of the design life. The expected elongation in the reinforcement under a given load can be found directly from the isochronous curves. Similarly, when a maximum allowable elongation has been specified, the corresponding maximum loadcan be found directlyfrom the isochronous curves.
2.3.3 Extrapolation for longterm properties Many geotextiles and their constituent polymer materials were developed relatively recently, and so extrapolation of data is often required to find the properties relevant to practical design lives for engineering works. Creep and creeprupture curves can be extrapolated by eye using the most plausible extension of a line or a curve, the extrapolation appearing more credible the a or informationcan be plotted to give straight line, fitted to an empiricalmathematical formula. However, while empirical laws are useful and appear to add credibility, they must be treated with caution unless they can be shown to relate to actual physical mechanismsin the material. All extrapolation, whether by eye or by calculation, depends on the mechanisms of creep and rupture remaining the same during the period of extrapolation. If they do not, the extrapolation is invalid (RILEM. 1988). Indeed it is the possibility that the mechanismsgoverning behaviour may change at times beyond the test period which is one of the greatest sources of uncertainty in extrapolation, since this can result in a discontinuous change in the measuredvariation of strength with time.
if
SpedaJ PubIicaton 1230 C$RIA
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2
Poiymer and geotextile properties
This phenomenon may occur due to a physical mechanism, as found in some unorientated polymer materials like polyethylene, for example. The result is that the actual period to rupture at lower stresses is shorter than found by extrapolating the rupture data from tests at higher stresses. To date, however, no evidence for such a physical transition has been found in the drawn polymers used to make mostgeotextiles (Greenwood, 1990). In order to resist and minimise the risk of physical mechanismscausing behavioural changes, polymertechnologists use additives and special processing in the manufacture of the raw materials of geotextiles. However, it is possible that chemical mechanisms may then cause similar discontinuous changes in behaviour, since the additives included to inhibit a mechanism of degradation in the polymer become used up or exhausted in some way, then the inhibited mechanism may eventually take place (Sotton, 1986; Wisse, 1988). As discussed earlier, the effect of temperature is to accelerate the mechanisms influencing polymer behaviour. Creep tests carried out over a range of temperatures provide the opportunityto support extrapolation by the superposition of results at higher temperature. That is, the samepattern of behaviour would be expected to be observed over a shorter test period at a higher temperature. Thus it is possible, in principle, to predict the longterm creep behaviour at ambient design temperaturesfrom the response measuredover a shorter period at higher temperatures. Care is needed in the use of accelerated testing. Typically the elevated test temperature should not exceed the design temperature by more than about 30°C, and should not approach the temperatureswhere material transitions occur such as the glass transition temperature for polyester at about 50 to 60°C There are accepted limits to the amount of extrapolation which is reasonable. It is sensible,and recognised as good practice, not to extrapolate the properties ofa polymer material (at a given temperature) by more than one log10 cycle in time without other supporting evidence. Even allowingextrapolation by this factor, a 100year design life would require results based on 10 years of testing. Since geotextiles are relatively new, and are being used in longlife applications, extrapolation of data by up to two log10 cycles oftime is frequently required. It is recommendedthat this should be supported by data from accelerated testing (at higher temperature) wherever possible, and that increasedsafety margins should be adopted in view of the greater uncertainty. Significantscatter is common in stressrupturedata and many repetitions oftests are needed confidence limits are to be placed on the measuredproperties.
if
if
2.3.4 Aged life of geotextiles The work of Sotton (1986), Verdu (1988) and Wisse eta!., (1990) suggests that the possible chemical breakdown of a geotextile in the very long term should be formally assessed. Such chemical breakdown sets an absolute limit
22
to the design life of the
SpecialPublication123 © CIRIA
Measurement of reference properties
2.4
geotextile irrespectiveof the magnitude of the applied load. A test for chemical breakdown exists in the electrical industry (CEI, 1990), but no similar test has been developed for geotextiles. Chemical ageing tests are carriedout at high temperatures with the material exposed to appropriate chemical environments. The time of failure at various temperatures is measured and plotted on a logarithmic scale against the inverse of temperature (for processes governed by the Arrhenius equation). This allows extrapolation ofthe data to the design temperature to find the aged life of the material, te,r, Figure 2.7. In effect, chemical ageing tests aim to prove that a polymerreinforcement material can resist the active chemical processes that would otherwise leadto complete chemical breakdown in the long term. Given the high temperature of testing and the uncertainty in extrapolation, it is suggested that the aged life, c,,1., should be required to exceed the design life of the structure by a factorof the order 3 (one half of one log10 cycle).
2.4 Measurement of reference properties Referencepropertiesare measured on exworks geotextile products.
The range of the data should include ambient temperatures equal to or greater than those which the reinforcement will experience in the ground. Separate allowance is made for the change in the properties caused by installation damage and the chemical and biological environment in the ground (Section 2.5.3). These changes depend on the soil and conditions at each site. The test defined by BS 6906 Part I (BSI, 1987) is recommended to determine index properties(Section 2.2.1). At least five specimens should be tested to determine mean values. Properties for a geotextile are usually measured in both the longitudinal and the Timetochemicalbreakdown:days 10
2.0
100
1000
10,000
tell
0 2.5
E C, 3.0 C
T
3.5
(After Wisse, 1988)
Figure 2.7 Time to chemical breakdown as a function of temperature for a spunbonded polypropylene geotextile (after Wisse, 1988) Special Pubiication 123 © CIRIA
23
2
Polymer and geotextile properties
transverse directions. The index loadelongation curve, maximum load and breaking load (if different) and the associated elongations for each should be reported (Figure2.8). Both the referencestrengthand referencestiffnessproperties for a geotextile should be determined under similar conditions to those above, but from creep tests where the loadis applied rapidly and subsequentlyheldconstantat the desired level. Thetestin BS 6906 Part 5 (BSI, 1991) is recommended to determine the creep properties for a geotextile (Section 2.2.2). The test arrangement is similar to the index test, but the load is applied rapidly (between 2 to 60 seconds) and held constant thereafter. Higher loads are chosen to observe rupture during creep tests to allow creeprupture properties to be extrapolated (Figure2.9). It is necessary to repeatthe test several times reid rrprve
a C
J
hrrprure Elongation: O/ a)
z c
0 J
Elongation: % (b) (After 8S6906: Part 1: 1987)
Figure 2.8 Typicalloadelongation responsefrom index tests: (a) linearbehaviour and (b) nonlinear behaviour 24
Special Publication 123
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Damage and durability of geotextiles
2.5
Data
Extrapolation
strength (tdTd)
.3
•
—
Datapoints Averagestrength
F
Characteristic strength
4 Design life
t
Log (time)
Figure 2.9 Creepruptureproperties for a geotextile material at each load level becauseof the scatter found in creeprupture data. Ideally, the aim should be to determine the variation of the safe characteristic strength of the material with time, commonly defined as the value only 5% of samples fail to achieve. The accuracy with which a characteristic valuemay be found depends on the number of test observations, and standard procedures are given in BS 2846 Part 2 (BSI, 1975). Reference properties for a geotextile should be measured over a range of temperatures, including 10°C and 20°C the typical range for ground temperatures in temperate countries (Murrayand Farrar, 1988). Data at higher temperaturesare needed for applications in tropical climates, and at lower temperatures for colder regions.
2.5 Damage and durability of geotextiles 2.5.1 Mechanicaldamage Polymer reinforcement can be damaged during construction. Physical damage of geotextiles can include punctures, tearing, piercedholes in which the yarns are separated but not torn, as well as abrasion of the yams themselves. Such damage can reduce the life ofthe geotextile under load. In the caseofgeogrids, damagecan result in cuts, splits and local crushing of members. There have been many tests in which geotextiles have been buried in soil, extracted and tested, usually under index test conditions, as reviewed by Cohn et al. (1986). The effects ofconstruction on the properties of geogrid reinforcement buried in various soils is reviewed by Bush (1988), and recent tests on geotextiles by Watts and Brady (1990). One effect of mechanical damage is to reduce locally the crosssection of material supporting load, thereby increasing the stress at these damaged places. This increased loading reduces the time to cause stress/rupture.Local stress concentrations caused by damagecan also initiate failure by tearing in a geotextile, but a suitable test for this has not yet been devised. Because damage is local in nature, the overall loadelongation Special Publication 123 © CIRIA
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2
Polymer and geotextile properties
properties, which
are dominated by the bulk of undamaged material, usually remain
largely unchanged. Thus mechanical damage reduces the strength properties of polymerreinforcement materials while leaving the overall stiffness properties substantially unchanged. The elongation to rupture, though, is reduced. Until more extensive longer term testing of damaged materials has been carried out, it has to be assumed that the reduction in strength caused by mechanical damage to geotextiles which is measured in relatively shortterm tests will apply in the same proportion over longer periods (Figure 2.10). Thus the procedure is to subject samples of geotextile to damage caused by a range of installation procedures and fill materials, and to measure the loss of strength caused by the damage (Billing et a!., 1990; Paulson, 1990; Watts and Brady, 1990). This measured loss in strength is represented by a damage factor,fd,which when applied to the reference strength allows for the anticipated damage to the geotextile in the ground. Recommended damage factors determined in this way for some uniaxially drawn geogrid materials are summarised in Table 2.1 (Bush, 1988). Similar factors for woven polyester geotextiles and some polyestergeogrids are given in Table 2.2 (Troost and Ploeg, 1990). Proper allowance for damage must be based on tests for each individual geotextile product, and this productspecific data should be supplied by manufacturers. The relevance of the data may be checked by independent testing on specific projects.
2.5.2 Chemical and biological durability The ability of geotextiles to withstand the chemical and biological environment in the soil over a long period of time has attracted considerable study (RILEM, 1988). The Reference propeiesfrom Figure 29
I
J
Data
k
—_l Extrapolation
*4
Reference strength strength
Pdm Damaged
(fordamagedmaterial)
=
tDes lifet, Log (time)
Figure 2.10 Idealisation of mechanical damage reducing strength by a constant factor irrespective of time 26
Special Publication123 © CIRIA
Chemicaland biological durability
2.5.2
Table 2.1 Factors to allow for mechanical damage for some geogrid reinforcements made from drawn HDPE (Bush, 1988, Netlon, 1990)
Wellgradedfill maximum size Fill type Coarsegrained soils and crushed rocks Coarse grained soils, cobbles and gravel Sands Medium and fine sand, clay and PFA
Values offd for Tensar
geogridS
Dmax (mm)
SRSS
SR8O
SR 110
Dmax
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10
Retainingwalls
In summary,theresultsindicatefor reinforced soil walls comprising granularfill and backfillthat the minimum reinforcement length for overall andmoment equilihirum is of the order, 0.7 L/H 0.5.
10.4 Internal equilibrium: practical corrections Twopractical corrections to the idealised internalequilibrium are required to allow for bond and compaction stresses, as described previously for steep slopes (Section 8.3). The same corrections apply for walls and, again, it is the minimum requiredstress to Overall equilibrium
J 0 C,
c 0) C 0 J
Angleoffriction, 4rd(deg) (a)
Momentequilibrium
I J
0 C,
C
0) C 0 J
35
40
Angle offriction, 'Nd (deg) (bI
Figure 10.11 Minimum reinforcement length for balancedequilibrium (case: °d = Yb = Yr' level backfill, and A1 = 1/Ab)
d'
158
SpecialPublication123 © CIRIA
10.4
Internal equilibrium: practical corrections
allow for compaction that usually dominates the internal equilibrium at shallow depth = l5kN/m2, for the minimum stress for (Equation 8.7). A prescriptive value, internal equilibrium is recommended. The value to be used may be checked once the compaction equipment has been selected using Equation 8.7. Although itcan be argued that with time polymeric reinforcement materials may creep and hencerelieve any lockedin compaction stresses, it is normally not onerous to satisfy the 'shortterm'required stress due to compaction. Practical factors influence thechoice of the reinforcement material and spacing near the crest of reinforced soil wall, which often leads to sufficient reinforcement near the crest of the wall to resist the effects of Overallequilibrium
I
J
0 Ct
=
0) C
0 J
Angleoffriction,
41:d (degl
(al
Moment equilibrium 1.0
0.9
I
0.8
J
0 It
0.7
=
0) 0.6
C 0 J
0.5 0.4 0.3 30
35
Angle of friction, 4'rd (degl (b)
Figure 10.12 Minimum reinforcement length for balancedequilibrium (case: %d — 5° Yb = y,. level backfill, and A1 1/Ab) Special Publication123 © CIRIA
159
Retainingwalls
10
bond and compaction without any further adjustment.This is illustrated in the design example (Section 10.8). In the case where external concentrated loads are applied directly to the reinforced zone, it is necessary to carry out a separate wedge analysis to check the internal equilibrium, as described in Section 10.9.
10.5 External equilibrium Theundesirabledesign situations forexternal equilibriumare foundation failurebeneath the reinforced soil wall and possible slip failure entirely around the reinforced structure. These were outlinedin Chapter 7 (Figures 7.5 and 7.6),and lead to the four mainchecks on external equilibrium:
I. direct outward sliding of the reinforced zone over the foundation 2. excessively eccentric loading at the base of the reinforced zone 3. bearing capacity failure in the foundation beneath the reinforced zone 4. external failure on slip mechanisms passing around the reinforced zone.
10.5.1 Direct sliding The required reinforcement length to prevent direct sliding, (L/H)dS, for a wall with a level backfill (Figure 10.13) is
\H) 7
iç,
=
(Yb
tan
"S
L
qh
y,JI
...(l0.9)
Pb
Figure 10.13 Directsliding at foundation level 160
Special Publication 123 © CIRIA
Direct sliding
10.5.1
where design values for the parameters are used, and the active earth pressure coefficient Ku,, = (1 sin + sin The lesser resistance of the fill, qç,, and thefoundation, is adoptedfor the resistance to directsliding, tan An appropriate valuefor thecoefficient, âdc, should be usedfor direct sliding between thereinforcement and the fill or the foundation soil. The above analysis is recommended even where the reinforced zone is embedded in the foundation to a depth, D. Any lateral (passive) resistance that could be provided is disregarded to allow for the risk of a trench being dug adjacent to the toe of the wall. Where the required length to resist direct sliding is greater than that for a balanced overall equilibrium (Section 10.3), the longer length, (L/H)€,, must be adopted lowerin the wall. Thereinforcement length maybe reduced higher in the wall to the lesser value found for overall equilibrium. However, the depth, z/II, at which the reinforcement length may be reduced must be chosen (a) to avoid direct sliding higher in the wall, and (b) to guardagainst a combined mechanism involving directsliding over a shorter length at the base of the wall (Figure 10.14). To avoid direct sliding in thereinforced fill where thereinforcement length is reduced to L/H, the change should be made no deeper than
.
d)/(l
,,
=
2a,tan,
y.
K41,
Yb
(L
\H,/
y,,H
...(lO.l0)
To resist the combined mechanism involving direct sliding on the shorter length, L/H, at the base of the wall (Figure 10.14) the reinforcement length should be reduced
at a depth less than
_________________________
=
()2 .7l
4
2e1(,S tan
AhKd
(L—L)H
...(lO.ll)
_
Figure 10.14 Possible directsliding mechanisms when LdS > L Special Publication123 © CIRIA
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10
Retaining walls
Equation (10.11) is suitable forpreliminary design purposes, but the influence ofbond
on the equilibrium in this case may be greater than determined from the standard bond allowance, A,, (Section 10.3.2). In detailed design, the bondallowance should be found by considering each individual reinforcement layer intersected.
Direct sliding on clay foundation soils
When a reinforced soil wall is founded on clay soil, possible direct sliding at the end of construction due to undrained shear across the surface of the foundation soil should be considered (the drained case being analysedas described above). Equation (10.9) is
modified in this case,
=
0012)
adV
\2s,,i s,d,J where s,, is the design value for the undrained shear strength of the foundation, and the superscript, ( )", representsthe undrainedanalysis.
10.5.2 Excessive eccentricity To satisfy overall equilibrium, the reinforcement length was chosen to maintain the resultant thrust at the base of the reinforced zone within the central third. This ensures satisfactory moment equilibrium for the foundation (Section 10.3.4). 10.5.3 Bearing capacity The bearingcapacity at the base of a reinforced soil wall may be analysed as an equivalent strip footing of effective width, L (Figure 10.15). The force resultants which 4
L
= 7fD
I_tt—
2e—
zw
Figure 10.15 Equivalent foundation for theanalysis ofbearing capacity 162
Special Publication 123 © CIRIA
10.5.4
External stability
act on the foundation are due to the surcharge and selfweight loading in the fill, and from the thrustofthe retained backfill. As usual,design valuesfor all theproperties and loadings should be used. The loading can be fully described in terms of the resultant vertical force, R,, and horizontal force, Rh, which act at an eccentricity, e, from the centreline. The combined = Rh/Ri.. loading acts at an inclination, tan The equations for the analysis of foundation bearing capacity are given in Section 5.4. The loading atthe base ofthe reinforced zone (Figure 10.15) maybe compared with that on a strip footing (Figure 5.18). For the case of a reinforced soil wall with level backfill and uniform surcharge load (Figure 10.15), the forces acting at the base of the reinforced zone are:
R, = y,h'L Rh
=
1+— Yr'1
Kab
_
(L/H) \y111 2 y,J Kab ((qb/y,JI) + (yd3y,M 2(L/H) (1 + (q/y,JI))
yJIL
e —H
(10.13)
tan 6=
Kab
((qb/y,H) + (Yi,/2Yr))
(L/H)
(1
+ (q,Jy,JJ))
(10.14)
(10 IS) ...(10.16)
Two of the limiting cases discussed earlier may be found from the above equations. The reinforcement length for the limiting eccentricity, e/L = 1/6, (Equation 10.8), may be recovered from Equation (10.15). Similarly, the reinforcement length for incipient direct sliding, tan 6 = tYd. tan (Equation 10.9), may be found from
,
Equation (10.16). The analysis for bearing capacity is illustrated by the design example in Section 10.8.
Undrained bearing capacity for clay
For a reinforced soil wall on a clay foundation, the shortterm, undrained bearing capacity should be considered in addition to the longterm, drained bearing capacity. The same loads act on the foundation (Equations 10.13 to 10.16) and the equations for undrained bearing capacity are given in Section 5.5. In broad terms, the undrained case should be carefully considered where y,R/s,, > 2, while drained bearing capacity would normally govern where, y,H/sj < 2.
10.5.4 External stability Conventional methods of stability analysis are used to examine the equilibrium on potential slip mechanisms passing entirelyaroundthe reinforced zone. The analysis for Special Publication 123 © ORIA
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Retainingwalls
external stability is needed to check that the planned earthworks will not disturb the general stability, and avarietyofpossible failure mechanisms should be examined using conventional slope stability methods. The analysis also provides an additional checkon foundation bearing capacity when potential failure mechanisms of the form shown in Figure 10.lba are examined. These may be compared with the mechanism implied by the analysis of local bearing capacity described in Section 10.5.3 (Figure blob).
10.6 Deformation
of walls
Progresshas been madein the analysis of deformation in reinforced soil walls caused by
the elongation in the reinforcement, and for the progressive horizontal and vertical displacements at the crest of a reinforced soil wall due to creep in the reinforcement. However, wall displacements can be influenced significantly by other factors, such as the immediate and consolidation deformation in the foundation, and the analysis for these other components of displacement is beyond the scope of this book. 10.6.1 Deformation of the reinforced till Charts forestimating the deformation in reinforced soil walls caused by elongation of the reinforcement layers were derived by considering the internal and the overall equilibrium described in the previous sections. The analysis and the resulting charts for horizontal and vertical wall displacements may be found in Jewell and Milligan (1989). The charts agree reasonably well with the field measurements where sufficient data allows back analysis, and with the behaviour of the instrumented walls reported by Jarrett and McGown (1988). The latter walls enabled a second source of displacement caused by the incremental nature of wall construction to be identified. During construction, initially unstressed layers of reinforcement higher in the wall are incorporated into an already deforming structure. In other words, the initial position of the endsof the unstressed reinforcement
(a)
(b(
Figure 10.16 Check on foundation stability: (a) bearing capacity analysis, and (b) analysisofexternal slip mechanisms
164
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Deformation of the reinforcedfill
10.6.1
layers is not on the initial (planned) alignment ofthe face. (Theexception is the wall built
with a fullheight facing panel that is firmly propped during filling, thereby controlling the initial position of the reinforcement layers, Section 10.7.3.) In practice, the influence ofconstruction is counteracted by initially tilting thefacing panels backward towards the fill. The exact measures and construction procedures adopted significantly affect the face deflection. The analytical solutions for wall displacement due to reinforcement elongation are useful (a) to assess the need for construction measures, such as the tilting of facing panels,to providegood alignment of the wall face, and (b) to estimate the progressive wall displacements caused by creep in the reinforcement, or subsequent loading by surcharge. A simplified chart ofmaximumhorizontal displacement for walls built with granular = 32°, and uniformly spaced reinforcement, is given in Figure 10.17. The fill, maximum horizontal displacement, â,nax/H, is expressed in terms of a maximum reinforcement elongation, h,,e/f' and the mobilised angleoffriction in the fill, irn. The mobilised reinforcement force at the base of the wall is defined as,
,.
"base
= (Kar)m5S(pH+ q,.)
...(l0.17)
where (Kar)n, is the active earth pressure coefficient in the reinforced fill for the mobilised angle of friction. The secant stiffness for the reinforcement, f, should reflect the time period over which it has been subject to load (Section 2.3.2). Limits to the likely wall displacements can be foundby examining different mobilised shearing resistances in the fill, as discussed in Section 7.3.1. For granular fill, the Angle of dilation 10
0.5
20
Uniform spacing
jO
H
54
Angle ot friction,
4
50
4'rn,
Figure 10.17 Chart for maximum horizontal movement in reinforced soil walls (after Jewell, 1990) Special Publication123 © CIRIA
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Retaining walls
maximum likely displacements are found by assuming that only the critical state angle offriction is mobilised, %,, = while the minimumlikely displacements would occur
if the peak shearing resistance of the fill were mobilised,
4, = 4.
Calculation of deflection To calculatethe displacement due to elongation in the reinforcement, chose a mobilised angle of friction for the fill and determine the value, OUIaXJ/HPoaSe, from Figure 10.17. The maximum wall deflection, órnjx/H, depends on the secant stiffness of the reinforcement,J, and the mobilised reinforcement force, phase' calculated from Equation (10.17). To evaluate the creepdisplacement, simply calculate the deflection for two values of reinforcement stiffness,J,to represent conditions at the beginning and end ofthe loading period. The difference between the two calculated deflections is the displacement due to creep. (In practice, the strain in the soil caused by creep in the reinforcement could enable a higher soil friction angle to be mobilised, and thereby reduce the required reinforcement force and the corresponding additional elongation below that envisaged above.) Ifan increment of uniform vertical surcharge, Aq, is applied to the wall, theresulting increase in reinforcement force willcause a corresponding displacement at the wall face. Again, the incremental displacement is found from the difference between the total displacement with and without the surcharge loading. Only the maximum horizontal displacement is given in Figure 10.17, but the corresponding maximum settlement, ÔIJH, at the crest of the wall (due to elongation in the reinforcement) is normally of the same order as, or just less than, the horizontal displacement, ÔmaJH. More detailed analysis of both horizontal and vertical displacement may be made using the charts given in Jewell and Milligan (1989).
10.6.2 Deformation caused by foundationmovement Conventional methods ofassessing foundation displacement need to be used,suchas the
analysis for foundations on granular soils by Burland and Burbidge (1984). The influence of shortterm undrained displacements and consolidation settlements should be considered for loading on clay foundations. The consolidation settlement at the back of the reinforced zone can exceed the settlement at the toe of the wall, the edge of the loaded region (Figure 10.18). This can cause the face of the wall to 'tip backward' into the fill, as discussed by Jones and Edwards (1980). It is important to recognise that thefinal vertical alignment of the faceof a reinforced soil wall depends on at least four separate factors, namely: I. the deformation caused by elongation in the reinforcement 2. the deformation caused by alignments during construction 3. the immediate, undrained displacement in the foundation, and 166
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Practicalaspectsinfluencing design
10.7
Wall displacement atthe end of
Wall displacement atthe end of conslruction
consolidation
Settlement duetoconsolidajion inthe softclay
Soft Clay flAY,'
Hard stratum
Figure 10.18 Resultant wall displacements following consolidation 4. the consolidation settlement in the foundation caused by the loading from the reinforced fill and the backfill.
10.7 Practical aspects influencing design 10.1.1 Thrust from the backfill In theanalysis for walls it has been assumed that the backfill exerts a horizontal thrust on the back of the reinforced zone, equivalent to the thrust on a smooth retaining wall. In most cases, allowing for roughness on this boundary, so that the thrust from the backfill would be angled downward, would enhance the equilibrium. But equally, ifthe thrustfrom thebackfill were angled upwardit would leadto a more critical equilibrium (O'Rourkeand Jones, 1990). The assumption of a horizontal thrust is made for two main reasons. First, the assumption of a thrust from the backfill angled downward implies that the backfill soil moves downward with respect to the reinforced zone. But as shown from the analysis of foundation displacement, it is far from clear that this should be the case, a priori, particularly oncethe influence of consolidation settlement in the foundation is considered (Section 10.6.2, Figure 10.18). Likewise, the foundation might contain a layerofcompressible soil deeper beneath the back of the reinforced zone than at thetoe, again implying a 'backward'rotation caused by consolidation settlement. Second, the analysis for reinforced soil using a full twopart wedge mechanism (Section 8.1) shows the critical planes are angled from the vertical, and that the assumption of a vertical interwedge boundary is a simplification for design. Special Publication123 © CIRIA
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Giventhese uncertainties, it is prudent not to rely on a more advantageous inclination of thethrustfrom thebackfill thanthe horizontal direction. Indeed a detailed justification should be given if a more advantageous assumption is to be made.
10.7.2 Connections There is a need to connect the reinforcement to the facing in most reinforced soil walls,
whether multiple panels, modular blocks or fullheight facing units are used. Two important designconsiderations are (a) an allowance for relative vertical displacement between the settling reinforced fill and the facing (which is often relatively incompressible and stiffened at the base by a small footing), and (b) detrimental factors reducing the strength ordurability ofthe connection with the face. These considerations are interrelated, since the development of a stress concentration at the connection due to relative settlement could cause rupturein the reinforcement. In general, the reinforced soil zone will settle to some extent with respect to the wall facing, and the connection should allow for adequate relative vertical displacement.This may be achieved with a sliding connection, and a variety of connection details are available (Jones, 1988). An alternative is to allow the face to 'settle' with the fill by incorporating compressible materials in joints between facing units, to allow them to 'concertina'together. Thereinforcement strength may be reduced locally at the connection with thefacing. This could be caused by mechanical damage, for example at the frictional/shear connection of reinforcement with modularblocks (Figure lO.19a), or stress concentration where a joint is made with the reinforcement material wrapped around a shear connector (Figure lO.19b). Because of the variable influence of construction, it is not considered reliable in design to assume that the force in the reinforcement at the connection with the face will always be less than at some distance away from the face. Indeed, any relative settlement PotentiaLmechanical damage lo reiniorcement
tacing units
Reinforcement
Shear bar
reinforcement (a) Monoblockface
(b) Shearconnector
Figure 10.19 Connectionsat the face (a) Monoblock face (b) Shear connector 168
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10.7.3
Fullheight facing
fill and the face potentially could cause a 'stress concentration' in the reinforcement at the connection with the face. Thus whatever detail is used, the appropriate designstrength used in the calculation of internalequilihtiumshould be the lesser of the strength at the joint or in the main reinforcement material. between the
10.7.3 Fullheight facing
The useof a fullheight facing can significantly affect the behaviour of reinforced soil walls compared with walls with flexible facing, such as panel or 'wraparound' facing. First, ifa fullheight faceis propped externally while the reinforced fill is being placed and compacted, the props only being removed near the end of filling, this largely eliminates the component of displacement due to construction (Section 10.6.1). Second, fullheight facing normally has a significant rigidity and strength to inhibit potential failuremechanisms passing out through the face ofthe wall. Stresses from the fill can be transmitted to the face causing significant vertical and horizontal forces to be transmitted through the face to the underlying foundation soil (Figure 10.20). These forces can greatly increase stability, thereby reducing the amount of force that must be provided by the reinforcement layers. Thus fullheight facing can provide a structural role and contribute to the stability of reinforced soil. However, to perform such a structural role, special measures must be taken to ensure that the necessary forces can be transmitted reliably from the face to the foundation. Unless such measures are taken, the possibility that a trench may be dug adjacent to the toe of the wall should always be considered (Figure 10.20). The reinforcement would have to support the extra load caused by the loss of support for the face. In general, the appropriateassumptionfor ultimate limitstate design is to ignore the contribution to stability derived from the Jice. However, account can be taken in
Possible trench excavalion
//AVA\
Figure 10.20 Forces transmitted through fullheight facing Special Publication 123 © cIRIA
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Retaining walls
serviceability calculations
of the extra stiffness provided by the face. This applies
equally to reinforced soil walls with other facings.
10.8 Design example
for a retaining wall
10.8.1 Data and design values Notethat while the calculated results have been roundedoff to an appropriate accuracy, the underlying value, rather than the roundedoff value, has been carried forward in the calculation (i.e. as in a spreadsheet). This can cause small discrepancies between the quoted results and those calculated using the roundedoff values.
Slope details
A retaining wall
up to Sm high is to be included in the landscaping of a housing development. A stonefaced (modular block) wall has been chosen to provide an attractive finish. The facing blocksare 200mm high, 500mm wide and 400mm deep and aredesigned to stackat a gradient 10: 1, = 84°.The soil willbe reinforced by polymer grids, and the structure is to be designed as a vertical wall. The Sm height includes for embedding the wall 0.3m, so that the base of the monoblock face, and of the reinforced backfill, is 0.3m below final ground level. Site investigation reveals a predominantly medium dense, sandy Thames gravel. SF!' values of 27 to 40 blows/300mm, and direct shear tests on samples recompacted to the field density, indicate that the peak strength of the gravel is about 48° 45°. The strain of friction measured in direct shear tests is 33°. large angle The large strain angle offriction is selected to represent the strength ofthe foundation = 33°. (This gives a similar mobilised angle soil for ultimate limit state calculations, of friction for design as would apply if a conventional factor of safety, FSç = 1.5, were applied to a representative peak angle of friction for the soil, Ø = 45°, as discussedin Section 5.2.2.) The minimum expected unit weight ofthe foundation soil is yf = l9kN/m3, andthehighest estimated water table is at lOm below ground level. Both these parameters are used directly in design. An imported granularfill will be used for construction. Compaction to 95% of the maximum dry density gives an expected bulk density for the fill, y = 2lkN/m3. Compactedby this amount in a shear box, the peak angle of friction was measured to be 49° 46° for appliedstressesin the range l5OkN/m2 5OkNJm2, relevant to the reinforced fill and backfill. The large strain angle of friction was measured to be not less than #r = 33w. For ultimate limit state calculations, the critical state angle of friction for the fill is = 33° = selected for design, together with a slightly higher than expected soil = = 22kN/m3. density. A nominal uniform surcharge = q,, = IOkN/m2 is assumed for design to allow for temporary overfilling, and other variable surcharges. A prescriptive allowance for
y
170
,
,,
q
Special Publication 123 © CIRIA
Data and design values
10.8.1
compaction stress is assumed, comp = l5kN/m2,and the compaction equipment will be chosen not to exceed this value (Section 10.4).
Reinforcement details
A design life of 50 years is chosen for the wall, and a design temperature in the ground 20°C is considered appropriate. Polymer reinforcement grids are to be used, and apartly frictional, partly dowelled connection for the reinforcement between the facing blocks, coupled with protection measures for the reinforcement, allows the full design strength in thereinforcement to be developed at the facing. Three grids are offered, and the manufacturer recommends the following allowances for degradation,f = 1.35 and f,,05, = 1.15, to allow for the soil, and the effects of construction and the environmental conditions at the site (Sections 2.5 and 6.4). Extrapolation ofthe material properties data by I log10 cycle of time is required to reach the design life, and a material factor, f,,, = 1.50, is chosen following the guidance in Table 6.1. The characteristic value of the index and reference strength supplied by the manufacturer foreachproductand the resulting design strength are summarised in Table 10.1.
When the grids are subjected to a force equal to the design strength (Table 10.1) for a 20day period they exhibit a cumulative elongation of about 2%. The estimated total
cumulative elongation under this loadby the end ofthe designlife is 3%. The appropriate values for the reinforcement stiffness for serviceability are given in Table 10.2. The constituent material of the polymer grids has a coefficient of skin friction, tan 6 = 0.6 tan 4?, and all three grids have a similar geometry, a., = 0.35, and, S/a,,B = 30, (Section 4.4). The coefficient of direct sliding may be calculated as, ds = 0.21 + 0.65 = 0.86, from Equation (4.3). Thebearing stress ratioin the reinforced = 8.8, from Equation (4.8), and the bond coefficient is, = 0.21 + 0.19 fill is, = 0.40, from Equation (4.6).
h
Table 10.1 Characteristicstrengths for the reinforcement grids in kN/m. (td = 50 years and Td = 20°C) Index strength kN/m
Reference strength
i'"tdTd
(Ppe&j)
70 50 30
42
27
IS
30
19
12.5
18
11.5
Field strength
Design strength
0d
7.5
Notes: Characteristic index and reference strength frommanufacturer Field strength for degradationf = 1.35 andf, = 1.15, Materialfaclorf 1.50 for I log10 cycle ofextrapolation. Strengths roundeddown to nearest 0.5kN/m.
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Table 10.2 Characteristic stiffnesses of the reinforcement grids in kN/n. years and Td = 20°C)
?sok'.v:
Index strength kN/m
End of construction
Design life
JSOOhours,2OC
iSO years, 2OC
70 50 30
900 640 390
430
(t = 50
600
260
Stillness is serviceabilitystrength over cumulativeelongation. Stiffnessrounded to nearesl lOkN/m.
Limit states Deformation for this wall is not critical and a maximum allowable elongation in the reinforcement, 5%, over the design life of the structure is considered acceptable for serviceability. This elongation is greater than would be caused by a force equal to the design strength (3%, see above) and so the serviceability strength for the reinforcement is limited by the design strength. Thus the reinforcement layoutwill be governedby the ultimate limit state analysis (see Section 6.4.1). The expected deformations for the wall will be calculated using the reinforcement stiffness values listed in Table 10.2. The main design steps below follow the flow chart in Figure 10.3.
10.8.2 Design steps (ultimate limit state)
Internal equilibrium Earth pressure The earth pressure coefficientfor the reinforced fill is = 0.295, Equation (10.1). coefficient There are various ways to proceed with design. In this example, the effects ofbond and loadshedding will he matched, A15 = IIAh, as recommended in Section 10.3.2. The bondallowance is normally quitesmallfor grid reinforcement, and thus only a nominal valuefor the loadshedding allowance, A15 = will be assumed initially. Once the has been selected, the bond allowance can be checked to insure reinforcement layout that sufficient loadshedding has indeed hee,z allowed. The design can he revised
I.]
necessary.
f
A provisionalvalue forthe loadshedding allowance, A, = LI, Required stress
172
is assumed initially (see above). The design value for the earth = 0.324. pressurecoefficient is then, Kd = The distribution of required stress for internal equilibrium is shown in Figure 10.21, allowing for the surcharge, Special Publication123 © CIRIA
Design steps (ultimate /imit state)
10.8.2
01105
0a (kNit2)
30
20
40
= lOkN/m2 10
0
22 kS/rn
=0 3
4
=33
rn)
v=l9kN/n12
(b)
(a)
Figure 10.21 Design example: wall details and required stresses for internal equilibrium
q=
lOkN/m2, and the minimum stress = l5kN/m2.
due to compaction,
The maximum required stress at the base of the wall is = 0.324 >< (5 >< 22 + 10)or (Req)max = 38.9kN/m2. (URCq)max The 200mm high facing units set thepossible vertical spacings for the reinforcement = 0.2m, 0.4m and 0.6m. The range of available design stress providedby the reinforcement grids at these spacings, and the depth Zmax below the slope crest to which the spacings apply, are summarised in Table 10.3.
Reinforcement selection
s
Table 10.3 Available stress from reinforcement, 0Av in kN/m2, and the maximum permissible depth for each reinforcement below the crest, Zmax in m
Index strength index
Spacing = O.2m
Spacing
Spacing
= O.4m
s
= O.6m
0Av
Zmax
9Av
Zmax
°Ar
Zmax
90.1 64.4
12.1 8.5
45.1 32.2
5.8
30.0
3.7
50
30
38.6
4.9
19.3
4.0 2.2
21.4 12.8
2.5 1.3
70
Notes: Design strength from Table 10.1. Available stress P/s.,for continuous layers. = (P,/KJy.s.) — (q/y,). Maximumallowable depth Availablestresses and maximumdepths roundeddown.
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A practical
choice is to use one reinforcement material at different spacings to match the required and available stresses. The reinforcement layout can be found by drawing, starting from the base of the wall. The grid with the intermediate strength, 'indev = 5OkN/m, would require a layoutwith the first = 0.2m, the next four layers at seven layers spaced at = 0.4m and the finalthree layers at s. = 0.6m, giving a total 14 layers (Figure (10.22a).
Trial layout
s
In a detailed design study, the benefits of other reinforcement arrangements would be examined. For example, the use of the stronger grid, jndt't• = 7OkN/m, would require a layout with five layers spaced at = 0.4m, and five more layers spaced at
s
= 0.6m (Figure l0.22b). The bond length at the base of the wall for the reinforcement
Bond length
with an index strength.
P1,
= 5OkN/m, with uniform width,
im, is LB/H = 0.044, from Equation (8.2) (Section
Wr =
10.3.2).
Overall equilibrium Overall failure mechanisms
The design charts for steep slopes described in Chapter 8 may be used for an initial assessment of the minimum length for overall stability (Figure 8.21). For a design angle of friction, Aeq 0Av (kN1m2)
60
50
40 I
I
30
10
20
0 0
3layers
— 1
0' 06Dm Available stress
(040
/
Required stress
—
2
—
3
—4
_______________________7 layers
I
c,,
Reinforcement P0 = 125 kN/m
5
Ia)
Figure 10.22 Design example: trial reinforcement layout to provide the required stresses (a) one reinforcement material (b) use of stronger grid at base
174
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Design steps (ultimate limit state)
10.8.2
Eccentricity at the base
= 33°, the minimum length for overall stability is, Lit! = 0.56. This may be found also from Figure 10.1 Ia, for the case with no surcharge, q/y,II = 0. When allowance is made for the surcharge, qIy,H = 0.1, but ignoring the beneficial influence of surcharge on the reinforced fill, q,JyjH = 0, the results in Figure 10.1 Ia indicate a greater minimum length for overall stability, (LIH)).d = 0.62.
Practical effects on internal equilibrium
The minimum length to maintain satisfactory moment equilibrium can be found from Equation (10.8) or Figure 10.1 lb. Again, accounting for the surcharge on the backfill hut disregarding that on the reinforced zone, gives a minimum length for moment equilibrium, (LIII).. = 0.62. The main external factor affecting internal equilibrium is compaction, and a prescribed minimum required stress, comp = l5kNIm2, is used to allow for compaction (Section
Summary
The above analyses for overallequilibrium indicate a minimum
10.8.1).
required reinforcement length, L/H = 0.62.
External equilibrium Directsliding
Drained bearing capacity
Stress at the base
of wall
Bearing capacity factors
Assuming that direct sliding occurs beneath the lowest reinforcement layer and the underlying foundation soil, = 33°, the minimum length to resist direct sliding is (L/H)dc = 0.31, from Equation (10.9). (Recall, dc = 0.86.) The minimum required length for overall equilibrium is, LIH = 0.62. Assuming this length, the equivalent foundation loading and dimensions at the base of the reinforced zone can be found from the Equations (10.13) to (10.16) in Section 10.5.3: Rjy,JJL = 1.09, R,jy,RL = 0.28, tan c5f = 0.26 and
e/H = 0.092. The equivalent footing width at the base of the wall is then L/H = 0.62—2 >( 0.092 = 0.435,orL = 2.18m. The average vertical bearing stress is then = RVIL = 1.09 >< 22 x 5 >< 3.l2I2.l8kNIm2, or
aj=
l7lkN/m2.
= 330, The bearing capacityfactors for the foundation soil, = 35.2, from Table 5.3. The reduction and Nq = 26.1 and factors for load inclination, fortan = 0.26, are = 0.55 and i,, = 0.41, from Equations (5.23) and (5.24) respectively.
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Allowable bearing stress
External stability
Summary
Ignoring the benefit of embedment, assuming D = Om, the allowable vertical bearing stress from Equation (5.19) is = 0.5 x 0.41 35.2 2.18 19 = 298kN/m2. The design value of foundation bearing capacity, 0hc = 298kN/m, is more than sufficient to support the design value of applied vertical stress at the base of the wall, = l7lkN/m2. (Recall that both the bearing stress and the bearing capacity have been calculated with pessimistic design values for the loadings and resistances, and that no additional factor of safety is required, Chapter 6.) A general slope stabilityanalysis forpotential slip mechanisms passing entirely around the reinforced zone indicates satis
/
/ /
factory external stability. The reinforcement length for design is governed by overall equilibrium rather than external equilibrium. The provisional reinforcement length for design is then, LI!! = 0.62, or
L = 3.lm. Check for bond Check the bond allowance
In the analysis above, an additional allowance of 10% on the required reinforcement stresses was included to counterbalance the effects of bond (i.e. a loadshedding allowance,
= 1.1, was assumed). Required loadshedding allowance
For the reinforcement used, the bond length at the base of the slope is, LBIH = 0.044 (see the results above for internal equilibrium, bond length). The reinforcement length is, LIII = 0.62,givingabondratio,L2IL = 0.044i0.62 = 0.071, and a bond allowance, A,, = I — LBIL = 0.93.
As discussed in Section 10.3.2, the required loadshedding allowance to exactly balance the effectof bond isAk = lIAh,so that the required loadshedding allowance isA, = 1.08. Since a greater allowance has been assumed,A1ç = 1.1, the design is satisfactory (i.e. it includes a marginally greater provision of reinforcement than required).
10.8.3 Check on serviceability The simplified chart for wall deflection (Figure 10.17) was derived for the case of reinforcement at constant spacing. In the present design, the lower pan of the wall is reinforced by seven layers spaced at 200mm, and four layers spaced at 400mm. The displacement due to elongation in the reinforcement will be calculated assuming all the 176
Special Publication 123 © CIRIA
Check on serviceability
10.8.3
reinforcement is at one or the other of these spacings. The maximum deflection for the
actual reinforcement layout should fall within this range. = Two values of mobilised angle of friction in the reinforced fill will be used, = 33° and 44m2 45°, to represent the limits to the likely value (Section 10.6.1). The deflection both at the end of construction and at the end of the design life will be calculated, using the reinforcement stiffness, = 640kN/mand,I, = 430kN/m,for the two cases respectively (Table 10.2). = q,, = OkN/m2, and the expected bulk No permanent surcharge is expected, density of the reinforced fill is, Yr = 2lkN/m3. The calculation of the maximum deflection for the wall is summarised in Table 10.4 (Section 10.6.1). The maximum wall deflections are all relatively small, the largest valuebeing 56mm. As discussed in Sections 7.3 and 10.6, the expected equilibrium is most likely to occur once the soil has mobilised a relatively high proportion of the peak shearing resistance. In the design example, the seven layers at the closer 0.20m spacing are expected to dominate the deformation response of the wall. Allowing for these factors, an appropriate estimate for the likely deflection in the wall would be of the order: ãmax = 14mm at the end of construction, increasing to 6max = 21mm at the end of the design life, implying creep during the design life ófllax = 7mm. The deflections due to reinforcement elongation could, in practice, be smaller still if forces are transmitted through the modular block facing of the wall to the foundation (Section 10.7.3). This mechanism increases stability, thereby relieving the reinforcement of some load.
J
q
Table 10.4 Summary of displacementcalculations for the design example End of construction
J = 64OkN/m Sv
Tm
/'maxJ\I
m
deg
\HPbase!
0.20 0.20 0.40 0.40
33° 45° 33° 45°
0.39 0.25 0.39 0.25
base
kN/m 6.2 3.6 12.4
7.2
max
H
mm
0.0037 0.0014 0.0075 0.0028
19
7 38 14
End of design life = 43OkN/m J
—
Creep
during design
life
H
max
ama'
mm
mm
0.0056 0.0021 0.0112 0.0042
28
II
9 4
56
19
21
7
ömax
Notes: Oma,J/HPhaw values fromFigure 1017 from Equation(10.17)
ae
Displacements rounded
to nearest mm.
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Retaining walls
It is important to emphasise, however, that the deflections discussed above aredue to elongation in the reinforcement only. Other causes of wall movement can be just as significant, such as any tilting caused by immediate or consolidation settlement in the foundation (including differential settlement along the wall), constructioninduced movements or effects due to temperature changes, for example (Section 10.6).
10.8.4 Design crosssection The wall crosssectionis shownin Figure 10.23. Note the practical details such as a levelling pad for the facing blocks and the coarser gravel included behind the face, connected to the toe drainage arrangements. Also note the collector drain at the crest of the wall to minimise water infiltration into the wall.
10.9 Point loads Point loads may be applied to the ground surface, either on the reinforced fill or the backfill, due to traffic loading or abutment forces, for example. These forces are simple Security lence
Surfacewaterdrain
L
3 layers @ 0.60m
0.2rn
}
5ni
4 layers @ 0.4m
} 7layers @ 0.2m
Levelling pad
Drainpipeconnected tosuitableoutlet Reinforcemeni grid ,de. = 5OkN/m
Figure 10.23 Design example: final crosssection 118
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Internal equilibrium
10.9.1
to incorporate intoa planewedge analysis ofinternalequilibrium,and a twopan wedge analysis of overall equilibrium.But there is no simple stress analysis for this case, such as given for the walls described in Sections 10.2 and 10.3. Approximations have to be introduced (which are consistent with the results of wedge analysis) to allow for the effects of point loads on the requiredstressesfor equilibrium in the soil. 10.9.1 Internal equilibrium
It is conventional to separate the vertical and horizontal components of the applied loading (BSI, 1991; DTp, 1978). When the applied load bears eccentrically, it is also conventional to calculate the effective widthof the loaded area, B, and the distance, X, from the edge of the crest (Figure 10.24). An important planewedge mechanism is the one at the critical inclination for selfweight loading, fi = 450 + 4,/2, which justcontains the loaded area, B (Figure 10.24). Theadditional required force for equilibrium on this critical wedge, caused by the point loading, is
= Qh + V'CQ. ...(l0.18) It is conventional to distribute the first component, the horizontal force, as an additional required stress reducing linearly from a maximum value at the crest of the slope to zero at the pointof intersection between the critical wedgeand the wall face, at a depth, h1. = (X + B/2) tan(45 + d/2) (Figure 10.25). The maximum additional stress at the crest due to the horizontal loading is, (GReq)h = 2Qh/h B
h,
I
AP,eq
L
Figure 10.24 Inclined loadon a reinforced soil wall Special Publication123 © CIRIA
179
10
Retaining walls Hë/2
—1
Additional required stress
20h/h)
.4
I
,qz
4
L
Figure 10.25 Additionalrequired stress due to a horizontal point load Following this approach,the additional required stress for internal equilibrium due to the vertical point load, Q., may be taken equal to a uniform stress, a(aReq). = (QVK)/h, which acts over the same depth, (Figure 10.26). Vertical loading on the reinforced zone may influence the required stresses lower in the wall, below the depth he.. The approximation of a loadspreading of vertical stress
h
II B
r Required stress a. Vkar/hc
Qv
7
JO
0, ha,
z
L
Figure 10.26 Additional required stress due to a vertical point load 180
Special Publication123 © CIRIA
Allowance for bond
10.9.2
throughthe fill provides an alllowance for this (BS1, 1991). Loadspeading at 2: I would cause an additional vertical stress in the reinforced fill, for z > h, equal to = QAX ÷ B/2 + z/2). The correspondingincreasein the required stress for internal equilibrium for, z > h, would be, A(UReq)! = KaiA(Uv), as illustrated in Figure 10.26.
If the applied loads act only over a limited length of the wall, for example as would apply for the support ofa bridge deck on an abutment, then the benefit ofloadspreading in the second direction, along the length of the wall, may also be considered. The above components of required stress for a wall with uniform vertical surcharge
subject to an inclined line loading behind the crest are illustrated in Figure 10.27. Note the required stresses to resist point loads are additive to the required stresses due to self weight and vertical surcharge (Figure 10.27), but do not add to the stress induced by compaction (which itself is caused by a moveable, vertical point load). Only if it is greater than the stress caused by point loading would the compaction stress still govern at shallow depth.
10.9.2 Allowance for bond While the above stress analysis may be used to proportion the reinforcement layout, a separate wedge analysis must be carried out to determine whether the reinforcement has sufficient bond to resist the applied point loads (Figure 10.28). Plane wedges may be used, intersecting the front face of the wall at a varietyof elevations, usuallyjust above a reinforcement layer. A wide range of possible wedge angles 6 should be checked. As before, design values for thesoil and thereinforcement parameters should be used in the analysis. The available force in the reinforcement layers intersected will be determined by the lesser of the design strength or the mobilised bond force, as appropriate (Figure 10.7). Required stress
a. Uniform surcharge b. Selfweight loading c. Horizontal point load d. Vertical pointload
z
Figure 10.27 Requiredstress for internal equilibrium with point loading Special Publication123 © CIRIA
181
10
Retaining walls
Availableforce Requiredforce
2.0
1.0
•4
/
mm
0
—
(a)
/ Q
/
I. (b)
Figure 10.28 Wedgeanalysis to check internal equilibrium
Oneaspectofdesignnot yet resolved is how to allow for any increased bondcapacity due to the imposed point loading. It is recommended that when vertical pointloading is continuously present, the increased normal effective stress acting on the reinforcement (estimated by means of loadspreading) should be allowed when calculating bond. Care is needed, however, when sudden or repeated loading is applied. Here it is usual to check that the reinforcement bond is adequate when not allowing for the increase in vertical stress that occurs under the sudden (rapid) load (i.e. use the preexisting effective stresses). In cases of cyclic applied loading, the possibility of a degradation of the bond capacity (below that prior to the applied loading) should be considered, and special analysis will be required. The results maybe summarised on a plot of the minimum ratio, (Av/Req)' foundfor potential wedges intersecting the wall face at each depth (Figure lO.28a). 10.9.3 Overall and foundation equilibrium Where pointloads are applied to the backfill behind the reinforced zone, the most critical anglefor the backwedge (in a twopart wedge analysis) will depend on factors suchas the position, inclination and magnitude of the loads. It is necessary to carry out separate wedge analysis to find the variation with depth of the required force for overall 182
Special Publication 123 © CIRIA
Sloping fill
10.10
equilibrium (i.e. it is not possible simply to modify the equation given in Section 10.3.3).
If the point loads are applied only to the reinforced zone, the expression for the required force for overall equilibrium given earlier can be modified (Section 10.3.3). These statements apply equally to the assessment of the worst loading acting at the base of the reinforced zone, for the analysis of foundation stability.
10.10 Sloping fill or behind the reinforced zone The for overall (Figure 10.29). wedge analysis stability and internal stability can be carriedout as before simply allowing for the sloping fill geometry. The higher stresses in the soil beneath sloping fill may also be calculated from the active earth pressure coefficients given in Figure 10.30. When a sloping fill at an inclination, i, to the horizontal extends to the edge of the crest, the appropriate active earth pressure coefficient for the stress analysis of internalequilibrium would be the value, (Kar)j (Figure 10.30). If the backfill slopes up for a considerable distance behind the reinforced zone, a similar active earth pressure coefficient, (K,,)1, may be used for the backfill loading. Ifthe sloping backfill only rises a shortdistance, to a level plateau at a height, H1,, the resulting horizontal stresses acting on the back of the reinforced zone, L, may be estimated using the approximation shown in Figure 10.31. To a certain depth the horizontal stress at the back of the reinforced zone is governed by the sloping fill and the higher active earth pressure coefficient, (K,,,)1, (Figure 10.30). At greater depth, the Reinforced soil walls may include sloping fill above
I
•1__ 4
L
—
Figure 10.29 WaIl with sloping fill Special Publication 123 © CIRIA
183
10
Retainingwalls 1.5
i.e 0.6 0.7
0.G 0.5 0 0,
0.4
C 0.3 0.2 0.15 0.1
rt 15
10
20
25
30
35
40
1.00
.0.80 0.60
—l 2 \ yHJ
...(1L2)
S,d(/
196
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11.2.2
Overall stability
wheredesign values for the parameters should be used (Chapter 6 and Section II .7). The inclusion of reinforcement at the base of an embankment improves dramatically theresistance to this potential sliding mechanism. For example, if the reinforcement can support the lateral thrustin the fill, then it willeliminate entirely the drivingforce for this slip mechanism (Figure Ii.2d). Deeperseated failure in the foundation is usually the more critical condition for both unreinforced and reinforced embankments.
Stability in the foundation Vertical embankmentloadingcausesan increase in the vertical stress in the foundation soil and a corresponding increase in the horizontal stress. Therefore, a lateral thrust develops in the foundation soil beneath the embankment crest which can eventually cause the foundation soil beneath the embankment sideslope to displace laterally. A simplified analysis illustrates this behaviour. Consider a zone of the soft clay beneath the embankment sideslope, the soil block oabc (Figure II .9a). It may be assumed that the vertical stress applied by the = yH, acts uniformly through the limited depth of soft clay, and that embankment, the principal axes of stress in the clay are vertical and horizontal on either side of the block oahc (Figure II .9a). The soil block then experiences a net horizontal stress,
a
a
I Ii,
t
t
—*—(o—2s)
2ud t/A\V/A'
C
—
—
b
Hard stratum
D
/IAVIA\
5ud
0
0
1 I
1y/yy>7yyy/y/ z/0f
0
z/D
0
z/0
Figure 11.9 Foundation stability: (a) applied stresses, (b) and (c) shear on horizontal planes, and (d) shear displacement, for the case v = 0 Special Publication 123 © CIRIA
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Embankmentson soft soil
11
—
2s,, on the righthand boundary ab, and a net resisting stress, 2Su, on the lefthand
boundary or, the selfweightterms in the level foundation having a neutral effect. Consider first the equilibriumwhere there is neitheroutwardnor inward shear stress acting on the top of soil block, on the surface oa, a = 0 (Figure 11 .9a). The applied vertical loading on the foundation and the net lateral thrust on the soil in the foundation both increase as the embankment height is raised. Eventual lateral sliding of the soil block is resisted by the available shear strength on horizontal planes, nHs,,d. This strength is mobilised and the limitingequilibriumreachedwhen the embankment height and sideslope satisfy the relation,
ii
= yD S,d
4D
...(ll.3)
H
yHIs,, > 5. Equation (11.3) is for the case of zero shear stress to the foundation surface, a = 0, whichassumes that reinforcement supports the applied lateral thrust in the fill. for
cases where,
Deformation in the foundation Consider now the shearstress on horizontal planes within the block oabc (Figure11.9b). The solid linerepresentsthe limitingconditionof Equation (11.3). when the undrained strength is mobilisedon the most highly stressed plane brat the base ofthe block (Figure .9a). The dotted lines in Figure 11 .9b indicate the shear stress at earlier stages of loading. The corresponding shear strain on horizontal planes, for clay with a constant shear modulus, ny = G, are shown in Figure 11.9c, from which the lateral sheardisplacement in the foundation may be found by integration (Figure .9d). The maximum lateral displacement at the ground surface, at the limiting equilibrium, is,
II
II
= Yrnax1 = 1axD 2
where Tm,x and
Ymax are
...(11.4)
2G
the maximum shear stress and shear strain at the base
of the
slidingblock. In the limit. Tfl)ax = s,,, Ymax = s,1/G, so that (Ofl)niax = s,,1D/2G.Again, this result is for the case of zero shear stress on the foundation surface, a = 0. What eventually limits the embankment height is the maximum shearing resistance mobilised on critical planes through the foundation. Only once this maximum resistance is mobilised can gross displacements on a 'failure mechanism' occur through the foundation. In the present example, that would occur on the slip surface dchef(Figure 11.10).
The above analysis highlights the following features of behaviour: 1. Thefoundation soil experiencesincreasing shearloadand sheardeformationas the embankment is built. 198
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Overall stability
112.2
b
C Sod
Figure 11.10 Overall stability: envisaged rigid bodyfailure mechanism 2. The 'prefailure' lateral deformation at the surface of the foundation governs the compatibility with the reinforcement. 3. Additional lateral displacements occur on the critical failure mechanism (Figure 11.10), but these would not normally be considered for compatibility because of the potential loss of strength in the soft clay resulting from intense shearing on localised slip surfaces.
Influence of reinforcement extensibility The above analysis was for zero shear stress applied to the surface of the soft clay, a = 0 (Figure 1 1.9a). For the analysis to apply, the net extension in the reinforcement, caused by the axial tension mobilisedto support the thrust in the fill, must be compatible with the lateral deflectionat the surface of the soft clay. Thus the lateral displacement at the clay surface and the net lateral displacement of the reinforcement (with respectto the embankment centre line) must be compared. The initial assumption of zero shear stress at the ground surface would be unreasonable if it implied a greater extension in the reinforcement than the lateral deflection in the softclay. The reinforced embankment couldnot displace outward with respect to the foundation without inducing outward shear stress on the clay surface, and some of the fill thrust would thus be supported by the foundation, reducing the force carried by the reinforcement. The opposite would be the case if the reinforcement extended less than the lateral deflection in the clay, which would also be unreasonable.The reinforced embankment could not displace inward relative to the foundation surface without applying inward shear stress to the clay surface (a > 0, Figure 11 .9a), in which case there would be greater axial tension in the reinforcement than due to the fill thrust alone. Where geotextile reinforcement is in contact with the clay surface, the permissible range for the coefficient, a, is limited by the applicable interaction coefficient for the reinforcement product (Section 4.4). Special Publication1230 CIRIA
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Embankmentson soft soil
The equilibrium with (a) full outward shear stress, a = —1, (b) zero shear stress a = 0, and (c) full inward shear stress, a' = +1, on the surface of the clay is illustrated in Figure 11.11. The relative heights oftheembankments may be found from thegeneral
expression summarised in Table 11 .1. Note that the outward shear stress in an unreinforced embankment depends on the thrust in the fill and on the sideslope, as indicated by Equation (2) in Table 11.1. The lateral deflection in the foundation is illustrated to show how the 'prefailure' deflections in the foundation reduce in more highly reinforced embankments (Figure 1 I 11). A situation of diminishing returns can be seen to apply to reinforced embankments. To be more effective, the reinforcement must carry greatertensileforce, first supporting the thrust in the fill and then restraining the foundation surface. But in becoming more effective, the reinforcement reduces the magnitude of 'prefailure'
,i
H/D
6hID
41
1.25
0
0
0.88 0.50
S.d/2C
1
sjG
Figure 11.11 Foundation stability: limiting embankment crosssections and 'prefailure' lateral deflections in the foundation for the cases, a = ÷1,0,—I Table 11.1 Equationsfrom simplified analysisfor an embankment on a foundation of uniform undrained strength, 5ud' and limiteddepth, D 4D
Embankment height
H =
. embankment a tot an unreintorced
a =—
Lateral deflection at the ground surface
6,,
(yD)/s,,,
— (1 + a)n
(2)
2ns ,D
= (I
—
(I)
a)
(3)
Note: applicable range yH/s, > 5. 200
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Construction rate and drainage
11.3
deflection in the foundation. Thus, much greater stiffness is required for the reinforcement to support greater tensile force at lower tensile elongation. This demonstrates why a 'fully reinforced' embankment (a = +1) is unlikely to be achieved in practice. Not only do all geotextiles elongate under load, but the interaction coefficient between the reinforcement and the soft clay may limit the magnitude of inward shear stress that can be exerted on the foundation surface. The embankments indicated by the dotted lines in Figure 11.11 illustrate typical reinforced, a +0.5, and unreinforced, —0.5, embankment cases.
a
11.3 Construction rate and drainage The rateof filling and the rate of drainage in the soft clay are important factors in the design of reinforced embankments on soft soil. 11.3.1 Construction period Reinforcement is generally required to maintain stability in an embankment on soft soil only until the excess porewater pressures caused by the embankment construction have dissipated (Figure 11.1). Thus, the same embankment crosssection could be built, without reinforcement, simply by filling slowly enough so that minimal excess porewater pressures develop. This behaviour was illustrated in Figure 11. I, and may be represented in terms of the maximum required reinforcement force versus time (Figure 11.12). The highestforce is required if the embankment were built 'instantaneously'. Lesser force is needed with
a. 0) 0 0 C 0, E
1 Log (time)
Figure 11.12 Relationbetween the maximum required reinforcement forceandthe rate of construction Special Publication123 © CIRIA
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Embankmentson soft soil
11
more practical rates
of filling which permit some drainage in the foundation during
construction. Only very slow and gradual filling would allow the foundation strength to keep pace with the increased embankment loading so that reinforcement is not required. Reinforcement is found to be attractive for many reasons:
On very soft ground, reinforcement doubles as a construction expedient that prevents local loss and intermixing of the fill and the soft soil, and improves the bearing capacity for construction equipment. 2. In comparing reinforced and unreinforced alternatives, the reinforced embankment will cost less ifthe fill saved, due to steeper side slopes, and the economies ofmore rapid construction, exceed the cost of the reinforcement. This is often the case, and the reinforcement can bring the additional benefit of more uniform embankment settlement and an ability to bridge over localised 'soft spots' in the foundation. 3. Major embankments on soft soil are often built in several stages. The use of reinforcement is attractive in this case because a greater embankment height can be built in any one stage. This leads to extra improvement in the foundation strength during consolidation, and reduces the number of stages required, aM hence the construction time. Reinforcement is particularly effective when combined with vertical drains for stage construction. 1.
11.3.2 Drained and undrained shear A critical feature for the stability analysis of embankments on soft soil is the drainage conditions in the soft clay at failure (Ladd, 1991). This is illustrated by an example of secondstage tilling where the clay beneath the embankment berm is normally consolidated, and the porewater pressures are known (Figure 11.13). Consider the element of clay indicated in the figure. When the shearing resistance for this element of clay is estimated from an effective stress analysis, based on the current porcwater pressures. the maximum available tan resistance is anticipated to be at point (I) in Figure Il. 13h. i, = Rapid shear in the clay, due to the second stage of filling, would cause an undrained response that is limited by the current undrained strength, 1 = point (2) in Figure I l.13b. There is a dramatic difference in available resistance between these two cases which stems entirely from the excess porewater pressures induced by undrained shear. These were not allowed for the effective stress analysis. When the factors of safety from the two analyses are compared for typical embankment cases, they are found to differ by a factor about 1.5 to 2.5 (Ladd. 1991). In other words., an effective stress analysis which does not anticipate the excess porewater pressures which will be induced by rapid shear in the soft clay may overestimate the factor of safety by about a factor of 2.
,.
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11.3.2
Drained and undrained shear
Crest
/
Stage 2
Stage1
— thc
4'; 4..
0
tf =
0
r
0)
U)
a
\_—Currentyieldenvelope
\
Normal effectivestress, a (b)
Figure 11.13 The response of soft clay to rapid stage 2 loading beneath an embankment (after Ladd, 1991) Theissue,then,is not one oftotal versus effective stress analysis, but ratherone ofan appropriate allowance for the porewater pressures induced by rapid, undrained shear. In the design of an embankment, a sudden, unexpected change in loading is a possibility which must be guarded against. Ladd (1991) concludes that it is preferable to assess the stability ofembankments on soft soil in terms ofthe current undrained shearing resistance in the soft clay, which may be estimated with relative confidence from the consolidation history and current insitu effective stresses in the clay (Section 5.3). It is relatively difficult, in comparison, to evaluate the change in porewater pressure that will occur when the clay is sheared rapidly to failure. It is helpful to consider standard laboratory tests as a reference for the loading cases that may apply for soft clay. A conventional undrained analysis may he compared with an unconsolidated undrained(UU) test in which no consolidation, with respect to the applied stresses, occurs before undrained shear to failure. A conventional drained analysis may be compared with a consolidated drained (CD) test in which therehas been fullconsolidation, with respect to the applied stresses, and no excess porewater pressures are induced by shear. The undrained strength analysis, which is recommended for the design of embankments on soft soil, may be compared with a consolidated undrained (CU) test in which there has been partial or full consolidation, with respect to the applied stresses, and a corresponding increase in undrained strength, before undrained shear to failure. Special Publication123 © CIRIA
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Embenkmentson soft soil
11.3.3 Design strategies Two main design strategies are used for reinforced embankments on soft soil which are built in one stage. One approach starts with the final embankment crosssection after consolidation in the foundation is complete, and determines first the unreinforced crosssection that will provide the required longterm factor of safety. Reinforcement is then viewed simply as an expedient to boost the intermediate endofconstruction stability, and the stability during consolidation. The amount of reinforcement required depends on the rate of construction, the rate of filling and whether wick drains are used in the foundation. An alternative approach starts with the stability at the end of construction. Various possible embankment crosssections are examined, and the required quantity and type of reinforcement, and the volume of fill, compared for each. The longterm stability, after consolidation, is checked separately. It is desirable that embankments on soft soil should have an adequate longterm factor of safety without reinforcement. It is fortunate, therefore, that reinforced embankments which are stable in the short term, after rapid construction, are usually found to be stable in the long term without need for reinforcement (see Figures 11.1 and 11.12). The measurement of porewater pressures is an important means of monitoring embankment performance. But the insitu effective stresses determined from these measurements are best considered as consolidation stresses from which the current undrained shearing resistance in the clay may be estimated for use in stability analysis. The properties of the fill material for embankment construction are generally not known prior to construction. The routine procedure is to design the embankment with assumed fill properties, and then to specify the fill and control the construction to ensure that the properties in the field either equal or exceed those assumed in design.
11.3.4 Significance of foundationstability It has been emphasised that the bearing capacity of the soft clay foundation limits the
improvement that can be achieved by reinforcing an embankment on soft soil. The important first step in design, therefore, is to check that the desired embankment crosssection will not cause bearing failure in the foundation. In addition to the reinforcement force needed to maintain stability in the foundation, the reinforcement must also support the thrust in the fill. This latterloading can be very significant, and some reinforced embankments are designed assuming that the reinforcement only supports the lateral thrust in the fill.
11.4 Concepts from plasticityanalysis was derived from plasticity theory (Terzaghi, 1943), and this same theory is relevant to embankments on soft soil. Rather than focus
Conventional bearing capacity analysis
204
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Plasticity solutions
11.4.1
on the overall bearing capacity, as for a surface footing (Figure 11.5), it is more helpful for embankments to determine the variation of vertical stress that can be applied to the foundation surface with distance from the edge of the loading (Figure 11. l4a). As explained earlier,reinforcement enables a soil clay foundation to support greater betweenthe point of maximum vertical loading. This reduces the requireddistance, beneath the crest of the and the toe embankment, loading (Figure 11. 14b). 11.4.1 Plasticity solutions Solutions have been derived for a foundation with shear strength, linearly with depth, z, according to the relation,
s,, that increases
+ pz ...(l 1.5) S,r = where, s,40, is the shear strength at the ground surface, and the linear rate of increase in strength is p. The results (Figure 11.15) for a fully restrained foundation, a' = + I (rough footing), and for no restraint at the foundation surface, a' = 0 (smoothfooting), werederivedby Davis and Booker (1973).The analysis was extended to the other loading cases by Houlsby and Jewell (1988). The corresponding results for a foundation of uniform shear strength, s,, and limited depth, D, were derived by Mandel and Salençon (1969 and 1972), for the same two loading cases, a' = +1 and a' = 0. Theseresults can be matched by simpler limit Embankment toe
forstaility (a)
'
Desired embankment loading 7H
11
Soft clay foundation
x
Desired loading yH
Required distancefrom the toelx) (b) _______ Comparative unreintorced and reinforced designs
Figure 11.14 Bearingcapacityexpressedin terms oftheallowable vertical loading versus distance from the edge of loading, relevant to embankment design Special Publication123 © CIRIA
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11
Embarikmentson soft soil 20 18 16
I0 0 0
14 12
10
b
0 0 C) 0 cc 0
t
8 6 4 2
0 0
1.0
2.0
3.0
Distance fromedge
4.0
5.0
so
Figure 11.15 Plasticitysolutions forstrength increasingwith depth (afterDavis and Booker, 1973, and Houlsby and Jewell, 1988) equilibrium analysis which has been used to derive the loading cases shown in Figure 11.16 (JewelI, 1988).
11.4.2 Application of plasticitytheory The applicationof the plasticity solutions for the design of embankments is illustrated in Figure 11.17. The simplest embankment shape that closely reproduces the results
0 0 In
C
0 0 a) In
t>0
u
cc
a)
2
Figure 11.16 Solutions
4
6
8
—1
10
for a foundation of uniform strength and limited depth
above a rough stratum
206
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Limit equilibrium analysis
11.5
t (a) Design curve
px —
— X
s
HF,,
H

x
Xd
(b) Praclical crosssection
j
—
Ild
4———
x
(c) Uniform sideslope
Figure 11.17 Practical embankment crosssections derived from plasticitysolutions from plasticity theory is shown in Figure 11.1 7b. Studies using limit equilibrium analysis and finite element analysis have shown empirically that an embankment with a uniform sideslope, as defined in Figure 1 1.l7c, preserves the same equilibrium and factor of safety (Russell, 1992). Thus the solutions in Figures 11.15 and 11.16 are a convenient tool for the preliminary sizing of embankments.
11.5 Limit equilibrium analysis Limit equilibrium methods have proved effective for the design of reinforced embankments on soft soil. Rotational stability on circularmechanisms and translational stability on wedge mechanisms may both be used. There are some limitations to slip circle analysis which are discussed below. Special Publication123 © CIRIA
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Embankmentson soft soil
11
11.5.1 General considerations A more sophisticated approach is demanded for the limit equilibrium analysis of reinforced embankments than for unreinforced embankments. While it is necessary to checkthe overall stability in both reinforced and unreinforced embankments, other stability checks are as important for reinforced embankments. For example, the stability in the foundation must be examined to ensure that there is sufficient bearing capacity to support the weight of the embankment. In more detail, the mainfailure mode for an unreinforced embankment is largescale movement on a failure mechanism passing through both the embankment fill and the foundation. Settlement and spreading ofthe embankment, and the period over which this occurs, influences the serviceability of unreinforced embankments. The main failure modes in a reinforced embankment are as follows:
I. Where thereinforcement is relatively inextensible but has adequate strength, there may be foundation failure which causes lateral spreading and heave in the soft clay, resulting in excessive settlement of the embankment. 2. Where the reinforcement is relatively inextensible but has insufficient strength, the reinforcement may become overloaded and rupture, triggering a similar failure mode to that in an unreinforced embankment. 3. Where the reinforcement has adequate strength but is too extensible, it may only be abletomobilise theforcesrequired for equilibrium at excessive elongation. The embankment would then settle andspreadlaterally to an unacceptable degree, with heave at the embankment toe and tension cracks in the crest. Guidance on selecting reinforcement strength and extensibility parameters is given in Section 11.7.
11.5.2 Rotational stability:slip circle analysis conventional slip circle analysis for an unreinforced embankment is shown schematically in Figure 11.18. The portions of the slip circle in the fill and in the foundation may be considered separately to identify the two main disturbing forces,
A
namely: 1. The lateral thrust in the fill, generated on the portion of the slip circle within the till (Figure 1 l.18b). and 2. The vertical loading due to the selfweight of the embankment above the highly stressed zone in the foundation (Figure ll.18c). Jndeed a conventional slip circle analysis may be represented as shown in Figure 1 l.lXd. when the lateral thrust, P1;111, is calculatedfrom the same circle. (The thrust has been assumed to act horizontally.) Thecrosssection of a reinforced embankment is ultimately restricted by thecapacity of the foundation to support the vertical embankment loading. The slip circle analysis for 208
Special Publication 123 © CIRIA
Rotational stability: slip circle analysis
11.5.2
(a)
H I
__ Soft clay
(c)
//X\ /A\\ (b)
PEril
Softclay (d)
Figure 11.18 Componentsofslip circle analysisin the fl/land the foundation this case is shown in Figure 1 l.19a, where the disturbing lateral thrust in the fill (Figure 11.1 8d) is supported by the reinforcement (i.e. not supportedby the foundation soil). The reinforcement can provide restraint on the foundation, an inward shear stress, which = FnJfl' which can be used in the slip circle analysis mobilises a net restoring force, (Figure ll.19a). There are two ways of proceeding with limit equilibrium analysis ofan embankment on softsoil. One way is to assumethat the desiredfactor ofsafety applies on all potential slip surfaces, and then to calculate the reinforcement force required to achieve this for each. This gives a distributionof maximum required reinforcement force for stability (for example, Figures I l.19c and d). The reinforcement is then checked to ensure that the available force in the reinforcement (Figure 11.1 9b), limited by the reinforcement material and interaction parameters, everywhere exceeds the required force. This method is recommended and used throughout the book (Section 7.1). An alternative approach starts with the variation of the maximum available force in the reinforcement (Figure 11.19b). Thefactor of safety on potential slip surfacesis then calculated using the maximum force corresponding to where the reinforcement is
R
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Embankmentson soft soil
///$
/
P
Reinforcement
f,'flVtA'\
Soft clay
(a)
Limitstoavailable reinforcement force
C a) E
P,
a) u
20 CO
Material propefties
a, =
C,
C
It
Cu
> C
Position
in embankment lx)
t Embankment toe (x
(b) C 0 E
0 0
2a, Co
0)
Locus of maximum required force
______ Foundation stability
= Positioninembankment
>1 (x)
o
0
PFill
= Co
__________
— PFnan
(d)
Overall stability
Position inembankment (x)
Figure 11.19 Slip circle analysis for reinforced embankments: (a) foundation stability, with (b) availableand (c) required forces;(d) overall stability, required forces intersectedby the trial slip mechanism. The factor of safety is calculated for all potential
slip mechanisms to check that in every case this exceeds the desired minimum value.
11.5.3 Foundation and overall stability The requiredforce to maintain stability in the foundation beneath an embankment may be found from limit equilibrium analysis. The distribution of the reinforcement force depends on the design loadings and resistances, and on the embankment crosssection. Themaximum available reinforcement force is governed by the reinforcement material properties and by the limiting shear interaction with the surface of the soft clay (Figure I l.19b). 210
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Limitations of slip circle analysis
11.5.4
at a distance, x, from the Thesoil interaction limitsthe maximum available force, toe of the embankment, that candevelop to maintain foundation stability. In the general case. =
...( 11.6)
where S110j is the design shear strength of the clay at the ground surface, and a a coefficient of interaction.Where the reinforcement is in directcontactwith the soft clay, a = ads, the coefficient of direct sliding (Section 4.5). Limitequilibrium analysis proceeds by trial and error. Design values for the material
parameters and a trial embankment geometry are selected, and the required reinforcement force evaluated using a range of trial slip surfaces. For example, many different combinations ofslip circle centres and radiiwould be examined to intersect the reinforcement in various positions. The distribution of maximum required force along the reinforcement foundfrom this analysis (Figure 1 l.l9c) must be less than or equal to the available force (Figure 1 l.l9b). A reinforced embankment that satisfies the above design check may be supported in equilibrium without exceeding either the design shear strength of the foundation soil or the limiting interaction between the foundation and the reinforcement. It remains, then, to check that the reinforcement is able to carry the additional thrust from the till and hence to provide satisfactory overall stability (Figure 1 l.l9d).
11.5.4 Limitations of slip circle analysis The limitation to slip circle analysis occurs where failure in the foundation is constrained to occur on shallow slip surfaces, due to a hard stratum beneath the soft soil, for example. Slip circle analysis underestimates the thrust in the fill in such cases and therefore overestimates embankment stability (Gudehus, 1981, and Leroueil eta!., 1985). This error can be avoided by using a logarithmic spiral mechanism which both cuts steeply upward through the embankment fill (like an active wedge) while reducing to a slip circlein the foundation (Leshchinsky, 1987). Alternatively, the analysis for thethrust in the fill may be decoupled from the search for critical slip circles in the foundation, and a Coulomb wedge, or Rankine earthpressure theory, usedinstead to calculate the active thrust. Even using the above techniques, slip circle analysis is still found to be inadequate for very shallow foundations. This is illustrated in Figure 11.20 by comparing the loads calculated from slip circle analysis and plasticity theory (for a = 0 in this case). While slip circle analysis performs well for foundations with strength increasing with depth (Figure 1 1.20a), it overestimates considerably the stability in foundations of limited depth (Figure II .20b). It is preferable to use a translational wedge analysis for this latter case (Section 11.5.5). Special Publication 123 © CIRIA
211
11
Embankmentson soft soil
t/s, = 0
F
verticalloading only
Slip circleanalysis
15
10
'Plasticity solution )Davis and Booker,1973)
(a) cJ
Slipcircleanalysis
15
1972)
_____
(b)
x/d
Figure 11.20 Comparison of slip circle analysis with plasticity solutions: (a) strength increasing with depth, and (b) foundation of limited depth
In general terms, the error in slip circle analysis could exceed 10% for reinforced embankments where x/D > 2, and for unreinforced embankments where x/D > 3. The critical distanceis between the toe of the embankment and the edge of the crest, so that xID = nilID, for a sideslope I: n. 11.5.5 Translational stability: wedge analysis In a wedge stability analysis, critical wedges and sliding blocks are examined to check horizontal equilibrium. In other respects the analysis and the steps that should be followed are the same as those described above for slip circle analysis. A typical wedge mechanism for an embankment on soft soil is illustrated in Figure 11.10. The exploded view in Figure I 1.2 Ia emphasises once more the separate roles played by the reinforcement to support the thrust in the fill and to provide lateral restraint at the foundation surface. Satisfactory foundation stability is achieved when the design shearing resistance in the soft clay, and the available force from the reinforcement, are sufficient to provide horizontal equilibrium in the foundation subject to the vertical loading from the embankment (Figure 1 l.21b). 212
Special Publication 123 © CIRIA
Method of slices
11.5.6

nkment— T
Reinforcement
PFiPI
= TX
Fndn = USydX
USUa
Softclay
Sod
(a)
x 0) 0
0
PAy = USJdX
Available force
C 0) E 0)
0 0 =
Foundation stability
0) Er
Position in embankment (x)
(b)
0)
0 0
Available force
C 0) E
Design strength
d
0)
0 0 =
0) Er
(cI
Required
force4zrd Positioninembankment
Overall stability
(x)
Figure 11.21 Wedgeanalysis for reinforced embankments: (a) exploded view of limiting stresses, (b) check on foundation stability, and (c) check on overall stability
To check overall stability, the design strength of the reinforcement must be greater thanthemaximum force required to support the lateral thrustin thefill, Fjf/' in addition to the maximum required force to maintain foundation stability (Figure I l.2lc). 11.5.6 Method of slices More generalmethodsof limitequilibrium analysis may be applied to embankments on soft soil, such as the method of slices. Both force and moment equilibrium may be examined, and more detailed consideration given to the equilibrium on interslice boundaries. Whatever method is used, it is essential that both foundation stability and overall stability are examined for a reinforced embankment. The simple slip circle analysis and translating wedge analysis described in this chapter are adequate for preliminary design purposes, and in many cases for final design. The methods give very similar results to more sophisticated analyses, and capture well the SpecialPublication 123 © CIRIA
213
11
Embankmentson soft soil
main mechanics in reinforced embankments. The uncertainty in evaluating the current soil shearing resistance, the interaction between the reinforcement and the foundation, and the design strength for the reinforcement, will often outweigh the gain in computational accuracy. More complex slip mechanisms with multiple slices are useful, however, where many different strengths apply in soil zones within the embankment and foundation. An example would be the analysis for stage construction where the clay experiences different levels of applied stress and degree ofconsolidation, giving different undrained strengths depending on position beneath the embankment.
11.6 Analytical solutions Analytical solutionsare useful for preliminary design investigations, and for making rough checks on designs, as an adjunct to limitequilibrium methods. Theirbenefit is that they can be applied quickly and without computation. Analytical solutions have been derived for foundations of uniform strength and limited depth, and strength increasing with depth, and have been shown to give results comparable with more sophisticated methods, over the applicable range. The derivation of the equations is not given here for reasons of length (see Jewell, 1988). Horizontal equilibrium of a rectangular block in the foundation is considered (Figure 11.22). The most critical loading is at the edge of the crest and this defines the q + dq q
nr
0b

—
—,
dx
afl+doh
D
L__J
IIA\VFA\
su (a)
Edgeof loading suo
yH
nil
SU
x 2s.
= yH j— z
z
FS,
(b)
Figure 11.22 Assumed equilibrium for analytical solutions: (a) foundation of limited depth, and (b) foundation with strength increasing with depth 214
Special Publication 123 © CIRIA
11.6.1
Foundation of uniform strength and limited depth
critical length,nH, for an embankment of height. H, and uniform sideslope, I: n. The equations below are for this most critical case. The more general use of the analysis to find therequiredreinforcement forceat other positions in the embankment is illustrated in the design example (Section 11.8). The equations are expressed in terms of the factor of safety and maximum required reinforcement force. This reflects the use of the equations to check stability and evaluate the maximum required force. As usual, the factor of safety, FS, defines the proportion of the representative soil shearing resistance, s,, that is mobilised, S,,,,,, to maintain stability (Section6.3.4), Sum
(11.7)
=—
and design values are used for the other parameters in the analysis. The solutions apply for embankments which exert significant loading on the foundation clay, consistent with the definition of 'soft clay' given earlier. In general, FSyH 'u
yH =—5
(11.8)
5um
It is the coefficient, a which defines the magnitude of inward shear stress applied
to the foundation surface, a'sum, and is a critical parameter for design. The ultimate limit to this interaction is the maximum shear stress that can be developed between the soil and the underside of the reinforcement. But the compatibility between the extension in
the reinforcement and thedeformation in thefoundation may influence the magnitude of the coefficient which can be mobilised. In an unreinforced embankment, there is a net outward shear stress acting on the foundation surface because of the thrust in the fill,
ftc 0.
11.6.1 Foundation of uniform strength and limited depth The analysisis for a foundation of uniform undrained shear strength, 4' and limited depth, D, underlain by a roughstratum. The equations are found from integration ofthe incremental equilibrium shown in Figure 1 l.22a. The integration is over a distance, x = nH, between the toe and crest of the embankment where the maximum loading is
= yH.
The factor of safety in a reinforced embankment is:
Suf' YH\
n/A
...(ll.9)
and the maximum reinforcement force required to provide the above stability is: Special Publication123 © CIRIA
215
Embankmentson soft soil
11
/
K
ctnD
P=yH2I
,
...(lI.lO)
2/
\4D+(l+ct')nH
where the design value of the active earth pressure coefficient, Kd, is for the design i.e. angle of friction, — sin
= 1
...(ll.ll)
. + sin
If the reinforcement were not included, the factor of safety in the unreinforced embankment would be:
s
/8Di2nH\I ES. = —I
...(11.12)
yH\2D+K0,H)
Please note the range for which the solutions apply (Equation 11.8).
11.6.2 Foundation with strength increasing with depth
Now considera foundation with an undrained shear strength, 5,:, that increases linearly with depth, :, at a rate,p, from an initial shear strength at the ground surface, S,,0 (Figure I 1.22b). Again, the solution considers the horizontal equilibrium ofa rectangular block of soil in the foundation, the critical depth of which is determined by calculus. The factor of safety in a reinforced embankment is, ES
s, /
pnll =—I4+——+2
yti
\
/2(1 + ct)pnil\
/
S'()
I
Silo
...(ll.13)
,)
and the maximum required reinforcement force mobilised to maintain the above equilibrium is:
= yH2I7 (1115,,,, + \ESyH
—I 2
...(ll.l4)
where the factor of safety, ESç, is defined by Equation (II. 13), and the mobilised earth pressure coefficient, K,,d, found from Equation (11.11). The critical depth of the sliding block is:
= .' /'(I
+ 2p
...(1 1.15)
The factor of safety for an unreinforced embankment is also found from Equation (11.13) but using the value for a' corresponding to the outward shear stress exerted by the unreinforced fill: 216
Special Publication 123 © CIRIA
11.6.3
Reinforcementstiffness
FSyH
—
2n
...(ll.16)
s,,0
An initial guess, a = —0.5, in Equation (11.13) gives an initial factorof safety, FS, that may be substituted intoEquation (11.16) to recalculate a. Convergence is rapid. The critical depth of the sliding block may be found from Equation (11.15). As before, the range for which the solutions apply is defined by Equation 11.8. 11.6.3 Reinforcement stiffness Theanalysismaybe extended to assess the required reinforcement stiffness by equating the lateral deflection at the surface of the foundation with the extension of the reinforcement, caused by the force exerted by the fill and the shear stress mobilised between the foundation and the reinforcement. An approximate (slightly conservative) expression for the extension in the reinforcement due to the thrust in the fill is,
=
l K,,yH2
J
2
( \3
+—
(1 1.17)
2/
where L. = niI is the length of the embankment sideslope, L,j2 is the halfwidth of the crest, and J is the stiffness of the reinforcement, the other parameters having been
defined previously. An approximate expression for the extension in thereinforcement caused by the shear stress (a 0) appliedby the foundation surface is,
=
as(L+D)
(11.18)
The corresponding lateral deflection at the surface of a foundation of uniform strength and limited depth is given in Table 11.1 (from the analysis in Section 11.2.2). The requiredreinforcement stiffness, Req' for the envisaged equilibrium may now be found by equating the soil deflection and the reinforcement extension to give,
/
G /nH L,\ q = (I — a)s0 (K",yH2 (—+ —1—}+as",D \3D 2D/ I
\
+—I D
//
(11.19)
I
a
The following should be noted. Equation (11 .19) is valid for cases, 0, and to applies embankments on foundations of uniform strength and limited depth (Section 11.6.1). The embankment should be proportioned using Equations (11.9), with a selected design value, a, to determine the factorof safety, F'S.. Only these values should be used in Equation (11. 19). The design shearing resistance in the foundation is defined as, = s,,/FS., and the design earth pressure coefficient is defined in Equation (11.11). Special Publication123 © CIRIA
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Embankmentson soft soil
The adequacyof the reinforcement stiffness is a question of serviceability ratherthan stability, as is discussed further in Section 11.7.Ifitwereassumed, forexample,that9O% of the representative values of thefoundation and fill shearing resistance were mobilised in the working equilibrium, then the value of a' in Equation (11.9) would be reduced by trial and error to find the equilibrium with FS 1.1, corresponding with O.9Os,. of force in the and hence the factor analysis, Reducing reduces the reinforcement safety. The lesservalue of a corresponding to the newequilibrium with ES5 1.1 would then be used in Equation (II . 19) together with the serviceability values of s,1 and Kadto define the required reinforcement stiffness for serviceability. In effect the analysis provides an expression of compatibility which links the elongation in the reinforcement to the assumed maximum (allowable) shear strain in the soft clay. The link is through the parameter, G/sUd, which is evaluated by selecting the magnitude of shear strain, Yrnax' required to mobilise the design shearing resistance, Sud. The secantshearmodulusfor the clay, G = iVy, then has a value, G/Sud = 1/yrnax, when the design shearing resistance is mobilised. The analysis above is for a foundation with uniform strength and limited depth. The more general analysis of serviceability is described in Section 11.7.3.
a
11.7 Parameters for design The selectionof design values for the ultimate and serviceability limit state analysis of reinforced embankments on soft soil is described in the following sections. The application of the limit state concepts is considered first. 11.7.1 Limit states The separate limit states of ultimate collapse and serviceability should be considered in
thedesign ofa reinforced embankment. At leasttheconditions at theend ofconstruction and at the end of foundation consolidation have to be examined. Stability at the end of the service life of the embankment would also need to be considered where the reinforcement was intended to play a longterm role, but this is not the usual case for embankments on soft soil and is not discussed further below. Forultimate limit state analysis, design values areselected for the ultimate resistances of the soil and the reinforcement, for their interaction parameters, and for the embankment selfweight and any externally applied loads. The design values must apply to the design situations being considered (Section 6.1). Analysis is usedto demonstrate that the internal stability, the foundation stability and the overall stability in the embankment are sufficient to guard against the envisaged ultimate limit states. These must cover critical stages of embankment construction, loading, and foundation consolidation. 218
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Ultimate limit states
11.7.2
The consequence of an ultimate limit state is either collapse of the embankment involving rupture of the reinforcement or gross sliding of the foundation or fill relative to the reinforcement. Expected values of the parameters are adopted in the analysis of serviceability (Sections 6.2 to 6.5) in which the lateral deformation and the settlement of the embankment are the major concerns. In contrast to the ultimate limit state, where the design strengthofthe reinforcement is governed by the risk ofrupture, the serviceability strength is governed by an allowable tensile elongation in the reinforcement (Section 6.4.1). The limit equilibrium methods of analysis for serviceability described below have proved adequate for routine design purposes. It is emphasised, however, that only a numerical analysis (such as the finite element method) can predict in detail the embankment and foundation deformations, and their development with time.
11.7.2 Ultimatelimit states The design values and safety margins recommended below follow the guidance in Sections 6.2 to 6.4.
Loadings and water pressures The maximum expected unit weight of the fill, Ymax' should be selected, together with the most critical embankment crosssection in the chainage covered by the analysis. Usually no allowance is made for porewater pressures or waterfilled tension cracks in freedraining fills. However, possible constructioninduced porewater pressuresand tension cracks in clayeyor finegrained fillsshould be considered. A waterfilledtension crack can significantlyaffect embankment stability. The worst expected live loadings should be used, allowing for equipment and stockpiled materials during construction. A minimum vertical surcharge on the crest, q = 5 kN/m2, is recommended in all cases as a prescriptive measure to allow for unexpected overfilling or surcharge loading.
Soil properties
,
Relativelylarge deformations may occur in embankments on soft soil and the critical state angle of friction for the soil fill, is recommendedfor design. This applies to all
fills, so that ç = 0 and
=
A representative value of the current undrained shearing resistanceat large strain in
the soft clay is the relevantstrength for the analysis of ultimate limit states. Methods to measureand predict this strength are discussedin Section 5.3.4. Any consolidation in the foundation with respect to the applied stresses from the embankment loading should always be taken into account (Section 11.3.2). When the representative undrained strength is selected conservatively, as recommendedabove, only a relativelysmall additional partial factor of safety need be applied Special Publication 123 © CIRIA
219
Embankmentson soft soil
11
to definethe design strength, Slid = s,/FS. The partial factor, FS, would typically be in the range 1.1 to 1.5, with the value reflecting the confidence in the knowledge of the foundation soil properties, the consequences of the envisaged limit state, and the duration of the envisaged design situation. A higherpartial factor of safety on the undrained shearing resistance of the soft clay would normally be used for the longterm stability following consolidation (Section 11.3.2).
The most appropriate analysis for the longterm stability of an embankment on soft soil remains under discussion, however (Section 11.3.2). Thus it is necessary to think carefullyof the uncertainties being guarded against and the risk that these could lead to a suddenchange in loadingand failure. Thereserveof strength in softclay to resist rapid (undrained) shear is significantlyless than to resist slow (drained) shear (Figure 11.13). It is pragmatic to use both undrained strength analysis (as recommendedin this chapter) and effective stress analysis when investigating the longterm stability of embankments on softsoil. But the factorof safety required in the effective stress analysis should reflect the potential shortcomings of the analysis for this application(Section 11.3.2). The recommendedsoil properties for ultimate limit state analysis are summarised in Table 11.2.
Reinforcementmaterial properties
The case where the reinforcement only maintains the shortterm stability of an embankment is considered here. The strength of geotextile materials gradually reduce with time (Section 2.4), and to ensure that an adequate allowance for time has been made, the design strength should be selected assuming that the reinforcement has to support the design load continuously until consolidation in the foundation is complete. The recommended design loading period, ta,, is the sum of the time required for embankment construction and the time to achieve 90% consolidation in the foundation. Table 11.2 Recommended soil properties for ultimate
limit state analysis
Foundation soil
Criterion for design
Design
Foundation shearing resistance
Largestrain value
s
Safety margin
Construction (ES) Longterm (ES)
I. I to 1.3
to
1.3
s1 =
1.5
5,
Granularfill Unit weight
Maximumexpected
Shearing resistance
Largestrain value
220
y1,
= =
Yrnax
Special Publication 123 © CIRIA
Ultimate limit states
11.7.2
Thedesign strength for thegeotextile reinforcement must allow for the conditions in the ground which requires an allowance for the reduction in strength due to mechanical damage,fd' anddue to the soil environment, fe,' (Section 6.4). The materialfactor,frn' provides a margin of safety between the design strength and
the expected rupture strength of the reinforcement at the end of the design loading period, and would normally have a value in the range 1.3 to 1.5 (Table 6.1). Because of the relatively short period under load in embankments on soft soil, the lower partial factor is usually adequate. The main reinforcement properties for ultimatelimit stateanalysis are summarised in Table 11.3.
Interaction properties There are two main interactions between the reinforcement and the soil which need to be considered, between the reinforcement and the fill above it, and between the reinforcement and the soft clay below it. The bond coefficient and the direct sliding coefficient are equal for continuous reinforcement materials that separate the soil on either side, such as woven geotextiles, (Section 4.4). For these materials in freedraining fill, the appropriate interaction coefficient is typically in the range, 0.90 0.60, depending on the surface of the material. There are fewer data on the interaction between roughness geotextile geotextiles and softclay under rapid shear, where additional factors such as the drainage conditions at the interface need to be considered. The direct sheartests by Garbulewski (1990),however, indicate that a relativelyhigh proportionof the strength of clay can he mobilisedat a claytogeotextile interface.
a.
Table 11.3 Recommended
reinforcement properties for ultimate limit state
analysis Strength
Criterion for design
Design life Design temperature Reference strength Mechanical damage Influence of soil environment
Time for 90% consolidation Maximum buried temperature Reference strength at (t,T,) Fill type and construction procedure Soil and waterexposure for (t7, Ti,)
Design
=
T
(Ri),r f,
Expected field strength
Material factor
=
Margin between design and expected field strength, typically 1.3
Design strength
Special Publication123 © CIRIA
t9J
(R1)
j
(Pf11)H (Pd), = ;:,
221
11
Embankmentson soft soil
The interactionbetweena geotextile and the top surface of a soft clay foundation can be influenced by several factors. 1. The undrained shear strength at the surface of the clay may be greaterthan at some depth, 200 mm or 500 mm say, below the ground surface (Section 5.3.3). 2. The surface of the soft clay, at the interface with the geotextile, is a drainage boundary at which the excess porewater pressures caused by construction would dissipate quickly. 3. When the geotextile is placed on existing (unprepared) ground, the interface may be affected by plant materials, roots and other surface detritus. No general recommendation can be made for such variable conditions. Rather, it is suggested that at leastthreemodesof relative slippage between the foundation clay and the reinforced embankment be considered. I. Undrained slip at the claytogeotextile interface for which an 'undrained' direct of the order 0.3 to 0.5, might be assumed (i.e. 30 to 50% sliding coefficient, of the undrained strength at the clay surface may be mobilised). 2. Partially or fully drained slip at the same interface, analysed in terms of effective stress, the effective angle offriction for the soft clay and a frictional directsliding coefficient, hi1s (Section 4.5). 3. Slip entirely within the clay, away from the reinforcement, just below a strong surface crust. Sometimes the reinforcement is placed above the clay on a working platform of granular fill. In this case the direct sliding at the reinforcement level would be within the granular fill. Consideration would then need to be given to the filltosoftclay interface. What is being sought are the possible mechanisms that could limit the load transfer between the base of the reinforced embankment and the soft clay. In the limit, a pessimistic assumption of no load transfer at this interface, a = 0, could be examined. The case for geogrids (as opposed to woven geotextiles) is complicated by the different interaction coefficients for direct sliding and bond mechanisms of interaction (Section 4.4), and by the possible penetration of soil through the grid apertures. The distinguishing feature between the bond and direct sliding modes of interaction is whether the soil on one side of the geogrid is moving laterally with respect to the geogrid only, or with respect to both the geogrid and the soil on the other side (Figure 4.6). For example, foundation failure in the soft clay beneath a stable reinforced embankment (Figure 11.10), or internal failure by direct sliding of the embankment fill over the
a,
reinforcement layer (Figure 11.7), are both failure modes for which the coefficient of direct sliding would be the relevant interaction parameter. The coefficient of direct sliding between geogrids and freedrainage soil is typically in the range, 0.90 a'1 0.70, depending on the geogrid material and geometry, and 222
Special Publication 123 © CIRIA
Analysis for serviceability
11.7.3
the soil properties(Section4.5).Again, there are few dataon the directsliding resistance of soft clay over geogrids. A different valueof the interaction coefficient is normal on the upperand lowersides of reinforcement that separates dissimilar soils.
11.7.3 Analysis for serviceability The finite elementmethodhasbeenused to carry out theoretical investigations into the influence of reinforcement stiffness on embankment performance and are summarised by Rowe and MyllevilIe (1989) and Hird and Kwok (1900). In general, the shearing strength in the foundation and the fill are found to be mobilised relatively rapidly compared to the development of tensile force in the geotextile reinforcement at the embankment base. Unfortunately it is not possible to develop a compatibility curve for embankments on soft soil similarto that for steep slopes and walls.But the same pattern of behaviour applies, namely rapid mobilisation of soil strength compared to reinforcement force so that at the working equilibrium much of the safety resides in unused capacity of the reinforcement. The reinforcement stiffness defines the relation between load and elongation, and depends on the time under load and the ambient temperature (Section 2.3.2).
t.T
= "P
...(ll.20)
The influence of the reinforcement stiffness on the equilibrium at the end of construction, for an embankment that is just stable when unreinforced, is illustrated by the numerical results in Figure 11.23. (The unreinforced case is with 'zero' reinforcement stiffness.) The maximum lateral displacement in the unreinforced embankment, 750mm (Figure 11 .23a), and the maximum (immediate) vertical settlement, 250mm (Figure 11 .23b), are both markedly reduced by the reinforcement. The improvement due to the reinforcement depends critically on the reinforcement stiffness, but with diminishing returns (as discussed in Section 11.2.2). A balance must be found between the improvement and the cost of the reinforcement. Limit equilibrium analysis can be usedto investigate serviceability. Expected values for the soil strength and the loadings are used in theanalysis to calculate the distribution ofmaximum required forcefor the expected, serviceability equilibrium (Figures 11.19d and 1 1.2 Ic). The elongation of the reinforcement is then determined from the reinforcement stiffness properties. It is the reinforcement deformation that is used to assess embankment serviceability. The maximum reinforcement elongation, and the total extension in the reinforcement between the centreline and the toe of the embankment, are both considered (Figures II .23a and b). The reinforcement extension indicates the likely lateral deflection at the toe of the embankment. Special Publication 123 © CIRIA
223
11
Embankmentson soft soil Vertical sethement
Horizontal displacement
800
400
E
E E 400
0
200
0 0
(a)
7500
15000
(b)
Reinforcement force
Reinforcement extension
8 6
E
z
S 4
0
2 0 0 (c)
7500
J (kN/m)
7500
15000 (d)
15000
J (kN/m)
Figure 11.23 Influence of reinforcement stiffness on the maximum values of embankment displacementand reinforcement elongation (after Hird and Kwok, 1990) The acceptablemagnitudeof reinforcement elongation and lateral deflection depend on the amount of deformation that may be tolerated in the embankment. In cunent practice, a limit to the maximum reinforcement elongation is often set in the range 2 to S%, with the higher values being appropriate to relatively low embankments on very soft soils.
Discussion on parameters for serviceability Guidance on the choice ofexpected values for the designparameters is given in Sections 6.2 to 6.4. The assumed shearing resistance in the fill and the foundation dominate the results of the analysis, however, and these are considered further below. The concern for embankment serviceability is the behaviour at modest deformation, before any significant zonesof localised shear deformation have developed in the fill or the foundation soil. When the deformation is limited, it may be reasonable to assume that the representative peak angle of friction is developed in the fill, since this is already a cautious estimate of the peak strength (Section 6.3.1). Otherwise the guidance in Section 6.3.3 should be followed, and a partial factor of the order 1.25 applied to the 224
Special Publication123 © CIRIA
11.7.4
Reinforcementmattress design
,
representativepeak shearing resistance to derive a mobilised strength for the analysis of = tan The critical state shearing resistance, should be serviceability,
used if this is greater.
/l.25.
.,
Where significant deformation may be tolerated, the representative undrained shearing resistance in the soft clay mightbe used for the analysis of serviceability with only a small partial factor of the order,s,,,, = s,,/1.1. However, where the deformation in the embankment must be more strictly controlled, a partial factor of the order 1 .25 may be applied to derive a mobilised strength foranalysis,Sm = sfl/I .25 (Section 6.3.4.). But note that finite element analysis should be used in cases where embankment deformation is critical. More rapid drainage in the soft clay than allowed for in design is often observed to occur. Thin bands of more permeable soil, and the naturally greater horizontal permeability of soft clay are two reasons for this behaviour. Enhanced drainage may increase the shearing resistance in the soft clay more than is allowed for in design. This will reduce the immediate displacements in the embankment and the force in the reinforcement. The expected reinforcement stiffness, ,T' is normally useddirectly in serviceability analysis. Note also that because the loadings are smaller, and the assumed soil shearing resistances greater, than in the ultimate limit state analysis, the reinforcement interaction parameters do not normally enter into the analysis of serviceability.
Embankment settlement The main source of settlement beneath an embankment on soft soil is due to consolidation in the foundation, and so unreinforced and reinforced embankments settle to a similar degree. However, by restraining the foundation against lateral displacements, the immediate settlements caused by undrained shear will be reduced by reinforcing an embankment (Figure 1 1.23b). More uniform settlement in reinforced embankments is also frequently observed, and this can improve serviceability, for example where a road pavement is to be constructed before the end of consolidation. Some lateral displacement often occurs during consolidation, and this can further extend the reinforcement. The phenomenon is simply mentioned, since it has not been observed to cause any problems to date in the performance of reinforced embankments designed as described above.
11.7.4 Reinforcement mattress design Cellular reinforcement mattressesformed from polymer grids have been used successfully forconstruction on soft sites (see Figure 3.3). The cellular mattress provides a relatively stiff working platform, which can bridge over weak spots, as described by Paul (1988). It wasthoughtthat new stabilising mechanisms mightstem from the bending stiffness when the mattress is filled with compact granular soil. However, the evidence suggests Special Publication 123 © CIRIA
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11
that
Embankmentson soft soil
it is the tensile properties which govern behaviour, and the tensile force in the
mattress that improves stability (Bonaparte and Christopher, 1987). This has been demonstratedin numerical analyses by Symes (1984), Lowand Duncan (1985) and Hird and Kwok (1990). Trial embankmentsbuiltto compare the performance of mattress and horizontal reinforcement arrangementsshowed no marked difference (Busbridge et a!., 1985).
With the present knowledge, therefore, it is recommended that the tensile properties of a reinforcement mattress should meet the same design criteria as if the reinforcement were simply placed horizontally. In otherwords, the net tensile force in the mattress is what improves the embankment stability.
11.8 Design example The design example illustratesthe analysis for an embankment on soft soil under conditions at the end of rapid construction, including analysis for the reinforcement stiffness.
11.8.1 Embankment details
A 200mlength ofa 4m high road embankment, witha crestwidth lSm, will crossan area of up to 4m depth of soft clay, which is underlain by stronger alluvial deposits. The representative undrained strength of the clay is found from a field vane and laboratory triaxial compression tests to be s,, = 15 kN/m2, almost constantwith depth. Possible unreinforced and reinforced alternatives for the embankment are to be considered in a preliminary designreview, assuming the embankment is builtrapidly in one stage. Thus the endofconstruction stability is the focus in the calculations below. Granular fill is available in the area and it is assumed that this will be used for construction. The fill has a maximum unit weight 21 kN/m3, but the expected unit weight, afterfieldcompaction, is 20kN/m3. The representative peak angle of friction for = 400, and the strength at large the compacted fill measured in direct shear tests is = 330 (Section 5.2.2). strain is Woven geotextiles made from polyester are to be considered for the reinforcement, and these are available with a range ofindex strengths between 100 kN/m and 400 kNIm. It is assumed for the preliminary design investigation that 90% of foundation consolidation will be achieved within two years of the end of filling, and that the embankment will then be stable, without need for reinforcement (Section 11.3.1). The analysis for foundation consolidation and settlement, the potential application of wick drains, and the longterm stability in the embankment, are important aspects of the embankment design which are not included below for reasons of length. From the above, a maximum design loading period for the reinforcement is selected, td = 2.5 years, together with a representative temperature for conditions in the ground, 226
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Ultimate limit state
11.8.2
= 20°C. Under these conditions, the manufacturer's data show that the reference strength at the end of the design life is 60% of the index strength (Table 11.3). An allowance for damage to the reinforcement from construction and compaction of the granular fill, fd = 1.2, is selected (Table 2.2). A relatively small allowance for = 1 .1, is assumed because of the chemically neutral environmental degradation, conditions at the site and the relatively short design life. The minimum recommended partial factor of safety between the expected reinforcement strength in the ground and the design strength.f, = 1.3, is chosen (Table 11.3). Theproperties for two of theavailable woven polyestergeotextiles aresummarised in Table 11.4. For the design conditions, the loadelongation properties of the polyester reinforcementmaybe approximated to be linear,with a cumulative elongation at rupture of 10%. Thus the secant stiffness of the reinforcement, ttT = Rt'f/° I, may be determined and the values are given in Table 11.4. The coefficient of direct sliding between granular fill and the woven geotextile is = 0.70. The actual coefficient is likely to be higher, and this will be assumed to be, checked for the actual combination of fill and reinforcement selected for the project. A limiting value for the interaction between the reinforcement and the surface of the soft clay, a' = 0.5, is selected for design. As part of the design study, an alternative design is considered in which the reinforcement is assumed only to support the lateral thrust in the fill, a' = 0.
a
11.8.2 Ultimatelimit state The greatestexpectedunit weight of the fill and the critical state angle of friction are appropriate for the analysis ofultimate limitstates, Yd = 21 kN/m3 and = 33°. It may be noted that this assumed design strength in the fill is equivalent to a partial factor, = tan Ø,/I.3. An embankment height, H, = 4.5m, is assumed to make some tan allowance at this design stage for immediate and consolidation settlement of the embankment (i.e. overfilling), and any unexpected temporary surcharges (see Figure
i
11.24).
Two different levels of safety (or strength mobilisation) in the soft clay are to be investigated, with a partial factor of safety on the foundation strength, ES, = 1.30 and 1.10. Although the second design is less safe, it can be an attractive option where greater Table 11.4 Two available woven polyester geotextiles Index strength (kM/rn) Reference strength (kN/m) Field strength (kN/m) Design strength (kM/rn) Secant stiffness (kM/rn)
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P/Ith.
200
(PR'f)
120
(pjejj) i (JRJ),
91
70 1200
400 240 182 140
2400
227
11
Embankmentson soft soil
Unreintorced FS, = 1.3
Case B
CaseA
Case 0
Ii
'Reinforcement
Soft day
I Hard stratum
Figure 11.24 Possible embankment crosssectionsfor the design example embankmentdeformation is acceptable and observational control of the construction can
be adopted. The latterrequires provision in the contract for a halt to filling for a suitable
rest period where excessive deformation or porewater pressures are observed. The design analysis below uses the equations presented in this chapter, and can be followed through numerically (Tables 11.5 and 11.6 for the cases shown in Figure 11.24). In practice this would only be a first stage that would be followed by more Table 11.5 Ultimate limitstate results to achieve FS = 1.3 on the clay strength Case A
Case B
Unreinforced
ReinforcedFS Shearon foundation UnreinforcedFS Side slope
ES5
1.30
1.30
—
0.00
ES
Eqn.(ll.12)
—0.24 1.30
n
Eqn. (11.9)
0.50 0.93 1:2.5
Sideslope angle
/3
15°
12°
Required force (kN/m)
P,
Eqn. (11.10)
22° 127
62
0
Notes:
P,, =
a
=
Case C
ReinforcedFS Shearon foundation Unreinforced FS
ES,
a
ES n
Side slope Sideslope angle Required force (kN/m)
228
=
1:3.7
1:4.9
63kN/rn
Table 11.6 Ultimate limit state results to achieve FS5 =
Votes: P,.,, =
III
Eqn. (11.12) Eqn. (11.9)
/3
R
Eqn. (11.10)
1.1
on the clay strength Case D
Unreinforced
1.10
1.10
—
0.50
0.00 0.94
—0.24 1.10
0.81
1:1.75
1:2.6
1:3.6
30° 116
21° 63
0
16°
63kN/rn
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Ultimate limit state
11.8.2
detailed investigation using limit equilibrium analysis. In cases where
the deformation is critical, the design crosssection would also be checked using finite element analysis. The two standard products in the range of woven polyester geotextiles that would satisfy the embankment design strength requirements are those with an index strength 400kN/m and 200kN/m, respectively. The design strengths for these materials are given in Table 11.4, and in both cases the standard products are slightly stronger than strictly required. In a later stage of refinement, the design would normally be adjusted to make full use of the available strength of the reinforcement. A point to be noted is that the geometry ofeach of these six embankments is as close to collapse as permitted in design. Thecollapse limit would be reached should thepeak soil strength turn out to be lowerthan anticipated and equal to the design value(possibly because ofpoorerfill material orcompaction in the embankment, and weaker foundation soil than anticipated from site investigation), and should the reinforcement strength be less than anticipated and equal to the design strength (perhaps due to more damage and degradation than expected, or through a quality control error). Such a combination of factors would cause collapse involving both rupture of the reinforcement (in the reinforced embankments) and overall slip failure. Foundation failure is also imminent in the two 'fully' reinforced embankments (Cases A and C). If in addition to the conditions in the foundation described above the maximum sliding resistance between the underside of the reinforcement layer and the surface of the soft clay turned out to be worse than expected, and equal to the assumed design value, = 0.5, then failure with lateral sliding of the foundation relative to the reinforced embankment would also occur. In these two embankments, whether the collapse involved the reinforcement rupturing or lateral sliding in the foundation would depend on the particular combination of factors leading to the limit state (i.e. in some cases the reinforcement strength might be adequate and sliding occur first, and in other cases the opposite might apply with collapse being triggered by rupture of the reinforcement).
a
Internal stability Theinternalstabilitymechanismof sliding across the surface of the reinforcement layer must be considered. Using a coefficient of direct sliding ar,. = 0.70, in the analysis presented in Section 11.2.1, gives a limiting maximum embankment slope, I 0.65 or /3 = 57° (Equation 11.1). That such a relatively steep sideslope could be built before internal direct sliding became critical supports the observation in Section 11.2.1 that collapse by internal direct sliding is seldom critical for an embankment on soft soil. A more critical internal stability limit to the embankment side slope is the stability on shallow slip surfaces in the slope face. For granular fill, a limitto the sideslope angle, Special Publication123 © CIRIA
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fJ
Embankmentson soft soil
4k would normally suffice. This givesa limiting slope, /3 = 33° or I : 1.6, which
is satisfied by all four reinforced embankment designs. The possibility of directsliding over the surface of thefoundation in the unreinforced embankments may also be checked to complete the designs (Section 11.2.1). The worst case is with the largest factorof safety on the foundation clay, FSç = 1.3, for which the steepest slope angle that prevents direct sliding is, /3 = 40°, or I 1.2 (Equation 11.2). The slope angle is much steeper than overall stability would permit, which supports the observation that sucha mechanism is unlikely to be critical in embankments on soft soil (Section 11.2.2). The conclusion from the ultimate limit state analysis is that readilyavailable woven polyester geotextiles would allow significant steepening of the side slopes for the proposed road embankment (Figure 11.24). It is necessary now to check whether the reinforcement products can meet the serviceability requirements in the embankments.
11.8.3 Serviceability limit state
The expectedconditionsshouldbe assumed in the serviceability analysis. The expected unit weight of the fill, Yd = 2OkN/m3, would be used together with the representative peak strength in the fill, = 40°. (The latterchoicemayappear bold but it reflects two facts: (a) that the peak angle of friction in compact granularsoil under relatively low confining stress is usually underestimated by standard laboratory testing, and (b) that the peak strength is mobilised rapidly in an active mode of deformation, as discussed in Section 5.2.2.) The expected shearing resistance that would be mobilised in the soft clay foundation under working conditions is assumed to be, s,,,, = s,j1 .1, or 90% of the representative peak strength (Section 11.7.3). This gives a serviceability strength, sn,,, = 13.5kN/m2. Again, this reflects the knowledge of geotextile reinforced embankment behaviour in which the soil strength is mobilised relatively rapidly with respect to the development of force in the reinforcement (Section 11.7.3). The embankment geometry in eachcase was determined from the ultimate limitstate analysis (Tables 11.5 and 11.6). The analysis is now repeated for each embankment to find the maximum required force forequilibrium with the combination of parameters for serviceability. The procedure when using the design equations is to reduce the parameter, a', to increase the magnitude of outward shear on the foundation, until the envisaged serviceability equilibrium is found, ES = 1.1. The results of the serviceability analysis are summarised in Table 11.7. Several points arise from the results in Table 11.7. First, note the increase in the unreinforced factorof safety when the expected values ofthe parameters are used in the analysis rather than the worst expected values assumed for the ultimate limit state. For embankment Case B, the unreinforced factor of safety for serviceability is actually
4
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Serviceability limit state
11.8.3
Table 11.7 Serviceability limit state to achieve FS5 = 1.1
Sideslope angle Unreinforced FS Shearon foundation Required force (kN/m) Allowable strain I' Req. stiffness (kN/m)
/3 ES,.
Toedeflection(mm) Req. stiffness (kN/m) t
R
Eqn. (11.12) Eqn. (11.9) Eqn. (11.10)
Case A
Case B
Case C
Case D
22° 1.01
l5°
300
1.21
0.89
—0.2!
0.31
0
77
21° 1.03 —0.12 25
—0.08 32
Ean
3°70
'Req
PRrqIEaIl
3% 0
3% 2580
3%
1058
6h
Tab.(11.1)
242 0
225
'Req
215 (1700)
138
Eqn. (11.19)
5400
(1340)
830
= K,,,,yf12/2 44 kN/m, Assumedmaximum allowablestrain in reinforcement in range2 to 5% (Section 11.7.3). = 10%, giving G/s,, = tO ISeclion 11.6.3). Assumed maximum shearstrain in clay
Notes: Pr,,,
v,
greater thanthe required value, 1.21 > 1.10, and so no additional reinforcement force is needed for this case (Table 11.7). It is interesting to compare thedifference between the maximum required force in the ultimate and serviceability limitstates by comparing the results in Tables 11.5, 11.6 and 11.7. Design based simply on an ultimate limit state analysis and a relatively high factor of safety will lead to reinforced embankment crosssections in which little or no reinforcement force is mobilised under normal serviceability conditions. Contrast embankment design Cases A and B with Cases C and D, for example. In the limit, if the representative shear strength in thefoundation was fully mobilised, F'S5 = 1.0, but all the other parameters and loadings were at their expected values, only embankment Case C would actually need assistance from the reinforcement to maintain equilibrium (see Table 11.7, where F'S, = 0.89 c 1.0 for embankment Case C).
Reinforcement stiffness The conventionalapproachto checking serviceability has been to set a limit to the maximum allowable elongation in the reinforcement, and a value, s111 = 3%, is typical in design (Table 11.7). Thus the required stiffness of the reinforcement may he determined to enable the required force for serviceability to he mobilised at this limiting tensile elongation, as shown in Table 11.7. The expected stiffness of the woven geotextiles,ff = 2400kN/m forembankment Cases A and C, andfk,.f = l200kN/m for embankment Cases B and D (Table 11.4), meet this check on serviceability, and there is only a marginal discrepancy for embankment Case C. The criterion would he met in the latter case if the reinforcement were allowed to extend by S = 3.2%, which would probably be considered acceptable. The simple analysis for lateral deflection at the embankment toe has been applied to the embankments under serviceability conditions, assuming a limiting maximum shear Special Publication123 © CIRIA
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Embankmentson soft soil
= 10%. This corresponds to a secant shear modulus, G/S11d = 10 (Section 11.6.3).The expected lateral deflections are of the order 220mm, which is not strain in the clay, Yrnax
unreasonable. A second estimate for therequired reinforcement stiffness comes from comparing the total extension in the reinforcement with the lateral displacement at the toe of the embankment. This comparison can be made using the analytical solution presented in Section 11.6.3 to give the results recorded in Table 11.7. (Note the results given in brackets are where < 0 for which the analysis willbe slightly in error, Section 11.6.3.) This suggests that the selected geotextile reinforcement for embankment Cases A and B are adequate, and would also be so for embankment Case D if a slightly greater maximum shear strain in the clay were allowed, Ymax = 11%. However, the analysis indicates a problem with the serviceability in embankment Case C, where much higher reinforcement stiffness, or much more shear strain in the foundation, would be needed to develop the serviceability equilibrium. This illustrates the aspect of 'diminishing returns' that applies to reinforced embankments on soft soil (Sections 11.2.2 and 11.7.3) whereby markedly increased reinforcement stiffness is needed if the embankment is to be strengthened beyond an optimum point (Figure 11.23).
a
11.8.4 Conclusions for the design example
The conclusionfrom the design study would be that embankment CasesA or D provide the most suitable reinforced design (Figure 11.24) to give a side slope 1:2.5. Compared to the unreinforced designwith a side slope 1:5, this would provide an approximate fill saving, 50m3/m, and a saving in landtake, 22m2/m, for the additional cost of the reinforcement, 37.5m2/m (all values are expressed per unit length of the embankment). The cost of the reinforcement depends significantly on the decision made concerning thefoundation equilibrium. The use of a lowerfactorof safety on theclaystrength brings great benefit, but at increased risk.For the designcases above, the difference is between reinforcement with an index strength, 400kN/m and 200kN/m. There is an argument to justify a lower factor of safety for a reinforced embankment which considers the additional reserve of strength in the reinforcement. The increased risk of foundation instability may be counterbalanced to an extent by assuming an artificially low value for the interaction between the reinforcement and the foundation clay, a. This provides a reserve ofstabilising inward shear stress that would be mobilised if the foundation became distressed. Should this happen, increasing lateral deflection would be seen at the toe ofthe embankment, or through inclinometers, and a temporary halt to filling would be called to permit some consolidation and increase in foundation strength. Where the risk of a temporary halt to filling is acceptable, the choice of a low factor of safety on the end of construction strength in the foundation clay, used together with 232
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Case histories
a low designvalue for the interaction between the reinforcement and the foundation, a 0, is likely to yield the most costeffective reinforced embankment design (Embankment Case D, above). A similar low factorofsafety on the foundation could not be justified for a comparative unreinforced design because there is no extra reserve of safety from reinforcement.
11.9 Case histories There are many published case histories of reinforced embankments, and a review
of
project details for 37 case histories was published by Humphrey and Holtz (1986). A discussion on the field experience may be found in Bonaparte and Christopher (1987), and an early review on reinforced embankments by Milligan and La Rochelle (1985) is recommended. There is much published information on the analysis of reinforced embankments, particularly using the finite element method. Papers describing predictions for the behaviour of trial reinforced embankments were presented at two conferences (Bassett and Yeo, 1988, and Koerner, 1987). More general investigations of reinforced embankment behaviour have been made using the finite element method in order to quantifythe influence of the reinforcement stiffness. Notable work has been carried out by Rowe and coworkers (see Rowe, 1982, to Rowe and Mylleville, 1990), and by Hird (see Hird and Kwok, 1990). Duncan eta!. (1987) describe a major reinforced embankment project that was designed using limit equilibrium methods, checked by finite element analysis, and compared with data from the instrumentation in the field. Published case histories using mattress reinforcement are given by Edgar (1984), Busbridge eta!. (1985) and Paul (1988).
11.10 Synopsis of Chapter 11
(I) The main disturbing forces for an embankment on soft soil are the vertical
selfweight loading of the embankment and the outward lateral thrust in the fill.
(2) Reinforcement acts to support the outward thrust from the embankment fill and to restrain the surface of the foundation soil against lateral displacement. (3) Three main limits for a reinforced embankment are: with reinforcement of adequate strength and stiffness; failure in the foundation causing excessive settlement of the embankment and lateral spreading and heave in the foundation. with reinforcement of inadequate strength; the reinforcement may rupture and cause the same type of failure as in an unreinforced embankment.
• •
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Embankmentson soft soil
•
with reinforcement of inadequate stiffness: the required forces may not be mobilised to prevent the embankment settling and spreading laterally, causing tension cracks in the fill. Limit (4) equilibrium methods of analysis can be applied to reinforced embankments on soft soil. A modified slip circle analysis and a translating wedge analysis are described. (5) Two approximate analytical solutions for the stability in unreinforced and reinforced embankments are presented as a tool for making preliminary design estimates. (6) Guidance is given on the selection of design values and safety marginsfor design. Procedures are described to allow limit equilibrium analysis to be used to check embankment serviceability. Key refeiinces Davis. E.H. and Booker, JR. (1973). The effect of increasing strength with depth on the bearing capacityof clays. Géotechnique, Vol. 23, No.4,551—563. — Humphrey, D.N. and Holtz, RD. (1986). Reinforced embankments a review of case histories, Geotextiles andGeornembranes, Vol. 4, 129—144. Jewell, R.A. (1988). The mechanics of reinforced embankments on soft soils, Geoteivtiles and Geomembranes,Vol. 7, No. 4, 237—273. Leroueil, S., Magnan,J.P. and Tavenas. F. (1985). Remblais sur Argues Molles. Lavoisier. Paris.
234
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Working platforms and unpaved roads
The working platforms and unpaved roads considered in this chaptercomprise a layerof granularfill overlying a soft clay subgrade (Figure 12.1). Geotextile or polymergrid reinforcement may be placed between the fill and the subgrade to improve the loadcarryingcapacity. While additional reinforcement can be placed toward the surface of the granular fill, to boost the bearing capacity of the fill itself, this is not common and is not considered here. The design of working platforms and unpaved roads has traditionally been based on semiempirical methods (Hammitt, 1970; Giroud and Noiray, 1981). Spurred by the successful application of geotextiles to reinforce these structures, a more fundamental understanding of behaviour has been developed, so that the benefit from the reinforcement, and the required reinforcement properties, may be determined more precisely.
There are strong similarities between the action of reinforcement in a working platform or unpaved road and in an embankment on soft soil (Chapter 11). The critical factor is the deterimental effect of outward shear stress on the bearing capacityof the clay subgrade (Section 12.1). The analysis for a working platform subjected to a temporary, or slowly moving, live load is considered first (Section 12.2). Practical examples include working platforms to install wick drains ahead of embankment construction or for the construction ofa bridge abutment to be piled through soft clay. A twodimensional loading is assumed to be applied by the tracked vehicles in these cases. The analysis must be extended to account for the threedimensional effects of a wheel loading on an unpaved road (Section 12.5). The static analysis applies only fora few load axIe
Live loading
Softclay
HO
p
p
Granylar
fill
Reinforcement
Figure 12.1 Typicalarrangement for an unpaved road Special Publication123 © CIRIA
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Working platforms and unpaved roads
repetitions, and empirical relations must be introduced to allow for the fatigue caused by repeated loading from traffic (Section 12.7).
The existing empirical guidance for unreinforced unpaved road design is reviewed and compared with the results from the new analysis (Section 12.9.1). The design procedure for reinforced unpaved roads developed by Giroud and Noiray (1981) is also compared with the new analysis to show the similarities, and where the improvements have been made (Section 12.9.2). The knowledge of the response of soil to repeated loading, particularly under the conditions in an unpaved road, is at the limit of the understanding of soil mechanics. Thus a reliance on empiricism still remains in unpaved road design (Section 12.10). 12.1 Mechanics of reinforcement action The parameters used to define the twodimensional loading on a working platform are shown in Figure 12.2. The pressure at the ground surface, p. is applied over a width, 28, and is assumed to spread outward at an angle, /3. through a thickness of granular fill, D. The underlying soft clayhas a uniform undrained shear strength with a design value, s,,,, and is loaded over the larger area,28', as a result of loadspreading. The granular fill has unit weight, y, and a design value of the angle of friction. The applicationof vertical load at the ground surface causes increased vertical and horizontal stresses to develop in the granular fill which displaces laterally from beneath the loaded area. The principal stresses are vertical and horizontal beneath the centreline, and the minimum horizontal stress, a, = is governed by the active earthpressure coefficient. K1 = (1 — sin ,)/( I ÷ sin A horizontal thrust. develops in the granular fill, and normally this is only the lateral, partially supported by passive resistance in the adjacent (unloaded) soil, L' limited lateral resistanceis available because of the low selfweight (Figure 12.3).Only
.
,).
ti
Granular fill 7,
U
Softclay
H\_ O
//x/
Figure 12.2 General definitions for the twodimensional loading on a working platform 236
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Mechanics of reinforcement action
12.1
/J\D i
//Z\X//
iB——i
P
'1D
Unreintorcedcase
Figure 12.3 Combined loading on the subgrade in the unreinforced case stresses in the unloaded fill, and the balance of the horizontal thrustis transmitted to the
underlying soft clay as an outward shear stress (Figure 12.3). As described previously, the consequence ofoutward shear stress is to reduce the bearing capacity by as much as 50% (Section 5.5 and Equation 5.25). Reinforcement placedjust above the claycan support the outward shear stress, and the fullbearing capacity of theclaycan be maintained if thereinforcement is ableto support all the lateral thrust (Figure 12.4). This is the main mechanism of reinforcement. A second, minor mechanism ofreinforcement stems from inward shear stress that can be exerted by the reinforcement on the surface of theclay beyond the loaded area, B', as indicated in Figure 12.4. At best, full inward shear stress at this location, = Sj, would improve the bearing capacity of the clay by an additional 11%. Analysis shows, however, that it is prudent to disregard this source of improvement for routine design. Only a small confining stress, yD, acts at the interface between the clay and the geotextile, limiting the shear stress that can be mobilised. Further, when good shear contact is assumed in analysis, a much greater reinforcement stiffness is needed if this mechanism of improvement is to be mobilised within the serviceable range of surface displacement. The action of reinforcement described above (Figures 12.3 and 12.4) explains why vertical loadcarrying capacity in a working platform or unpaved road can be improved with little or no rutting (Houlsby eta!., 1989). The reinforcement need not deform into
r
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Working platforms and unpaved roads
PFII,
N Soft cLay
Reinforced case
Figure 12.4 Action
of the
reinforcement to relieve subgrade of outward shear
stress
a curved tensionmembrane before it can act, and thus it can be effective against load applied anywhere on the ground surface. Studies suggestthat the benefitfrom typical geotextilesactingas a tensionmembrane is only significant after rutting ofthe order, 6,128 > 0.20. Giroud eta!. (1985) found for the typical wheelsof heavy vehicles that the benefit from a tensionmembrane was negligible up to a rut depth, 6. 75mm,and contributed only a 10% improvement at a rut depth 6 150mm.The plastic deformation in the clay at such displacement would make the road susceptible to repeated loading. Indeed failure is usually observed to occur rapidly under repeated loading once rutting exceeds ñ 75mm (Webster and For these it is Watkins, 1977). considered prudent in routine design to ignore the reasons, potential benefit from the reinforcement acting as a tensionmembrane. The exception to the above is where carefully channelled traftic is maintained over a significantly rutted reinforcement layer, with the fill being regraded to allow for the rutting. This special case is not considered here. Anchorage of the reinforcement beyond the loaded area. B'. is seento be less critical than previously thought (Figure 12.2). The main tension in the reinforcement is due to the outwardshearstress transmitted from the fill to the reinlbrcement surface within the areaof vertical loadspreading (Figure 12.4). Relatively high vertical stress acts on this critical interface between the fill and the reinforcement, and an average ratio ofshear to normal stress, T,JUr < 0.40, is typical under twodimensional loading. It is the modulus ofthe reinforcement that is of greater significance since it governs the force that can be mobilised with acceptable deformation in the soil. The design method presented below is based on the above concepts which have been supported by the evidence from laboratoryscale tests and from field data (Milligan 238

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Analysis for working platforms
12.2
et al., 1990). The basic mechanisms have been confirmed by detailed finite element studies (Burd and Brocklehurst, 1990). But most importantly, the new understanding explains the central empirical assumptions made in the previous design methods for reinforced unpaved roads (Section 12.9). In other words, analysis is catching up with the empirical knowledge.
12.2 Analysis for working platforms Stability is governed by the bearing capacity of the soft clay, and the analysis is expressed directly in terms of the loading that must be supported by the clay (the required stresses) and the limiting resistance of the clay (the available stresses).
12.2.1 Subgrade bearing capacity
The analysisfor the bearing capacityof a clay foundation undercombined vertical and shear loading is described in Section 5.5. The combinations of (available) shear stress, ;,, and normal stress, a,, that can be supported by the clay are defined in Equations (5.25), which for the case of a working platform are: yD) =
=
I
2
cos'
+
l
—
...(l2.l)
where, Ne,, is the available bearingcapacity factor, and the granular fill provides a surcharge on the clay, yD. Outwardshear stress is defined as positive, ;, 0, to give simpler equations. The limiting resistance of the clay is represented by the envelope ABCE in Figure 12.5.The full bearing capacity, N.0 = (2 + ,r) is only mobilised when thereis no outward
a,
(I irI2)
t2+)
Nc N, Figure 12.5 Envelope of available subgrade resistance (ABCE) and the stress applied by surface load (GCH) SpecialPublication 123 © CIRIA
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Working platforms and unpaved roads
12
r, = 0 (point E in Figure 12.5). The bearing capacity is reduced by half, = (I + 42), when the outward shear stress reaches the limiting value, r, = Slid,
shear stress, N.1,
(point B in Figure 12.5). Lateral sliding on the surfaceof the clay can then occur, under a bearing stress in the range, 0 (1 ÷ jr/2). 12.2.2 Stresseswithin the fill The vertical stress within the fill is found by assuming a uniform loadspreadangle, /3, to give an average verticalstress at depth, pB
...(12.2)
'TB+:tanf3
which applies within the loaded region ABED (Figure 12.6), and where p is the average pressureapplied at the ground surface. Elsewhere in the granular fill, =
...(12.3)
Thefill tends to displace outwardfrom beneath the surface load and, in the limit, the = K1,o,.. The minimum horizontal horizontal stress on the centreline reduces to on the surface is then: thrust. Ejf/' acting AD,
o
Eill
=
K,pB
In
tan/3
/B'\
K,,yD2
\B,J
2
(—j +
...(12.4)
= B + D tan /3 is the halfwidth of the loaded area of clay (Figure 12.6). Lateral, passive pressure is mobilised in the surrounding soil to resist the outward
where B'
movement
of fill,
and a lateral resistance,
L' develops on the surface CE (Figure
12.6),
K,,,1yD2
L
...(12.5)
2
The mobilised passive resistance will be in the range, Kik, Kpm K0, where the passiveearth pressure coefficientK,, = 1IK111. Becausesignificant lateral displacement is needed to mobilise passive resistance, a smaller earth pressure coefficient may be
!'
B
C'
H__ B
Figure 12.6 Elemental block of fill beneath the surfacepressure 240
Special Publication123 © CIRIA
Unreinforced design
12.2.3
= 2K1k,/3, or, K,,/2. The coefficient of earth pressureat rest, K0, sets the lowerlimitfor no lateral displacement in the soil at the surfaceCE (Section 5.1).The full assumed,K,,,,,
passive resistance is usually assumed for the analysis of ultimate collapse, with a reduced resistancefor the analysis of serviceability. Shear load at the surface ofthe granular fill, such as caused by a cornering force, can be defined in proportion to the vertical load. An inclination, tan 6, defines a lateral loading,pBtan 6, (Figure 12.7). (Notethat an outwardacting surface load is defined by a negative inclination, tan 6 < 0.) The shearstress at the surface of the clay, r,., dependson the applied pressure, p. and can be found by considering the horizontal equilibrium of the rectangular block of soil
ABCED(Figure 12.7),
B
/ K,,, In /B"\ I—I
r. = p—I B'
\tan /3
\BJ
tan 61
+ (K
/
Ki" ) yD2
...(12.6)
2B'
12.2.3 Unreinforced design The shear stress,
t,
and the net vertical stress on the clay, pB/B', are linked through which defines a straight line (GCH) in Figure 12.5. The limiting Equation (12.6) equilibrium in the unreinforced case is reached when the required bearing capacity to support the applied load, N,., equals the available bearing capacity, N,.0. This is the point of intersection, C, of the line representing the applied loading, GCH, with the envelope representing the limiting resistance of the clay, ABCE (Figure 12.5). Equation (12.6) may be rewrittenin a nondimensional form to relate the shear stress on the clay, tjc,,,,, directly to the required bearing capacity factor,N,.r = (o yD)Iic,. Note that the vertical stress on the clay surface is 0r = pB/B' + yD, so that the required bearing capacity factor is N,. = pB/s0,,B'. Equation (12.6) becomes:
7K
/
/B'\
(— —tan6 +(K,k/—K,,fl) / \tan fi \B /
N,.(
In
yD2 2s0,,B
,
(12.7)
The limiting equilibrium is sometimes reached with sliding at the clay surface, = whenthe line GCH intersectsthe resistanceenvelope in the segmentAR (Figure pBtan3 A
B
KaJckd:
Figure 12.7 Horizontal forces consideredin the equilibrium analysis Special Publication 123 © CIRIA
241
12
Working platforms and unpaved roads
12.5). In other cases,bearing failure can occur, N,.,. = N,.,, = (2 + yt), before any outward shear stress acts on the clay (point E in Figure 12.5). This happens when the lateral resistance in the till entirely balances the thrust in the fill. The intersection at point C (Figure 12.5) defines the limiting equilibrium for an unreinforced working platform. The solution may be found by numerical or graphical means, since it cannot be expressed conveniently in a single formula. The limiting pressure that may be applied to an unreinforced working platform, p", depends directly on the unreinforced bearing capacity factor, N, which is defined by the equilibrium,
Nf = N,r =
N,.,,.
p' =
B'
= tVs,,,, B
+
D tan fi
(12.8)
B
12.2.4 Reinforced design The reinforcedcasefollows simplyfrom the above. If the reinforcement can support the outward shear stress at the base of the fill (Figure 12.8), the full bearing capacity in the clay can be mobilised, N. = N,.,, = (2 + r). to give a limiting resistance to surface loading. p' (Equation 12.8):
= (2 + Jr)s,
/
l
+
Dtanfi\ B
...(12.9)
)
The corresponding maximum tension in the reinforcement, R' due to the surface pressure, p', is then (Equation 12.9 and Figure 12.8):
B' = p'B
=
(t'n ()
— tan
+ (K0,, —. K,,,,,)
yD2 2
...(12.lO)
The equilibrium for the unreinforced and reinforced working platforms. and the outward shear stress that must be supported by the reinforcement, are illustrated in Figure 12.9. pBtand
B PR
Reinlorcement
Figure 12.8 Outward shear stress supported by the reinforcement 242
SpecialPublication 123 © CIRIA
12.2.5
Fill bearing capacity
I
1.0
A
Stding
H
B
C,,
0
(I + x12) N0,, Nor,
(2 + pB
:
Figure 12.9 Interaction diagram showing the unreinforced and fully reinforced equilibrium 12.2.5 Fill bearing capacity Theaboveanalysismay leadto values of allowable surface load that are greaterthan the available bearing capacity of the fill. This can be checked using conventional bearing capacity theory (Vesic, 1975). The limiting surface load that the fill can support,p),, =
...(12.l I)
where N.,, is the bearing capacity factor corresponding to the design angle of friction, (Note that the apparently missing factor 1/2 in Equation (12.11) is due to the width of the loaded area, 2B.) The bearing capacity of the fill may act as a cutoff to the envelope of available resistance as shown by the line FDH in Figure 12.10. In many practical cases,however, the point F falls to the right of point F, p,fl,B/s,JB' > (2 + r), andthe fill bearing capacity is not a critical factor (Figure 12.10). The analysis for bearing capacity is summarised in Section 5.4 where values for the bearing capacity factor, N, are listed (Table 5.3).
,.
Direct sliding Thepossibilityof direct sliding ofthe fill over the reinforcement must be considered. A good stress transferbetween the fill and the reinforcement is highly desirable, and a substantial coefficient of direct sliding resistance is a beneficial property of reinforcement material. The interlock afforded by geogrids can be a positive advantage in this respect. Special Publication 123 © CIRIA
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Working platforms and unpaved roads
N,
1.0
U,
0
(I + r/2) Nca. Nc,
Figure 12.10 Limit imposed by the bearing capacity of the fill (N = pyBIsB') The averageratio of shear to normal stress applied to the reinforcement, ;1o c 0.4, is rather low under twodimensional loading. However, the main shear interaction between the fill and the reinforcement occurs over the outer half of the contact length, B'/2, and it is recommended to check for potential direct sliding in theultimate limit state as follows, 2(r,ja) < ar,, (Section 4.5).
Loadspread angle An assumed loadspread angle in granular materials of 2: I or /3 = 26.6°, has been
conventional in foundation engineering. However, substantially more load spreading can occur in relatively strong soils over soft ground, when the loadspread angle may even exceed /3 = 45°, in certain cases. It is suggested that a loadspread angle, /3 = 27°, is likely alwaysto be conservative, and even an angle /3 = 31°, as assumed by Giroud and Noiray (1981), is likely to be representative of the lower values in the range. Greater loadspreading in the range /3 = 35° to 45° can occur in well compacted granular fill over soft clay, and this is demonstrated later.
12.2.6 Serviceability for known reinforcement properties An important part of limit state design is to check serviceability using expected values for the loadings and the soil resistances (Chapter 6). The geotextile or geogrid reinforcement must be shown to support the required force under the working equilibrium at a deformation that is compatible with a serviceable structure. In common with the other applications of reinforced soil, acceptable serviceability is defined most simply in terms of a maximum allowable elongation in the reinforcement. 244
Special Publication123 © CIRIA
Serviceabilityfor known reinforcement properties
12.2.6
Thusultimate and serviceability limit states are investigated in design (Section 12.3), and the maximum reinforcement force is limited by the design strength in the ultimate limit state analysis, and by the allowable force in the serviceability limit state and analysis. The allowable forcedepends on the maximum allowable elongation, 8a11' and a value in the range 2 to 5% is often chosen, depending on the degree of deformation that is acceptable. The allowable force then depends on the reinforcement stiffness (modulus), for the relevant loading period and design temperature, aII = J,,TE3U (Section 6.4). The case examined here is where the loadcarrying capacity is governed by serviceability (i.e. the reinforcement has sufficient strength but insufficient stiffness). This occurs when the allowable reinforcement force is less than the maximum required force for the fully reinforced equilibrium, alI C PR under working loads. The required is found from Equation (12.10), and in this case the working platform can only force, support a reduced load, Pan < p' The equilibrium described above is one in which thereinforcement supports only part of the outward shear stress, ;., up to the limit v.,11 = Pan/B', with the remainder of the shear stress being supported by the clay, as shown in Figure 12.11,
R'
t,
= "all B'
;, =
...(12.l2)
The equilibrium is found by graphical or numerical methods. For example, a trial load is selected, a,, = pB/B',to determine the required outward shear stress (Equation 12.6), and the shear stress that can be suported by the clay, ç,, (Equation 12.1). Possible
r
.1
(NJ,,
1.0
0)
0
(2+x)
(1 +,t12)
N,
N
3,0
Figure 12.11 Limit imposed by the allowable reinforcement force SpecialPublication 123 © cIRIA
(P = tauB') 245
Working platforms and unpaved roads
12
equilibrium is checked using Equation (12.12) to see whether the allowable reinforcement force is sufficient to support the balanceof outwardshear stress, and the surface load is adjusted until the equilibrium is satisfied. A simpler, approximate solution is available for preliminary analysis. If a linear approximation is made to the curved envelope of available stress (i.e. the dotted line versus the curve CE in Figure 12.11), the allowable equilibriumdepends simply on the proportion of the full outward shear stress that can be supported by the reinforcement. PaH
= p' + P." ——(p'
—
p")
...( 12. 13)
12.2.7 Serviceability for a known applied loading The analysis above found the maximum pressure that could be applied to a working platformwhen the equilibriumis governed by the known stiffness of the reinforcement. Where a range of potential reinforcement materials is to be investigated, an ultimate limit state analysis is used first to define the required strength of the reinforcement. The maximum required force is then determined for serviceability under the expected surface load. Following this, the required reinforcement stiffness is determined to enable this force to be mobilised within the range of allowable tensile strain in the working platform. The above is illustrated by a worked example (Section 12.4.2). Briefly, the interaction diagram is derived from the serviceability loadings, dimensions and resistances (i.e. Figure 12.11) and the required bearing capacity is derived, (Ne)Req = pjB/s,,jB'. One of three cases may be found (Figure 12.11): I. the required bearing capacity is less than the unreinforced capacity of the clay, (Ne)Req < N, no reinforcement force is needed to maintain serviceability. 2. the required bearing capacity is greater than the fully reinforced value, N., thenequilibriumcannot be achieved under serviceability conditions. (NC)Re,, (However, this should never be the case since the design resistances should be higher and the design loadings lower for serviceability than for ultimate
If If
c
conditions.)
3. The serviceabilityequilibrium usually falls between the above limits, and the maximum required reinforcement force corresponding to the bearing capacity, (NC)Req, is found from the difference between the outwardshear stress caused by — the loading, and the shear stress supported by the clay, Req = ijB'.
12.3 Procedure for working platform design The design stepsand the choice ofdesign values should follow the general guidance set out
in Chapters 6 and 7. The commentary below offers specific guidance for
application 246
the
of the general methods to working platforms. Special Publication123 © CIRIA
12.3.1
Ultimate limit state analysis
A designer would normally consider stability first (the ultimate limit state), allowing for the worst expected loadings and the lowest likely resistances. The required reinforcement tension to maintain the equilibrium underthe expected loadings would be
investigated subsequently. A suitable reinforcement material would have sufficient strength to maintain stability at the ultimate limitstate, and sufficient stiffness to enable the required force to be mobilised for the expected equilibrium without exceeding a specified maximum elongation in the reinforcement. Usually, the fill thickness is the unknown and is requiredto support a known loading with a specified margin of safety. Given the properties of the subgrade soil and the granular fill, it is usually convenient to consider a range of possible fill thickness to derive a plot of the unreinforced and reinforced loadcarrying capacity, and the maximum required force, versus the fill thickness. This provides a 'design chart' of fill thickness against loadcarrying capacity. 12.3.1 Ultimate limit state analysis The guidancein Chapter 6 should be followed, and stability assessed for the worst expected loading. The unsatisfactory limits include rupture of the reinforcement (Section 12.2.4), bearing capacity failure in the fill (Section 12.2.5), and direct sliding across the surface of the reinforcement (Section 12.2.5). The worst expected load should be assumed (the most heavily loaded equipment) acting on a slightly thinner than expected thickness of granular fill (to allow for variability across the site). A partial factor of safety. FS = 1.25, is recommended to derive the design shearing resistance for the fill, tan Ø = tan 1',/l .25, and foundation soil, Sa = s/1 .25 (Section 6.3). It is helpful to consider the linkbetween thepeak angleoffriction, therelative density, and the confining stress in granular fill when interpreting laboratory test data to select a representative peak strength for design (Section 5.2.2). The choice of a representative strength for the clay subgrade should account for the relatively shallow depth involved in any slip failure (Figures 12.3 and 4). Theaverage strength over a depth, \[2B', would normally be appropriate, but a greater depth might be considered where a relatively strong but thin crust overlies much weaker clay. The worst expected (i.e. longest) period that the equipment may remain stationary determines the time that the reinforcement must support sustained load, re,, and this loading should be assumed to coincide with the highest expected ambient temperature of the reinforcement in the ground, Td (Section 6.4). The reference strength of the reinforcement is chosen to reflect these conditions. Allowance for mechanical damage, Id' and the effects of the soil environment,f,,,, should then be made to derive the field strength. A partial factor of safety,f = 1.3, would normally suffice as the margin of safety between the expected field strength, and the assumed design strength of the reinforcement. Special Publication123 © CIRIA
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Working platforms and unpaved roads
12
Thecoefficientofdirect sliding, th' is the relevant interaction parameter for granular fill sliding over woven or nonwoven geotextiles (Section 4.5). Allowance could be made in a detailed investigation of this property for the possible migration of water and fine soil particles through the geotextile if this could reduce the direct sliding resistance. The sliding resistance offered by geogrid reinforcement depends on whether the reinforcement is placed over a geotextile separator layer, or direct on to the clay subgrade, or just within the granular fill. Care is needed in a test programme to examine the relevant direct sliding interface. This may involve: granular fill over (a) geogrid placed on a textile separator, (b) geogrid placed on the clay subgrade, (c) geogrid underlain by granularfill, or (d) some other combination.
12.3.2 Serviceability limit state analysis Theexpectedvaluesfor the design parameters are usedin the analysis of serviceability. A high proportion of the representative soil shearing resistances can be assumed to be mobilised, and a partial factor of safety ofthe order,FS, = 1.15, would be appropriate. This reflects the knowledge of the working equilibrium in which the soil resistance tends to be mobilised before that of the reinforcement. It also reflects some conservative aspects in the analysis of working platforms, such as the assumed twodimensional loading when, in practice, a tracked vehicle has only a limited length. A reduced lateral resistance in the fill should be assumed for the analysis of serviceability, perhaps only one halfor one third ofthe full passive earth pressure, to account for the smaller lateral deformations. The analysis with the expected loadings and resistances gives a maximum required reinforcement force for serviceability (the expected working condition). The required stiffness of the reinforcement then depends on the maximum allowable elongation, normally in the range, San = 2 to 5%.
12.4 Design example: working platform A rig weighing 350kN has to be brought on site for the construction of a piled bridge abutment. The rig has two 400mm wide tracks, spaced 2m apart, each 2.5m long and applying an essentially twodimensional loading, p = l75kN/m2.The rig will be used in various positions on the working platform, but stored off it. Therepresentative strength in the top Im of thesoft clay is found to be, s,, = 2SkN/m2, and direct shear tests on the granularfill indicate a representative peak angle of friction, = 42°, for the expected relative density in the field. The unit weight of the fill,
y = 2OkN/m3.
A runge of likely fill thickness, B = O.3m, O.4m and O.5m, isto be investigated.
12.4.1 Stability are selected for the ultimate limit state analysis. The halfwidth of the track defines the size ofthe loaded area,B = 0.2m. A slightly greater than The following parameters
248
Special Publication123 © CiRIA
Stability
12.4.1
expected loading from the rig is allowed, 400kN, giving a design loading, Pd = 200kN/m2, over a total area of contact, 2m2. The rig is assumed to apply vertical load only, 6 = 00. = 2OkN/m2, are The design strengths of the fill, i% = 35°,and of the foundation, = factor of 1.25. The full found by applying a partial passive resistance in safety, FS,
s,,
thefill is assumed to be mobilised atcollapse, and the relevant earthpressure coefficients = 3.69. Conventional loadspreading at 2:1 is are, Kd = 0.0271, and, K,,,,, = = assumed, an angle /3 26.6°. Substituting these design values into Equation (12.7) gives the required stresses, which forD = 0.4m are: pB — 0.684 0.376N.. —0.684 = 0.376
(12.14)
Sud
where, Ar,., = pBIs,,B'.
The requiredstressesareplotted in Figure 12.12, the line GCJH, together with the limiting available resistance of the clay (Equation 12.1). The point of intersection, C, gives the unreinforced design, N' = 3.89, when, T/S,,j = 0.78(Section 12.2.3). The unreinforced limit occurs for a surface load (Equation 12.8), B, (12.15) p" = N;fs,,,,—= 156kN/m2 which is less than the required design load, Pd = 200kN/m2. If the fill is reinforced, and assuming the reinforcement can support the necessary outward shear stress, N. = 5.14, (point H in Figure 12.12), corresponding to a surface load, p' = 206kN/m2 (Equation 12.9). This is just greaterthan the required value, and the reinforcement has provided a 32% increase in loadcarrying capacity.
1.0 '0 0.5
N,,, N,,,
Figure 12.12 Required and available stresses for working platform example Special Publication123 © CIRIA
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Working platforms and unpaved roads
The maximum requiredreinforcementforce is then (Equation 12.10), a/
= pB (
\tan/3
In
B'
\B/
— tan
6
)+
—K,)
yD2
7
2
=
lOkN/m
...(12.16)
The shear stress exerted at the base of the fill in the reinforced case is = 125, (Equation 12.14,and point H in Figure 12.12), which represents an average shear stress ratio at the reinforcement interface, r',ia,. = 1.251(5.14 ÷ 0.4) = 0.23, allowing for the weight of the fill. It is recommended that the direct sliding resistance should exceed twicethis value (Section 12.2.5), so that the minimum required coefficient of direct sliding resistance for the reinforcement at,, > 0.46. The bearing capacity of the fiti must be checked. The design angleof friction gives a bearing capacity factor, N1 = 48 (Table 5.3), or a bearing capacity, p, = l92kN/m2 (Equation 12.11). This is slightly less than needed to support the design load, = 200kN/m2. The fill bearing capacity would then control the maximum load, as indicated by the vertical line FJ3J in Figure 12.12, at an equivalent bearing capacity factor, N. = 4.79. However, the sensitivity of the bearing capacity to the assumed angle of friction should be considered. If the design angle of friction were one degree higher, 0' = 36°, there would be satisfactory bearing capacity, p7 = 225kN/m2. The assumption, = 36°, is likely to be acceptable since it corresponds to a partial factor of safety on the fill strength, FS = 1.24, or a lumped factor of safety on the fill bearing capacity, = 42°, Table 5.3). FS = 2.76, (where, N7 = 156, for The results for the three trial depths of fill are shown on the 'design chart' of Figure 12.13. This indicates the savings in fill thickness that can be obtained by reinforcing the 300 Fill bearing 250
' z
Reinforced subgrade failure
200
N
0. 150
N
Unreinforced subgrade failure
100
I
0T 0
0.1
0.2
0.3
0.4
0.5
0.6
D(m)
Figure 12.13 Design chart for working platform example 250
SpecialPublication 123 © CIRIA
12.4.2
Serviceability
working platform, and the maximum required reinforcement force in each case. The limit set by the fill bearing capacity is also clearly represented. (The lines VW and XY dotted on Figure 12.12 are the required stresses forD = 0.3 and 0.5m, respectively.)
12.4.2 Serviceability
P
= l75kN/m2, would be The expectedgeometryand the expected surface loading, used to check serviceability (Section 12.2.7). The mobilised resistance in the soil is found by assuming FS = 1.15, to give mobilised soil resistances, = 38° and = 21.7kN/m2. Less lateral resistance in the fill is assumed, K,,,,, = K,,,/2, to reflect the smaller displacements underworking conditions (Section 12.2.2). These parameters define the required stresses for equilibrium (Equation 12.7), and forD = 0.4m
r.
0.33N —0.34
(12.17)
and the unreinforced equilibrium occurs with, Ti/Sad = 0.854, and N = 3.63 (Equations 12.1 and 12.7). Since more than the unreinforced bearing capacity is needed to support the serviceability load, (N•)Req = 4.03 > 3.63,reinforcement will be needed to maintain the serviceability equilibrium (Section 12.2.7). The outward shear stress, ;js,,, = 0.986, and the available resistance from the clay, Ta/Saa = 0.720, under the serviceability loading, are found from Equations (12.17) and (12.1), respectively. These define the maximum required reinforcement force, Req = Ta)B' or Req = 2.3kN/m. (This equilibrium was illustrated by the line ILM in Figure 12.11, showing a total outward shear stress, IM, an available resistance from the clay,IL, and the portionof shear stress carried by the reinforcement, LM.) If the maximum allowable elongation is aH = 3%, the minimum required reinforcement stiffness would be f,, 2.3/0.03 = 77kN/m.
(
12.4.3 Reinforcement properties A reinforced fill of thickness, D = 0.4m, would be sufficient to support the assumed design loading. A satisfactory geotextile reinforcement for this application would need a designstrength lOkN/m, a secant stiffness, J,T 77kN/m, and a coefficient of direct sliding resistance, a'dS 0.46. The selection ofa suitable reinforcement might proceed as follows. A worst expected design loading period, td = I week, could be assumed and a highest expected ground temperature, Td = 20°C. A range of polyester grid products could be considered for which the manufacturer's datashow a reference strength for the requireddesign loading conditions of not less than 65% of the index strength (Section 6.4). Allowing for mechanical damage,f, = 1.2 (Table 2.2), but assuming no environmental degradation in the temporary structure,ft,, = 1.0, while allowing for a margin of safety between the Special Publication123 © CIRIA
251
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Working platforms and unpaved roads
ft
= 1.3 (Table 6.1), would expected strength in the ground and the design strength, define the minimum required index strength for the grid material, jnde. = 24kN/m. The reference strength of the grid that just satisfies the above would be = 15.bkN/m. If the data show that this load causes a cumulative elongation, = 10%, for the design conditionsof one week loading at 20°C under the design load, = l56kN/m. the relevant secant stiffness is When placed within the granular fill, the polyester grid has a measuredcoefficientof direct sliding resistance, a',5 > 0.8. The material properties for the above product would satisfy the three main design criteria.
rT
12.4.4 Comparative designs Themaximum increasein loadcarrying capacity in the above example was of the order of 30% (Figure 12.12). A comparatively greater reduction in fill thickness is found to support the same design load, a saving of up to 50%. For example, an unreinforced fill, D = 0.4m, would support an applied stress, p = l5OkN/m2, which could be supported on a reinforced fill thickness, D = 0.2m (Figure 12.12). A wider comparison has been madefor the typicalparameters,B = 0.2m, tan /3 = 0.5, and y = 2OkN/m3 (Table 12.1). This illustrates that reinforcement is beneficial only when there is an appropriate combination of fill and foundation material properties. The analysis shows that the capacity ofa 'weak' fill over a 'strong' subgradeis always governed by bearing failure in the fill. Placing reinforcement at subgrade level will not help. Similarly, a 'strong' fill is wasted over weak' subgrades because the available Table 12.1 Ratio of loadcarrying capacity for reinforcedand unreinforceddesigns (twodimensional loading case) Subgrade
Fill depth
Ø
Ø
s,,1 (kNJm2)
D (m)
30°
38°
45°
10
tO
0.20 0.40
1.29 1.30
1.10 1.02
1.00
30 30
0.20 0.40
1.00
(1.14)
80 80
0.20 0.40
t 1
t t
1.22 1.31
1.11
1.09
(1.06)
t t
1.16 1.25
value in bracket where fill failure intervenes flU failure governs in both unreinforced and reinforced cases
252
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Static analysisfor unpaved roads
12.5
lateral resistance in the fill can always counterbalance the fill thrust, and the subgrade is
subjected only to vertical loading whether or not reinforcement is included.
12.5 Static analysis for unpaved roads
A twodimensionalanalysis was usedfor working platforms (Section 12.2),where a load of much greaterlength thanwidthwas idealised as being infinitely long (i.e. plane strain conditions were assumed). Typical wheel loads on unpaved roads have a similar width and length, and this requires a threedimensional analysis which may be idealised by assuming a circular load (i.e. axisymmetric conditions are assumed). The basic mechanics described in Section 12.1 still apply and the analysis follows the same basic steps (Section 12.2). The main difference between the two cases is the enhanced bearing capacity of clay under circular (as opposed to strip) loading, the greaterbenefit from loadspreading in threedimensions, and theeffectofthe radial shear stress loading on the reinforcement. A slice through an unpaved road is shown in Figure 12.14. A circular load of radius, R, is assumedto act on the surface of a fill thickness, D. Loadspreading at an angle, /3, increases the area over which the load acts in the ratio, (R'/R)2. 12.5.1 Subgrade bearing capacity The combinationof outward shear stress, t,, and normal stress, ar,, that can be resisted by clay under axisymmetric loading conditions cannot be expressed analytically. Numerical values for the bearing capacity factor may be calculated by the method of characteristics, and these are summarised in Table 12.2, and may be compared with the values for plane strain loading (Section 12.2.1).
/
D
p
Rz
t
tt
Figure 12.14 Generaldefinitions for the threedimensionalloading on an unpaved road Special Publication123 © CIRIA
253
Working platforms and unpaved roads
12
Table 12.2 Variation of bearing capacityfactor with outward shear stressfor plane strain (2D) and axisymmetric (3D) loading Shear
2D loading
30 loading
a = 1/s.
(NC.)2Dt
(N)314 5.69 5.59 5.48 5.35
0.0
5.14 5.04 4.92 4.79 4.65 4.48
0.! 0.2 0.3 0.4 0.5
20 loading
Shear
a = r/s
(N<
0.6 0.7 0.8 0.9
5.21
3D loading
)2t
(N,.)2D*
4.30 4.08 3.8! 3.46
4.86 4.64 4.37 4.00
2.57
1.0
3.07 0.00
0.00
5.05
Equation (12.1)
Houlsby and Jewell (1990)
As before, the data in Table 12.2 define the maximum resistance of the clay in terms = as,,,, and normal stress, of the available combinations of shear stress, = yD + N,.s,,,,, that can be supported. 12.5.2 Stresses within the fill The surfaceload,p, acts over acirculararea of radius, R. A vertical slice through this axisymmetric loading reveals a block of soil that looks similar to the previous twodimensional case (compare Figures 12.2 and 12.14). However, the active pressures beneath the loaded area act on the radial sections shown, the surface ABCD, and the lateral (passive) resistance of the surrounding fill acts around the circumference. Vertical stress, a, reduces with depth beneath the surface load, p, and at a depth, z, the load acts over an area of radius, R = R + z tan /3. The vertical stress is then = yz ÷ p(R/R)2. Active stresses are assumed to develop in the fill beneath the load, = and the horizontal stress, acts over an incremental area, 2R4z, (Figure in 12.14). The total lateral thrust the fill may be found by integration,
h
21
j
2K0,pR in UirRdz =
0
Lateral, passive pressure
tan/3
/R"\
\RJ
+
K,,yD2 2
/
j2R+
4D tan I
3
(12.18)
is mobilised in the surrounding soil to resist the radial
displacement of the fill, and a net lateral resistance, P,, opposes the lateral thrust, "Fl/I'
= (See Section 12.2.2 for coefficient, K,,,,.) 254
a
K 1yD2 ( 2
12R+
4D tan
3J I
...(12.l9)
discussion on the mobilised passive earth pressure
Special Publication123 © CIRIA
12.5.3
Unreinforced design
Now consideraplan view at the level ofthe clay (Figure 12.1 5a). The net lateral thrust on any diameter, (Fll, — EL), must be supported in shear, but because of axialsymmetry the required shear stress acts radially outward at everypoint, so that the magnitude ofthe shear stress, t., (PFill
—
LI
7\2 I
I
=pI—I
ad
\R'/ tan/3
loge
7, — R
+ (Kad — K,)yD2
+ 2R"\
t
3R'2
)
.02.20)
Note that the effect of radial shear on the surface of the fill has been omitted for simplicity (see Section 12.2.2).
12.5.3 Unreinforced design The shearstress,t., and the net vertical stress, p(R/R')2, acting on the clay are linked through Equation (12.20). As before, the required stresses plot as a straight line on the nondimensional interaction diagram of required and available bearing capacity (see Section 12.2.3 and Figure 12.5). The limiting capacity of the unreinforced unpaved road is reached at the intersection of the line of the required stresses (found from Equation 12.20) with the envelope of limiting resistance for the clay (found from Table 12.2). The pointof intersection gives the solution, Nf = N.1 = Nm,, which maybe found graphically or by numerical methods, and which defines the capacity of the unreinforced unpaved road, p", 2
=
...(12.21)
Nsud—)
12.5.4 Reinforced design The reinforcedcase follows simply from the above (Section 12.2.4). The full bearing capacity in the claycan be mobilised when the reinforcement supports the outward shear stress at the base of the fill. Recalling that a greater bearing capacity factor applies for axial symmetry, N. = 5.69 (Table 12.2). the fully reinforced capacityis then, 2
p1 = 5.69s,
...(l2.22)
Now consider a plan view of the reinforcement (Figure 12.lSb). When the reinforcement supports all the applied shear stress.,.,an equilibrium analysis shows that the reinforcement tension (force per unit width) varies across the diameter from zero at the edges to a maximum value, ;R', at the centre. The average tensionis ;R'/2. It is suggested that the average tension is most relevant for design since it would correspond to the average loading in a biaxial test (Figure l2.15c). Biaxial testing is SpecialPublication 123 © CIRIA
255
12
Working platforms and unpaved roads
———A
—
s——A
—
Pd
(a)
(b)
Ut
_ "ft
Li (c)
Figure 12.15 Shear loading under axisymmetricconditions: (a) shear stresses,(b) force in the reinforcement, and (c) average biaxial conditions 256
Special Publication123 © CIRIA
Fill bearing capacity
12.5.5
likely to be the most practical way to measure the strength and stiffness parameters for geotextiles under loading conditions relevant to unpaved road design, and it is emphasised that the strength and stiffness properties of a given geotextile will differ depending on whether the product is subjected to uniaxial or biaxial load. In theremaining text, the required reinforcement tension refers to the average tension defined above. Note that this average tension corresponds to a force per unit width, (Fu, — PL)/2R', (Figure l2.15a). The required tension in the fully reinforced unpaved road, pr, may now be found, (Equations 12.20 and 12.22), PR
s0,R2 =—= 5.69 2
R' tanfl
log,' I—
+ (K1 — Kim)
7D2 —
IR + 2R'\ 3R'
)
...(12.23)
When a lesser surface load is applied, but one that exceeds the unreinforced capacity,p" c p C p',the intermediate loading case that was discussed in Section 12.2.7 will apply. The required shear stress, ;., would be partially supported by the reinforcement and partially by the clay, r,, so that the required tension in the reinforcement is: "Req =
(t
—
;,)
...(12.24)
12.5.5 Fill bearing capacity It is recommended that the surface bearing capacity of the granular till should be assessed as described in Section 12.2.5. Previously there has been a reliance on semiempirical measures, such asthe California Bearing Ratio(CBR) test, or compliance with a grading and compaction specification. This is likelyto be because ofthe critical nature of the bearing capacity, due to the relatively high contact pressure exerted over a small surface area. A high mobilised angle of friction is needed to maintain the equilibrium in this case, which demands a thorough assessment of the frictional properties of the fill underthe field loading conditions, if an adequate margin of safety is to be demonstrated (Section 5.2.2). Two other features of the analysis are important. First, the bearing capacity of a circular load on frictional till increases rapidly with settlement, 6,. so that small settlements have a significant impact. Second, for small contact areas, R < 0.2m, particle size effects may become important where the average particle size, D50, is significant relative to the size ofthe surface load, D5(J2R > 0. 1. Some allowance should probably be made for the beneficial influence of particle size on the bearing capacity Special Publication 123 © CIRA
257
12
Working platforms and unpaved roads
factors in such cases, perhaps along the lines introduced for the bond capacity of grids
(Section 4.6 and Figure 4.11). The analysis for plane strain bearing capacity (Equation 12.11) maybe adapted for a circular load by using a shape factor, 0.6 (Vesic, 1975). Allowing for the surcharge due to settlement in the fill, Y&' the bearing capacity for a circularload is ...(12.25) p, = 0.6NRy+ (1 + tan Ø)N1óy
where the bearing capacity factors, N,,, and Nqd. correspond to the design angle of friction, Ø', (Table 5.3).
Other influences The commentsmadein Section 12.2.5 on potential direct sliding in working platforms apply equally to unpaved roads. The shear stress at the level of the reinforcement, Tr/Gr, should be checked to ensure that the reinforcement has sufficient direct sliding resistance. The comments on loadspread angles also apply, namely that relatively high loadspread angles can develop in wellcompacted frictional soils, as illustrated in Section 12.9.
12.5.6 Serviceability
The approachto the analysis of serviceability described in Sections 12.2.6 and 12.2.7 may be applied to unpaved roads. Briefly, the limiting allowable load in the reinforcement would be found from the reinforcement stiffness, J,, measured in a biaxial test, and from a specified maximum allowable elongation. Alternatively, the maximum required tension may be defined by the analysis of serviceability. In this case, a minimum required reinforcement stiffness would be determined from the maximum required tensile force and the maximum allowable elongation (Section 12.2.7).
12.5.7 Design charts Thecalculations above for unreinforced unpaved roadsare too complex to be expressed in a single formula or a single diagram, although they are readily carried out by computer. The results of such analysis, covering a range of cases, may be summarised in design charts. Two types of design chart are presented. The first allows the required thickness of fill to be determined for a specified loading, for both reinforced and unreinforced unpaved roads (Figure 12.16a). The fill thickness is defined in terms of the radius of the loaded area, DIR, and the surface load is defined in terms of the strength of the soft clay, pls,,. The second design chart gives the maximum required reinforcement force for the reinforced equilibrium (Figure 12.1 6b) expressed as a nondimensional quantity, PRIS,,R.
Thedesigncharts are for vertical loading only. Subject to this restriction, the relation between the surface load, pu,,, and the required fill thickness, DIR, for a given angle of 258
Special Publication123 © CURIA
12.5.7
Design charts 30
0
a 0 0 a) 0 a)
a a
Depth of fifl (DIR) (a)
a:
0
I
0. a) C)
0
0 0)
a:
(b)
Figure 12.16 Design chart for unreinforced and reinforced stability under axisymmetric loading: (a) required fill thickness, and (b) required reinforcement force
,
friction, depend only on the assumed loadspread angle, /3, and the valueof the nondimensional quantity, sIyR. The latter quantity has a lower value for weak subgrades and the large loaded areas. A set of design charts was published by Houlsby and Jewell (1990) for the cases, /3 = 450, 35°, and, 25°, and for, s0/yR = 20, 10 and 5. The chart for the central case, /3 = 35° and sIyR = 10, is given in Figure 12.16. Compared to this central case, the Special Publication123 © CIRIA
259
12
Working platforms and unpaved roads
charts in Figure 12.17 illustrate the influence of loadspread angle (/3 = 45° and 25°), while the charts in Figure 12.18 illustrate the influence of the parameter, s,/yR, for the case, /3 = 35°.
Interpolation between design charts is possible without too much lossof accuracy, but extrapolation should be treated with caution. The design charts are suitable for preliminary investigations, and for checking designs, but the design equations should be used for detailed studies.
12.6 Design example: static wheel loading Thestaticanalysisfor a wheel loading is the first part of the analysis for an unpaved road subject to traffic loading. An example of the static analysis is given here simply to illustrate the use ofdesigncharts. The loading capacity defined by static analysis applies only to a very few load repetitions.
Consider againthe working platform discussed in Section 12.4. Somematerials must be delivered to this site and the possibility of driving the delivery vehicle directly on to the working platform is to be investigated. An ultimate limit state analysis is to be used.
= 8OkN,and dual wheels on eitherside Thedelivery vehicle has a rear axle load, = 620kN/m2. Following the (a total four wheels on theaxle),inflated to a pressure, method proposed by Giroud and Noiray (1981), the average contact pressure between the tyres and the area of the ground surface loaded is assumed to be p = (Section 12.7.5). Assuming a circular area of contact for each pair of wheels, the applied piessur is p = p,./V2 = 438kN/nr, and the radius of the loaded area, R = (Patje/\/.iTp,v,.e) or R = 0.17m. The geometry for the loading on the working platform is DIR = 0.4/0.17 = 2.35, and the applicable design chart would be for s,/yR = 5.9. Recall that the design strength of = 35°. = 2OkN/m2,and the design angle of friction in the fill, the subgrade, The design chart selected for a conservative preliminary investigation is for a loadspread angIe, /3 = 25° and for se/yR = 10 (Figure 12.17a and b). The results corresponding to DIR = 2.35 are: a reinforced capacity p'is,, = 25, a required reinforcement force PR/SUR = 4.3, and an unreinforced capacityp"/s1, = 9, which have been marked by points A, B, and C, respectively. These correspond to a reinforced capacity. p' = SOOkN/m2, which is sufficient to support the wheel loading, = 438kN/m2. The capacity without reinforcement would be p" = l8OkN/m2. The required reinforcement force is = 146kN/m, whereasthe design strength for reinforcement in the working platform was (P,),1 lOkN/m. However, the above is for the limiting load, p1 = SOOkN/m2. whereas only p = 438kN/m2 is applied allowing the clayto support some outward shear stress. Thedesign load mobilises a bearing capacity, = 5. and the claycan support an outward shear, rjs, = 0.5 (Table 12.2). Also, the
R
260
Special Publication 123 © CIRIA
12.6
Design example: static wheel loading
0
0
= a 0
=
(sjdl ssenspeljddy
0
a
US/d) eoiojpoiinbo
0
0
0
0
=
a
fld)S9049 peJddy
a
(us/d)OJ0J Pei!flbOU
Figure 12.17 Designcharts for(s/yR = 10) illustrating theinfluenceofloadspread angle: (a) and (b) with f3 = 25°, (c) and (d) with 1 = 45° SpecialPublication 123 © CIRIA
261
L
6uDpoM swiofleid pue peAedun spew
:0
C 0
t S
C
lp/sj stress Applied
{Pe/sR) force Required
0
:0
C
C
V 0 C
0 V S C
0
u6iso speya §)ioj (q) LJJIM
L/'s
0)
—
0
{P/sRl force Requfred
(p/sj stress Applied
aJnb!J 8VZL
a
= '9
= (usE 6u'je4snj/' aq aauanjjui jo atp :jjij (9) pus' pus' (p) qJ'M aLf1s = oz
(3)
IB!adS uOi1B3qfl
Efl VililD
Allowance for traffic
12.7
total shearstressis reduced,us0 = 3, becauseofthe smaller applied load, i.e. Equation = 9kN/m (12.20), so that the net force to be supported by the reinforcement is (Equation 12.24). The surface bearing capacity must be checked. The results in Table 12.3, calculated from Equation (12.25) and the bearing capacity factors in Table 5.3, report the bearing capacity for three assumed angles of friction, 4, = 350, 40° and 45°, and for three settlements, 61 = 0, 75 and 150mm. The results indicate that the design loading, p = 438kN/m2, is at the limit of the = 42°. bearing capacityfor the fill strength assumed in the working platform design, Indeed, a settlement, O, = 37mm, would be needed to maintain the equilibrium. However, the sensitivity of surface bearing capacity to the mobilised angle of friction and to the amount of settlement is apparent from these results. In summary, the working platform is likely to have sufficient capacity to support the wheel loading without causing an overall failure. However, some difficulties with surface bearing capacity are expected, with the possibility of severe rutting. The judgement on whethera separate surfacing should be used, such as runner boards or a wearing layer, or whether the fill offers sufficient bearing capacity, will depend on the exact natureofthe fill material, including the particle size, the angularity and the degree of compaction (i.e. the assumed angleof friction for the working platform design might be unduly conservative). A compact, crushed limestone fill with a representative peak = 47°, for example, would almost certainly be considered adequate angle offriction, to resist the wheel loading.
4
4
12.7 Allowance for traffic So far the analysis has been for an idealised strip or circularload applied statistically to the surface of a granularlayer overlying a soft clay subgrade. This approximation is satisfactory for design where the loading is due to stationary or slowly moving vehicles acting only once or twice over any given location. Specific allowance for the effects of traffic is required wherethereis significant repeated loading, more than about five to ten load repetitions.
Table 12.3 Limiting bearing stress for a circular load, R = Settlement(ar) (mm)
0 75 150
O.17m
ø.i
ø.
350
40°
450
98 183 268
223
554
400
959
577
1364
Notes: Bearing stresses fromEquation (1225), in kN/ni2
SpecialPublication 123 © CIRIA
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12
Working platforms and unpaved roads
Static and repeated load tests of model unpaved roads have shown that the failure mechanisms under repeated loading are the same as those for static loading, and that it is reasonable to link the former to the latter (Fannin, 1987). The behaviour in the repeated load tests is essentially one with deformations accumulating gradually with each loadunload cycle but at an accelerating rate to a failure defined by a limiting acceptable settlement. A large study on fatigue in unreinforced unpaved roads was carriedout by Hammitt (1970), who used the data to derive an empirical relation between the pavement thickness, the size ofthe loaded area, the subgrade strength. the number of wheel passes and the applied load to cause a 75mm rut. This empirical correlation for unreinforced unpaved roads is replotted in Figure 12.19. This shows a trend of failure load against pavement thickness that is similar to that found from static tests, which appear to be roughly equivalent to five wheel passes. Tests at a relatively large scaleon reinforced pavements have also indicated a pattern of reducing capacitywith repeated loading, but at a lesserrate (Delmas et al., 1986; De 0
Nc of load applications blammit)1970)ls = 3OkPal Statictests, unrenforced 1
o
9kPa Fannin (1986) • s.s=33kPa 100
0 IC
80
60 0)
a 100
40
1000
0 C
1
2
4
D/R
Figure 12.19 Comparisonbetween static and repeatedloadtests on unreinforced unpaved roads (after Milliganet al., 1990) 264
Special Publication123 © CIRIA
Definition of failure
12.7.1
Groot et al., 1986). More fullscale trials
are needed, however, to provide data on
fatigue. A method to allow for traffic loading is described below, and provides a complete design procedure for unreinforced and reinforced unpaved roads (Section 12.8). The designmethod builds on the previous work, but incorporates the new knowledge on the mechanisms governing stability in unpaved roads. The analysis provides a more sophisticated interpretation of Hammitt's (1970) data for unreinforced unpaved roads, and extends the relations for reinforced unpaved roads suggested by Giroud and Noiray (1981).Agreement with the field data is demonstrated by the back analysis in Section 12.9.
12.7.1 Definition of failure
A simple definition of failure in an unpaved road is used, as illustrated in Figure 12.19
for the typical behaviour observed in static and repeated load tests on unpaved roads. In each case a relatively welldefined 'yielding' occurs after which displacements accumulate rapidly leading quickly to failure by excessive deformation. A simple bilinear interpolation is used to define the failure load in a static test, and the failure number of cycles in a repeated load test (Figure 12.20). The onset of large displacement typically occurs at settlement in the range, 0.2 (ó/R) 0.5, where R is the radius of the loaded area. llammitt (1970) adopted = 75mm, as a failure criterion, observing that rutting developed alimiting rut depth, thereafter. This criterion falls in the range, óJR 0.25 to 0.45, for the wheel rapidly sizes in the tests.
10,000
(p/s)1 0,
z
0
0
0.2
0.4
0.2
(al Staticloading
0.4
0.6
0.8
6)4
&/R (b) Repeated loading
Figure 12.20 Definition of failure in an unpaved road under static and repeated loading SpecialPublication 123 © CIRIA
265
12
Working platforms and unpaved roads
The results from trafficking trials on an unreinforced and two reinforced unpaved roads, all with the same thickness D = 0.36m, but with two markedly different reinforcement materials, are shown in Figure 12.21 (Webster and Watkins, 1977). The failure criterion defines a numberof load cycles to failure in the range causinga rutdepth = 75 to 150mm. When applied to similar data in Websterand Alford (1978), the failure criterion defines a number of load repetitions to failure corresponding closely with a rut depth, 6, = 75mm.
12.7.2 Rate effects A factor that contributes to the enhanced capacity of an unpaved road under traffic, compared to static loading is the influence of strain rate on the undrained shear strength of clay. Chandler(1988) has used the available data to derive a general expression for o/R 0.2
0.4
0.6
0.8
I
10.000
z
Reinforced section (T16reinforcement)
einfor::t
1000
0, =
I
with insufficient stiffness
mS
0 a, a,
0 cc 0
1.0
100
Unreintorced section
J
10
0
50
100
I
I
150
200
250
300
Sefflement 6.(mm)
Figure 12.21 Failure in unreinforced and reinforced unpaved roads subject to traffic (after Websterand Watkins, 1977) 266
Special Publication123 © CIRIA
Rate effects
12.7.2
the vane correction factor, Pr' to allow for the influence of strain rate. The strain rate is expressed in terms of the time to failure in minutes, t1•,
Pr = 1.05 — (0.015 + 0.0075 log t,)\/I,,
...(l2.26)
wheretheplasticity index, li,, is in units of percent, and the equation applies toclayswith I0,000mm. I,, > 5%.Equation(12.26)was derived from datain the range, 10mm The values of the vane correction factor are plotted in Figure 12.22. Bjerrum's (1973) vane correction factor is recovered for = 10,000 mm which is relevant to field embankment failures. In contrast, a loading that would cause failure with tf = 1 mm, would require no correction at all, Pr = I, of a standard vane test brought to failure in 1 minute (Chandler, 1988). The effect of strain rate in an unpaved road subject to a traffic loading that caused a medium plasticity clay to shear rapidly to failure could account for a 25% increase, or more, in the available shearing resistance, relative to the strength deduced using Bjerrum'scorrection factor. As shown below, rate effects are taken into account in the design of unpaved roads through the fatigue relation which equates a numberof repeated loadings, N, as being equivalent to a static loading (as implied by the data in Figure 12.19). 1,2
1.0
0.8
0 0 0.6
0.4
0.2
0
0
20
40 Plasticity index,
60
80
100
l, (°/o)
Figure 12.22 Vane correction factors to allow for the influence of strain rate on undrained shear strength (after Chandler, 1988) Special Publication123 © CIRIA
267
12
Working platforms and unpaved roads
12.7.3 Fatigue relation The field laboratorytest data on unpaved roads show a progressive reduction in loadcarrying capacity with repeated loading. The lossof strength occursrelatively rapidly at first but to a lesser extent under large numbers of load repetitions. The data also show a lesser rate of degradation in reinforced unpaved roads. A function that captures the measured pattern of degradation in unpaved roads is:
P
= (p/s,,) = (p/s,)
(N \N)
exp
=
...(12.27)
where a load equal to the static capacity, P, causes failure when applied a number of times, N, usually in the range 3 to 10. The capacity of the road to sustain N load repetitions is and the ratiobetween the static and trafficked capacity is defined by the coefficient of fatigue,ft. An exponential factor, exp = 0.30, fits the average degradation rate measured in unreinforced unpaved roads by Hammitt (1970), while De Grootet a!. (1986) measured an average value, exp = 0.16, from trafficking trials on reinforced unpaved roads. A similar rate of degradation in reinforced unpaved roads was observed in the trafficking trials by Delmas et a!. (1986), and in the laboratory tests by Fannin (1987). Unless there are other data on which to makea choice, it is suggested that the values N, = 5 andexp = 0.30 are appropriate for thegeneral analysis of unreinforced unpaved roads. The same relation to static loading, N, = 5. would apply to the reinforced case, but the rate of degradation, somewhere in the range, 0.30 exp 0.16, will dependon the properties of the reinforcement. In an extreme case, a fine tissue of reinforcement with little or no strength could not be expected to retard the degradation caused by traffic. While it is difficult to make a general recommendation, a safe design value, exp = 0.20, might be adopted for the design ofreinforced unpaved roads in which the reinforcement material fully meets the strength, stiffness and direct sliding criteria defined by the analysis. However, the expected rate of degradation in such cases would be exp = 0.16, and this is a more appropriate value for use in the backanalysis of field trials.
P,
12.7.4 Permanent road thickness For a given road geometry and soil properties, there should be a critical load below which an unpaved road can sustain an infinite number of load repetitions. Laboratory data from cyclic loading tests of surface footings on sand suggest that this may be a rather small proportion of the static capacity. lIammitt's (1970) empirical relation for unreinforced unpaved roads built on an earlier expression by Ahlvin (1959) which relates the required fill thickness, D, to the applied surface pressure. p. The equation can he expressed in terms of a circular loaded 268
Special Publication123 © CIRIA
Practicalwheel loading
12.7.5
area, A
= irR2, and using the standard correlation, CBR =
s,J30, gives the non
dimensional form, D R
=
f't //711.687—— II
(12.28)
)
s,,
The factor,f' c I, depends simply on the number of load repetitions, and equals unity when N = 100,000. (See Section 12.9.1 for further discussion.) It is suggested that Equation (12.28), with = 1, might be used to estimate the limiting unreinforced road geometry, DIR, that would be able to sustain any number of load repetitions, p/s,. The shortcoming of this approach, however, is that it does not account directly for the properties of the fill.
f'
An alternative approachis to define the permanentloadcarrying capacity of the road as a percentageof the static capacity. The percentageis likely to depend on the fill and foundation properties, but a residual strength of the order 10% ofthe full static capacity accords with Hammitt's empirical relation. (But note the considerable uncertainty in defining such a limiting capacity because of the scarcity of data on unpaved roads trafficked to this extent.) To allow for a residual capacity in the fatigue relation, Equation (12.27) would be modified as follows, p,,
7, ÷ CN\
P5
\N + CNV)

I
exp
(12.29)
I
where the constant, C = (Residua1)l1eP. The residual capacity has a value in the range zero to unity, so that a residual capacity 10% of the static capacity would define a constant, C = (olo)IIP The extendedform of the fatigue relation need only be used a very large number of load repetitions is involved. The simpler form of Equation (12.27) suffices for most
if
practicalpurposes. 12.7.5 Practical wheel loading The area of contact between a single wheel and the ground surface is simply a function = avfrI' and the averagecontact pressure, p. of the load applied by the wheel, with the soil, where ii, is the number of wheels on the axle (two or four). Hammitt (1970) measured both the tyre pressure, Ptv/r' and the average contact pressure,p. for various sizesand types of single wheel and found them to fall within the 0.8. The conservative choice for design would be to assume that a range, I wheel exerts a pressure on the soil, p = p,,1,. However, the assumption, single = p °9Ptwe' would on average provide a more realistic assessment of the average contact pressure. Thus for a single axle with two single wheels, the equivalent radius, R. of the area of soil loaded by each wheel is: Special Publication 123 © CIRIA
269
12
Working platforms and unpaved roads
I
R=4/
=
...(12.30)
'V
p,.
where the contact pressure, p, is the range, p A dual wheel configuration is widely used for heavy vehicles (two closely spaced wheels on either end of an axle), and each pair of wheels may be considered as providing a single load on the unpaved road. Giroud and Noiray (1981) suggested that the equivalent contact pressure exerted by a dual wheel configuration is p = Ptyre/V' allowing for the thin area of soil between the two wheels. The equivalent radius, R, of the area loaded by each pair of wheels on a dual wheel axle (total of four wheels) is then:
=
R=
__ \J
...(l2.3l)
12.7.6 Allowance for mixed traffic When an unpaved road is trafficked by different vehicles, or by the same vehicle carrying different loads, it is necessaryto derive an equivalent loading, (Peq,Neq), for analysis. As suggestedby Giroud and Noiray (1981). the equivalent loading may be defined either in terms of the greatest applied load or the greatest number of load repetitions. This is logical because the road may be damaged by excessiveloadingor by excessive load repetitions. It is recommended that both approaches are used, and the more critical result selected. Traffic is represented in terms of the axle load, P1. and the number of loadrepetitions over the design location. N1. The subscript. i, represents a set of different loadings, (P1.N,). The relation between differcnt load combinations is given by Equation (12.27), which can he written in terms of the applied axle load,
\
7
l/CXI)
=
1w. \ I—l
\ N,)
(12.32)
where (P,1,N,q) is an equivalent loading combination to (P,Nj. This is the form of equation tiscd by Giroud and Noirav (192 II who suggested a value. l/exp = 3.95. As shown earlier, the data for unreinforced unpaved roads sugest. l/exp = 1/0.3 = 3.33. and for typical reinforced unpaved roads, I/exp = 1/0.2 = 5 (Section 12.7.3). When the equivalent load is set equal to the greatest load exerted on the road, = the total traffic is then expressedin terms of an equivalent number of of this maximum loading, and from Equation (12.32): passes.
=
270
/
"(\(
p'
\ I
iiexp
(12.33)
i)maxj
SpecialPublication 123 © CIRIA
Procedurefor unpaved road design
12.8
Alternatively, the equivalent number of load repetitions may be set equal to the largest number, N1 = (Ni)max, in which case the total trafficis expressed in terms of an equivalent load,
(p')i/eM) = (p)i/exp (
\
N1
...( 12.34)
be carried out for both equivalent traffic loadings., (Pc.c,,Neii) and and the more conservative result selected. (Pq,Nq), It is worth noting that the loading applied by the front axleof a truck is usually found from the analysis to have an insignificant effect on the net traffic. Also, one pass of a truck with two equally loaded rear axles causes two load repetitions. Design should
12.8 Procedure for unpaved road design The elementsfor the design of unpaved roads have been introduced in the previous sections. The application of these to the design of unpaved roads is described below, where the method is correlated against the existing data (Hammitt, 1970; Webster and Watkins 1977; Giroud and Noiray, 1981). The response of soil to traffic loading is complex. The fatigue relation may be interpreted in two ways, and the method usedaffects the unreinforced analysis, although the difference is often insignificant. While a firm recommendation is made for design, a more detailed knowledge of the physical mechanisms governing fatigue in unpaved roads will only he developed through the backanalysis of a more extensive database of trafficking trials than is currently available. The analysis for unpaved roads is concerned with the failure of the road under repeated loading. In previous studies, no factors of safety are introduced on the design parameters and this approach is adopted here. Thus the representative valucs of thc peak strength of the soil are used directly in the analysis. An element of conservatism may hc introduced in design through the cautious choice of the soil properties, the design loading (both the magnitude and the number of repetitions). and the parameters which govern fatigue. The analysis below is expressed in terms of an applied load. P. repeated a numher of times. N. This is the same as an equivalent loading, (Peci.Neq). in a design for mixed traffic (Section 12.7.6). The subscript has been omitted for clarity.
12.8.1 Unreinforced design There are two parts to the calculation, namely a static analysis and an allowance for fatigue. Design analysis may be carried out to find the required fill thickness to sustain a specified loading, or to derive a design chart relating the required fill thickness to the applied loading (Figure 12.19). SpecialPublication 123 © CIRIA
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Theaxle load and wheel configuration of the vehicle define the applied loadintensity, p. and the size of the loaded area. R (Section 12.7.5). The maximum number of load repetitions. N, that may be applied to any position on the unpaved road is normally defined. A representative undrained shear strength, s,. for the near surface of the subgrade (extending to a depth of the order V2R') should be chosen based on the site investigation data and testing. Similarly, the representativeproperties of the compacted
fill,
,
and, y. should be measured in laboratory tests for the range of relative density and mean stress expected in the field. The above parametersdefine the intensity of the repeated loading, (p/s,,),,. that must be resisted.The required fill thickness to sustain this loading may be found from a static
(p/,j,
to allow for fatigue analysis using a greater (equivalent) loading intensity, The was defined in 12.23). (Figure equivalent loading Equation (12.27), and dependson = the coefficient of fatigue,f,,
/s)
=
(p/s,), =
/s,,),,
...( 12.35)
f,,
The values, N = 5 and exp = 0.30, are typical for unpaved roads (Section 12.7.3). Static analysis is used to find the required fill thickness, (D/R),,, to support the equivalent loading (Figure 12.23). As before, the solution must be found by trial and error using either numerical or graphical means (Section 12.5.3). The loadspreadangle in the till, must be chosen and reference to values found from backanalysis can be used for guidance (Section 12.9.1). The full passive resistance in the fill is usually assumed to be mobilised,K,,,,, = K,,. The derivation of design charts follows naturally from the above. A design chart applies for a specific combination of parameters,(s,,/yR) and /3. It is always conservative to use the design chart forthe initial value of (s,,/yR). In this case, the static analysis gives
.
N,
EquvenI
::::
Car Initial load
(DIR),
DIR
Figure 12.23 Derivation of road capacity after N load repetitions in terms
of an
equivalent static load
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12.8.2
Reinforced design
D/R
Figure 12.24 Design chart for unreinforced unpaved roads; applicable to specific values,sb/yR, and,
I
the baseline result (Figure 12.24). The current capacity of the road is defined by the equivalent load, (p/s,) x 1/f,, which allows for the appropriate number of load repetitions, where N > N. Using this approach, the results for a range of angles of friction can be plotted on one chart (Figure 12.14). This technique applies equally to the design charts given earlier when the equivalent load, (p/sn),, X I/f,,, rather than the initial load, (p/s,,),,, is used (Figures 12.16 to 12.18).
The conservatism in using a single design chart is that degradation in the strength of the subgrade reduces thequantity, sfl/yR. The fill then plays an enhanced role that is not accounted for by a single design chart corresponding to the initial value of this parameter.
12.8.2 Reinforced design Therequireddesignthickness fora reinforced unpaved road is found as described above, but the analysis is simpler as it canbe expressed in a single equation (Equation (12.22)). Therequiredthickness of reinforced unpaved road, (DIR),, required to support a design loading, (p/s,,),,, repeated N timesmay also be expressed analytically (Equations (12.22) and (12.27)),
(—I
=
//v \
/It/I tan /3 \( 1
"I—li\
\5.69f,,)
...(l2.36)
,/
= (NINYXP. It is possible to plot Equation (12.36) to derive a master design chart for the required thickness of reinforced unpaved roads that applies for all loading cases (Figure 12.25). where the fatigue coefficient,f,,
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12
o
I, 0
0
w
0
1
2
3
4
Required thickness,
Figure 12.25 Master design chart for reinforced unpaved roads (The parameter, s,/yR, does not enter into the analysis for the reinforced unpaved road thickness.)
Required reinforcement force There are few or no data available on the magnitude of the reinforcement forces that are
mobilised in reinforced unpaved roads under traffic loading. Ideally, measurements should be made ofthe development oftensile strain in the reinforcementthrough the life of the reinforced unpaved road. Without data on reinforcement forces, it is not possible to correlate the analysis directlyagainst measurements. It is recommended that the actual road geometry. (DIR),, and the actual applied loading. p. should be used in the analysis for the required reinforcement force. The increased load intensity. (plc,). is then attributed to a reduction in the undrained shear strength of the clay subgrade due to fatigue. (s,), = fs,,. The analysis then gives a required reinforcement force for equilibrium at point A in Figure 12.26. (Note that the is (s,),. and the applicable design chart is that applicable strength when calculating,
R'
for (s,,)/yR.) It might be argued that at the end of the design life, as the road starts to fail afterN load repetitions, the fill will have sheared sufficiently to reduce the mobilised angle of friction to the critical statevalue. This lowerangle of friction in the fill would cause force to be mobilised in the as illustrated by point, B, in Figure reinforcement, greater
'..
12.26.
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Comparisonsand backanalysis
12.9
(0
a
0
Figure 12.26 Determination of the required reinforcement force allowing for traffic Theapproachadoptedby GiroudandNoiray (1981)is to use static analysis to find the required force to resist the actual loading, (p/s11), applied to the minimum required thickness forequilibrium, (DIR)1 (rather than the actual thickness ofthe road, (DIR),). In otherwords, the actual load, p, and the initial properties of the subgrade, and the fill, are used in a static analysis to find the minimum required fill thickness, (DIR)1, and the corresponding required reinforcement force. This force is assumed to act in the thicker unpaved road subjected to trafficloading. The procedure is shown schematically in Figure 12.26 by thepointC. (Note that the applicable strength is so that the design chart for the initial conditions applies, (su)nIyR.)
s,
s,
12.9 Comparisons and backanalysis Thedesignmethodthat hasbeenpresentedbuildson the previous design guidance. The earlier design methods are summarised below in sufficient detail to be applied in design, but themainpurpose is tocontrast themethods in terms of thedataupon which theywere based. Special Publication 123 © CIRIA
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12
12.9.1 Unreinforced unpaved road design (Ilammitt, 1910) The empirical relation for unreinforced unpaved roads derived by Hammitt (1970) is widely used in practice, and is built into the analysis for reinforced unpaved roads by Giroud and Noiray (1981). The basic equation used by Hammitt was introduced in Section 12.7.4, Equation (12.28). and is repeated below,
=
[4(1
...(12.28 bis) SI,
where the fatigue coefficient,f', is:
= 0.1761og(N)+ 0.120
...(12.37)
The capacity of the road depends on the square of the thickness,p/s,, (DIR)2, which is the same as in the new analysis (see Equation 12.36, for example). Equation 12.28 is plotted in Figure 12.27 as a design chart for unreinforced unpaved roads based on Hammitt's work.
7 7/7!
/47 Y
£f
C 0,
C x 0 c
0 0J
0 0,
0
I
10
400
1Q00
10,000
100,000
Loadrepetitions, N
Figure 12.27 Correlation for unreinforced unpaved roads proposed by Hammitt (1970)
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Unreinforced unpaved road design (Hammitt, 1970)
12.9.1
12
.. .
Eqn (12.28),?
1
.
10
0 o
0
.
8
.
0 0
C
0
£3
0
0
0.
0
a
0
a
4
Fill strength
• CBR>12
2
O CBR< I/I', for the data where N1 > 10. There is a significant scatter, but a likely cause of this is the range of fill materials used in the trials. The strength ofthecompacted fill was reported in terms of CBR values, and tests on the stronger fills, ('BR > 12, have been plotted with a different symbol. This indeed confirms that the road behaviour depends on the fill properties. The limitation in Hammitt's approach is that no account is taken of the strength or the loadspreading ability of the till. These parameters are an integral part of the new analysis. Using the fatigue relation introduced in Section 12.7.3, Hammitt's data have been replotted in terms of the equivalent static capacity of each road tested. In other words, the fatigue coefficient,f (Equation 12.27), has been used to define the equivalent static loading, (p/s,4), x I/f,,, for each test result, i.e. Special Publication 123 © CIRIA
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12
Working platforms and unpaved roads 40
.
35
/, f. 3025
.
—
o
S
220=
(a
a
10
—
a
a
15
W
a
0
DO
B0
Fillstrength
•
5_ 0
a
a
CBR>12
0 CBR > 35°, whencomparedwith the newanalysis, as illustrated in Figure 12.31 (using the designchartofFigure 12.16a). The results for reinforced unpaved roads correspond very closely with those from the new analysis. The conclusion to be drawn for the static analysis is that the new design method is consistent with the equations proposed by Giroud and Noiray (1981), and that practically identical results are found for reinforced unpaved roads. The new analysis offers the advantage, however, of allowing the influence of the till properties to be taken into account, which is particularly significant for unreinforced unpaved roads. This is illustrated by the comparison in Figure 12.31, where the requiredfill thickness in an unreinforced road can vary by up to a factor of two, depending on the angle of friction in the fill. The analysis by Giroud and Noiray (1981) only gives an average thickness within the likely range. where the bearing capacity factor,
'
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Reinforcedunpaved road design (Giroud and Noiray, 1981)
12.9.2 Ju
25
20
0.
5
10
5
0
DIR
Figure 12.31 Comparison ofthenew analysiswith Giroud and Noiray (1981). (For the case, 1 = 35°, and, s0/yR = 10, Figure 12.16)
Allowance for traffic In a later paper, Giroud et al. (1985) conclude that the effect of reinforcement acting as a tensionmembrane in an unpaved road is negligible up to a rut depth of the order of 6, = 75mm. This corresponds with the rutting after which settlement develops leading rapidly to failure in reinforced unpaved roads, as illustrated in Figure 12.21 (Section 12.7.1).
Giroud and Noiray (1981) proposed that the designthickness for a reinforced unpaved road to resist traffic loading, ((pIs),N), was equal to the required fill thickness for the unreinforced road subject to traffic, as defined by Flammitt (1970), less the saving in fill thickness due to the reinforcement found from the static analysis of the initial loading conditions. To complete the above analysis, the results for Hammitt (1970) are defined by Equations 12.28 and 12.37, and have been plotted in Figure 12.27. When the potential benefit of the reinforcement acting as a tension membrane is disregarded (for design Special Publication 123 © CIAIA
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Working platforms and unpaved roads
c
against unchannelled traffic, or forlimited rutting, 6, 75mm), then the fill saving may be found directly from Equation (12.39), which is shown plotted in Figure 12.31. What is missed in the above procedure is the reduced rate ofdegradation that has been observedin trials on reinforced unpavedroads (Section 12.7.3).Tests have demonstrated the two main sources of improvement from reinforcement in unpaved roads. First, the increase in strength due to the mechanical action of the reinforcement supporting outward shear stress. Second, the reduction in the rate of degradation, or fatigue, in reinforced unpaved roads compared to unreinforced unpaved roads.The latter source of improvement can be at least as significant as the former.Both aspects of behaviour are included in the new analysis, the latter being allowed for by means of the coefficientof fatigue,f, (Section 12.7.3). This is illustrated by the backanalysis below.
12.9.3 Backanalysis of reinforced trafficking trials The influence of the different rates of fatigue in reinforced and unreinforced unpaved roads can be illustratedby the test sections reported by Webster and Watkins (1977), (Figure 12.21), and Webster and Alford (1978). Three test sections used the same reinforcement and filL, but two different fill thicknesses were tested in the reinforced case (Table 12.4).
F0
= 8OkN,actingon dualwheels (two pairs Thetest data are for a single axle load, = of tyres) inflated to a pressure, 48OkN/m2. The contact pressure, p = p,vreIV = 0.194m, as = 34OkN/m2, defines a radius of contact, R =
described in Section 12.7.5. The strength of the subgrade and the thickness of the fill are known, and the number of load repetitions to failure are found from the measured performance (Section 12.7.1 and Figure 12.21). The test on the thinner, reinforced road section reported by Webster and Alford (1978) did not fail after 15,000 load repetitions (Table 12.4).
Table 12.4 Traffickingtrials on a crushedstone fill over a clay subgrade,reinforced by a strong woven nylon membrane T16 Fill depth
D (m)
Unreinforced' Reinforced A1 Reinforced B2 Notes:
0.35 0.36 0.15
Subgrade s,, (kN/m2)
Loading (p/s11)
27 30
12.59
102
3.33
11.33
Failure
Fatigue
?If3
f,5
90 12000
0.42 0.29 0.28
(1500O)
I. Websterand Watkins(1977) itemsSand 7 2. Websterand Alford (1978) item 6 3. see Figure 12,21
4. Did not fail, 50mmrut depthafter 15,000 load repetitions 5. Equation(12.27)with N, = 5: exp = 0.30 Forunreinlorced roads, andexp = 0.t6. used forthe backanalysis ofreinforcedroads.
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12.9.3
Backanalysis
of reinforced trafficking trials
Reinforced testsections The reinforced caseis the simpler to analyse. Equation (12.36) and Figures 12.25 summarise the resultsfor reinforced unpaved roads, for any applied loading and number of load repetitions. Forthereinforced road A at failure, the equivalent load is (p/s,), >< I/f, = 11.3310.29 = 39.1, and from Figure 12.25 (or Equation 12.36), the road thickness that would lead to failure afterN = 12,000 load repetitions is D tan /3/R = 1.62. The size of the loaded area R = 0. 194m, so that the theoretical fill thickness for failure is D = 0.31, 0.37 and 0.45m, for assumed loadspread angles, /3 = 450, 40° and 35°, respectively. The actual fill thickness causingfailure was D = 0.36m (Table 12.4),suggesting that a loadspread angle of the order of /3 = 40° is appropriate for the crushed stone fill in the reinforced case. (The measured result is predicted to within an accuracy 10% by a loadspread angle in the range 44° /3 37°, for all 4/.) Thesamefill, reinforcementand traffic loading was used in road B, but with less than half the fill thickness, D = 0.1 Sm, and for a much stronger subgrade, s, = 1 O2kN/ni2. The equivalent loading in this case, (p/sfl),, x 1/f,, = 3.33/0.28 = 11.9, corresponds to a road thickness at failure afterN = 15,000 load repetitions of D tanfl/R = 0.42(Figure 12.25 or Equation 12.36). The theoretical fill thickness for failure for the same range of loadspread angles as above are D = 0.08, 0.10 and 0.12m, for /3 = 45°,40° and 35°, respectively. An expected loadspread angle, /3 = 40°, would predict failure after 15,000 load repetitions in a reinforced road of thickness, D = O.lOm. In fact the road was 50% thickerthanthis,D = 0.15m, and remained distant from failure at the end oftrafficking, as the analysis would suggest. The results for the second reinforced road, case B, couldbe found on thedesign charts in Figures 12.l7c and l2.16a, for /3 = 45°and35°,respectively, and for the equivalent static loading, (pls,,),, x 1/f, = 11.9. The result when [3 = 40°, would be deduced by interpolation. The equivalent load in the first trial, (p/s,,),, x I/f,, = 39.1, is beyond the range of the general charts presented.
Unreinforced test section In an unreinforced unpaved road, the influence of the fill is governed by the angle of friction, 4/, the loadspreadangle,/3, and by a nondimensional measure of the fill weight with respect to the subgrade strength, sfl/yR. It is always conservative in the analysis for repeated loading to use the chart for the initial value, s,,/yR (Section 12.8.1).
When fatigue is interpreted as reducing the undrained strength of the suhgrade, = f,,, the fill plays an increasingly important role as the value, (s,,)/7R, decreases. This can be seen by comparing the required fill thickness for unreinforced roads in the design charts for the same loadspread angle, /3 = 35°,but the two values,
s/
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s,jyR = 5 and 20 (Figure 12.18a and c). The higher the value, s,jyR, the greater the required fill thickness in the unreinforced road. To illustrate this point, the analysis for the unreinforced test section above has been carried out for the two extreme values, s,,/yR = 7 for the initial conditions, and (s0),,/yR = 2.9 after the 90 load repetitions (Table 12.4). In the first case, a loadspread angle in the range, 45° /3 40°, and a mobilised angle of friction, 45° 4? 40°, closely reproducethe measured failure, as illustrated in Figure l2.32a. Slightly less loadspreading would apply in the secondcase,40° 35°, forthe same range ofangle of friction in the fill, 45° 4? 40° (Figure12.32b). The range of values are consistent with the backanalysis of Hammitt's (1970) data on unreinforced unpaved roads (Section 12.9.1). As discussed earlier (Section 12.8), the approach that reflects most accurately the physical mechanisms governing fatigue in unreinforced unpaved roadswill only become clearer after further research. For now, designers need be aware ofthe two possibilities, and to allow for an appropriate degree of loadspreading. The merit of the first approach is that it is always conservative. However, it is considered more reasonable to expect that repeated loading willprogressively reduce the undrained strength of the subgrade, and that consequently there will be slightly less effective loadspreading in an unreinforced, compared to a reinforced, unpaved road, as the above analysis implies. Thus the second approach is believed to reflect more accurately the physical mechanisms at work, and is the approach that it recommended.
Required reinforcement force The requiredreinforcementforcefor the equilibrium in the reinforced unpaved road case B may be estimated following the procedures described in Section 12.8.2. The recommended procedure considers the equilibrium at failure, A/f = 12,000, and assumes that the actual load applies, p = 340kN/m2, and that the strength ofthe subgrade has deteriorated due to fatigue,f,, = 0.29, so that (s,,), = 30 x 0.29 = 8.7kN/m2. The initial loading, (p/s,,),, = 11.33, rises as a consequence of fatigue to an equivalent value at failure, (plc,), X I/f,, = 39.1. The actual fill thickness in this case is, (DIR),,
= 0.36/0.194 =
1.86.
For the fully reinforced equilibrium. N. = 5.69, and the loadspread angle that fits with the equivalent loading and the fill thickness is /3 = 41° (Equation12.36).The above parameters define the equilibrium at failure and may be substituted into Equation (12.23) to determine thecorresponding reinforcement force. Foran expected strength in the fill, 4? = 40°. the maximum required force is R = l.SkN/m. However,as discussed in Section 12.8.2, the conservative choice is to assume that at failure the fill has been remoulded sufficiently to reach the critical state. 4? = 4?,.. Making this assumption, 284
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Backanalysis
12.9.3
of reinforcedtrafficking trials
DIR
alE
0
I
2
3
DIR
Figure 12.32 Resultsfor thebackanalysisofthe unrein forced unpavedroadtested by Websterand Watkins(1977)
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12
.
= 35°, the maximum required reinforcement force increases to and with = 4.0kN/m. Giroud and Noiray (1981) (Section 12.8.2) examine the initial equilibrium in the reinforced case,p/s, = 11.3, (f, = 1). For a chosen loadspreadangle (/3 = 41° is used here to allow a direct comparison), the required fill thickness just to maintain the reinforced equilibrium is found, DIR = 0.46, (Equation 12.36). For the assumedangle = 3.7kNIm of friction, qi = 40°, the maximum required reinforcement force is (Equation 12.23). This latter case is within the range of the charts given earlier, s,jyR = 7.7, and the maximum required force in a reinforced unpaved road of depth, DIR = 0.46, may be found from Figures 12.l6b and 12.l7d, for the cases of /3 = 35° and /3 = 450, respectively, and for s,/7R = 10. The values, PR/SI)? =0.6 and 0.7, correspond to a = 3.5 and4kN/m,for the two mobilisedangle of friction, = 40°, andgive a force, cases respectively. Interpolation between the charts is needed, but at low values, DIR < I. the maximum required force does not depend greatly on small differences in loadspread angle. in design the maximum allowable tensile strain in the reinforcement had been = 3%•, the minimum required stiffness for the reinforcement would be specified as = 4/0.03 = I 35kN/m, based on the largest estimated value for the required reinforcement force. Themeasured stiffness from indextests on the T16 reinforcement = 200kN/m. fabric used in the road was
R
'
R
If
Reinforcementwith insufficient modulus When the reinforcement in an unpaved road has insufficient modulus to mobilise the maximum required reinforcement force at an acceptable elongation, failure will occur (due to excessive rutting) at an intermediate equilibrium, (N < N:.). In this case the reinforcement is able to support only a portion of the outward shear stress, and the remainder is transmitted to the underlying clay, as described in Section 12.2.6 (Figure 12.11).
Knowing the maximum allowable force in the reinforcement (derived from the reinforcement stiffness and the maximum allowable elongation for a serviceable road) it is possible to determine the limiting road capacity, which will fall between the reinforced and unreinforced N. > > cases, (Section 12.2.6). fully (N.)0 In an unpaved road that is deteriorating due to traffic, the undrained shear strength of the subgrade reduces progressively, s,,.f,,, and likewise the equivalent load increases, (p/s,,),. I/f,,. Where there is insufficientreinforcement, the capacity of the unpaved road is limited by an allowable bearing capacity, (Nc)aH, rather than by the (fully) reinforced capacity, N. (Figure 12.33). What is currently lacking is a method to assess how rapidly the deterioration in the road to this end point will occur. All that is certain is that the fatigue coefticient,f, is
m
N
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Discussion
12.10
A A: Fullyreinforced capacity B: Capacityset bytheallowable reinforcement force
0,
a
0:
Initial loading
Increasing equivalent load duetofatigue
D/R
Figure 12.33 Illustration of the increasing equivalent loaddue to fatigue and the limiting capacity caused by insufficientreinforcement modulus
likely to fall within the range established by the unreinforced and the (fully) reinforced cases, 0.30 exp 0.16. The pessimistic assumption would be to select the same rate of degradation in an insufficiently reinforced road as in an unreinforced unpaved road. This would set the lower limit to the expected number of load repetitions to cause failure (and is the approach implicit in Giroud and Noiray (1981) who build Flammitt's (1970) relation for unreinforced roads into their analysis for reinforced roads). At present there is no basis available on which tojudge by how much reinforcement with insufficient modulus can reduce the rate of degradation in an unpaved road, compared to the case with no reinforcement.
12.10 Discussion A substantial amount of design information has been presented on working platforms and unpaved roads, and some final remarks are warranted to help set it in context. The static analysis for working platforms is straightforward and falls well within the scope of reinforced soil design that was discussed in earlier chapters. The extension of the static analysis to a threedimensional loading, and the application of this analysis to design is also well within the conventional knowledge of reinforced soil, except for the loading applied to the geotextile reinforcement (Figure 12.15). The reinforcement is subjected to an outward radial shear which is likely to cause nonuniform tensionacross the loaded portion of the reinforcement. It was suggested that for static loading conditions it may well be adequate to compare the stresses in the reinforcement to those in a biaxial test, and to derive the necessary properties for the reinforcement from biaxial testing. For this reason, the average tension across the loaded portion of the geotextile was selected as the value to be reported by the analysis (Section 12.5.4). SpecialPublication 123 © CIRIA
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In the above cases involving (quasi) static loading, it is possible to apply the same procedures for the selection of design parameters and safety margins, and for checking
the fill bearing capacity, as used throughout this book. Extending the analysis to allow for traffic raises a number of new issues that are not well established for reinforced soil. For example, the testing methods to measure the parameters for geotextile reinforcement subjectedto the rapid loadunload cycles in an unpaved road, and over an extendedperiod,are not well established.Such shortcomings must be clearly recognised. However, it has proved possible to develop an analysis for unreinforced and reinforced unpaved roads in a way that is entirely consistent with the previous methods and data (Hammitt, 1970; Giroud and Noiray, 1981). The key to this development has been the recognition of the fundamental interaction between bearing capacity and outward shear stress. Through this mechanism, the properties of the fill have been introduced into the analysis, and this has shown that the earlier work gives results corresponding to the middle of the likely range for typical fill properties. But the range can be quite large. Thus the design method which has been presentedprovides a more versatile tool for the analysis of unreinforced and reinforced unpaved roads. However, some considerable uncertainties remain; e.g. in the rate ofdegradationthat will applywhen an unpavedroad is reinforced by a geotextile with insufficient modulus, or in the analysis for the fill bearing capacity under repeated traffic loading. Furtherdevelopments in the design method will be made as more researchis carried out and more data obtained on the behaviour of reinforced unpaved roads under traffic loading and on the behaviour of geotextile materials under repeated,multiaxial loading. The new analysis should provide a useful tool for the interpretation and future application of the data.
12.11 Synopsis of Chapter 12 (1) In an unreinforced working platform or unpaved road, outwardshear stress is applied to the subgrade, together with the vertical stress, and this results in a lower bearing capacity than if there was no outwardshear. (2) Reinforcement placed over a soft subgrade can support the outwardshear stress thereby increasing the bearing capacity, i.e. improving the loadcarrying capacity; without any ruts being formed. This does not depend on deformation (or rutting) taking place. (3) The analysis for unreinforced and reinforced fills on soft subgradesis derived for planestrain loading, relevant to tracked vehicles on working platforms, and for axisymmetric loading, relevant to wheel loading on an unpaved road. 288
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12.11
Synopsis of Chapter 12
(4) The loadcarrying capacity of unreinforced and reinforced unpaved roads may be summarised in design charts, and several examples are given. (5) The extension of the static analysis to allow for the fatigue caused by traffic loading has been presented. The analysis has been shown to provide a more complete interpretation of the field data of Hammitt (1990). (6) It has been observed that the rate of degradation due to traffic on a reinforced unpaved road is significantly less than in an equivalent unreinforced road. This important source of improvement from reinforcement has been included in the new analysis, based on the field observations of comparative reinforced and unreinforced test sections. A (7) complete design method for unreinforced and reinforced unpaved roads has been developed which offers much greaterversatility. The method reproduces the results from earlier methods. (8) The relative lack of knowledge of the behaviour of soils and geotextiles underrepeated loading should not be overlooked, and the design of unpaved roads must still rely on a substantial element of empiricism. Key references Dc Groot, M., Janse, E., Maagdenberg, T.A.C. and Van den Berg, C. (1986). Design method and guidelines for geotextile application in road construction. Proc. 3rd hit. ConJ on Geotextiles.Vienna, Vol. 3, pp. 741—7. Giroud, J.P. and Noiray, L. (1981). Geotextilereinforced unpaved road design. Proc. ASCE Journal Geotechnical Engineering. Vol. 107, No. GT9, 1233—54. Hammitt, G.M. (1970). Thickness requirements for unsurfaced roads and airfields, bare base support. US Army WaterwaysResearch Station. Vicksburg,TR2705. Houlsby,G.T. and Jewell,R.A. (1990) Design of reinforced unpaved roads for small rut depths, Proc.4th/nt. Cotifon Geotextiles, Geomembranes andRelatedProducts.The Hague, Balkema. Milligan, G.W.E., Jewell, RA., Houlsby, CT. and Burd, H.J. (1989). A new approach to the design of unpaved roads—Part 11. Ground Engineering, November, 37—42.
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From design to specification This bookintroducesthe concepts and purposes ofsoil reinforcement, describes the data to be gathered and assessed, and explains the analytical procedures. These arethe major elements of the design process but, in the course of a specific project, there is a continuing interaction between these elements, and with the development of the specification and quality assurance plan to ensure that the design assumptions are achieved. An important step in the analysis and checking process is to assessthe degree of uncertainty inherent in the methods, material properties or design parameters. This chapter, therefore, draws attention to matters which require special attention in the design of reinforced soil. Some concern overall planningfor the use of reinforced soil, some the uncertainties in current knowledge — where further research is needed — and some are points for specifications or construction detailing. For design and construction to come together successfully, these types of question have to be resolved. The chapter is introduced by a brief review of some likely future developments in reinforced soil which can already be foreseen. Somefinal remarks on reinforced soil are given at the end of the chapter.
13.1 Future developments over the past 10 to 15 years in reinforced soil techniques and in the geotextile and geogrid materials that may be used for these applications. Reinforced soil and geotextiles are now widely used in earthworks. The Dramatic advances have been made
progress continues apace, with increased knowledge and confidence stemming from successful applications, and with new developments in polymer materials and their manufacturing processes. The range and costeffectiveness of polymer reinforcement materials should be expected to increase in the foreseeable future. Four developments in reinforced soil which are likely to become widely established in coming years are identified below. Soil may be reinforced by fibres. Individual fibres when intermixed with granularsoil can provide a remarkable increase in shear strength and stability, which is not yet fully explained within the conventional principles of soil mechanics. Fibre reinforced soil could be used in all the main application areas of reinforced soil, and wider practical application will followthe development ofeffective mixing and placing techniques, with increased knowledge of likely damage and the resulting durability of fibres intimately Special Publication 123 © CIRIA
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mixed with soil, and in the methods ofanalysis. Fibre reinforced soil offersthe particular advantage of greatductility and tolerance to seismic loading. The reinforcement of soil in situ to form excavations and stabilise slopes is now well established, but with steel reinforcement. The increasing use of insitu soil reinforcement is likely to bring the application of polymerreinforcement materials to this form of construction. Anchored earthand loopanchor construction takes advantage ofthe available bearing resistance between reinforcement and soil, and these techniques are applied in the construction of steep slopes and walls (Figure 10.32). Widerapplication of this form of reinforced soil construction should be expected. The combination of functions in one material will increase. For example, there are composites which allow drainage as well as providing reinforcement, and these have allowed silty clay materials to be used for the construction of steep slopes. Another new technique is to use a substantial structural facing in combination with a reduced quantity of reinforcement to form retaining walls, with the faceplaying a vital structural role.
13.2 Designing reinforced soil structures 13.2.1 Concept As with any design, the conceptual thinking at the start of the project has to be clear. Reinforced soil structures have widened the options open to engineers and in some cases have provided viable solutions to otherwise costly if not intractable problems. In many instances, reinforced soil is one of various options, often as an alternative to either a reinforced concrete retaining wall or a conventional earth slope. But the choice of one or otherconstruction method depends on a numberof interactions: costs, time and space constraints, and available fill material or other resources.. Less obvious, perhaps, are questions of the structure's compatibility — with the foundation, with the external finish, with adjacent or internal structures — and how its structural form matches these functional requirements. All the main applications of soil reinforcement, described in this book, are suitable for relatively shortterm usages. Specifically, reinforcement of embankments on soft clay foundations is needed only until the foundation has gained strength by consolidation; hardstandings are construction expedients, and unpaved roads are often site haul roads; many vertical wall structures are builtas temporary worksduringa project. But vertical walls, steep slopes, embankment slip repairs and unpaved roads can all be longterm structures, and reinforced soil techniques are increasingly being used for them. Therefore clarity is needed in considering the appropriate length of the design life and the changes which occur during this period. 292
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Compatibility
13.2.2 Compatibility Perhaps the primary consideration for a reinforced soil structure is recognising (a) that it has to deform to develop its strength, (b) that it continues to deform, and (c) that, as a consequence, its available 'strength' is not constant, but variable (Chapter 4). This inherent flexibility is often advantageous: within limits, a reinforced soil structure can accommodate a degree of externally caused movement and is usually less sensitive to such movements than, say, a masonry alternative. Thus combining reinforced soil construction with other techniques of ground improvement, such as vertical drainsor stone columns in order to improve a poorfill, can achieve compatibility between a compressible foundation and the superimposed structure. Other components of a project, however, may be relatively more rigid, such as a bridge abutment and its wingwalls to which a reinforced soil embankment leads. The soilstructure interactions here are complex and depend very much on the construction sequence as well as on the detailing at the junction. Should, for example, the reinforced soil approach be constructed first and the abutment and wingwalls built as standalone units? Should there be some transitional foundation treatment beneath the embankment in the approach to the abutment? Two extreme examples from a very soft clay site illustrate the point. From a pontoon in a shallow estuarial creek, Hpiles had been driven to support a light vehicle bridge. The low approach embankment to the bridge was constructed over the soft clay using a strong, woven geotextile. Fill placing was with lowweight plant and carefully controlled but, despite this, mud waves were created ahead and to the side of the filling. The displacement of soft clayahead of the filling imposed high lateral forces on the steel piles and bent them, and new piles had to be installed later through the constructed embankment (Figure 13.1). A prefabricated steel culvert had to be constructed through a reinforced soil embankment on soft clay. The culvert is flexible and can accommodate a substantial amount of differential settlement, but at what stage in the construction of the embankment should it have been installed? If placed virtually upon the basal reinforcement prior to embankment filling, subsequent compression of the soft clay foundation could result in the culvert being at too low an elevation. If placed later after excavating a cut through the till, the embankment stability could be in jeopardydue to a failure in the longitudinal direction (i.e. at right angles to the direction for which the reinforcement was designed); and, at the least, there would be a risk of damaging the reinforcement in the excavation process (Figure 13.2). Later still, provided the culvert did not have to be inplace at an early stage, the foundation would have consolidated sufficiently to allow the cut to be made safely. These two examples epitomise the need for two types of compatibility: with external structures and with internal structures. The principles apply equally to vertical walls or Special Publication123 © cIRlA
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