Soil Parameters For Drained and Undrained Analysis

 

Soil Parameters for Drained and Undrained Anal sis Applied Theory Dr Minna Karstunen based on work by Dr H. Burd, University of Oxford

 

Introduction • The The a aim im is to di disc scus uss s the the cho choic ice e of param paramet eters ers for for tthe he Mohr-Coulomb model. • More More ad adva vanc nced ed soi soill mo mode dels ls ma may y hav have es som ome e adv advan anta tage ges s over the Mohr-Coulomb model (but require the specification of a larger number of parameters) • the soil parameters are briefly discussed. • It is als also o us usef eful ul,, h how owev ever, er, to es esti tima mate te valu values es o off soi soill properties on previous experience, and on correlationsbased with other soil parameters.

 

Undrained and Drained Loading • In ca carr rryi ying ng ou outt a any ny an anal alys ysis is in geotechnical engineering engineering it is usually necessary to distinguish between drained . • The The s soi oill m may ay al also so be pa part rtia ialllly yd dra rain ined ed which means that it lies between these two extremes.

 

Undrained and Drained Loading • drained an analysis appropriate when  – permeability is high  – rate of loading is low  – s or   erm e av or s no o n eres or pro em considered

• undrained analysis appropriate when  – permeability is low and rate of loading is high  – short term behavior has to be assessed

 

Undrained and Drained Loading Suggestion by Vermeer Vermeer & Meier (1998) T < 0.10 (U < 10%) T > 0.40 (U > 70%)

 

undrained analysis drained analysis

k E

T

k E oed =

D γw

2

t

= = oed γ w = D = t =

permeability stiffness in 1-d compression unit weight of water drainage length construction time

T U

dimensionless time factor degree of consolidation

= =

 

Drained Analysis Drained analysis may be carried out by using a constitutive model based on effective stresses in which the material mo e s spec e n terms o ra ne parameters.. parameters

 

Modelling Undrained Behavior with PLAXIS Method A (an Method (analy alysis sis in tterm ermss of effective  stresses): type of material behaviour: undrained   effective strength parameters (MC: c', ϕ', ψ   ‘) effective stiffness parameters (MC: E50',  ν ‘) Method B (an Method (analy alysis sis iin n term termss of effective  stresses): type of material behaviour: undrained   total strength parameters c = cu, ϕ = 0, ψ  = 0 effective stiffness parameters E50',  ν' Method Met hod C (an (analy alysis sis in tterm ermss of total  stresses): type of material behaviour: drained   total strength parameters c = cu, ϕ = 0, ψ  = 0 total stiffness parameters Eu,  νu = 0.495

Need to be careful in case of stiff OC clays!

 

Mohrand Coulomb Model for Drained Undrained Analysis • For Fo r drai draine ned lloa oadin ding, g,the a tota tMohr-Coulomb otall of 5 p para arame mete ters rs are required todspecify model. These are; two strength parameters (c' and φ ' ), ψ )   and two elastic parameters. a dilation angle ( ψ   • For For undra undraine ined d calc calcula ulatio tions, ns, a separ separate ate failu failure re model based on an undrained shear strength strength,, cu, is used. Note that cu is not a fundamental property of the soil; soil; it depends on the stress

level and also the stress history.

 

Mohrand Coulomb Model for Drained Undrained Analysis

Drained or Undrained pproac

AUndrained roach C

 

Mohrand Coulomb Model for Drained Undrained Analysis • To an anal alys yse e a pr prob oble lem m us usin ing g the eM Moh ohrr-Co Coul ulom omb b model, appropriate values ofth the material parameters must be selected to provide a good match with the soil being modelled. • The The sel selec ecti tion on of thes these e pa para rame mete ters rs is complicated by the fact that real soil behaviour often departs considerably from the fundamental assumptions on which the Mohr-Coulomb model is based.

 

The Mohr-Coulomb Model and Real Soil Behaviour a) Most real real soils do not exhibit linear elastic elastic behaviour behaviour prior to failure 󰀱      󰁝   󰀭      󰁛      󰀰      󰁇      󰁇    󰁳    󰁵      󰁬    󰁵      󰁤    󰁯

 

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The Mohr-Coulomb Model and Real Soil Behaviour b) The The stif stiffne fness ss of of soil soil tends tends to to inc increa rease se with with increasing stress level. In PLAXIS the stiffness can be specified to increase linearly with depth below the soil surface.

c) loading Unloa Unloadin ding g stiff stiffne ness ss diffe differs rs from from stiff stiffne ness ss in prim primary ary

 

The Mohr-Coulomb Model and Real Soil Behaviour

Triaxial compression test on a sample of Leighton Buzzard sand

 

The Mohr-Coulomb Model and Real Soil Behaviour d)

The friction angle of a sand depends on its density and . choice of φ  φ'  needs careful consideration of these factors.

 

The Mohr-Coulomb Model and Real Soil Behaviour

 

Drained Triaxial Test

 

Undrained Triaxial Test

 

Pressuremeter Test 

  G      L = ho + u P σ    c 1 + ln cu 

The undrained shear strength may be calculated from the limiting cavity pressure P L (for details see Clarke (1995).

 

Cone Penetrometer Test For penetration the tip resistance qt in is clays, given by:

q =  N   c + σ  where σ vo  vo  is the total vertical stress in the soil at the level of the cone and N kt  i s an empirical factor, typically in the range of 10 factor, to 20. For further details, see Lunne et al, (1997).

 

Correlations for Undrained Shear Stren th  c

 

Undrained Strength from MCShear Parameters

   '+  cu = sin φ '     φ   c' cot  1  + K 0  σ v '    2      

 

Example: Undrained from MC parameters

   '+  cu = sin φ '     φ   c' cot  1  + K 0  σ v '    2      

 

Example: Undrained from MC parameters

In this example:

cu = c uo + ρ  z where c uo =4.698 kPa and  ρ = 2.326 kPa/m.

 

Example: Undrained from MC parameters Note that the correlation is unlikely to give an accurate shear strength str ength profile for an overconsolidated clay clay.. A better estimate is obtained with Critical State models.   , Poisson’s ratio would be 0.5 (Method C) C).. However However,, this value cannot be used element calculations, because it would resultfor infinite an infinite value of bulk modulus. A suitable value of undrained Poisson’s ration for use in FE analyses is ν u =0.495. In this case, the appropriate value of undr undrained ained Y Young’s oung’s modulus would be 5537 kPa.

 

u based on Correlations for s Cam Clay A useful correlation that is based on Cam Clay theory (and confirmed by the results of laboratory testing) is:

    cu =  cu  (OCR ) µ  ' ' vi

vi

 NC 

where σ ’’ vi    is the vertical effective stress at the start of undrained loading and OCR (the overconsolidation ratio) is equal to σ’p / σ ’’ vi    , where σ’p is the vertical (effective) preconsolidation stress. According to data collected by Muir Wood (1990) µ is close to 0.8 and (c u  / σ  σ ’’ vi    )NC  lies between 0.1 and 0.35.

 

Example At an OC clay site, the water table is at the ground surface. The preconsolidation stre stress sses es co corr rres es on ond d to th the e application of a vertical effective stress of 500 kPa at the ground surface. Take (c u  / σ σ ’’   vi    )NC as 0.2,  µ  as 0.8 and the submerged unit weight of the soil as 8 kPa/m.

 

cu from Index Tests

 I  L =

w − wP w −w  L

 

P

cu = 2 × 100  

(1− I L )

NOTE: This is remoulded strength (intact strength can be much higher)

 

cu of London Clay

 

cu of London Clay

 

Friction and Dilations Angles for Sand

 

Correlations for Friction Angle Bolton (1986) proposes a relationship

φ ' = φ   ' cv +0.8 where φ ’’  cv is the critical state friction angle and ψ is the angle of dilation.

 

Correlations for Friction Angle A study by Bolton (1986 and 1987) on published sand test data, suggested that the maximum dilation rate of a sand depends on    p'    I  R =  I  D 5 − ln   150   − 1 

 for  p ' > 150 kPa

 I  R = 5 I  D − 1

 for  p ' < 150 kPa



 I  D =

emax − e emax − emin

  

 

Correlations for Friction Angle The following correlations were found by Bolton to give a good fit to the available database of test results:

φ ' peak  −  φ 'cv  = 5 I  R

for plane strain

φ ' peak  −  φ 'cv  = 3I  R

for triaxial test

  is For quartz sand, the critical state friction angle φ ’’ cv  approximately 33 degrees.

 

Correlations for Friction Angle

Determining the relative density of a sand deposit is rather difficult. For correlations that relate cone resistance to relative density are described in Lunne et al. 1997.

 

Estimation of Stiffness

 

Stiffness of Clay E 

problems here relatively large • strains Option Opti onare 1 - Use Us e 50 . For expected (e.g. for foundation bearing capacity and studies of the deformation of soft soil beneath an embankment). • Option Option 2 - Use a small small stra strain in Young's Young's modu modulus. lus. If the pro em nvo ves e ca cu a on o e orma ons o s clay under working conditions (e.g. the analysis of the interaction between a tunnel liner and the surrounding ground) • Opti Option on 3 - Use the unload unloading ing Youn Young's g's modulus modulus,, E ur . If the problem is dominated by unloading (as may be the case, for example, in an excavation problem)

 

Measurement of Stiffness in the Triaxial test

Not accurate for strains below 1%

 

Measurement of Stiffness in the Triaxial test

 

Correlations for Stiffness Jardine et al. (1984) conducted a series of triaxial tests on a range of soils, using local gauges to measure strains.

 

Correlations for Stiffness Jardine et al. (1984)

 

Correlations for Stiffness

Plate loading tests Buchignani (1976). Data correspond to strain about values 0.1% of

 

Correlations for Stiffness Data from Termaat, Vermeer and Vergeer (1985) may be used to suggest the following correlation for normally consolidated (Dutch) u

  15000cu

 E 50   ≈

 I P

 

Case Studies

Stiffness profile for various London clay site (Matthews et al, 2000, re-plotted by Simon and Menzies 2000)

 

Case Studies

Scott et al. (1999)

 

Stiffness Anisotropy • Rece Recent nt st stud udie ies so on n na natu tura rall cl clay ays s (no (norm rmal ally ly consolidated and overconsolidated) suggest that their stiffness may be . can be found e.g. in Gasparre et al. (2007)

 

Stiffness of Sands • Base Based do on n da data ta o on n un undr drai aine ned d tria triaxi xial al te test stin ing g of sandfs at different densities by Tokheim (1976) and Leahy (1984)Loose sand

 

Bibliography • this Furt Further her in infor forma matio tion on on tthe heintopi tothe pics cs discu discusse ssed d in in lecture can benfound following books: • Simo Simons ns,, N., N., Menz Menzie ies, s, B. an and dM Mat atth thew ews, s, M. (2002). A short course in geotechnical site investigation. Thomas Telford • Pott Potts, s, D. D.M. M. and and Z Zdr drav avkov kovic ic,, L. L. ((200 2001) 1).. F Fini inite te element analysis in geotechnical engineering. Application. Thomas Telford • Loo, Loo, B. (200 (2007) 7).. H Han andb dboo ook k of Geot Geotec echn hnic ical al Investigations and Design Tables. Taylor & Francis.