UDOT Hyperbolic Model Report

Report No. UT-11.XX

Hyperbolic Model Parameters and Settlement Modeling for the I-15 Reconstruction Project Prepared For: Utah Department of Transportation Research and Development Division Submitted By: University of Utah Civil & Environmental Engineering Authored By: Steven F. Bartlett Bret N. Lingwall Evert C. Lawton Michelle Cline

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August 31, 2011

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DISCLAIMER The authors alone are responsible for the preparation and accuracy of the information, data, analysis, discussions, recommendations, and conclusions presented herein. The contents do not necessarily reflect the views, opinions, endorsements, or policies of the Utah Department of Transportation or the US Department of Transportation. The Utah Department of Transportation makes no representation or warranty of any kind, and assumes no liability therefore.

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2. Government Accession No.

UT-11.???

1. Report No. 4. Title and Subtitle

3. Recipient's Catalog No.

5. Report Date

Hyperbolic Model Parameters and Settlement Modeling for the I-15 Reconstruction Project 7. Author(s)

AUGUST, 2011 6. Performing Organization Code

8. Performing Organization Report No.

Steven F. Bartlett, Bret N. Lingwall, Evert C. Lawton, Michelle Cline 9. Performing Organization Name and Address

Department of Civil and Environmental Engineering University of Utah 110 Central Campus Drive, Suite 2000 Salt Lake City, Utah 84112

10. Work Unit No. Project

Number

11. Contract No. Contract

Number

12. Sponsoring Agency Name and Address

13. Type of Report and Period Covered

Utah Department of Transportation Research Division 4501 South 2700 West Salt Lake City, Utah 84114-8410

Research from 1999 - 2011 14. Sponsoring Agency Code Project

ID Code No.

15. Supplementary Notes

Prepared in cooperation with the Utah Department of Transportation or U.S. Department of Transportation, Federal Highway Administration 16. Abstract

A series of laboratory triaxial tests were performed on specimens of Bonneville clay sampled from sites along I15 at North and South Temple Streets. The purpose of the triaxial tests was to determine the HNLE properties of Bonneville clays. Triaxial tests were performed drained on the majority of specimens, while undrained tests were performed on several specimens. The triaxial test data were examined to determine the required soil parameters for the HNLE model. The laboratory test results of HNLE parameters for the Bonneville clays were compared with the back calculated values determined from surface settlements during and after I-15 reconstruction. The laboratory and back calculated values of various HNLE model parameters compared very well. A summary of the HNLE model parameters found in this report for the Bonneville clays is presented. 17. Key Words

18. Distribution Statement

embankment settlement, numerical modeling, triaxial testing

UDOT Research Division 4501 South 2700 West – Box 148410 Salt Lake City, UT 84114

19. Security Classification (of this report)

21. No. of Pages

Unclassified

20. Security Classification (of this page)

???

Unclassified

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22. Price

23. Registrant’s Seal

Page Left Blank Intentionally

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Table of Contents Table of Contents.................................................................................................................5 Table of Figures...................................................................................................................7 Table of Tables.....................................................................................................................9 Abstract..............................................................................................................................10 Introduction........................................................................................................................11 Background....................................................................................................................11 Purpose..........................................................................................................................12 The Hyperbolic Constitutive Model for Soils...................................................................12 Theory............................................................................................................................13 Soil Parameters for Hyperbolic Model..........................................................................16 Friction Angle............................................................................................................17 Cohesion Intercept.....................................................................................................17 Poisson’s Ratio...........................................................................................................17 Initial Tangent Modulus Number and Exponent........................................................18 Unloading and Reloading Modulus Number.............................................................20 Bulk Modulus Number and Exponent.......................................................................21 Failure Ratio..............................................................................................................22 Application....................................................................................................................22 Limitations.....................................................................................................................23 Advantages....................................................................................................................23 Bonneville Clays................................................................................................................24 Site Description.............................................................................................................24 Soil Profile.....................................................................................................................24 Triaxial Testing..................................................................................................................27 Test Apparatus................................................................................................................27 Procedures......................................................................................................................31 Data Reduction..............................................................................................................36 Triaxial Test Results.......................................................................................................37 Back Calculation from Embankment Settlements.............................................................43 Conclusions........................................................................................................................54 6

Acknowledgements............................................................................................................55 References..........................................................................................................................56 Appendix............................................................................................................................59 Table of Contents.................................................................................................................2 Table of Figures...................................................................................................................3 Table of Tables.....................................................................................................................3 Abstract................................................................................................................................4 Introduction..........................................................................................................................5 Background......................................................................................................................5 Purpose............................................................................................................................6 The Hyperbolic Constitutive Model for Soils.....................................................................6 Theory..............................................................................................................................7 Soil Parameters for Hyperbolic Model............................................................................9 Friction Angle............................................................................................................10 Cohesion Intercept.....................................................................................................10 Poisson’s Ratio...........................................................................................................10 Initial Tangent Modulus Number and Exponent........................................................11 Unloading and Reloading Modulus Number.............................................................13 Bulk Modulus Number and Exponent.......................................................................13 Failure Ratio..............................................................................................................14 Application....................................................................................................................15 Limitations.....................................................................................................................15 Advantages....................................................................................................................16 Bonneville Clays................................................................................................................16 Soil Profile.....................................................................................................................16 Site Description.............................................................................................................17 Triaxial Testing..................................................................................................................17 Test Apparatus................................................................................................................18 Procedures......................................................................................................................20 Data Reduction..............................................................................................................25 Triaxial Test Results.......................................................................................................26 Back Calculation from Embankment Settlements.............................................................31 Conclusions........................................................................................................................35 Acknowledgements............................................................................................................36 References..........................................................................................................................37 7

Appendix............................................................................................................................40

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Table of Figures Figure 1 – Stress-Strain Curves - After Duncan and Wong (1974)....................................14 Figure 2 - Generalized Nonlinear Stress-Strain Curve......................................................16 Figure 3 - Derivation of Modulus Number and Exponent - From Geo-Slope International (2004).................................................................................................................................20 Figure 4 - South Temple CPT Layering.............................................................................26 Figure 5 - GEOCOMP Control Box..................................................................................28 Figure 6 - GEOCOMP Load Frame with Assembled Specimen.......................................29 Figure 7 - GEOCOMP FLOWTRACK II Flow Pumps....................................................31 Figure 8 - Cut Shelby tube ready for specimen extraction................................................32 Figure 9 - Bottom of triaxial cell.......................................................................................33 Figure 10 - Assembled triaxial cell....................................................................................34 Figure 11 - Flow Line Connections...................................................................................35 Figure 12 - Initial Tangent Modulus Plot for Upper Bonneville Clays.............................40 Figure 13 - Initial Tangent Modulus Plot for the Interbeds...............................................41 Figure 14 - Initial Tangent Modulus Plot for the Lower Bonneville Clays.......................41 Figure 15 - Bulk Modulus plot for the Upper Bonneville Clays .......................................42 Figure 16 - Bulk Modulus Plot for the Interbeds...............................................................42 Figure 17 - Bulk Modulus Plot for the Lower Bonneville Clays ......................................43 Figure 18 - 200 South Embankment - From Flint and Bartlett (2005).............................44 Figure 19 - 200 South Settlement Data and Estimates - After Flint and Bartlett (2005). 46 Figure 20 - Existing I-15 Embankment Analysis Comparison..........................................49 Figure 21 - Phase I of Reconstruction Analysis Comparison............................................50 Figure 22 - I-15 Reconstruction Phase II Analysis Comparison.......................................52 Figure 23 - Comparison of Measured Data and HNLE Models........................................53 Figure 24 - General Trend of all Initial Tangent Modulus Data........................................60 Figure 25 - General Trend of all Bulk Modulus Data........................................................61 Figure 26 - Comparison of Triaxial Test data to Calibrated HNLE values.......................62 Figure 27 - Comparison of Triaxial Test Results to Calibrated HNLE.............................63 Figure 28 - North Temple CPT Data..................................................................................64 Figure 29 - South Temple CPT Data..................................................................................65 Figure 30 - Stress:Strain Plot for B1 -14.00......................................................................66 Figure 31 - Stress:Strain Plot for B1 15.46........................................................................67 Figure 32 - Stress:Strain Plot for B1 15.48........................................................................68 Figure 33 - Stress;Strain Plot for B1 17.22........................................................................69 Figure 34 - Stress:Strain Plot for B2 10.2..........................................................................70 Figure 35 - Stress:Strain Plot for B2 13.3..........................................................................71 Figure 36 - Stress:Strain Plot for B2 14.8..........................................................................72 Figure 37 - Stress:Strain Plot for B3 7.1............................................................................73 Figure 38 - Stress:Strain Plot for B3 7.315........................................................................74 Figure 39 - Stress:Strain Plot for B3 8.7............................................................................75 Figure 40 - Stress:Strain Plot for B3 8.69..........................................................................76 Figure 41 - Stress:Strain plot for B3 11.56........................................................................77 Figure 42 - Stress:Strain Plot for B3 16.00........................................................................78 9

Figure 43 - Stress:Strain Plot for B3 17.260......................................................................79 Figure 44 - Stress:Strain Plot for B3 17.68........................................................................80 Figure 45 - Stress:Strain Plot for B3 18.532......................................................................81 Figure 46 - Stress:Strain Plot for B3 19.11........................................................................82 Figure 47 - Stress:Strain Plot for B4 6.25..........................................................................83 Figure 48 - Stress:Strain Plot for B3 7.98..........................................................................84 Figure 49 - Stress:Strain Plot for B4 11.07........................................................................85 Figure 50 - Stress:Strain Plot for B4 13.945......................................................................86 Figure 51 - Stress:Strain Plot for B6 16.84........................................................................87 Figure 52 - Stress:Strain Plot for B4 17.00........................................................................88 Figure 53 - SIGMA/W In-Situ Stress Analysis.................................................................89 Figure 54 - SIGMA/W Existing Embankment Analysis...................................................90 Figure 55 - SIGMA/W Phase I Analysis...........................................................................91 Figure 56 - SIGMA/W Phase II Anlysis............................................................................92 Figure 1 - Stress:Strain Curves - After Duncan and Wong (1974).....................................9 Figure 2 - Generalized Non-Linear Stress:Strain Curve....................................................10 Figure 3 - Derivation of Modulus Number and Exponent - From Geo-Slope International (2004).................................................................................................................................13 Figure 4 - South Temple CPT Layering.............................................................................19 Figure 5 - GEOCOMP Control Box..................................................................................21 Figure 6 - GEOCOMP Load Frame with assmebled Specimen........................................22 Figure 7 - GEOCOMP FLOWTRACK II Flow Pumps....................................................23 Figure 8 - Cut Shelby tube ready for specimen extraction................................................24 Figure 9 - Bottom of triaxial cell.......................................................................................25 Figure 10 - Assembled triaxial cell....................................................................................26 Figure 11 - Flow Line Connections...................................................................................27 Figure 12 - Initial Tangent Modulus Plot for Upper Bonneville Clays.............................31 Figure 13 - Inital Tangent Modulus Plot for the Interbeds................................................32 Figure 14 - Inital Tangent Modulus Plot for the Lower Bonneville Clays........................32 Figure 15 - Bulk Modulus plot for the Upper Bonneville Clays .......................................33 Figure 16 - Bulk Modulus Plot for the Interbeds...............................................................33 Figure 17 - Bulk Modulus Plot for the Lower Bonneville Clays ......................................34 Figure 18 - 200 South Embankment - From Flint and Bartlett (2005).............................35 Figure 19 - 200 South Settlement Data and Estimates - After Flint and Bartlett (2005). 36 Figure 20 - Existing I-15 Embankment Analysis Comparison..........................................39 Figure 21 - Phase I of Reconstruction Analysis Comparison............................................40 Figure 22 - I-15 Reconstruction Phase II Analysis Comparison.......................................41 Figure 23 - General Trend of all Initial Tangent Modulus Data........................................46 Figure 24 - General Trend of all Bulk Modulus Data........................................................46 Figure 25 - Comparison of Triaxial Test data to Calibrated HNLE values.......................47 Figure 26 - Comparison of Triaxial Test Results to Calibrated HNLE.............................48 Figure 27 - North Temple CPT Data..................................................................................49 Figure 28 - South Temple CPT Data..................................................................................50 Figure 29 - Stress:Strain Plot for B1 -14.00......................................................................51 Figure 30 - Stress:Strain Plot for B1 15.46........................................................................52 Figure 31 - Stress:Strain Plot for B1 15.48........................................................................53 10

Figure 32 - Stress;Strain Plot for B1 17.22........................................................................54 Figure 33 - Stress:Strain Plot for B2 10.2..........................................................................55 Figure 34 - Stress:Strain Plot for B2 13.3..........................................................................56 Figure 35 - Stress:Strain Plot for B2 14.8..........................................................................57 Figure 36 - Stress:Strain Plot for B3 7.1............................................................................58 Figure 37 - Stress:Strain Plot for B3 7.315........................................................................59 Figure 38 - Stress:Strain Plot for B3 8.7............................................................................60 Figure 39 - Stress:Strain Plot for B3 8.69..........................................................................61 Figure 40 - Stress:Strain plot for B3 11.56........................................................................62 Figure 41 - Stress:Strain Plot for B3 16.00........................................................................63 Figure 42 - Stress:Strain Plot for B3 17.260......................................................................64 Figure 43 - Stress:Strain Plot for B3 17.68........................................................................65 Figure 44 - Stress:Strain Plot for B3 18.532......................................................................66 Figure 45 - Stress:Strain Plot for B3 19.11........................................................................67 Figure 46 - Stress:Strain Plot for B4 6.25..........................................................................68 Figure 47 - Stress:Strain Plot for B3 7.98..........................................................................69 Figure 48 - Stress:Strain Plot for B4 11.07........................................................................70 Figure 49 - Stress:Strain Plot for B4 13.945......................................................................71 Figure 50 - Stress:Strain Plot for B6 16.84........................................................................72 Figure 51 - Stress:Strain Plot for B4 17.00........................................................................73 Figure 52 - SIGMA/W In-Situ Stress Analysis.................................................................74 Figure 53 - SIGMA/W Existing Embankment Analysis...................................................75 Figure 54 - SIGMA/W Phase I Analysis...........................................................................76 Figure 55 - SIGMA/W Phase II Anlysis............................................................................77

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Table of Tables Table 1- Consolidated Drained Triaxial Test Summary.....................................................38 Table 2 - Consolidated Drained Triaxial Test Results.......................................................39 Table 3 - Typical HNLE Properties for 200S.....................................................................45 Table 4 - Calibrated HNLE Properties...............................................................................45 Table 5 - Laboratory Triaxial HNLE Properties................................................................47 Table 6 - Comparison of Triaxial and Back Calculated Parameters..................................47 Table 1 - Consolidated Drained Triaxial Test Summary....................................................26 Table 2 - Consolidated Drained Triaxial Test Results.......................................................27 Table 3 - Typical HNLE Properties for 200S.....................................................................33 Table 4 - Calibrated HNLE Properties...............................................................................34 Table 5 - Laboratory Triaxial HNLE Properties................................................................34 Table 6 - Comparison of Triaxial and Back Calculated Parameters..................................35

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Abstract In order to evaluate the determine appropriate foundation stability of accelerated embankment construction and to predictestimate the subsequent foundation soil deformationsconsolidation settlement from large embankment construction, the use of finite element modeling is proposed using nonlinear soil properties. Such a method is preferred over over traditional limit equilibrium techniques because . Ffinite element modeling is a type of numerical modeling which can better estimate the model both theinduced stresses change and deformations of subsurface soils in a more realistic manner. A numerical model requires an appropriate soil constitutive relationship model for the soils located mass underneath the future embankment. One of the potentialse soil constitutive models is the Hyperbolic Non-Linear Elastic (HNLE) model developed by Duncan et.al (1980). This model includes volumetric changes and their effects on soil deformations under induced stress. It is a relatively simple, sophisticated constitutive relationship which includes the stress dependency of both shear and volumetric deformation in a non-linear framework. A series of laboratory triaxial tests were performed on specimens of Bonneville clay sampled from sites along I-15 at North and South Temple Streets. The purpose of the triaxial tests was to determine the HNLE properties of Bonneville clays. Drained tTriaxial tests were performed drained on the majority of specimens. The results of these tests , while undrained tests were performed on several specimens. The triaxial test data were examined to determine the required soil parameters for the HNLE model. Lastly, Tthe laboratory test results of HNLE parameters for the Bonneville clays were compared with the back- calculated values determined from surface settlement monitorings during and afterfrom the I-15 Rreconstruction Project. The laboratory and back- calculated values of various HNLE model parameters compared very wellwell. A summary of the HNLE model parameters found in this report for the Bonneville clays is presented in addition to the numerical modeling that was done with the applied HNLE parameters. 13

Introduction Background The I-15 Reconstruction Project, completed in 2001 in Salt Lake City, Utah,, incorporated several innovative embankment and foundation treatments as part of a fastpaced, 4-year, $1.5 billion design-build project. In many cases, these treatments were required to facilitate construction over compressible clayey foundation soils present along much of the alignment. ForemostPrinciple among the clayey foundation soils are the Bonneville Formation lacustrine deposits (primarily silt and clay with sandy interbeds). Prefabricated vertical (PV) drains were used in conjunction with surcharge preloading (i.e., surcharging) at soft soil sites to accelerate primary consolidation settlement and reduce secondary consolidation settlement. Expanded polystyrene (EPS) Geofoam was used as an extremely lightweight fill material in some utility corridors, so as not to trigger large and damaging settlement to underground lines (Bartlett et.al, 2001). Also, at one location, lime cement columns (LCCs) were employed to improve the foundation soils of a mechanically stabilized earth (MSE) wall. Details on these innovative technologies are presented in other technical reports.

To monitor the performance of foundation soil treatments, various types of instrumentation were installed at select sites to collect field performance data during and after

construction.

Installed

instrumentation

included

horizontal

and

vertical

inclinometers, magnet extensometers, strain gages, open and closed-ended piezometers, total pressure cells and survey settlement points. These instrument arrays were installed 14

by the design-build contractor to monitor construction performance and by the UDOT Research Division to monitor construction and post-construction performance. Performance has been monitored since construction began in 1998 and continued through 2011 at some locales s today (Bartlett and Farnsworth, 2004). The data from these instrument arrays have been reported, in part, in various publications and technical reports. The data from the instrumentation, as well as laboratory soil testing, will bring insights into innovative accelerated construction methods.

Purpose The purpose of the research for this report is to determine via, through laboratory testing , suitable hyperbolic non-linear elastic (HNLE) model parameters using methods developed by Duncan and Chang (1977) and Duncan et.al (1980). These parameters will be hyperbolic non-linear elastic (HNLE) model parameters for used in a finite element numerical model to evaluates of t the settlement and stability of the Bonneville clays under undrained embankment loading. Also, this report provides is to develop guidance for designers regarding thein selection of suitable hyperbolic model parameters from a laboratory test programing. Finally, this report is to demonstrates the effectiveness of back-calculation of hyperbolic model parameters in estimating settlement by comparison with from field instrumentation.

The Hyperbolic Constitutive Model for Soils There are several constitutive models that can be used in finite element analysis (FEA) or finite difference analysis (FDA) to numerically simulate the stress-strain behavior of soils. For example, the stress-strain relationship employed in the numerical model might be linear-elastic, bi-linear-elastic, elastic-plastic with a Mohr-Coulomb failure criteria or a variety of other constitutive relations, depending on the anticipated strain range or required complexity of the problem. One of the most popular advanced constitutive 15

models is the ‘hyperbolic’ model, where the stress-strain relationship is elastic-plastic and non-linear. The nonlinear at the stress-:strain relationship of soils is non-linear hashas been been observedstudied for many years. Konder (1963) proposed that the non-linear shape of the stress-:strain relationship is approximately hyperbolic for some soils, particularly for clays in particular, and he . As a result, a proposed a ‘hyperbolic’ model to explain the nonlinearity was proposed by Konder (1963).

Subsequently,

Tthe hyperbolic

mathematical model was further developed by Duncan and Chang (1970) and Duncan et .al. (1980), who addressed by addingthe stress dependency and volumetric nonlinearity. For soil-structure interaction problems, Clough and Duncan (1971) showed that a ‘hyperbolic’ model can be used to simulate the soil-structure interaction for lateral earth pressures on retaining walls. Duncan and Mokwa (2001) demonstrated that the hyperbolic model can accurately predict passive earth pressures in numerical model/test comparisons. They also noted the suitability of using the hyperbolic model for clayey soils. The Duncan and Chang (1977) and the Duncan et.al (1980) models are referred to as the Hyperbolic Non-Linear Elastic model (HNLE model) since they are non-linear models (the hyperbolic shape of the stress-:strain curve) and elastic (perfectly hysteretic unloading is assumed) prior to reaching a failure condition. For both of these models and aAfter the a failure condition has been reached, for both relationships is reached tthe models treat the soil as is perfectly plastic, following the formulation of the classic MohrCoulomb constitutive relationship for plastic flow.

Theory Konder (1963) noted that the stress-:strain relationship for soils, though hyperbolic in shape when plotted arithmetically, is approximately linear when transforming by plotting strain divided by stress against stress transformed as shown in Figure 1. Equation (1) shows the Konder arithmetic stress-:strain mathematical relationship, which is non-linear and hyperbolic in shape. Equation (2) shows the transformed mathematical relationship that is linear. The transformation is done by dividing the strain of a material by the deviator stress (principle stress difference) that induced that strain. This is plotted against 16

strain to find a line with the form of Equation (2). Equations (1) and (2) are shown graphically in Figure 1 from Duncan and Wong (1974).

 1   3  



1   Ei   1   3  ult

 1     1   3  Ei  1   3  ult

(1)

(2)

Figure 1 -– Stress-:Strain Curves - After Duncan and Wong (1974)

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Duncan and Chang (1970) added a stress dependency relationship to the hyperbolic form.relationship stress dependency. In their formulation, tThe modulus of a soil is dependant on the confining stress acting on it. In general, the higher the confining stress, the stiffer the material; hence (the greater the modulus). This allows the estimated values from thes the user to model to the cchange inwith modulus to better represent the material behavior

with the change in with increasing depth below ground surface.

accurately and continuously. The advantage of the Duncan et.al (1980) HNLE model is itsthe addition of the bulk modulus parameter, which was lacking from the previous hyperbolic models of Konder (1963) and Duncan and Chang (1970). The bulk modulus parameter is important in that it provides a volumetric parameter to explain volumetric change to accompany to go along with the non-linear distortional shear deformation parameters of the previous models. A volumetric deformation parameter that can changes with stress and strain conditions is important since the strength of a soil can change significantly when accompanied by contraction or dilation of the soil skeleton (Holtz and Kovacs, 1981). In addition, tThe bulk modulus is also a more fundamental soil property than Young’s Modulus for the deformation characteristics of a soil under partially to fully drained conditions (Wood, 1990 and Itasca, 2005).

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Soil Parameters for Hyperbolic Model There are nine required sSoil parameters used in the HNLE which . They include strength and volumetric parameters. The parameters required for analysis are: K, K ur, Kb, n, m, c, φ’, Δφ’, and Rf which are the: mModulus nNumber, uUnloading-rReloading mModulus nNumber, bBulk mModulus nNumber, mModulus eExponent, bBulk mModulus eExponent, internal apparent cohesion, initial friction angle, change in friction angle with stress, and fFailure rRatio. There parameters will be explained in the following sections. These parameters are found most commonly from laboratory triaxial testing or from the library of 150 soils in the Duncan et.al (1980) report. The generalized stress-:strain relationship for the HNLE model is shown in Ffigure 2, which shows that definitions of initial tangent and tangent moduli in the numerical implementation of the model graphically.

Figure 2 - Generalized Nonl-Linear Stress-:Strain Curve

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Friction Angle The HNLE model uses the drained or undrained internal friction angle of the soil being modeled. For a large range of confining pressures, it is appropriate to use a value of φ that varies with confining pressure in accordance with the following equation:  3    Pa 

   o  Log 

(3)

where  o = value of  when σ3 is equal to the reference stress Pa; and Δ = change in φ for a 10-fold increase in σ3. The term PPa term is the reference pressure in, 100 kPa (i.e., 1 tsf). The Duncan et.al (1980) report tabulates the friction angle of 150 soils. For cohesive soils with a very curved failure envelope, or one with a distinct overconsolidated failure envelope that differs from the normally consolidated envelope, Duncan et.al (1980) recommend using two sets of strength parameters ( and c) for the appropriate range of normal stresses on the soil. For cohesionless soils, Eequation (3) is recommended to account for a curved failure envelope.

Cohesion Intercept This value of the cohesion intercept is usually zero for drained conditions in un-cemented soils except those that are highly over-consolidated. The use of a cohesion intercept should be chosen carefully depending on the triaxial test the cohesion comes from. The unconsolidated-undrained ( UU) and consolidated-undrained ( CU) tests will give different values of cohesion intercept. Duncan et.al (1980) shows that for consolidated drained tests (CD), the cohesion intercept is nearly zero for many of theall soils tested. However, for the the undrained tests, Tthe cohesion for the undrained testsvalues ranged from 0 to 200 kPa tsf in the library of 150 soils tested for HNLE properties.

Poisson’s Ratio Though not included in the Duncan et.al (1980) formulation of the HNLE model except for the bulk modulus, Poisson’s rRatio is included in the finite element implementation of the model in most computer programs. It is also a part of the Duncan and Chang (1970) and the Duncan and Wong (1974) formulations of the HNLE model. Poisson’s rRatio is calculated directly from drained triaxial tests with volumetric strain measurements. For 20

an undrained triaxial test, or other saturated soil sheared in undrained conditions, Poisson’s Ratio is equal to 0.5. Poisson’s rRatio is calculated from test data by the equation:

 1    1  v 2 a

  

(4)

where  v is the volumetric strain of the specimen under triaxial shear, and  a is the axial strain of the soil specimen under triaxial shear. Values of ν are restricted to lower and upper limits of 0.1 and 0.49, respectively, for most finite element analyses. A value of 0.5 indicates that there is no volume change (i.e., no volumetric strain) and is used to model perfectly “undrained” soil conditions in most LE analyses. (Note that a ν of 0.49 must be used in many numerical models, including Sigma/W, to model “undrained” conditions. Sigma/W and other computer codes will not reach a solution if 0.5 is used.) Values of Poisson’s Ratio less than 0.5 indicate that a soil undergoes volume change during strain, and those values of PPoisson’s rRatio are called obtained from drained triaxial testing and are commonly referred to as “drained” values.

Initial Tangent Modulus Number and Exponent The initial tangent modulus used in the HNLE is also obtained from triaxial testing. (It is important to note that it is not the not the very small strain Young’s Modulus, Emax, which isobtained from geophysical testing the normal stress counterpart to Gmax obtained from shear wave velocity measurements for soils. The very small strain values of modulus from shear wave velocitiesgeophysical testing are 50% to 250% morehigher than the values of initial tangent modulus available from routineegular triaxial testing.) In the HNLE model, theThe HNLE model requires the initial tangent modulus from triaxial testing, which is the theoretical slope of the initial linear portion of the stress-:strain curve (Figure 2). The Duncan et .al. (1980) documentreport provides guidance on selection of the initial tangent modulus appropriate for the HNLE model. They also Duncan et.al (1980) showed that graphical tangent line methods of determining the initial tangent modulus are unreliable. They recommend fitting the hyperbolic shape of the stress-:strain

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curve at 70% and 95% of the failure stress level. The initial tangent modulus is then estimated from the functional form of the hyperbola. Once the initial tangent modulus has been determined for a soil at a variety of confining stresses, the modulus number can be calculated. This is done by first normalizing the initial tangent modulus to the reference pressure, Pa. The reference pressure is defined as by definition 100kPa. The normalized modulus is plotted on a log-log plot against normalized confining stress, σ’3 / Pa. A power regression fit to the data is used to find the modulus number and exponent. The intercept at unity on the log-log scale is the modulus number. The exponent of the power fit to the data is the modulus exponent. This is also the slope of the line in log-log space. The equation of the power fit is shown in Eequation 5:.   Ei t  Kp a  3  pa

n

  

(5)

wWhere Eit is the initial modulus, K is the modulus number and n is the modulus exponent. An example of the graphical determination of the modulus number and exponent is shown in Figure 3. In Eq. (5), K and n are unit-lessunit less, and Eit, Pa, and

σ3 are in consistent units. Duncan et al. (1980) report conservative values of n ranging from 0.25 to 0.6 for various types of soil.

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Figure 3 - Derivation of Modulus Number and Exponent - From Geo-Slope International (2004)

For the modulus of the soil beyond the initial linear range of the stress-:strain curve, the tangent modulus is used. The tangent modulus at any stress is calculated using Equation (6).

R f 1  sin    1   3    Et   1   Eit 2c cos   2 3 sin   

(6)

In Equation (6), Rf = failure ratio; φ = soil friction angle; ( σ1 - σ3 ) = deviator stress; and c = soil internal cohesion intercept. The failure ratio symbolizes the ratio between the asymptote to the hyperbolic curve and the maximum shear strength, and typically ranges from 0.5 to 0.9 for most soils. Equation. (6) indicates that Et is dependent on confining pressure and the percentage of shear strength mobilized.

Unloading and Reloading Modulus Number In the HNLE model, the modulus of a soil in unloading and reloading are assumed to be identical. They are found from triaxial testing,, and an example is shown in Figure 2. The 23

uUnloading and rReloading mModulus nNumber (Kur) is found by normalizing the unloading and reloading modulus of a soil to the confining stress and plotting on a loglog scale against the normalized confining stress as is shown in Figure 3. There is no unloading and reloading modulus exponent in the HNLE model. It is assumed to be identical to the Modulus Exponent (n). The form of the uUnloading and rReloading Modulus in the HNLE model is the same as for the mModulus nNumber and is shown in Eequation (7). E ur

   K ur p a  3  pa

n

 

(7) 

Equation. (7) accounts for the fact that strains occurring during primary loading are only partially recoverable on reloading, a common characteristic of inelastic soil behavior. For soil reloading, Kur is always greater than K. Often, unloading data is not available and thus Kur is assumed. For stiff soils, such as dense sands, K ur is approximately equal to 1.2K. For softer soils including loose sands, Kur is approximately equal to about 3K.

Bulk Modulus Number and Exponent The bBulk modulus represents the constant change in volume of a specimen with no change in shape (Wood, 1990). In contrast, Tthe shear modulus represents the change in shape of a soil with no change in volume. The HNLE model uses the bBulk mModulus, represented by the bBulk mModulus nNumber and eExponent, to show a change in volume and its effects on the stiffness and strength of the soil. The bulk modulus at a given confining stress is calculated from triaxial drained test data. It is not calculable from undrained triaxial test data, since the undrained test is constant volume in nature. The bBulk mModulus is related to sShear mModulus, Young’s mModulus and Poisson’s rRatio by elastic theory. It can be calculated directly from test data by use of volumetric measurements from the triaxial test as shown by Equation (8). B

 'd 3 v

(8)

In Equation (8),  ' d is the deviator stress at the 70% stress level or where the volumetric change curve reaches a horizontal tangent. The volumetric strain in Equation (8) is the volumetric strain that corresponds to the 70% stress level or tangent level. Note that the Bulk mModulus at a given stress lelvel is related to the sSecant Young’s mModulus at the 24

same stress level and Poisson’s rRatio by Eequation (9). If the bulk modulus is variable, Equation (9) allows for both the Young’s modulus and Poisson’s rRatio to vary with stress level. B

Es 31  2 

(9)

The Bulk mModulus number (Kb) and exponent (m) are calculated similar to the modulus number and exponent by normalizing the bulk modulus with confining stress and plotting on a log-log scale against confining stress normalized to the reference pressure. See Figure 3 for plotting details. The Bulk mModulus nNumber (Kb) is the normalized bulk modulus at unity, and the Bulk mModulus eExponent (m) is the slope of the normalized log-log curve. For most soils, m is in the range of 0.0 to 1.0. Equation (10) shows the HNLE equation for bulk modulus.  3   B  K b pa   p   a 

m

(10)

Failure Ratio The fFailure rRatio is a calculated parameter which represents the ratio of failure compressive strength of a soil to the asymptote of its stress-:strain curve (the ultimate strength, or critical state). The Duncan et.al (1980) document provides methodology on calculation of this parameter from the failure and ultimate states of stress on a purely dilative specimen. Equation (11) shows the calculation of the fFailure rRatio (Rf). Rf 

 1   3  f  1   3  ult

(11)

The fFailure ratio is always less than unity, and ranges from 0.5 to 0.95 according to Duncan et.al (1980). The failure compressive strength of a soil is defined by Eequation (12).

 1   3  f



2c  Cos  2 3 Sin 1  Sin

25

(12)

Application The HNLE model is used in nonlinear incremental analysis of soil deformations. In each increment of the numerical modeling, the small piece of the analysis is treated as a linear material with the stress-:strain behavior governed by the generalized Hooke’s lLaw. Hooke’s lLaw describes the relationship between stress-strain in the elastic behavior of materials, and can be used in an incremental manner for including soils. Numerical models such as finite element methods use Hooke’s lLaw in the formation of stiffness matrices for calculation of incremental stress-:strain response. The fundamental stiffness matrix of Hooke’s’ lLaw for soils in the HNLE model is represented for plane-strain conditions by:

(13) This equation is used in FEA or FDA so solve for the deformations of a soil element under a load. The variable E in Eequation (13) denotes Young’s mModulus, B is bBulk mModulus. Note that bBulk mModulus and Young’s mModulus are the key parameters. As has been noted before, these parameters are stress dependant, non-linear and elastic in the HNLE Model. The computer varies the values of modulus used in each increment as the stresses vary.

Limitations Despite its advantages over simpler elastic models, there are several limitations of the HNLE model. The HNLE relationships may not realistically predict soil behavior at or beyond the failure condition due to its lack of a specific plastic flow rule. Thus, In computer software implementation, the Mohr-Coulomb flow rule is used (Itasca, 19XX). Tthe HNLE stress-:strain relationships developed are primarily developed applicable for stable earth masses where the post-failure condition is not important. For earthen structures that reach failure or post-failure This means that earth structures at or beyond failure are not modeled accurately with the plastic flow rule used in FEA. In addition, Earthsoil masses with inherent anisotropy are not addressed. Further, tThe HNLE model 26

only accounts for volume change resulting from normal stresses; it does not account for volume changes due to shear stress, which may be important in complex three dimensional analyses, only normal stresses. which may be important in complicated three dimensional analyses.

Advantages There are several advantages for use of the HNLE model rather than alternative other models such as the Modified Cam Clay mModel. The HNLE model is simpler than Modified Cam Clay model. It requires fewer inputs, and the inputs are easier to obtain, than those needed in the Modified Cam Clay model. The HNLE model also has advantages over simpler constitutive models such as the linear-elastic model. These advantages include a non-linear stress-:strain relationship more realistic for (which soils really have) and volumetric change and its subsequent influence on shear strength. It also allows for a variation of stiffness with additional confinement, which is not allowed in older and simpler models. The HNLE model is also a proven method for numerical modeling. Another advantage of the HNLE model is that it’s parameters are easily obtained from drained or undrained triaxial testing. which is the standard strength test for clayey soils.

Bonneville Clays Site Description North and South Temple Streets cross the I-15 alignment at approximately 700 West in Salt Lake City, Utah. At the North Temple site, drilling, sampling, and CPT testing was done on the east side of the I-15 embankment just north of North Temple Street. At the South Temple site, drilling, sampling, and CPT testing was done underneath the I-15 mainline overpass. The terrain at these locales is flat, and the groundwater table varies from 8 feet to 15 feet below ground surface.

27

Soil Profile Foundation soils below the embankment at the North and South Temple sites consist of about 5 to 8 m (16 to 26ft) of interbedded, alluvial clays, silts and sands. This upper alluvium was deposited during the Holocene epoch by stream channels extending from the canyons of the nearby Wasatch Mountains and from the floodplain of the Jordan River. The upper alluvium is underlain by a 10-m (33-ft) to 13-m (43-ft) sequence of soft, compressible lacustrine soils commonly referred to as Lake Bonneville deposits. This Pleistocene sequence consists of interbedded clayey silt and silty clay, with thin beds of silts and fine sand near the middle of the unit. Beneath the Lake Bonneville deposits are about 3 m (10 ft) of interbedded Pleistocene alluvial and lacustrine sediments consisting of sands, silts, and clays. These interbedded deposits are in turn underlain by the Cutler Dam Lake sequence. These Pleistocene lacustrine deposits are about 4-m (13-ft) to 9-m (30-ft) thick and consist of clay with occasional seams and layers of silt and sand. Dense, alluvial sands and gravels underlie the Cutler Dam Lake sediments. Typically, groundwater is encountered within a depth of about 3 m (10 ft) below the ground surface in this area. For purposes of this study, groundwater was assumed to be located at a depth of 3 m (10 ft). The Lake Bonneville deposits are commonly referred to as the Bonneville cClays, and that will continue in this report. Other reports detail the various granulometry, plasticity, and consolidation properties. Ozer (2004) and Farnsworth (2008) detail these properties further. Strength parameters for the undrained shear strength of the Bonneville clays are available for the SHANSEP technique in Bay et.al (2005). Cone Penetration Test data for the North and South Temple sites are presented in the appendix. CPT data from I-15 Rreconstruction and University of Utah research projects from 2001 to 2005 are shown in the CPT plots in this report. Figure 4, below, shows the use of the Cone Penetration Test to determine the layering of the South Temple site.

28

Figure 4 - South Temple CPT Layering

29

Triaxial Testing A series of isotropically consolidated drained axial compression (CIDC) and K o consolidated undrained (CKoUC) triaxial tests were performed on specimens of Bonneville sediments from North Temple Street and South Temple Street in Salt Lake City. Drilling was done using hollow stem continuous flight augers. The soil samples were retrieved using Shelby tubes and piston sampling to reduce sample disturbance (Santaga and Germaine, 2002) and to increase laboratory testing reliability (Bay et.al, 2003). The Shelby tubes were sealed and stored in a 100% humidity room until samples were to be tested to preserve the in-situ moisture condition as closely as possible (Bishop and Henkel, 1962).

Test Apparatus Testing was done using GEOCOMP Corporation’s triaxial system. The GEOCOMP system is fully automated. The triaxial test cell used was rated to 1000 kPa. The system consists of 4 parts. The first part of the system is a PC computer that has the control software installed. This PC communicates with the other components of the system to run the test. The second part of the system is the load frame. This device holds the triaxial cell, applies the vertical load to the specimen, and monitors the force and displacements of the load piston. The GECOMP load frame is shown in Figure 6. The load frame interfaces with the rest of the triaxial compression system using a control box with an LCD display. This control box can be used to operate the load frame independently of the software if needed. The control box for the GEOCOMP load frame is shown in Figure 5. Note the numeric keypad used to operate the load frame. The control box also interfaces the load frame with the control software in the PC.

30

Figure 5 - GEOCOMP Control Box

31

LVDT S-Type Load Cell

Assembled Triaxial Cell with Specimen in Latex Membranes

Figure 6 - GEOCOMP LLoad FFrame with assmebledAssembled SSpecimen

32

The third and fourth components are the FLOWTRACK II flow pumps that apply the pressures for the triaxial cell. Flow lines connect the two pumps to the triaxial cell. One pump is for the cell pressure and the other pump is for the specimen. Each pump has a 250cc bladder that is pressurized as controlled by the computer. The use of two pumps is needed so that the specimen can be pressurized to a different pore pressure than the total stress applied from the cell. Each flow pump contains a calibrated pressure gauge to monitor the pressures continuously throughout the test. The pumps also adjust automatically to keep the pressures constant as required by the user. To keep the pressures constant, a volume of water flows in or out of the pump. This change in volume is monitored and allows for volumetric strain measurements on the specimen. The force applied to the specimen from the load piston is monitors using an S-type load cell. An LVDT measures displacements of the specimen in the vertical direction. The load cell and LVDT can be seen in Figure WW on the top of the GEOCOMP Load frame. Drainage of the specimen is allowed through the top and bottom pore stones. The GEOCOMP FLOWTRACK II flow pumps are shown in Figure 7.

33

Figure 7 - GEOCOMP FLOWTRACK II Flow Pumps

Procedures No ASTM test method exists for the consolidated drained triaxial test of a soil. ASTM standards D4746 and D2850 are test standards for undrained tests. A working standard is being developed and is designated as standard WK3821. The standard D4746 was followed as closely as possible for specimen preparation. Care was taken to minimize any sample disturbance during specimen preparation. For details on careful sampling and specimen preparation of Bonneville clays, see Bay et.al (2003). Each specimen was extruded from the Shelby tube after the tube had been trimmed to length using an electric ban saw. The Ccut Shelby tube ready for extraction of specimen is shown in Figure 8. 34

Figure 8 - Cut Shelby tube ready for specimen extraction

Specimens were extruded slowly from the Shelby tube, using a nearly constant rate. The specimens tested in the triaxial device were trimmed to 120 mm to 150 mm in length to meet a height to diameter ratio of 2 to 2.5. Each specimen was weighed, measured, and a moisture sample was taken from the cuttings to aid in the data reduction. After the specimen was measured, it was placed on the triaxial device base cap, with its saturated pore stone and filter paper. One or two latex membranes were place gently over the specimen to separate the specimen from the cell water. A top cap, and its pore stone and filter paper, was place on the top of each specimen. The triaxial cell was then assembled, filled with distilled water, and placed in the loading frame. Figures 9 to 11 show the assemblage of the triaxial cell. Figure 9 shows the base of the triaxial cell. Connections for flow lines are mounted on the bottom of the cell. The plastic bottom cap is also shown.

35

Plastic Bottom Cap for Specimen

Connections for flow lines to the flow pumps.

Figure 9 - Bottom of triaxial cell

36

Internal Flow Lines to allow top and bottom drainage of the specimen O-rings to isolate specimen and cell Clay Specimen in latex membranes

Figure 10 - Assembled triaxial cell

After the cell is assembled (Figure 10), it is placed on the load frame as shown in Figure 3. All flow lines were purged of air, connected to the triaxial cell, and the cell was lifted into place. The instrumentation was zeroed out and a very small vertical load was applied to seat the load piston. Flow lines are then attached as shown in Figure 11.

37

Specimen Bleed-off

Connection to the cell

Connection to the Specimen

Figure 11 - Flow Line Connections

To begin the triaxial test, an initialization stage was first undergone. The initialization phase consists of application of a nearly equal vertical stress, horizontal stress, and pore pressure to the specimen to check for leaks and compliance issues before the test proceeded. After the initialization pressure was held for a short time, the saturation phase was begun. All specimens were backpressure saturated to a Skempton’s porewater pressure B value greater than 0.95 (Holtz and Kovacs, 1981( (Skempton, 19XX). The GEOCOMP system automatically measures the pore pressure changes during the saturation phase and calculates the Skempton B parameter continuously. Pore pressures for the backpressure saturation ranged from 200kPa to 500kPa depending on the specimen, its hydraulic conductivity, and the initial level of saturation. Air in the system goes into solution at around 200kPa (Black and Lee, 1973).

38

After the specimen has reached a B value greater than 0.95 (which does not guarantee full saturation), a phase of consolidation is undertaken. The cell and vertical stresses are increased incrementally, while keeping the pore pressure constant to achieve an effective stress condition chosen for consolidation. Consolidation can be either isotropic or to an anisotropic Ko condition. Isotropic consolidation is always recommended in the literature for drained tests. Isotropic or Ko consolidation can be used for undrained test. This consolidation phase lasts until at least 95% consolidation has been achieved using the square root of time method. The GEOCOMP system monitors this automatically. After the specimen has consolidated, the test is paused for a short time to age the specimen at the stress level. This aging is recommended by several researchers (Bay et.al, 2005), especially for consolidation pressures that exceed the in-situ field conditions the specimen was taken from conditions for the specimen. Once the aging is complete, the specimen is then sheared. The shearing phase of the triaxial test is done either drained or undrained. Undrained tests a conducted at higher strain rates, with no drainage of the specimen allowed. Drained tests are conducted at slow strain rates based on the consolidation properties of the specimen. The slow strain rates allow for drainage. Several authors have noted that despite being drained, increasingly slow strain rates of loading lead to higher strengths in triaxial testing (Reference, 19MM). Strain rates were determined using the method recommended by Bishop and Henkel (1962) and Gibson and Henkel (1954) which is based on the coefficient of consolidation of the soil (Cv or t90). The GEOCOMP software monitors the force, displacement, stresses, and strains continuously thought the shear phase of the test. The specimen is sheared from 20% to 30% axial strain to assure that the critical state has been reached before end of shear. After the shear phase is completed, the specimen is removed from the triaxial cell and a final moisture specimen is obtained.

39

Data Reduction Data from a triaxial test is used to calculate the parameters for the HNLE model as was discussed in previous sections of this report. As with any test on real materials, the data does not plot to a perfect hyperbola, or transformed line when normalized by strain. Also, on some occasions the load rod was not initially placed snug into the load cap, and some displacement of the platform occurred as the load rod seated completely in the load cap before any load was applied to the specimen. This extra displacement had to be removed from several of the data files. This seating displacement problem was recognized by Duncan et.al (1980) in their formulation of the HNLE model from triaxial test data. They recommend the adjustments made to the test data to remove it from the data file and recalculate the strains from the adjusted displacements. In addition to the seating issue of the load rod and top cap, there are small strain nonlinearities of the stress-:strain relationship in clay soils that make an estimation of Initial tTangent mModulus (Eit) difficult by a visual or extrapolation method from triaxial test data (Santaga, Ladd and Germaine, 2007). For this reason the HNLE model uses a fit at 70% and 95% (of the peak stress) of the stress-:strain data to estimate Eit. If the 70% stress-level fit needs to be verified, plotting the strain divided by stress against stress, as shown in Ffigure 1, the intercept of the transformed stress-:strain curve is the inverse of the initial tangent modulus. For complete details on the reduction of the triaxial test data for the HNLE model, see Duncan et.al (1980).

Triaxial Test Results A summary of triaxial tests is found in Table 1RR. A summary of the results to the triaxial tests is found in Table 2RS. Stress-:sStrain plots for each test are shown in the appendix. HNLE model parameters were calculated as shown previously in this report. Included in the summary of results is the drained friction angle of the soil assuming zero cohesion and a linear Mohr-Coulomb failure envelope. It should be noted that the confining consolidation pressure for the tests vary in order to calculate the HNLE stress range. Tests were performed at various confining stresses, which included: (1) in-situ confining

40

stress, (2) the pPreconsolidation stress times Ko, (3) the horizontal stress from a 15-m high embankment, and (4) at 500 kPa for each layer.

41

Table 1- Consolidated Drained Triaxial Test Summary Site

Boring

Depth

Elevation

Layer

σ 'ff

σ '3

σ '3/Pa

σ 'df

σ '50

σ '70

φ'c=0

εaf

ε50

ε70

ST ST ST ST ST ST NT NT ST ST NT NT NT ST ST NT NT ST NT ST ST ST ST ST ST

B4 B3 B3 B4 B3 B3 B2 B1 B4 B3 B2 B1 B2 B3 B4 B1 B1 B3 B1 B4 B4 B3 B3 B3 B3

6.25 7.10 7.32 7.98 8.69 8.70 10.20 11.00 11.07 11.56 13.30 14.00 14.80 13.80 13.95 15.46 15.48 16.00 17.22 16.84 17.00 17.50 17.68 18.53 19.11

1282.07 1281.22 1281.01 1280.34 1279.63 1279.62 1279.31 1278.51 1277.25 1276.76 1276.21 1275.51 1274.71 1274.52 1274.37 1274.05 1274.03 1272.32 1272.29 1271.48 1271.32 1270.82 1270.65 1269.79 1269.21

Upper Bonn Upper Bonn Upper Bonn Upper Bonn Upper Bonn Upper Bonn Upper Bonn Upper Bonn Interbeds Interbeds Interbeds Interbeds Interbeds Interbeds Interbeds Interbeds Interbeds Lower Bonn Lower Bonn Lower Bonn Lower Bonn Lower Bonn Lower Bonn Lower Bonn Lower Bonn

200.6 201.6 1334.0 381.7 635.0 512.0 268.0 154.0 175.0 1618.0 533.3 248.0 659.3 235.0 315.6 1429.0 210.0 222.0 647.0 220.0 334.0 247.0 289.0 1233.0 264.0

60.5 45.0 450.0 125.0 240.0 165.0 98.0 60.0 55.0 450.0 125.0 80.0 220.0 70.0 73.0 500.0 80.0 110.0 240.0 95.5 113.0 136.7 89.0 500.0 100.0

0.6 0.5 4.5 1.3 2.4 1.7 1.0 0.6 0.6 4.5 1.3 0.8 2.2 0.7 0.7 5.0 0.8 1.1 2.4 1.0 1.1 1.4 0.9 5.0 1.0

140.1 155.5 884.0 256.7 395.0 347.0 170.0 94.0 120.0 1168.0 410.0 168.0 439.3 165.0 242.6 929.0 128.5 112.0 407.0 124.5 221.0 110.3 186.0 733.0 164.0

70.1 77.8 442.0 128.4 197.5 268.5 85.0 47.0 60.0 584.0 205.0 84.0 219.7 82.5 121.3 464.5 64.3 56.0 203.5 62.3 110.5 55.2 93.0 366.5 82.0

98.1 108.9 618.8 179.7 276.5 300.0 119.0 65.8 84.0 817.6 287.0 117.6 307.5 115.5 169.8 650.3 90.0 78.4 285.0 87.2 154.7 77.2 130.2 513.1 114.8

32.5 39.1 29.7 30.4 26.8 30.8 27.7 26.1 31.4 34.4 38.5 30.8 30.0 32.8 38.6 28.8 26.3 19.7 27.3 23.2 29.6 16.7 29.5 25.0 26.8

19.0 10.0 17.5 18.5 20.0 12.5 14.0 12.0 8.0 12.0 16.0 11.5 19.0 16.0 12.0 16.0 7.7 14.8 20.0 22.0 16.0 18.0 6.0 18.0 15.0

3.5 1.6 2.1 4.0 4.8 2.0 3.5 2.5 2.5 2.8 2.4 1.6 5.0 3.3 3.5 2.5 1.5 3.3 4.5 5.5 5.0 1.9 1.8 4.7 4.0

7.3 3.5 4.8 6.5 8.8 5.3 6.2 4.6 3.5 4.7 3.8 2.8 8.0 5.5 5.5 6.0 2.5 7.4 8.5 8.0 7.5 5.4 3.0 7.5 6.7

42

Table 2 - Consolidated Drained Triaxial Test Results

43

From Table 1, it can be seen that the drained friction angle increases in the Iinterbedss that are found overlying the predominantly clay layers. The upper Bonneville sediments tends to have higher friction angles than the lower Bonneville clays. The data from Tables 1 and 2 were plotted on log-log scales to determine the appropriate HNLE parameters. Figures 12 to 14 show the iInitial tTangent mModulius plots for the three primary Bonneville claysediment layers.

Figure 12 - Initial Tangent Modulus Plot for Upper Bonneville Clays

44

Figure 13 - Initial Tangent Modulus Plot for the Interbeds

Figure 14 - Initial Tangent Modulus Plot for the Lower Bonneville Clays

45

In the regression equations shown in Figuresplots 12 to 14, the y value is the Iinitial tTangent mModulus from the triaxial test reduction normalized to the reference pressure. The x value is the confining stress normalized to the reference pressure. There is some scatter in the data due to the variability of the clay deposits and sites. The bBulk mModulus plots are shown in Ffigures 15 to 17.

Figure 15 - Bulk Modulus plot for the Upper Bonneville Clays

Figure 16 - Bulk Modulus Plot for the Interbeds

46

Figure 17 - Bulk Modulus Plot for the Lower Bonneville Clays

In these figuresFrom figures 15 to 17, there is more scatter in the lower Bonneville clays than the other layers considered in the triaxial testing. This may be due in part to the definition of the The bBulk mModulus as given in the is also more arbitrary in the HNLE guidelines from Duncan et.al (1980). The use of the 70% stress level bulk modulus may introduce have more variability than the functional form used to define the initial tangent modulus. For the unloading and reloading modulus, only three tests were conducted, and it was found that the ratio of K to K ur is approximately 2.4 for the three primary layers of the Lake Bonneville deposits.

Back Calculation from Embankment Settlements Settlement data has been collected using settlement points, horizontal inclinometers, and magnet extensometers along the I-15 rreconstruction alignment since construction began in 1998. This data is presented and interpreted detailed in several publications and

47

reports available from UDOT. This report relies on the settlement profile measured at 200 South Street in Salt Lake City. Flint and Bartlett (2005) have used the settlement data to back calculate HNLE model parameters for the Bonneville clays at 200 South and I-15 and the Lime-Cement treated site at I-80 and I-15. In this report, tThey back calculated the drained HNLE parameters using soil layering properties and geophysical measurements only. No triaxial laboratory testing was available for their evaluation. The FEA program Sigma/W was used to model the surface settlement resulting from the determine the various soil properties from tfoundation layers and calibrated to that settlementhe settlement data. The sequencingstaging of the embankment construction was included in the analysis Figure . Figure 18 shows the embankment geometry and stagingsequencing used in the evaluationsanalysis by Flint and Bartlett (2005).

Figure 18 - 200 South Embankment - From Flint and Bartlett (2005)

The measured settlement dataprofile at the end of primary consolidation was plotted for the 200 South Street Array and compared to thesettlement estimates made with linear elastic (LE) Limit Equilibrium mmethods and consolidation properties developed for the during design of the I-15 Rreconstruction Project. These soil data and constructiondesign estimates appear in the following tables and figures, as well as the results of their calibrationback-calculation of HNLE parameters by Flint and Bartlett (2005). Figure 19 48

also shows Notice that only the Sigma/W analysis of Flint and Bartlett (2005), which included the calibrated calibrated HNLE model parameters. This Sigma/W analysis with the HNLE model provided the best matched to the actualmeasured settlement dataprofile. from the Sigma/W analysis. Table 3 shows the typical HNLE soils properties from the Duncan et.al (1980) library that Flint and Bartlett (2005) used to begin their FEA. The soil profile was divided into 6 layers, as was done in this report for the North and South Temple Street sites along I-15.

Table 3 - Typical HNLE Properties for 200S from Flint and Bartlett (2005)

Layer

K

Kb

Kur

m

n

Rf

Upper Alluvium

100

50

200

0.60

0.5

0.7

Upper Bonneville

60

50

120

0.45

0.2

0.7

Interbeds

150

75

300

0.60

0.5

0.7

Lower Bonneville

90

80

180

0.45

0.2

0.7

Deeper Alluvium

300

250

600

0.25

0.0

0.7

Cutler Dam

120

110

240

0.45

0.2

0.7

After a series of iterations, Flint and Bartlett developed calibrated model properties that are shown in Table 4. Note that the failure ratio is the same for each soil. This is because the settlement data did not need strength parameters to do the calculations, which the failure ratio is dependant on. Figure 19 shows the results of the analysis re-run using the calibrated soil parameters.

Table 4 - Calibrated HNLE Properties from Flint and Bartlett (2005)

49

Layer

K

Kb

Kur

m

n

Rf

Upper Alluvium

60

40

240

0.60

0.5

0.7

Upper Bonneville

30

20

120

0.45

0.2

0.7

Interbeds

50

40

220

0.60

0.5

0.7

Lower Bonneville

50

40

190

0.45

0.2

0.7

Deeper Alluvium

110

120

430

0.25

0.0

0.7

Cutler Dam

70

50

300

0.45

0.2

0.7

50

Figure 19 - 200 South Settlement Data and Estimates - After Flint and Bartlett (2005)

51

The HNLE model parameters developed directly from the triaxial testing done as part of this report can be input into the Sigma/W models constructed by Flint and Bartlett to show how well the laboratory testing represents the real worldmeasured field behavior of the soils. The summary of the HNLE parameters to be inputted into the Flint and Bartlett Sigma/W model is found in Table 5. These revised values were used to re-run the settlement analysis of the staged embankment at 200 South and compared with the measured settlement profile..

Table 5 - Laboratory Triaxial HNLE Properties Layer

K

Kur

Kb

m

n

Rf

Upper Bonneville

50

120

24

0.77

0.57

0.70

Interbeds

75

180

23

0.78

0.78

0.70

Lower Bonneville

39

100

29

0.77

0.35

0.70

Table 6 shows a comparison of the HNLE parameters developed by this report and those used by from Flint and Bartlett (2005). The results from of this report are presented in the first column for each parameter. The results from Flint and Bartlett (2005) are shown second column for comparison. For plots of the triaxial test data regression, see the appendix of this document. Table 6 - Comparison of Triaxial and Back Calculated Parameters

K

Kb

m

n

Rf

Upper Alluvium

50

60

30

40

0.6

0.60

0.57

0.5

0.7

0.7

Upper Bonneville

50

30

24

20

0.77

0.45

0.57

0.2

0.7

0.7

Interbeds Lower Bonneville Deeper Alluvium

75

50

23

40

0.78

0.60

0.78

0.5

0.7

0.7

39

50

29

40

0.77

0.45

0.35

0.2

0.7

0.7

NA

110

NA

120

NA

0.25

NA

0.0

NA

0.7

Cutler Dam

NA

70

NA

50

NA

0.45

NA

0.2

NA

0.7

52

The information in Table 6, was input into the finite element computer program SIGMA/W for analysis of the embankments. The embankment loading was modeled sequentially to simulate construction loading of the Bonneville deposits. The first analysises have several phases, each phase divided into embankment construction steps. Figure 18 demonstrates the phases and geometry. The analysis begins with an elastic analysis with no embankment to determine the in-situ stress state. The analysis then continues with the loading from the original 1960’s I-15 embankment. The first phase of I-15 reconstruction at 200 South is next, noted as “Phase I”. Finally, the second phase of I-15 reconstruction is modeled. This modeling progression is done for each set of HNLE model parameters. Figure 20, shows the comparison of the HNLE model parameter results for the original I15 embankment at 200 South prior to the I-15 reconstruction. In Figures 20 through 22, the “matched” settlement profile is from Flint and Bartlett (2005). The “lab” settlement profile is the results from this report using the laboratory determined values for the HNLE model. It can be seen that the two analyses match quite well. From Figure 20, the two analyses match well. Figure 21 shows the comparison of the HNLE model parameters results for the Phase I I-15 reconstruction at 200 South Street. Once again, From Figure 21, the two analyses match well.

53

Figure 20 - Existing I-15 Embankment Analysis Comparison

54

Figure 21 - Phase I of Reconstruction Analysis Comparison

55

From Figure 21, it can be seen that the laboratory triaxial HNLE parameters provide a good estimate of the measured field settlements at the 200 South Street array. In addition, observed. Thethe HNLE results from this report compare well with to the calibrated parametersthe modeling developed by Flint and Bartlett (2005). However, except that the maximum settlement at the toe of the embankment is slightly less for the analysis performed in this report using run with the laboratory-determined HNLE hyperbolic model parameters. This latter e lab parameter analysis was reanalyzedre-run with the HNLE parameters for the Upper Alluvium altered to better agree align with the HNLE parameters found for the underlying layers. The assumption is that some parameters, such as K and m, will be different than those for the Bonneville deposits, but not significantly differentso. This result is shown as the “parametric” profile in Figure 22. Table 6 includes the parameters for the Upper Alluvium used in the re-analysis. Figure 22 shows that altering the HNLE model parameters, from those found in the calibration done by Flint and Bartlett to those that align with the laboratory testing, the surface settlements match the observed settlements much closer. Finally, the results of the HNLE model analysis from laboratory triaxial testing can be compared to the actual measured surface settlement data for the 200 South site for the I15 reconstruction. Figure 23 shows a plot of the measured surface settlements (black line) compared to the HNLE analysis results for this report (red line).

56

Figure 22 - I-15 Reconstruction Phase II Analysis Comparison

57

Figure 23 - Comparison of Measured Data and HNLE Models

58

Conclusions Laboratory triaxial testing of carefully sampled specimens of Bonneville clay from the locations of the I-15 bridges over North and South Temple Streets in Salt Lake City were conducted to determine appropriate Duncan et al. (1980). Hypberbolic mModel parameters for estimating settlements from new embankment and MSE wall construction. The laboratory test data was used to develop the parameters, and finite element modeling of the 200 South Street case history from the I-15 Reconstruction settlement monitoring was done. This finite element modeling showed that the use of laboratory determined HNLE model parameters reasonably matched the observed settlements at the 200 South Street array..

59

Acknowledgements The authors of this report wish to express thanks to the following individuals: Clifton Farnsworth for his I-15 settlement data and . Kleinfelder Inc. for use of their constant humidity room to store Shelby tubes of clay samples.

60

References Bartlett, S., and Farnsworth, C. (2004). “Monitoring and modeling of innovative foundation treatment and embankment construction used on the I-15 Reconstruction Project, Project Management Plan and Instrument Installation Report,” Report No. UT04.19, Utah Department of Transportation Research Division, Salt Lake City, Utah. Bartlett, S.F., Farnsworth, C., Negussey, D., and Stuedlein, A.W. (2001), “Instrumentation and Long-Term Monitoring of Geofoam Embankments, I-15 Reconstruction Project, Salt Lake City, Utah.” Proceedings of the 3rd International EPS Geofoam Conference, December 2001, Salt Lake City, Utah. Bay, J.A., Anderson, L.R., Colocino, T.M., and Budge, A.S. (2005), “Evaluation of SHANSEP Parameters for Soft Bonneville Clays,” Utah Department of Transportation, Salt Lake City, Utah, Report No. UT-03.13. Utah State University Department of Civil and Environmental Engineering. Bay, J. A., L. R. Anderson, J. C. Hagen, and A. S. Budge. (2003). “Factors affecting sample disturbance in Bonneville clays”. Report No. UT-03.14, Utah Department of Transportation, Salt Lake City, Utah. Bishop, A.W., and Henkel, D.J (1957). The measurement of soil properties in the triaxial tests. Edward Arnold Ltd., London, England. Bishop, A.W., and Henkel, D.J (1962). The measurement of soil properties in the triaxial tests. Edward Arnold Ltd., London, England.

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Black, D.K., and Lee, K.L. (1973), “Saturating laboratory samples by back pressure”. J. of Geotech. Engrg. Div., ASCE, 99(1), 75-93. Clough, G.W., and Duncan, J.M. (1971). “Finite element analysis of retaining wall behavior.” Journal of Soil Mechanics and Foundations Division, ASCE., 97(12), 16571673. Duncan, J.M., and Chang, C.Y. (1970), “Non-linear analysis of stress and strain in soils”. J. of Geotech. Engrg. Div., ASCE, 96(5), 1629-1953. Duncan, J.M, and Wong, K.S. (1974), “Hyperbolic Stress-Strain Parameters for NonLinear Finite Element Analysis of Stresses and Movements in Soil Masses”. Report TE74-3 National Science Foundation, University of California, Berkeley. Duncan, J.M., Bryne P., Wong K.S., and Chang, C.Y. (1980), “Strength, stress-strain, and bulk modulus parameters for finite element analysis of soils”. Report UCB/GT/80-02, University of California, Berkeley. Duncan, J.M., and Mokwa, R.L. (2001). “Passive earth pressures: theories and tests.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, (127)-3, 248-257. Farnsworth, C. (2008). Geo-Slope. (2004). SIGMA/W version 5 user’s guide. Geo-Slope International Ltd., Calgary, Canada. Gerber, T. M. (1995). “Seismic ground response at two bridge sites on soft-deep soils along Interstate 15 in the Salt Lake Valley, Utah,” Masters thesis, Dept. of Civil and Envir. Engrg., Brigham Young University, Provo, Utah.

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Gibson, R.E., and Henkel, D.J. (1954), “Influence of duration of tests at constant rate of strain on measured drained strength”. Geotechnique., London, England, 4(1), 6-15. Holtz, R. D., and Kovacs, W. D. (1981). An Introduction to Geotechnical Engineering, Prentice-Hall, Inc. Englewood Cliffs, New Jersey. Itasca (2005). FLAC version 5.0 user’s guide. Itasca Consulting Group Inc, Minneapolis Minnesota. Kondner, R. L. (1963). “Hyperbolic stress-strain response: Cohesive soils.” J. Soil Mech. and Found. Div., (98-1), 115–143. Ozer, A.T., and Bartlett, S.F. (2004). “Estimation of Consolidation Proerties from In-Situ and Laboratory Testing”. Report No. Ut-03. Utah Department of Transportation, Salt Lake City, Utah. Santaga, M., Germaine, J.T., Ladd, C.C. (2007). “Small-strain nonlinearity of normally consolidated clay.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE. (??)-?, 72-82. Santaga, M., Germaine, J.T. (2002). “Sampling disturbance effects in normally consolidated clays.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE. (??)-?,997-1006. Skempton, A.W. (1954), “The pore pressure coefficients A and B”. Geotechnique., London, England, 4(3), 143-147. Skempton, A.W., and Bjerrum, L. (1957), “A contribution to the settlement analysis of clays”. Geotechnique., London, England, 7(4), 168-178.

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Wood, D.M. (1990). Soil Behavior and Critical State Soil Mechanics. Cambridge University Press, Cambridge, UK.

Appendix

64

Figure 24 - General Trend of all Initial Tangent Modulus Data

65

Figure 25 - General Trend of all Bulk Modulus Data

66

Figure 26 - Comparison of Triaxial Test data to Calibrated HNLE values

67

Figure 27 - Comparison of Triaxial Test Results to Calibrated HNLE

68

North Temple Tip Resistance

North Temple Sleeve Friction

5000

10000

15000

20000

0

25000

100

CPTu - 1

1286

SC - 32

Fr 600

800

0

1284 SC - 35

SC - 35

1288

RC -12

SC - 32

1286

SC - 34

SC - 34 1284

1290

SC - 33

SC - 33

SC - 34

400

SC - 31

SC - 31 1286

SC - 33

1284

SC - 35

1282

1282

1280

1280

1280

1280

1278

1276

1278

1276

1278

1276

E le v a tio n(m )

1282

E le v a tio n(m )

1282

E le v a tio n(m )

E le v a tio n(m )

1288

RC -12

SC - 32

200

CPTu - 1

CPTu - 1

1288

SC - 31

1284

0

200 1290

RC -12

1286

150

1290

1290

1288

50

North Temple Normalized

Uexcess (kPa)

fs (kPa)

qt (kPa) 0

North Temple Pore Pressures

1278

1276

1274

1274

1274

1274

1272

1272

1272

1272

1270

1270

1270

1270

1268

1268

1268

1268

1266

1266

1266

1266

1264

1264

1264

1264

Figure 28 - North Temple CPT Data

69

3

6

SouthTemple Sleeve Friction

5000

10000

15000

20000

0

25000

1286.00

1284.00

100

CPTu - 2 SC - 128

SC - 128

SC - 130

SC - 130

SC - 139

SC - 139

SC - 140

SC - 140 1284.00

400

600

800

0 1290.00

1288.00

SC - 128 SC - 130

1286.00

SC - 131

1286.00

SC - 139 SC - 140 1284.00

SC - 143

1284.00

SC - 143

1282.00

E l e v a t i o n ( m )

1282.00

E l e v a t i o n ( m )

E l e v a t i o n ( m )

1276.00

1288.00

SC - 131

1286.00

SC - 131

200

CPTu - 2

CPTu - 2

1288.00

1282.00

1278.00

0

200 1290.00

SC - 143

1280.00

150

1290.00

1290.00

1288.00

50

South Temple Norma

Uexcess (kPa)

fs (kPa)

qt (kPa) 0

South Temple Pore Pressures

1280.00

1278.00

1276.00

1280.00

1278.00

1276.00

1282.00

E l e v a t i o n ( m )

South Temple Tip Resistance

1280.00

1278.00

1276.00

1274.00

1274.00

1274.00

1274.00

1272.00

1272.00

1272.00

1272.00

1270.00

1270.00

1270.00

1270.00

1268.00

1268.00

1268.00

1268.00

1266.00

1266.00

1266.00

1266.00

1264.00

1264.00

1264.00

1264.00

70

3

6

Figure 29 - South Temple CPT Data

Figure 30 - Stress:Strain Plot for B1 -14.00

71

Figure 31 - Stress:Strain Plot for B1 15.46

72

Figure 32 - Stress:Strain Plot for B1 15.48

73

Figure 33 - Stress;Strain Plot for B1 17.22

74

Figure 34 - Stress:Strain Plot for B2 10.2

75

Figure 35 - Stress:Strain Plot for B2 13.3

76

Figure 36 - Stress:Strain Plot for B2 14.8

77

Figure 37 - Stress:Strain Plot for B3 7.1

78

Figure 38 - Stress:Strain Plot for B3 7.315

79

Figure 39 - Stress:Strain Plot for B3 8.7

80

Figure 40 - Stress:Strain Plot for B3 8.69

81

Figure 41 - Stress:Strain plot for B3 11.56

82

Figure 42 - Stress:Strain Plot for B3 16.00

83

Figure 43 - Stress:Strain Plot for B3 17.260

84

Figure 44 - Stress:Strain Plot for B3 17.68

85

Figure 45 - Stress:Strain Plot for B3 18.532

86

Figure 46 - Stress:Strain Plot for B3 19.11

87

Figure 47 - Stress:Strain Plot for B4 6.25

88

Figure 48 - Stress:Strain Plot for B3 7.98

89

Figure 49 - Stress:Strain Plot for B4 11.07

90

Figure 50 - Stress:Strain Plot for B4 13.945

91

Figure 51 - Stress:Strain Plot for B6 16.84

92

Figure 52 - Stress:Strain Plot for B4 17.00

93

Figure 53 - SIGMA/W In-Situ Stress Analysis

94

Figure 54 - SIGMA/W Existing Embankment Analysis

95

Figure 55 - SIGMA/W Phase I Analysis

96

97

Figure 56 - SIGMA/W Phase II Anlysis

98