Passive Earth Pressures: Design Parameters for Common Force ...

Passive Earth Pressures: Design Parameters for Common

Force-Displacement Approaches

Reynold David Meyer II

A project submitted to the faculty of Brigham Young University

in partial fulfillment of the requirements for the degree of

Master of Science

Kyle M. Rollins, Chair Norman L. Jones

Fernando S. Fonseca

Department of Civil & Environmental Engineering

Brigham Young University

April 2012

Copyright © 2012 Reynold David Meyer II

All Rights Reserved

ABSTRACT

Passive Earth Pressures: Design Parameters for Common

Force-Displacement Approaches

Reynold David Meyer II

Department of Civil & Environmental Engineering, BYU

Master of Science

Prior large scale lateral load testing was performed on pile caps with varying geometries

and backfill configurations. The testing simulated the lateral response of backfill against bridge abutments. The backfill soil included clean sand, silty sand, fine gravel, and coarse gravel. In this report, the backfills were considered either loose or dense depending on their relative densities. Several of the tests were performed using wingwalls in an effort to assess the contribution of plane strain effects. The purpose of this testing was to determine the lateral passive resistance of several types of backfills against bridge abutments.

The purpose of this project was to first collect and tabulate the data from previous studies

and then to compare the results. The measured force-displacement relationships for each backfill were then compared with common force-displacement approaches. The common force-displacement methods used were: PYCAP, ABUTMENT, and Shamsabadi’s general hyperbolic force-displacement relationship. The analytical models were fit with the measured data and appropriate design parameters were back-calculated. The design parameters can be used to model the force-displacement relationship and to determine the total lateral passive resistance of various backfills against bridge abutments.

Keywords: passive resistance, ABUTMENT, PYCAP, backfill

v

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................................................... ix

LIST OF FIGURES ................................................................................................................... xiii

1 Introduction ........................................................................................................................... 1

1.1 Objectives ....................................................................................................................... 2

2 Literature Review ................................................................................................................. 3

2.1.1 Caltrans Seismic Design Approach............................................................................. 3

2.1.2 PYCAP ........................................................................................................................ 5

2.1.3 ABUTMENT .............................................................................................................. 8

2.1.4 Closed-Form Modified Hyperbolic Force-Displacement (HFD) Equation .............. 10

3 Testing .................................................................................................................................. 13

3.1 Rollins & Cole (2006) ................................................................................................... 13

3.2 Kwon (2007) ................................................................................................................. 15

3.3 Valentine (2007) ........................................................................................................... 16

3.4 Pruett (2009) ................................................................................................................. 16

3.5 Cummins (2009) ........................................................................................................... 18

3.6 Nasr (2010) ................................................................................................................... 19

3.7 Heiner (2010) ................................................................................................................ 19

3.8 Strassburg (2010) .......................................................................................................... 20

3.9 Bingham (2012) ............................................................................................................ 21

3.10 Jessee (2012) ................................................................................................................. 22

3.11 UCLA (Stewart et al., 2007) ......................................................................................... 23

4 Results .................................................................................................................................. 25

4.1 Loose Clean Sand (2D) ................................................................................................. 25

vi

4.2 Loose Clean Sand (3D) .................................................................................................27

4.3 Dense Clean Sand (2D) .................................................................................................30

4.4 Dense Clean Sand (3D) .................................................................................................34

4.5 Loose Silty Sand (3D) ...................................................................................................37

4.6 Dense Silty Sand (2D) ...................................................................................................39

4.7 Dense Silty Sand (3D) ...................................................................................................42

4.8 Loose Fine Gravel (3D) .................................................................................................45

4.9 Dense Fine Gravel (3D) ................................................................................................47

4.10 Loose Coarse Gravel (3D) .............................................................................................50

4.11 Dense Coarse Gravel (3D) ............................................................................................52

5 Comparison of Results .........................................................................................................55

5.1 Friction Angle, φ ...........................................................................................................55

5.2 Cohesion ........................................................................................................................65

5.3 Initial Soil Modulus, Ei .................................................................................................70

5.4 Strain at 50% of Ultimate Strength, ε50 .........................................................................77

5.5 Modified HFD: Fult/Beff ................................................................................................81

5.6 Modified HFD: yave .......................................................................................................84

5.7 Passive Earth Pressure Coefficient, Kp .........................................................................87

5.8 Caltrans ..........................................................................................................................96

6 Conclusion ...........................................................................................................................103

6.1 Conclusions .................................................................................................................103

6.1.1 Friction Angle ............................................................................................................104

6.1.2 Cohesion ................................................................................................................104

6.1.3 Initial Soil Modulus ...................................................................................................105

6.1.4 Strain at 50% of Ultimate Strength, ε50 .....................................................................106

vii

6.1.5 Modified HFD: Fult/Beff .......................................................................................... 106

6.1.6 Modified HFD: yave................................................................................................. 107

6.1.7 Passive Earth Pressure Coefficients ........................................................................ 107

6.1.8 Caltrans ................................................................................................................... 108

6.2 Recommendations for Future Research ...................................................................... 108

References .................................................................................................................................. 109

ix

LIST OF TABLES

Table 2.1: Stiffness Ranges for Various Soil Densities (Duncan and Mokwa, 2001) .....................8

Table 2.2: Typical Adhesion Factors (NAVFAC, 1982) .................................................................8

Table 2.3: Ranges of ε50 for Various Soil Types (Shamsabadi et al., 2007) .................................10

Table 2.4: Suggested HFD Parameters for Abutment Backfills (Shamsabadi et al., 2007) ..........12

Table 3.1: Summary of Backfill Soil Parameters (Rollins and Cole, 2006) ..................................14

Table 3.2: Unit Weights and Shear Strength Parameters for Backfill Materials (Rollins and Cole, 2006) ..................................................................................................................14

Table 3.3: Summary of Backfill Soil Parameters (Kwon, 2007) ...................................................15

Table 3.4: Gradation Properties of the Fine Gravel (Pruett, 2009) ................................................17

Table 3.5: Results of Direct Shear Testing for Fine Gravel (Pruett, 2009) ...................................17

Table 3.6: Gradation Properties for the Coarse Gravel (Pruett, 2009) ..........................................18

Table 3.7: Results of Direct Shear Testing for Coarse Gravel (Pruett, 2009) ...............................18

Table 3.8: Direct Shear Results for Loose Clean Sand (Cummins, 2009) ....................................19

Table 3.9: Gradation Parameters for Loose Well-Graded Sand (Strassburg, 2010) ......................21

Table 3.10: Soil Properties for Dense Clean Sand (Jessee, 2012) .................................................23

Table 4.1: PYCAP Parameters for Loose Clean Sand (2D) ..........................................................26

Table 4.2: ABUTMENT Parameters for Loose Clean Sand (2D) .................................................27

Table 4.3: Modified HFD parameters for Loose Clean Sand (2D) ................................................27

Table 4.4: PYCAP Parameters for Loose Clean Sand (3D) ..........................................................29

Table 4.5: ABUTMENT Parameters for Loose Clean Sand (3D) .................................................29

Table 4.6: Modified HFD Parameters for Loose Clean Sand (3D) ...............................................29

Table 4.7: PYCAP Parameters for Dense Clean Sand (2D) ..........................................................33

Table 4.8: ABUTMENT Parameters for Dense Clean Sand (2D) .................................................33

Table 4.9: Modified HFD Parameters for Dense Clean Sand (2D) ...............................................34

x

Table 4.10: PYCAP Parameters for Dense Clean Sand (3D) ........................................................36

Table 4.11: ABUTMENT Parameters for Dense Clean Sand (3D) ...............................................36

Table 4.12: Modified HFD Parameters for Dense Clean Sand (3D) .............................................37

Table 4.13: PYCAP Parameters for Loose Silty Sand (3D) ..........................................................38

Table 4.14: ABUTMENT Parameters for Loose Silty Sand (3D) .................................................38

Table 4.15: Modified HFD Parameters for Loose Silty Sand (3D) ...............................................39

Table 4.16: PYCAP Parameters for Dense Silty Sand (2D) ..........................................................41

Table 4.17: ABUTMENT Parameters for Dense Silty Sand (2D).................................................41

Table 4.18: Modified HFD Parameters for Dense Silty Sand (2D) ...............................................42

Table 4.19: PYCAP Parameters for Dense Silty Sand (3D) ..........................................................44

Table 4.20: ABUTMENT Parameters for Dense Silty Sand (3D).................................................44

Table 4.21: Modified HFD Parameters for Dense Silty Sand (3D) ...............................................45

Table 4.22: PYCAP Parameters for Loose Fine Gravel (3D) ........................................................46

Table 4.23: ABUTMENT Parameters for Loose Fine Gravel (3D) ..............................................46

Table 4.24: Modified HFD Parameters for Loose Fine Gravel (3D) .............................................47

Table 4.25: PYCAP Parameters for Dense Fine Gravel (3D) .......................................................49

Table 4.26: ABUTMENT Parameters for Dense Fine Gravel (3D) ..............................................49

Table 4.27: Modified HFD Parameters for Dense Fine Gravel (3D) ............................................50

Table 4.28: PYCAP Parameters for Loose Coarse Gravel (3D) ....................................................51

Table 4.29: ABUTMENT Parameters for Loose Coarse Gravel (3D) ..........................................51

Table 4.30: Modified HFD Parameters for Loose Coarse Gravel (3D) .........................................52

Table 4.31: PYCAP Parameters for Dense Coarse Gravel (3D) ...................................................54

Table 4.32: ABUTMENT Parameters for Dense Coarse Gravel (3D) ..........................................54

Table 4.33: Modified HFD Parameters for Dense Coarse Gravel (3D) ........................................54

Table 5.1: Ranges for the PYCAP Friction Angles .......................................................................57

xi

Table 5.2: Ranges for the ABUTMENT Friction Angles ..............................................................57

Table 5.3: Ranges for the PYCAP Cohesion Values .....................................................................67

Table 5.4: Ranges for the ABUTMENT Cohesion Values............................................................67

Table 5.5: Stiffness Ranges for Various Soil Densities (Duncan and Mokwa, 2001) ...................71

Table 5.6: Ranges for the Initial Soil Modulus ..............................................................................72

Table 5.7: A Comparison of Relative Density with the Initial Soil Modulus of the Silty Sand....................................................................................................................................73

Table 5.8: A Comparison of Relative Density with the Initial Soil Modulus of the Clean Sand....................................................................................................................................73

Table 5.9: A Comparison of Relative Density with the Initial Soil Modulus of the Loose Gravel .................................................................................................................................74

Table 5.10: A Comparison of Relative Density with the Initial Soil Modulus of the Coarse Gravel.....................................................................................................................74

Table 5.11: Ranges of Initial Soil Modulus for Different Relative Densities ...............................74

Table 5.12: Ranges for the Strain at 50% of Ultimate Strength ....................................................78

Table 5.13: Ranges for Fult/Beff for the Modified HFD Equation .................................................82

Table 5.14: Ranges of yave for the Modified HFD Equation .........................................................85

Table 5.15: Ranges for the Measured Passive Earth Pressure Coefficient ....................................90

Table 5.16: Comparisons of the Measured Kp Value with the Rankine and Coulomb Methods for the Silty Sands ...............................................................................................91

Table 5.17: Comparisons of the Measured Kp Value with the Rankine and Coulomb Methods for the Clean Sands .............................................................................................91

Table 5.18: Comparisons of the Measured Kp Value with the Rankine and Coulomb Methods for the Fine Gravels ............................................................................................92

Table 5.19: Comparisons of the Measured Kp Value with the Rankine and Coulomb Methods for the Coarse Gravels ........................................................................................92

xiii

LIST OF FIGURES

Figure 2.1: Passive Force-Deflection Relationship for Caltrans Seismic Design Model

(Adapted from Caltrans Seismic Design Manual (2004)) ...................................................4

Figure 2.2: Hyperbolic Passive Force-Displacement Curve (Duncan and Mokwa, 2001) ..............7

Figure 2.3: Mobilization of the Passive Resistance of a Backfill Material (Shamsabadi et al., 2007) ....................................................................................................................................9

Figure 2.4: Hyperbolic Force-Displacement Curve (Shamsabadi et al., 2008) .............................11

Figure 3.1: Grain Size Distribution for Clean Sand (Heiner, 2010) ..............................................20

Figure 3.2: The Particle-Size Distribution for a Clean Sand. (Bingham, 2012) ............................22

Figure 4.1: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Clean Sand (2D) (Strassburg, 2010). .........26

Figure 4.2: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Clean Sand (3D) (Cummins, 2009). ..........28

Figure 4.3: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Clean Sand (3D) (Strassburg, 2010). .........28

Figure 4.4: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (2D) (Bingham, 2012). ...........30

Figure 4.5: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (2D) (Jessee #1, 2012). ..........31

Figure 4.6: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (2D) (Jessee #2, 2012) ...........31

Figure 4.7: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (2D) (Jessee #3, 2012) ...........32

Figure 4.8: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (3D) (Rollins & Cole, 2006). .................................................................................................................................34

Figure 4.9: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (3D) (Heiner, 2010). ..............35

Figure 4.10: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (3D) (Bingham, 2012). ...........35

xiv

Figure 4.11: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Silty Sand (3D) (Kwon, 2007).................. 37

Figure 4.12: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Silty Sand (2D) (Stewart et al., 2007) ...... 40

Figure 4.13: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Silty Sand (2D) using the Plane Strain Friction Angle (Stewart et al., 2007) ...................................................................... 40

Figure 4.14: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Silty Sand (3D) (Rollins & Cole, 2006) ................................................................................................................................. 42

Figure 4.15: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Silty Sand (3D) (Valentine, 2007)............ 43

Figure 4.16: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Fine Gravel (3D) (Pruett, 2009) ............... 45

Figure 4.17: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Fine Gravel (3D) (Rollins & Cole, 2006) ................................................................................................................................. 47

Figure 4.18: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Fine Gravel (3D) (Kwon, 2007) ............... 48

Figure 4.19: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Fine Gravel (3D) (Pruett, 2009) ............... 48

Figure 4.20: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Coarse Gravel (3D) (Pruett, 2009) ........... 50

Figure 4.21: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Coarse Gravel (3D) (Rollins & Cole, 2006) ................................................................................................................................. 52

Figure 4.22: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Coarse Gravel (3D) (Pruett, 2009) ........... 53

Figure 5.1: Comparison of the PYCAP Friction Angles for All of the Soil Types. ..................... 56

Figure 5.2: Comparison of the ABUTMENT Friction Angles for All of the Soil Types. ............ 56

Figure 5.3: A Comparison of the PYCAP Friction Angles with Relative Density for the Unconfined Backfills. ....................................................................................................... 59

xv

Figure 5.4: A Comparison of the PYCAP Friction Angles with Relative Density for the Unconfined, Non-Cohesive Backfills. .............................................................................. 60

Figure 5.5: A Comparison of the ABUTMENT Friction Angles with Relative Density for the Unconfined Backfills. ................................................................................................. 61

Figure 5.6: A Comparison of the ABUTMENT Friction Angles with Relative Density for the Unconfined, Non-Cohesive Backfills. ........................................................................ 62

Figure 5.7: A Comparison of the PYCAP Friction Angles for the Unconfined (3D) Backfills. ........................................................................................................................... 63

Figure 5.8: A Comparison of the PYCAP Friction Angles for the Dense Backfills. ................... 63

Figure 5.9: A Comparison of the ABUTMENT Friction Angles for the Unconfined (3D) Backfills. ........................................................................................................................... 64

Figure 5.10: A Comparison of the ABUTMENT Friction Angles for the Dense Backfills. ........ 65

Figure 5.11: Comparison of the Cohesion Values used in PYCAP for all of the Soil Types....... 66

Figure 5.12: Comparison of the Cohesion Values used in ABUTMENT for all of the Soil Types. ................................................................................................................................ 66

Figure 5.13: A Comparison of the PYCAP Cohesion Values for the Unconfined (3D) Backfills. ........................................................................................................................... 68

Figure 5.14: A Comparison of the PYCAP Cohesion Values for the Dense Backfills. ............... 69

Figure 5.15: A Comparison of the ABUTMENT Cohesion Values for the Unconfined (3D) Backfills.................................................................................................................... 69

Figure 5.16: A Comparison of the ABUTMENT Cohesion Values for the Dense Backfills. ...... 70

Figure 5.17: Comparison of the Initial Soil Modulus for All of the Soil Types. .......................... 71

Figure 5.18: A Comparison of Initial Soil Modulus, Ei, against Relative Density. ..................... 75

Figure 5.19: A Comparison of the Initial Soil Modulus Values for the Unconfined (3D) Backfills. ........................................................................................................................... 76

Figure 5.20: A Comparison of the Initial Soil Modulus Values for the Dense Backfills. ............ 77

Figure 5.21: Comparison of the Strain at 50% of Ultimate Strength for All of the Soil Types. ................................................................................................................................ 78

Figure 5.22: A Comparison of the Strain at 50% of Ultimate Strength against Relative Density for the Unconfined Backfills. .............................................................................. 79

xvi

Figure 5.23: A Comparison of the Strain at 50% of Ultimate Strength for the Unconfined (3D) Materials. ...................................................................................................................80

Figure 5.24: A Comparison of the Strain at 50% of Ultimate Strength for the Dense Materials. ...........................................................................................................................81

Figure 5.25: Comparison of Fult/Beff for All of the Soil Types. ....................................................82

Figure 5.26: A Comparison of the Fult/Beff Values for the Unconfined (3D) Backfills. ...............83

Figure 5.27: A Comparison of the Fult/Beff Values for the Dense Backfills. .................................84

Figure 5.28: Comparison of yave for all of the Soil Types. ............................................................85

Figure 5.29: A Comparison of yave for the Unconfined (3D) Backfills. ........................................86

Figure 5.30: A Comparison of yave for the Dense Backfills. .........................................................87

Figure 5.31: Comparison of the Passive Earth Pressure Coefficient for All of the Soil Types. ....90

Figure 5.32: A Comparison of the Passive Earth Pressure Coefficients against Relative Density for the Unconfined Backfills. ...............................................................................93

Figure 5.33: A Comparison of the Ultimate Passive Resistance per Effective Area against Relative Density for the Unconfined Backfills. .................................................................94

Figure 5.34: A Comparison of the Passive Earth Pressure Coefficients for the Unconfined (3D) Backfills.....................................................................................................................95

Figure 5.35: A Comparison of the Passive Earth Pressure Coefficients for the Dense Backfills. ............................................................................................................................95

Figure 5.36: A Comparison of Pult for the Caltrans Method and the Measured Results for a Wall Height of 3.67 ft. .......................................................................................................97

Figure 5.37: A Comparison of K for the Caltrans Method and the Measured Results for a Wall Height of 3.67 ft. .......................................................................................................98

Figure 5.38: A Comparison of Pult for the Caltrans Method and the Measured Results for a Wall Height of 5.5 ft. .........................................................................................................99

Figure 5.39: A Comparison of K for the Caltrans Method and the Measured Results of the Dense Materials with a Wall Height of 5.5 ft. .................................................................100

Figure 5.40: A Comparison of Pult for the Caltrans Method and the Measured Results for Loose Materials with a Wall Height of 5.5 ft. .................................................................101

Figure 5.41: A Comparison of K for the Caltrans Method and the Measured Results for Loose Materials with a Wall Height of 5.5 ft. .................................................................102

1

1 INTRODUCTION

Pile foundations and abutment walls are critical in the lateral stability of a bridge under

seismic and wind loadings. The lateral stability comes through the interactions of the piles and

soil as well as the abutment wall and the backfill soil. As the abutment wall is subjected to lateral

loading and displaces, passive resistance within the backfill develops. This passive resistance can

provide much of the lateral stability during seismic and wind loadings. The passive resistance of

a backfill material depends on several factors including the magnitude and the direction of

movement, the strength and stiffness of the soil, the friction between the abutment and the soil,

and the geometry of the abutment wall (Duncan and Mokwa, 2001).

Engineers use the passive resistance of a backfill to determine the lateral strength and

performance of bridge foundations. Several methods, such as Rankine, Coulomb, and log-spiral,

are used to estimate the ultimate passive resistance under static loading. However, using the

ultimate passive resistance in design is not always an appropriate approach. There are cases in

which the magnitude of the abutment wall deflection needed to develop ultimate passive

resistance may exceed the limit specified for a particular bridge. There are also displacement-

based design approaches in which the structure is designed for a specific amount of movement,

which may not allow the full development of passive resistance.

Due to displacement limitations, engineers can use several methods to develop force-

displacement relationships for a given abutment backfill. These methods include simple linear

2

elastic as well as hyperbolic models that will predict the passive force at any given abutment wall

displacement. Duncan and Mokwa (2001), Shamsabadi (2007), Shamsabadi (2008), and

CALTRANS (2004) each provide engineers with models to predict the force-displacement

relationship for an abutment backfill.

1.1 Objectives

Developing the force-displacement backbone curve for a particular abutment-backfill

system can often be complex and uncertain. Although easier methods have been developed to

assist engineers in their design (e.g. Caltrans, PYCAP, ABUTMENT, and a general hyperbolic

force-displacement relationship), determining the soil parameters to be used in these methods

can also be difficult. Engineers need a quick and accurate method for producing soil parameters

to be used in the development of force-displacement backbone curves.

There have been several tests performed by Dr. Kyle Rollins and his students at Brigham

Young University (BYU) to determine passive force-deflection curves for various soils and soil

geometries against bridge abutments. However the results from these tests have generally been

analyzed one test at a time without much consideration of how one relates to other test results. In

this study, the results of all these tests were collected and tabulated, and then the results were

compared with one another. Using the collected data and common methods for approximating

the force-displacement relationships of various soils, appropriate soil parameters were back-

calculated for the various design approaches. Knowing the type of backfill material, this data set

gives engineers access to parameters for use in developing force-displacement curves without

extensive geotechnical testing.

3

2 LITERATURE REVIEW

This chapter provides a summary of the analytical methods used in developing force-

displacement relationships for soil against a bridge abutment or pile cap. These methods include

Caltrans, PYCAP, ABUTMENT, and a closed-form modified Hyperbolic Force-Displacement

(HFD) equation (Shamsabadi, 2008). In this report, the Caltrans approach was used only as a

comparison to the measured data. PYCAP, ABUTMENT, and the modified HFD equation were

used to back-calculate soil parameters that would provide a best fit to the measured data.

2.1.1 Caltrans Seismic Design Approach

The Caltrans seismic design approach was developed from research performed by

Maroney (1995) and Romstad et al. (1996) at the University of California, Davis. The testing

was performed on large scale abutments against (1) a well-graded silty sand and (2) a silty clay.

The Caltrans approach uses equations for the abutment stiffness and ultimate passive force to

form a bi-linear force-displacement relationship. Figure 2.1 demonstrates this bi-linear

relationship. Equations for the abutment stiffness and ultimate passive force are shown in

Equations (2-1) and (2-2).

4

Figure 2.1: Passive Force-Deflection Relationship for Caltrans Seismic Design Model (Adapted from Caltrans Seismic Design Manual (2004))

𝑘𝑎𝑏𝑢𝑡 = (20 𝑘𝑖𝑝/𝑖𝑛./𝑓𝑡) ∗ 𝑤 ∗ (𝐻

5.5 𝑓𝑡) (2-1)

𝑃𝑢𝑙𝑡 = (5.0 𝑘𝑠𝑓) ∗ 𝐴𝑒𝑓𝑓 ∗ (𝐻

5.5 𝑓𝑡) (2-2)

where

kabut = stiffness of the backfill material, kip/in.

w = effective width of the abutment, ft

H = height of the abutment, ft

Pult = ultimate passive force, kips

Aeff = effective area of the abutment

In 2011, Caltrans revised Equation (2-1) to include a value of 50 kip/in./ft instead of 20

kip/in./ft. Both the 2004 and 2011 versions of the equation are used in the Comparison of Results

section. Equations (2-1) and (2-2) include a height proportionality factor (H/5.5 ft) based on the

5

abutment height used for the UC Davis testing (5.5 ft). The Caltrans approach is meant to be

used for dense materials only and does not account for the type of backfill material used; thus the

equations are only a function of the dimensions of the abutment. This method was later adopted

in the Caltrans Seismic Design Criteria manual (2004).

2.1.2 PYCAP

Duncan and Mokwa (2001) concluded that the Log Spiral Theory, when corrected for 3D

effects, provides an accurate method for determining the ultimate passive pressure of a soil.

PYCAP is an excel spreadsheet that is based on the Log Spiral Theory and provides an efficient

method for determining the ultimate passive resistance of a soil. Using the ultimate passive

resistance along with an estimated value for soil stiffness and a hyperbolic expression, the

passive force-displacement relationship can be estimated for a particular backfill material.

Duncan and Mokwa (2001) also concluded that the passive resistance of a soil depends on the

magnitude and direction of the abutment movement, the strength and stiffness of the soil, the

frictional resistance between the soil and the abutment, and the shape of the abutment.

Duncan and Mokwa (2001) developed a Microsoft Excel spreadsheet, known as PYCAP,

which incorporates the factors and methods mentioned previously. PYCAP provides users with a

quick and effective method for determining the passive force-displacement relationship for a

backfill material. PYCAP is limited to cases in which the wall is vertical, the ground surface is

horizontal, and any surcharge is uniform (Duncan and Mokwa, 2001). The spreadsheet includes

the Brinch-Hansen (1966) correction factor for three-dimensional (3D) end effects. Equation (2-

3) shows the Brinch-Hansen correction factor for 3D end effects.

6

𝑅𝑅𝑜

= 1 + 𝑅𝑜23� �1.1𝐴4 +

1.6𝐵1 + 5 𝑙 ℎ⁄

+0.4𝑅𝑜𝐴3𝐵2

1 + 0.05 𝑙 ℎ⁄�

(2-3)

where

R = resistance factor

Ro = resistance factor in the basic case (h = H, l = L)

A = 1 - h/H

B = 1 – (l/L)2

l = actual length of the anchor slab or pile cap

h = actual height of the anchor slab or pile cap

L = distance between the centers of two consecutive slabs

H = distance from the lower edge of the slab to the ground surface.

The passive force-displacement relationship is approximated in PYCAP by the

hyperbolic relationship shown in Equation (2-4).

𝑃 =𝑦

� 1𝐾𝑚𝑎𝑥

+ 𝑅𝑓𝑦𝑃𝑢𝑙𝑡

� (2-4)

where

P = passive resistance, kips

y = deflection, in.

Kmax = initial stiffness, kip/in.

Pult = ultimate passive resistance, kips

Rf = failure ratio, Pult/hyperbolic asymptote

7

Figure 2.2 displays the passive force-displacement relationship as approximated by

Equation (2-4).

Figure 2.2: Hyperbolic Passive Force-Displacement Curve (Duncan and Mokwa, 2001)

The backfill soil and abutment properties required for PYCAP include: cap width (b), cap

height (H), embedment depth (z), surcharge (qs), cohesion (c), soil friction angle (φ), wall

friction (δ), soil modulus (Ei), Poisson’s ratio (υ), soil moist unit weight (γm), adhesion factor

(α), and the maximum deflection normalized by the wall height (Δmax/H). Poisson’s ratio can be

calculated using Equation (2-5). Table 2.1 provides a range of stiffness values for different soils

densities as described in Duncan and Mokwa (2001). Typical values for the adhesion factor are

shown in Table 2.2. Duncan and Mokwa (2001) recommends a value of 0.04 for the maximum

deflection normalized by the wall height, which is the estimated amount of movement necessary

to fully develop passive pressures.

𝜐 =1 − 𝑠𝑖𝑛 𝜑2 − 𝑠𝑖𝑛 𝜑

(2-5)

8

Table 2.1: Stiffness Ranges for Various Soil Densities (Duncan and Mokwa, 2001)

Table 2.2: Typical Adhesion Factors (NAVFAC, 1982)

2.1.3 ABUTMENT

Shamsabadi et al. (2007) developed the computer program, ABUTMENT, which uses a

mobilized logarithmic-spiral failure surface and modified hyperbolic stress-strain behavior to

estimate the passive force-displacement relationship of a backfill material. In order to develop

the force-displacement relationship, ABUTMENT assumes that mobilized passive wedges are

formed for each level of wall displacement, and as a result, intermediate passive forces are

determined using force-based, limit-equilibrium equations. The ultimate passive resistance is

developed when the displacement is large enough to fully mobilize the shear strength of the soil.

Figure 2.3 shows the mobilization of intermediate passive wedges and how they relate to the

passive force-displacement curve.

9

Figure 2.3: Mobilization of the Passive Resistance of a Backfill Material (Shamsabadi et al., 2007)

The force-displacement curve is a function of the backfill soil properties and the

movement of the abutment. The backfill soil and abutment properties used in ABUTMENT

include: abutment height, abutment effective width, soil friction angle (φ), wall friction angle (δ),

soil cohesion, abutment adhesion, soil density, strain at 50 percent of the failure stress (ε50),

Poisson’s ratio (υ), failure ratio (Rf), and surcharge. The effective width of the abutment is

calculated by multiplying the Brinch-Hansen (1966) 3D correction factor with the actual width

of the abutment. Recommended ranges of ε50 for various soil types are displayed in Table 2.3

10

Table 2.3: Ranges of ε50 for Various Soil Types (Shamsabadi et al., 2007)

2.1.4 Closed-Form Modified Hyperbolic Force-Displacement (HFD) Equation

The modified HFD equation was developed by Shamsabadi et al. (2008) to provide a

simpler method for estimating the passive force-displacement curve of a given backfill material.

The closed-form equation was developed from testing performed at the University of California,

Davis (Romstad et al., 1995), the University of California, Los Angeles (Stewart et al., 2007),

and BYU (Rollins & Cole, 2006). The passive force-displacement relationship can be described

by the general hyperbolic form shown in Equation (2-6). A typical hyperbolic force-

displacement curve is shown in Figure 2.4.

𝐹(𝑦) =𝐶𝑦

1 + 𝐷𝑦 (2-6)

11

Figure 2.4: Hyperbolic Force-Displacement Curve (Shamsabadi et al., 2008)

The variables C and D are functions of the following soil parameters: average soil

stiffness (K), ultimate passive resistance (Fult), maximum displacement (ymax), and the

displacement corresponding to half of the ultimate passive resistance (yave). For a granular

backfill, Shamsabadi et al. (2008) used 90.84 for C and 2.70 for D, and for a cohesive backfill,

45.42 was used for C and 1.35 for D. Equations (2-7), (2-8), and (2-9) show how the values of C

and D are calculated. Suggested HFD parameters for pressure, average soil stiffness, and

maximum displacement are shown in Table 2.4.

𝐶 = �2𝐾 −𝐹𝑢𝑙𝑡𝑦𝑚𝑎𝑥

� (2-7)

𝐷 = 2 �𝐾𝐹𝑢𝑙𝑡

−1

𝑦𝑚𝑎𝑥� (2-8)

𝐾 =12𝐹𝑢𝑙𝑡𝑦𝑎𝑣𝑒

(2-9)

12

Table 2.4: Suggested HFD Parameters for Abutment Backfills (Shamsabadi et al., 2007)

Shamsabadi et al. (2008) developed a height adjustment factor that can be applied to

Equation (2-6) to account for abutments in which the height is not 5.5 ft. The height adjustment

factor for granular materials is shown in Equation (2-10).

𝑓𝑠 = �𝐻

5.5 𝑓𝑡�1.5

(2-10)

The height adjustment factor was applied to the modified HFD equation to compare with

test data on an abutment with a height of 3.67 ft at BYU (Rollins and Cole, 2006). Shamsabadi et

al. (2008) showed that the force-displacement curve calculated from the adjusted modified HFD

equation agreed reasonably well with the measured data from BYU.

13

3 TESTING

The measured data used for this project came from a variety of tests performed by Dr.

Kyle Rollins and several graduate students at BYU. Testing data from UCLA (Stewart et al.,

2007) is also included. Both full-scale and small-scale tests were performed. For the full-scale

tests at BYU, steel pipe piles were driven and reinforced pile caps were built on top of the piles.

The dimensions of the pile caps varied for each of the tests. For the small-scale tests, a 4-in. thick

concrete panel was pushed against compacted backfill material. In some of the tests the width of

the backfill was confined to the width of the pile cap in order to simulate wingwalls and

eliminate 3D end effects. For the UCLA test, a hydraulic actuator provided the vertical force to

keep the abutment from moving upward during lateral loading.

The tests were performed using different backfill materials at varying densities. The pile

caps were loaded laterally using hydraulic actuators to develop the passive force-displacement

curves. The passive resistance curve of each backfill material was calculated by subtracting the

force against the pile cap without backfill from the force against the pile cap with backfill.

3.1 Rollins & Cole (2006)

Rollins and Cole (2006) performed large-scale testing on four different backfill materials:

clean sand, silty sand, fine gravel, and coarse gravel. The height of the pile cap was 3.67 ft and

the width was 17 ft. The soil was not confined by wingwalls and extended 5 ft beyond the width

14

of the pile cap on each side to capture 3D end effects. The results of a mechanical sieve analysis

as well as the plasticity index of each backfill material are shown in Table 3.1.

Table 3.1: Summary of Backfill Soil Parameters (Rollins and Cole, 2006)

The specific gravity was 2.66, 2.68, 2.70, and 2.80 for the clean sand, silty sand, fine

gravel and coarse gravel, respectively. In-situ direct shear tests were performed on all of the

backfill materials except the clean sand, which was performed in the laboratory. The in-situ

moisture contents (w), dry unit weights (γd), relative densities (Dr), friction angles (φ), cohesion

(c), and interface friction ratio (δ/φ) are shown in Table 3.2.

Table 3.2: Unit Weights and Shear Strength Parameters for Backfill

Materials (Rollins and Cole, 2006)

15

3.2 Kwon (2007)

Kwon (2007) performed large-scale testing on two different backfill materials: loose silty

sand and dense fine gravel. The silty sand and fine gravel were the same material tested in

Rollins and Cole (2006). The height of the pile cap was 3.67 ft and the width was 17 ft. The soil

was not confined by wingwalls and extended 5 ft beyond the width of the pile cap on each side to

capture 3D end effects. The results of a mechanical sieve analysis as well as the plasticity index

of each backfill material are shown in Table 3.3.

Table 3.3: Summary of Backfill Soil Parameters (Kwon, 2007)

The specific gravity of the silty sand was measured to be 2.68, the average dry unit

weight was 99.9 pcf, and the average moisture content was 11.1%. The specific gravity of the

fine gravel was measured as 2.70, the average dry unit weight was 132.6 pcf, and the average

moisture content was 6.1%.

A laboratory direct shear test was performed on the silty sand. The friction angle was

determined to be 32.4° and the cohesion was 230 psf. Due to the difficulty of performing a direct

shear test on the fine gravel, no test was performed. However, a direct shear test was performed

on a similar material and the friction angle and cohesion of that material were determined to be

44° and 410 psf, respectively.

16

3.3 Valentine (2007)

Valentine (2007) performed large-scale testing on a dense silty sand. The height of the

pile cap was 3.67 ft and the width was 17 ft. The soil was not confined by wingwalls and

extended 5 ft beyond the width of the pile cap on each side to capture 3D end effects.

The silty sand used in Valentine (2007) was the same material used in Rollins and Cole

(2006). A mechanical sieve analysis determined the silty sand to be composed of 5.6% gravel,

53.6% sand, and 40.8% fines. The coefficient of uniformity was 14.8 and the coefficient of

gradation was 2.8. The average dry density and moisture content of the silty sand were 110.8 pcf

and 10.7%, respectively. Direct shear tests were performed both in the laboratory and in-situ.

The laboratory friction angle was 28.8° and the cohesion was 363 psf and the in-situ friction

angle was determined to be 29.1° with a cohesion of 148 psf.

3.4 Pruett (2009)

Pruett (2009) performed large-scale testing on two different backfill materials: fine gravel

and coarse gravel. Each material was tested in both a loose state and a dense state. The height of

the pile cap was 5.5 ft and the width was 11 ft. The soil was not confined by wingwalls and

extended 6 ft beyond the width of the pile cap on each side to capture 3D end effects.

The results of a mechanical sieve analysis on the fine gravel are displayed in Table 3.4.

The relative densities of the dense fine gravel and loose fine gravel were 74% and 35%,

respectively. These values were estimated from the relative compaction using the correlation

developed by Lee and Singh (1971). For the dense fine gravel, the average in-situ dry density

17

was 125.4 pcf and the average moisture content was 9.7%. For the loose fine gravel, the average

in-situ dry density was 114.6 pcf and the average moisture content was 6.6%.

Table 3.4: Gradation Properties of the Fine Gravel (Pruett, 2009)

Direct shear tests for the loose and the dense fine gravel were performed both in the

laboratory and in-situ. The results of this testing are shown in Table 3.5. Modified direct shear

testing was performed to determine the interface friction angle (δ) for the backfill material

against concrete. The interface friction angle for the dense fine gravel was determined to be 30.5

degrees, resulting in a δ/φ ratio of 0.61.

Table 3.5: Results of Direct Shear Testing for Fine Gravel (Pruett, 2009)

The results of a mechanical sieve analysis on the coarse gravel are displayed in Table 3.6.

The relative densities of the dense coarse gravel and loose coarse gravel were 82% and 48%,

respectively. These values were estimated from the relative compaction using the correlation

developed by Lee and Singh (1971). For the dense coarse gravel, the average in-situ dry density

18

was 135.0 pcf and the average moisture content was 2.9%. For the loose coarse gravel, the

average in-situ dry density was 125.4 pcf and the average moisture content was 1.9%.

Table 3.6: Gradation Properties for the Coarse Gravel (Pruett, 2009)

An in-situ direct shear test was performed for both the dense coarse gravel and the loose

coarse gravel. The results of this testing are shown in Table 3.7. Also displayed in Table 3.7 is

the friction angle estimated using a correlation with relative compaction as developed by Duncan

(2004). The same δ/φ ratio developed for the fine gravel (0.61) was used to determine the

interface friction angles of the coarse gravel. For the dense coarse gravel, the interface friction

angle was between 32° and 33°. For the loose coarse gravel, the interface friction angle was

30.5°.

Table 3.7: Results of Direct Shear Testing for Coarse Gravel (Pruett, 2009)

3.5 Cummins (2009)

Cummins (2009) performed large scale testing on loose clean sand. The height of the pile

cap was 5.5 ft and the width was 11 ft. The backfill soil was not confined by wingwalls and

extended 2.4 ft beyond the width of the pile cap on each side to capture 3D end effects.

19

From a mechanical sieve analysis, the clean sand was determined to contain 6% gravel,

92% sand, and 2% fines. The coefficients of uniformity and curvature were 8.7 and 1.2,

respectively. The average dry density of the sand was determined to be 98.6 pcf and the moisture

content was 8%. Using the Lee and Singh (1971) correlation, the relative density was estimated

as 44 %. Laboratory direct shear tests were performed on the sand to determine the soil friction

angle, wall friction angle, and cohesion. These values are shown in Table 3.8.

Table 3.8: Direct Shear Results for Loose Clean Sand (Cummins, 2009)

3.6 Nasr (2010)

Nasr (2010) used results from previous testing to determine the effects on the total

mobilized passive resistance of a backfill due to plane strain stress effects and 3D geometric end

effects. The data was taken from research performed by Kwon (2007), Pruett (2009), and Cummins

(2009). Nasr (2010) back-calculated soil parameters from the passive force-displacement curves

created using the PYCAP and ABUTMENT programs.

3.7 Heiner (2010)

Heiner (2010) performed large-scale testing on a dense clean sand. The height of the pile

cap was 5.5 ft and the width was 11 ft. The soil was not confined by wingwalls and extended 5.5

ft beyond the width of the pile cap on each side to capture 3D end effects.

20

The clean sand used in Heiner (2010) contained less than 5% fines and could be generally

classified as concrete sand. The grain size distribution curve is shown in Figure 3.1. The average

dry density and moisture content of the clean sand were 106.5 pcf and 9.0%, respectively. The

minimum void ratio was 0.48 and the maximum void ratio was 0.96. The relative density of the

clean sand was calculated to be 80% using the minimum and maximum void ratios. Several

direct shear tests were performed in the laboratory. The friction angle of the dense clean sand

was determined to be 40.5° with a cohesion value of zero.

Figure 3.1: Grain Size Distribution for Clean Sand (Heiner, 2010)

3.8 Strassburg (2010)

Strassburg (2010) performed large-scale testing on a loose well-graded sand. The height

of the pile cap was 5.5 ft and the width was 11 ft. Two tests were performed on the loose sand:

an unconfined test in which the soil extended 5.5 ft beyond the width of the pile cap on each side

to capture 3D end effects and a confined test with slip planes to simulate plane strain conditions.

Table 3.9 contains the results of a mechanical sieve analysis performed on the sand. The

in-situ dry unit weights for the loose sand unconfined (3D) and loose sand slip plane (2D) were

21

107.0 pcf, and 109.5 pcf, respectively. The average moisture content of the loose sand

unconfined (3D) was 5.6% and the loose sand slip plane (2D) was 7.9%.

Table 3.9: Gradation Parameters for Loose Well-Graded Sand (Strassburg, 2010)

Direct shear and triaxial tests were performed in the laboratory. The friction angle of the

sand was determined to be 36.0° and there was no cohesion. Using the Lee and Singh (1971)

correlation, the relative densities of the loose sand were calculated. For the loose sand

unconfined (3D) the relative density was 31% and for the loose sand slip plane (2D) it was 41%.

3.9 Bingham (2012)

Bingham (2012) performed large-scale testing on a dense well-graded sand. The same

sand was used for testing performed by Strassburg (2010). The height of the pile cap was 5.5 ft

and the width was 11 ft. Two tests were performed on the dense sand: an unconfined test in

which the soil extended 6 ft beyond the width of the pile cap on each side to capture 3D end

effects and a confined test with slip planes to simulate plane strain conditions.

Figure 3.2 shows an average particle-size distribution curve obtained from multiple

mechanical sieve analyses performed during testing. Table 3.9 shows some results from the

mechanical sieve analysis. The in-situ dry unit weights for the dense sand unconfined (3D) and

dense sand slip plane (2D) were 120.3 pcf, and 118.9 pcf, respectively. The average moisture

content of the dense sand unconfined (3D) was 7.7% and for the dense sand slip plane (2D) the

average moisture content was 8.8%.

Gravel Sand Fines D60 D50 D30 D10 Cu Cc

% % % in. in. in. in.Well-graded Sand 12 87 1 0.056 0.042 0.021 0.006 8.91 1.26

Backfill Soil

22

Figure 3.2: The Particle-Size Distribution for a Clean Sand. (Bingham, 2012)

Direct shear and triaxial shear tests were performed in the laboratory. The friction angle

of the sand was determined to be 43.1° and the corresponding cohesion was 823 psf. Using the

Lee and Singh (1971) correlation, the relative densities of the dense sand were calculated. For

the dense sand unconfined (3D) the relative density was 84% and for the dense sand slip plane

(2D) it was 79%.

3.10 Jessee (2012)

Jessee (2012) performed small-scale testing on a dense clean sand. A 4 in. thick concrete

panel, with a height of 2 ft and width of 4.125 ft, was pushed against the compacted backfill

material. The width of the backfill was limited to the width of the concrete panel using slip

planes. The test was performed three times with the same backfill conditions.

The sand classified as a clean poorly-graded material. The coefficients of uniformity and

curvature were 3.7 and 0.7, respectively. The average dry unit weight for the clean sand was

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.010.1110100

Particle diameter (mm)

Perc

ent F

iner

23

determined to be 111 pcf and the average moisture content during testing was 8.0%. Direct shear

tests were performed in the lab to determine the shear strength parameters of the clean sand. The

drained friction angle (φ) was found to be 49° and the cohesion was 90 psf. The interface friction

angle (δ) between the sand and concrete was measured to be 33°. This provided an interface

friction angle to soil friction angle ratio (δ/φ) of 0.68. Other soil parameters for the dense clean

sand can be found in Table 3.10.

Table 3.10: Soil Properties for Dense Clean Sand (Jessee, 2012)

3.11 UCLA (Stewart et al., 2007)

The UCLA testing was performed on a seat-type abutment with a height of 5.5 ft and a

width of 15 ft. Plywood was placed on each side of the abutment to simulate wingwalls and

confine the backfill width to 16 ft. The backfill material was a well-graded sand with silt. The

fines content was 10% and the D50 ranged from 0.7-0.85 mm.

Backfill Soil Properties USCS Classification SP

Cu 3.7 Cc 0.7 Gs 2.65 e 0.49

ϕ (°) 49.0 δ (°) 33.2

Modified Proctor γd(max)

115.4

wopt 16.0 Avg. γd 111.0

Avg. w (%) (during compaction) 11.3

Avg. w (%) (during testing) 8.0

Avg. S (%) 43.5 Avg. ψ (kPa) 9.6 Avg. ca (kPa) 3.8

24

Sand cone testing was used to determine the unit weight and moisture content of the sand.

The dry unit weight was 118.3 pcf and the median moisture content was 6.5%. A specific gravity

of 2.7 was assumed to calculate the median in-situ void ratio as 0.38 and from this value the

relative density was calculated as 92%. A triaxial test determined the friction angle to be 40° and

the cohesion range from 300-500 psf. The interface friction angle between the soil and the

relatively smooth concrete wall was determined to be 14°.

25

4 RESULTS

Testing was performed on 11 categories of backfill material, each with varying soil types

and configurations. For each soil, the measured passive force-displacement curve was used to

back-calculate parameters that could be used in common approaches for developing the passive

force-displacement relationship. The common approaches include PYCAP, ABUTMENT, and

the modified hyperbolic force-displacement equation. For each test on a dense material, the

measured passive force-displacement curve is compared with the bi-linear force-displacement

model formulated using the Caltrans Seismic Design approach. For the cases in which end

effects were accounted for (3D), the effective width computed using the Brinch-Hansen equation

was used in the ABUTMENT program. For the modified HFD equation, the maximum

displacement was assumed to be 5% of the pile cap height.

Many of the parameters used herein were determined previously or discussed in Chapter

3. ABUTMENT parameters for the Rollins & Cole (2006) testing were taken from Shamsabadi

(2007). Parameters for PYCAP and ABUTMENT on the Kwon (2007) testing were taken from

Nasr (2010).

4.1 Loose Clean Sand (2D)

Strassburg (2010) performed testing on loose clean sand confined to the width of the wall

by slip planes in order to negate 3D end effects. The measured results of this testing was fit to

26

curves from typical methods for determining the passive force-displacement relationship. The

force-displacement curves are found in Figure 4.1.

Figure 4.1: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Clean Sand (2D) (Strassburg, 2010).

The back-calculated parameters for PYCAP, ABUTMENT, and the modified HFD

equation are summarized in Table 4.1, Table 4.2, and Table 4.3, respectively.

Table 4.1: PYCAP Parameters for Loose Clean Sand (2D)

0

50

100

150

200

250

300

350

0 0.5 1 1.5 2 2.5 3 3.5

Forc

e (k

ips)

Displacement (in.)

MeasuredPYCAPABUTMENTModified HFD

Cap width b 11 ftCap height H 5.5 ftCohesion c 60 psfSoil friction angle φ 42.0 degreesWall friction angle δ 31.5 degreesInitial soil modulus Ei 400 ksf

Poisson's ratio υ 0.25 -Moist unit weight γm 118.2 pcf

Parameter UnitStrassburg

(2010)Symbol

27

Table 4.2: ABUTMENT Parameters for Loose Clean Sand (2D)

Table 4.3: Modified HFD parameters for Loose Clean Sand (2D)

4.2 Loose Clean Sand (3D)

Cummins (2009) and Strassburg (2010) performed testing on unconfined loose clean

sand. The measured results of these tests were fit to curves from typical methods for determining

the passive force-displacement relationship. The force-displacement curves are shown in Figure

4.2 and Figure 4.3.

Cap width b 11 ftCap height H 5.5 ftSoil cohesion c 0.13 ksfSoil friction angle φ 42.0 degreesWall friction angle δ 31.5 degreesSoil density γ 0.1182 kcfStrain at 50% of ultimate strength ε50 0.01 -

Poisson's ratio υ 0.25 -Failure ratio Rf 0.9 -

Parameter SymbolStrassburg

(2010) Unit

Ultimate passive resistance/effective width Fult/beff 30 kip/ftMaximum displacement/Height ymax/H 0.05 in/inDisplacement at half of the ultimate passive resistance yave 0.8 in


(2010) Unit

28

Figure 4.2: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Clean Sand (3D) (Cummins, 2009).

Figure 4.3: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Clean Sand (3D) (Strassburg, 2010).

0

20

40

60

80

100

0 0.5 1 1.5 2 2.5

Forc

e (k

ips)

Displacement (in.)


0

50

100

150

200

250

300

350

0 1 2 3 4

Forc

e (k

ips)

Displacement (in.)


29


equation are summarized in Table 4.4, Table 4.5, and Table 4.6, respectively.

Table 4.4: PYCAP Parameters for Loose Clean Sand (3D)

Table 4.5: ABUTMENT Parameters for Loose Clean Sand (3D)

Table 4.6: Modified HFD Parameters for Loose Clean Sand (3D)

Cap width b 11 11 ftCap height H 5.5 5.5 ftCohesion c 10 60 psfSoil friction angle φ 27.7 36.0 degreesWall friction angle δ 20.8 27 degreesInitial soil modulus Ei 200.5 210 ksf

Poisson's ratio υ 0.35 0.25 -Moist unit weight γm 110 113 pcf


(2010) UnitCummins

(2009)

Cap width b 11 11 ftCap height H 5.5 5.5 ftSoil cohesion c 0.01 0.01 ksfSoil friction angle φ 27.7 36.0 degreesWall friction angle δ 20.8 27 degreesSoil density γ 0.11 0.113 kcfStrain at 50% of ultimate strength ε50 0.003 0.006 -Poisson's ratio υ 0.35 0.25 -Failure ratio Rf 0.97 0.94 -


(2010) UnitCummins

(2009)

Ultimate passive resistance/effective width Fult/beff 8.7 16.3 kip/ftMaximum displacement/Height ymax/H 0.05 0.05 in/inDisplacement at half of the ultimate passive resistance yave 1.0 0.8 in


(2010) UnitCummins

(2009)

30

4.3 Dense Clean Sand (2D)

Bingham (2012) and Jessee (2012) performed testing on dense clean sand confined to the

width of the wall by slip planes in order to negate 3D end effects. Jessee (2012) performed three

different tests on small-scale abutments. The measured results of both the Bingham (2012) and

Jessee (2012) tests were fit to curves from typical methods for determining the passive force-

displacement relationship. The passive force-displacement curves are shown in Figure 4.4,

Figure 4.5, Figure 4.6, and Figure 4.7.

Figure 4.4: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (2D) (Bingham, 2012).

0

100

200

300

400

500

600

700

800

0 0.5 1 1.5 2 2.5 3 3.5

Forc

e (k

ips)

Displacement (in.)

Measured PYCAPABUTMENT Modified HFDCaltrans

31

Figure 4.5: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (2D) (Jessee #1, 2012).

Figure 4.6: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (2D) (Jessee #2, 2012)

05

101520253035404550

0 0.5 1 1.5 2

Forc

e (k

ips)

Displacement (in.)


05

101520253035404550

0 0.5 1 1.5 2

Forc

e (k

ips)

Displacement (in.)


32

Figure 4.7: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (2D) (Jessee #3, 2012)

These results show that the Caltrans method underestimates the passive force-

displacement relationship for dense sands confined by slip planes. The back-calculated

parameters for PYCAP, ABUTMENT, and the modified HFD equation are summarized in Table

4.7, Table 4.8, and Table 4.9, respectively. The same parameters were used for all three Jessee

(2012) tests except in the modified HFD method.

05

101520253035404550

0 0.5 1 1.5 2 2.5

Forc

e (k

ips)

Displacement (in.)


33

Table 4.7: PYCAP Parameters for Dense Clean Sand (2D)

Table 4.8: ABUTMENT Parameters for Dense Clean Sand (2D)

Cap width b 11 4.125 ftCap height H 5.5 2 ftCohesion c 60 90 psfSoil friction angle φ 48.3 50.0 degreesWall friction angle δ 34.8 33.5 degreesInitial soil modulus Ei 680 1000 ksf

Poisson's ratio υ 0.23 0.20 -Moist unit weight γm 129.3 120.0 pcf

Parameter Symbol UnitBingham

(2012)Jessee (2012)

Cap width b 11 4.125 ftCap height H 5.5 2 ftSoil cohesion c 0.06 0.13 ksfSoil friction angle φ 49.9 50.0 degreesWall friction angle δ 35.9 33.5 degreesSoil density γ 0.1293 0.12 kcfStrain at 50% of ultimate strength ε50 0.008 0.004 -Poisson's ratio υ 0.23 0.20 -Failure ratio Rf 0.92 0.95 -

UnitBingham

(2012)Parameter SymbolJessee (2012)

34

Table 4.9: Modified HFD Parameters for Dense Clean Sand (2D)

4.4 Dense Clean Sand (3D)

Rollins & Cole (2006), Heiner (2010), and Bingham (2012) performed testing on

unconfined dense clean sand. The measured results of these tests were fit to curves from typical

methods for determining the passive force-displacement relationship. The passive force-

displacement curves are shown in Figure 4.8, Figure 4.9, and Figure 4.10.

Figure 4.8: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (3D) (Rollins & Cole, 2006).

Ultimate passive resistance/effective width Fult/beff 58.9 50.7 48.5 47.8 kip/ftMaximum displacement/Height ymax/H 0.05 0.05 0.05 0.05 in/inDisplacement at half of the ultimate passive resistance yave 0.68 0.20 0.14 0.15 in

Parameter SymbolJessee

(2012) #3 UnitBingham

(2012)Jessee

(2012) #1Jessee

(2012) #2

0

50

100

150

200

250

300

0 0.5 1 1.5 2 2.5 3

Forc

e (k

ips)

Displacement (in.)

MeasuredPYCAPABUTMENTModified HFDCaltrans

35

Figure 4.9: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (3D) (Heiner, 2010).

Figure 4.10: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Clean Sand (3D) (Bingham, 2012).

0

100

200

300

400

500

600

0 0.5 1 1.5 2 2.5 3

Forc

e (k

ips)

Displacement (in.)


0

100

200

300

400

500

600

700

800

900

0 0.5 1 1.5 2 2.5 3

Forc

e (k

ips)

Displacement (in.)


36


equation are summarized in Table 4.10, Table 4.11, and Table 4.12, respectively. For Rollins &

Cole (2006) and Heiner (2010), the effective widths were used in the ABUTMENT program.

The Brinch-Hansen 3D factor for Rollins & Cole (2006) was 1.360 and for Heiner (2010) the 3D

factor was 1.636.

Table 4.10: PYCAP Parameters for Dense Clean Sand (3D)

Table 4.11: ABUTMENT Parameters for Dense Clean Sand (3D)

Cap width b 17 11 11 ftCap height H 3.67 5.5 5.5 ftCohesion c 0 0 60 psfSoil friction angle φ 40.7 40.5 43.5 degreesWall friction angle δ 31.3 31.2 31.3 degreesInitial soil modulus Ei 775 800 450 ksf

Poisson's ratio υ 0.26 0.26 0.23 -Moist unit weight γm 116.8 105 129.5 pcf

Parameter SymbolBingham

(2012) UnitRollins &

Cole (2006)Heiner (2010)

Cap width b 23.1 18 11 ftCap height H 3.67 5.5 5.5 ftSoil cohesion c 0.08 0.1 0 ksfSoil friction angle φ 39.3 41.5 43.3 degreesWall friction angle δ 30.3 32 31.2 degreesSoil density γ 0.1168 0.1161 0.1295 kcfStrain at 50% of ultimate strength ε50 0.002 0.0065 0.007 -Poisson's ratio υ 0.27 0.29 0.23 -Failure ratio Rf 0.98 0.91 0.92 -

UnitRollins &

Cole (2006)Heiner (2010)Parameter Symbol

Bingham (2012)

37

Table 4.12: Modified HFD Parameters for Dense Clean Sand (3D)

4.5 Loose Silty Sand (3D)

Kwon (2007) performed testing on unconfined loose silty sand. The measured results of

these tests were fit to curves from typical methods for determining the passive force-

displacement relationship. The force-displacement curves are shown in Figure 4.11.

Figure 4.11: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Silty Sand (3D) (Kwon, 2007).

Ultimate passive resistance/effective width Fult/beff 19.5 27.0 37.7 kip/ftMaximum displacement/Height ymax/H 0.05 0.05 0.05 in/inDisplacement at half of the ultimate passive resistance yave 0.16 0.58 0.85 in

Parameter SymbolBingham


Cole (2006)Heiner (2010)

0

20

40

60

80

100

0 0.5 1 1.5 2 2.5

Forc

e (k

ips)

Displacement (in.)


38


equation are summarized in Table 4.13, Table 4.14, and Table 4.15, respectively. The Brinch-

Hansen correction factor used for this material was 1.177.

Table 4.13: PYCAP Parameters for Loose Silty Sand (3D)

Table 4.14: ABUTMENT Parameters for Loose Silty Sand (3D)


Poisson's ratio υ 0.35 -Moist unit weight γm 110 pcf

Parameter Symbol UnitKwon (2007)

Cap width b 20.0 ftCap height H 3.67 ftSoil cohesion c 0.06 ksfSoil friction angle φ 27.7 degreesWall friction angle δ 20.8 degreesSoil density γ 0.11 kcfStrain at 50% of ultimate strength ε50 0.003 -Poisson's ratio υ 0.35 -Failure ratio Rf 0.97 -


39

Table 4.15: Modified HFD Parameters for Loose Silty Sand (3D)

4.6 Dense Silty Sand (2D)

UCLA (Stewart et al., 2007) performed testing on confined dense silty sand. The

measured results of this testing were fit to curves from typical methods for determining the

passive force-displacement relationship. The force-displacement curves are shown in Figure 4.12

and Figure 4.13. Two scenarios were used in comparing the measured data with the common

methods for the UCLA dense silty sand (2D): the triaxial friction angle and the plane strain

friction angle. According to Kulhawy and Mayne (1990), the plane strain friction angle is about

10/9 of the triaxial friction angle. The use of the plane strain friction angle allowed for lower

values of cohesion to be used.

Ultimate passive resistance/effective width Fult/beff 8.3 kip/ftMaximum displacement/Height ymax/H 0.05 in/inDisplacement at half of the ultimate passive resistance yave 0.7 in


40

Figure 4.12: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Silty Sand (2D) (Stewart et al., 2007)

Figure 4.13: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Silty Sand (2D) using the Plane Strain Friction Angle (Stewart et al., 2007)

0

100

200

300

400

500

600

0 1 2 3 4 5 6

Forc

e (k

ips)

Displacement (in.)


0

100

200

300

400

500

600

0 1 2 3 4 5 6

Forc

e (k

ips)

Displacement (in.)


41


equation are summarized in Table 4.16, Table 4.17, and Table 4.18, respectively. The use of the

plane strain friction angle allowed for the cohesion to be reduced in both PYCAP and

ABUTMENT.

Table 4.16: PYCAP Parameters for Dense Silty Sand (2D)

Table 4.17: ABUTMENT Parameters for Dense Silty Sand (2D)

Cap width b 15 15 ftCap height H 5.5 5.5 ftCohesion c 380 190 psfSoil friction angle φ 40.0 44.4 degreesWall friction angle δ 14.0 15.6 degreesInitial soil modulus Ei 1000 1000 ksf


Parameter Symbol UnitUCLA (Stewart

et al., 2007)UCLA Plane

Strain

Cap width b 15 15 ftCap height H 5.5 5.5 ftSoil cohesion c 0.3 0.05 ksfSoil friction angle φ 39 44.4 degreesWall friction angle δ 29.25 33.3 degreesSoil density γ 0.126 0.126 kcfStrain at 50% of ultimate strength ε50 0.0036 0.0036 -Poisson's ratio υ 0.27 0.27 -Failure ratio Rf 0.98 0.98 -

UnitUCLA (Stewart

et al., 2007)Parameter SymbolUCLA Plane

Strain

42

Table 4.18: Modified HFD Parameters for Dense Silty Sand (2D)

4.7 Dense Silty Sand (3D)

Rollins & Cole (2006) and Valentine (2007) performed testing on unconfined dense silty

sand. The measured results of these tests were fit to curves from typical methods for determining

the passive force-displacement relationship. The passive force-displacement curves are shown in

Figure 4.14 and Figure 4.15.

Figure 4.14: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Silty Sand (3D) (Rollins & Cole, 2006)


Parameter Symbol UnitUCLA (Stewart

et al., 2007)

0

50

100

150

200

250

300

350

0 0.5 1 1.5 2 2.5 3

Forc

e (k

ips)

Displacement (in.)


43

Figure 4.15: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Silty Sand (3D) (Valentine, 2007)



Cole (2006) and Valentine (2007), the effective widths were used in the ABUTMENT program.

The Brinch-Hansen 3D factor for Rollins & Cole (2006) was 1.187 and for Valentine (2007) the

3D factor was 1.271.

0

50

100

150

200

250

300

350

0 0.5 1 1.5 2 2.5 3

Forc

e (k

ips)

Displacement (in.)


44

Table 4.19: PYCAP Parameters for Dense Silty Sand (3D)

Table 4.20: ABUTMENT Parameters for Dense Silty Sand (3D)

Cap width b 17 17 ftCap height H 3.67 3.67 ftCohesion c 570.2 650 psfSoil friction angle φ 27.9 30 degreesWall friction angle δ 20.9 26.3 degreesInitial soil modulus Ei 800 800 ksf


Parameter SymbolValentine


Cole (2006)

Cap width b 20.4 21.6 ftCap height H 3.67 3.67 ftSoil cohesion c 0.647 0.5 ksfSoil friction angle φ 27 30.5 degreesWall friction angle δ 21 22.9 degreesSoil density γ 0.1209 0.1226 kcfStrain at 50% of ultimate strength ε50 0.003 0.003 -Poisson's ratio υ 0.35 0.33 -Failure ratio Rf 0.97 0.97 -

UnitRollins &

Cole (2006)Parameter SymbolValentine

(2007)

45

Table 4.21: Modified HFD Parameters for Dense Silty Sand (3D)

4.8 Loose Fine Gravel (3D)

Pruett (2009) performed large scale testing on unconfined loose fine gravel. The

measured results of this testing were fit to curves from typical methods for determining the

passive force-displacement relationship. The passive force-displacement curves are shown in

Figure 4.16.

Figure 4.16: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Fine Gravel (3D) (Pruett, 2009)


Parameter SymbolValentine


Cole (2006)

0

20

40

60

80

100

120

140

160

180

200

0 0.5 1 1.5 2 2.5 3 3.5

Forc

e (k

ips)

Displacement (in.)


46

The parameters for PYCAP and ABUTMENT were taken from Pruett (2009). The back-

calculated parameters for PYCAP, ABUTMENT, and the modified HFD equation are

summarized in Table 4.22, Table 4.23, and Table 4.24, respectively. For PYCAP the Brinch-

Hansen 3D factor used was 1.54 and for ABUTMENT program, the 3D factor was 1.48.

Table 4.22: PYCAP Parameters for Loose Fine Gravel (3D)

Table 4.23: ABUTMENT Parameters for Loose Fine Gravel (3D)



Parameter UnitPruett (2009)Symbol

Cap width b 16.28 ftCap height H 5.5 ftSoil cohesion c 0 ksfSoil friction angle φ 33.0 degreesWall friction angle δ 25.0 degreesSoil density γ 0.1221 kcfStrain at 50% of ultimate strength ε50 0.005 -


Parameter SymbolPruett (2009) Unit

47

Table 4.24: Modified HFD Parameters for Loose Fine Gravel (3D)

4.9 Dense Fine Gravel (3D)

Rollins & Cole (2006), Kwon (2007), and Pruett (2009) performed testing on unconfined

dense fine gravel. The measured results of these tests were fit to curves from typical methods for

determining the passive force-displacement relationship. The passive force-displacement curves

are shown in Figure 4.17, Figure 4.19, and Figure 4.19.

Figure 4.17: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Fine Gravel (3D) (Rollins & Cole, 2006)



0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Forc

e (k

ips)

Displacement (in.)


48

Figure 4.18: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Fine Gravel (3D) (Kwon, 2007)

Figure 4.19: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Fine Gravel (3D) (Pruett, 2009)

0

50

100

150

200

250

300

350

0 0.5 1 1.5 2 2.5

Forc

e (k

ips)

Displacement (in.)

Measured

PYCAP

ABUTMENT

Modified HFD

Caltrans

0

100

200

300

400

500

600

700

0 0.5 1 1.5 2 2.5 3 3.5 4

Forc

e (k

ips)

Displacement (in.)


49



Cole (2006) and Pruett (2009), the effective widths were used in the ABUTMENT program. The

Brinch-Hansen 3D factor for Rollins & Cole (2006) was 1.260, for Kwon (2007) the 3D factor

was 1.403, and for Pruett (2009) the 3D factor was 1.950. The cohesion in PYCAP for Pruett

(2009) was changed from 84 psf to 0 psf to attain better agreement with the measured data.

Table 4.25: PYCAP Parameters for Dense Fine Gravel (3D)

Table 4.26: ABUTMENT Parameters for Dense Fine Gravel (3D)

Cap width b 17 17 11 ftCap height H 3.67 3.67 5.5 ftCohesion c 79.4 0 0* psfSoil friction angle φ 34.0 41.0 44.0 degreesWall friction angle δ 25.5 30.75 27 degreesInitial soil modulus Ei 706 600 670 ksf

Poisson's ratio υ 0.31 0.26 0.30 -Moist unit weight γm 132.2 141.0 137.8 pcf

*Pruett (2009) used c = 84 psf


Rollins & Cole (2006)

Kwon (2007)

Cap width b 21.4 24.4 21.5 ftCap height H 3.67 3.67 5.5 ftSoil cohesion c 0.084 0.015 0.084 ksfSoil friction angle φ 34.0 42.0 44.0 degreesWall friction angle δ 26.0 31.5 27.0 degreesSoil density γ 0.1322 0.141 0.1378 kcfStrain at 50% of ultimate strength ε50 0.0015 0.004 0.004 -Poisson's ratio υ 0.31 0.25 0.30 -Failure ratio Rf 0.98 0.95 0.98 -

UnitRollins &

Cole (2006)Kwon (2007)Parameter Symbol

Pruett (2009)

50

Table 4.27: Modified HFD Parameters for Dense Fine Gravel (3D)

4.10 Loose Coarse Gravel (3D)

Pruett (2009) performed large scale testing on unconfined loose coarse gravel. The

measured results of this test were fit to curves from typical methods for determining the passive

force-displacement relationship. The passive force-displacement curves are shown in Figure

4.20. The parameters for PYCAP and ABUTMENT were taken from Pruett (2009).

Figure 4.20: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Loose Coarse Gravel (3D) (Pruett, 2009)

Ultimate passive resistance/effective width Fult/beff 15.3 23.1 31.0 kip/ftMaximum displacement/Height ymax/H 0.05 0.05 0.05 in/inDisplacement at half of the ultimate passive resistance yave 0.095 0.24 0.66 in



Kwon (2007)

0

50

100

150

200

250

300

350

0 0.5 1 1.5 2 2.5 3 3.5 4

Forc

e (k

ips)

Displacement (in.)

Measured

PYCAP

ABUTMENT

Modified HFD

51


equation are summarized in Table 4.28, Table 4.29, and Table 4.30, respectively. For both the

ABUTMENT program and PYCAP, the Brinch-Hansen 3D factor used was 1.72.

Table 4.28: PYCAP Parameters for Loose Coarse Gravel (3D)

Table 4.29: ABUTMENT Parameters for Loose Coarse Gravel (3D)



Parameter UnitPruett (2009)Symbol

Cap width b 18.6 ftCap height H 5.5 ftSoil cohesion c 0 ksfSoil friction angle φ 40.0 degreesWall friction angle δ 24 degreesSoil density γ 0.1278 kcfStrain at 50% of ultimate strength ε50 0.0074 -



52

Table 4.30: Modified HFD Parameters for Loose Coarse Gravel (3D)

4.11 Dense Coarse Gravel (3D)

Rollins & Cole (2006) and Pruett (2009) performed testing on unconfined dense coarse

gravel. The measured results of these tests were fit to curves from typical methods for

determining the passive force-displacement relationship. The passive force-displacement curves

are shown in Figure 4.21 and Figure 4.22.

Figure 4.21: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Coarse Gravel (3D) (Rollins & Cole, 2006)



050

100150200250300350400450500

0 0.5 1 1.5 2 2.5 3

Forc

e (k

ips)

Displacement (in.)


53

Figure 4.22: Comparison of Measured Passive Force-Deflection Curves with Curves Computed using Various Methods for Dense Coarse Gravel (3D) (Pruett, 2009)


equation are summarized in Table 4.31, Table 4.32, and Table 4.33, respectively. For each of the

coarse gravel tests, effective widths were used for the ABUTMENT program using the Brinch-

Hansen 3D factor. For Rollins & Cole (2006) the 3D factor was 1.4 and for Pruett (2009) the 3D

factor was 1.89.

0

100

200

300

400

500

600

700

800

900

0 0.5 1 1.5 2 2.5 3 3.5

Forc

e (k

ips)

Displacement (in.)


54

Table 4.31: PYCAP Parameters for Dense Coarse Gravel (3D)

Table 4.32: ABUTMENT Parameters for Dense Coarse Gravel (3D)

Table 4.33: Modified HFD Parameters for Dense Coarse Gravel (3D)

Cap width b 17 11 ftCap height H 3.67 5.5 ftCohesion c 150.4 286 psfSoil friction angle φ 41.3 41 degreesWall friction angle δ 31.0 26.65 degreesInitial soil modulus Ei 600 830 ksf




Cap width b 23.8 20.8 ftCap height H 3.67 5.5 ftSoil cohesion c 0.251 0.286 ksfSoil friction angle φ 40 41.0 degreesWall friction angle δ 30 30.75 degreesSoil density γ 0.1472 0.1384 kcfStrain at 50% of ultimate strength ε50 0.005 0.0037 -Poisson's ratio υ 0.30 0.30 -Failure ratio Rf 0.95 0.98 -

UnitRollins &

Cole (2006)Parameter SymbolPruett (2009)




55

5 COMPARISON OF RESULTS


method are summarized in this section of the report. The parameters summarized include the

friction angle, cohesion, initial soil modulus, the strain at 50% of ultimate strength, the ultimate

passive force normalized by the effective width, and the displacement at 50% of the ultimate

strength. The passive earth pressure coefficient of each test is also summarized and compared to

the Rankine and Coulomb theories and the ultimate passive pressure and stiffness of each test are

compared with the Caltrans 2004 and 2010 methods.

5.1 Friction Angle, φ

The soil friction angle is one of the more important parameters in developing the passive

force-displacement relationship in PYCAP and ABUTMENT. The friction angles back-

calculated using PYCAP and ABUTMENT for all of the tests are shown in Figure 5.1 and Figure

5.2 respectively. The values shown are the minimum, 25th quartile, median, 75th quartile, and the

maximum. Values shown as small boxes, e.g. Loose Silty Sand 3D, contained no variation and

represent a single point. The ranges of the friction angles for all of the soil types are summarized

in Table 5.1 and Table 5.2.

56

Figure 5.1: Comparison of the PYCAP Friction Angles for All of the Soil Types.

Figure 5.2: Comparison of the ABUTMENT Friction Angles for All of the Soil Types.

25

30

35

40

45

50

55

LooseSiltySand3D

DenseSiltySand2D

DenseSiltySand3D

LooseCleanSand2D

LooseCleanSand3D

DenseCleanSand2D

DenseCleanSand3D

LooseFine

Gravel3D

DenseFine

Gravel3D

LooseCoarseGravel

3D

DenseCoarseGravel

3D

PYC

AP

Fric

tion

Ang

le (d

egre

es)

25

30

35

40

45

50

55

LooseSiltySand3D

DenseSiltySand2D

DenseSiltySand3D

LooseCleanSand2D

LooseCleanSand3D

DenseCleanSand2D

DenseCleanSand3D

LooseFine

Gravel3D

DenseFine

Gravel3D

LooseCoarseGravel

3D

DenseCoarseGravel

3D

AB

UTM

ENT

Fric

tion

Ang

le (d

egre

es)

57

Table 5.1: Ranges for the PYCAP Friction Angles

Table 5.2: Ranges for the ABUTMENT Friction Angles

The results from the friction angle comparisons are consistent with anticipated results.

The tests in which the backfill was confined to the width of the wall (2D) resulted in higher

friction angles than the tests on the same material that were unconfined (3D). Soils under plane

strain conditions typically provide higher strength than those in an unconfined condition.

Kulhawy and Mayne (1990) observed the plane strain friction angle to be about 10/9 of the

triaxial friction angle.

In most cases, the friction angles of the backfill materials in the dense state were higher

than those of the loose state. The higher compactive effort provided a higher relative density as

Soil TypeLoose Clean Sand 27.7 - 36.0Dense Clean Sand 48.3 - 50.0 40.5 - 43.7Loose Silty SandDense Silty Sand 40.0 - 44.4 27.9 - 30.0Loose Fine GravelDense Fine Gravel 34.0 - 44.0Loose Coarse GravelDense Coarse Gravel 41.0 - 41.3

2D 3DPYCAP Friction Angle (degrees)

n/an/an/a

n/a

n/a

42.0

27.7

31.0

37.4

Soil TypeLoose Clean Sand 27.7 - 36.0Dense Clean Sand 49.9 - 50.0 39.3 - 43.3Loose Silty SandDense Silty Sand 39.0 - 44.4 27.0 - 30.5Loose Fine GravelDense Fine Gravel 34.0 - 44.0Loose Coarse GravelDense Coarse Gravel 40.0 - 41.0

40.0

33.0

27.7

42.0

n/a

n/a

n/an/an/a

ABUTMENT Friction Angle (degrees)2D 3D

58

well as a higher strength for the backfill material. The friction angles for the dense clean sand

were higher than those of the dense coarse gravel, which was unexpected. This may be a result of

using higher values for cohesion instead of increasing the friction angles of the dense coarse

gravels in PYCAP and ABUTMENT. For the dense clean sand (3D) cases, very little to no

cohesion was used in developing the passive force-displacement relationships whereas in the

dense coarse gravel (3D) cases, 150 psf to 286 psf were used to match the passive-force

displacement curves with the measured results.

The friction angles back-calculated from PYCAP are shown as varying with the relative

density in Figure 5.3 and Figure 5.4. The plots include only the friction angles of the unconfined

(3D) backfill materials to prevent plane strain conditions from influencing the results. Figure 5.4

includes only the non-cohesive materials, since the non-cohesive materials typically had lower

friction angles due to the use of cohesion in PYCAP. In most cases the friction angles for both

methods are the same but for there is a slight difference. The plots show that the friction angles

for the soils increase as the relative density also increases, which is consistent with the expected

results.

59

Figure 5.3: A Comparison of the PYCAP Friction Angles with Relative Density for the Unconfined Backfills.

φ = 0.1773Dr + 25.119 R² = 0.3155

25.0

29.0

33.0

37.0

41.0

45.0

30 40 50 60 70 80 90

PYC

AP

Fric

tion

Ang

le (d

egre

es)

Relative Density, Dr (%)

60

Figure 5.4: A Comparison of the PYCAP Friction Angles with Relative Density for the Unconfined, Non-Cohesive Backfills.

The friction angles back-calculated from ABUTMENT are shown as varying with the

relative density in Figure 5.5 and Figure 5.6. The plots include only the friction angles of the

unconfined (3D) backfill materials to prevent plane strain conditions from influencing the

results. Figure 5.6 includes only the non-cohesive materials, since the non-cohesive materials

typically had lower friction angles due to the use of cohesion in ABUTMENT. In most cases the

friction angles for both methods are the same but for some there is a slight difference. The

comparisons show that the friction angles of the soils increase as the relative density also

increases, which is consistent with the expected results.

φ = 0.235Dr + 23.051 R² = 0.6391

25.0

29.0

33.0

37.0

41.0

45.0

30 40 50 60 70 80 90

PYC

AP

Fric

tion

Ang

le (d

egre

es)


61

Figure 5.5: A Comparison of the ABUTMENT Friction Angles with Relative Density for the Unconfined Backfills.

φ = 0.1703Dr + 25.905 R² = 0.2819

25.0

29.0

33.0

37.0

41.0

45.0

30 40 50 60 70 80 90

AB

UTM

ENT

Fric

tion

Ang

le (d

egre

es)


62

Figure 5.6: A Comparison of the ABUTMENT Friction Angles with Relative Density for the Unconfined, Non-Cohesive Backfills.

The average friction angle of each soil type is shown in Figure 5.7 and Figure 5.8. Figure

5.7 shows the average PYCAP friction angles of the dense and loose unconfined (3D) soils.

Figure 5.8 shows the PYCAP friction angles of the confined and unconfined dense materials.

The back-calculated values for the friction angles are consistent with the expected results. The

dense materials exhibited higher friction angles than the loose materials. Because of plane strain

conditions, the confined material friction angles are higher than those of the unconfined

materials.

φ = 0.2216Dr + 24.279 R² = 0.6158

25.0

29.0

33.0

37.0

41.0

45.0

30 40 50 60 70 80 90

AB

UTM

ENT

Fric

tion

Ang

le (d

egre

es)


63

Figure 5.7: A Comparison of the PYCAP Friction Angles for the Unconfined (3D) Backfills.

Figure 5.8: A Comparison of the PYCAP Friction Angles for the Dense Backfills.

The average friction angle of each soil type is shown in Figure 5.9 and Figure 5.10.

Figure 5.9 shows the average ABUTMENT friction angles of the dense and loose unconfined

(3D) soils. Figure 5.10 shows the ABUTMENT friction angles of the confined and unconfined

25

27

29

31

33

35

37

39

41

43

Silty Sand Clean Sand Fine Gravel Coarse Gravel

PYC

AP

Fric

tion

Ang

le (d

egre

es)

Dense MeanLoose Mean

25

30

35

40

45

50

55

Dense SiltySand

Dense CleanSand

Dense FineGravel

Dense CoarseGravel

PYC

AP

Fric

tion

Ang

le (d

egre

es)

2D Mean3D Mean

64

dense materials. As with the PYCAP friction angles, the back-calculated values for the friction

angles are consistent with the expected results. The dense materials exhibited higher friction

angles than the loose materials, although the difference between the dense and loose coarse

gravel average friction angles is much closer than those of PYCAP. Because of plane strain

conditions, the confined material friction angles are higher than those of the unconfined

materials.

Figure 5.9: A Comparison of the ABUTMENT Friction Angles for the Unconfined (3D) Backfills.

25

27

29

31

33

35

37

39

41

43


AB

UTM

ENT

Fric

tion

Ang

le (d

egre

es)


65

Figure 5.10: A Comparison of the ABUTMENT Friction Angles for the Dense Backfills.

5.2 Cohesion

The cohesion value is an important parameter in developing the passive force-

displacement relationship in PYCAP and ABUTMENT. The cohesion values back-calculated

using PYCAP and ABUTMENT are shown in Figure 5.11 and Figure 5.12, respectively. The

ranges of the cohesion values for all of the soil types are summarized in Table 5.3 and Table 5.4.

25

30

35

40

45

50

55


AB

UTM

ENT

Fric

tion

Ang

les (

degr

ees)

2D Mean3D Mean

66

Figure 5.11: Comparison of the Cohesion Values used in PYCAP for all of the Soil Types.

Figure 5.12: Comparison of the Cohesion Values used in ABUTMENT for all of the Soil Types.

0

100

200

300

400

500

600

700

LooseSiltySand3D

DenseSiltySand2D

DenseSiltySand3D

LooseCleanSand2D

LooseCleanSand3D

DenseCleanSand2D

DenseCleanSand3D

LooseFine

Gravel3D

DenseFine

Gravel3D

LooseCoarseGravel

3D

DenseCoarseGravel

3D

PYC

AP

Coh

esio

n (p

sf)

0

100

200

300

400

500

600

700

LooseSiltySand3D

DenseSiltySand2D

DenseSiltySand3D

LooseCleanSand2D

LooseCleanSand3D

DenseCleanSand2D

DenseCleanSand3D

LooseFine

Gravel3D

DenseFine

Gravel3D

LooseCoarseGravel

3D

DenseCoarseGravel

3D

Abu

tmen

t Coh

esio

n (p

sf)

67

Table 5.3: Ranges for the PYCAP Cohesion Values

Table 5.4: Ranges for the ABUTMENT Cohesion Values

As expected, the dense silty sands had the highest cohesion, ranging from 300-647 psf.

However, the loose silty sand needed a much smaller value for cohesion, 60 psf, in order to

develop a passive force-displacement curve that matched the measured data. Most of the clean

sands needed cohesion values between 60 and 90 psf to obtain good fits. Some cohesion was

calculated from the direct shear and triaxial tests. The dense coarse gravel needed higher

cohesion than would be expected, 150-286 psf. The reason for these cohesion values is because

the dense coarse gravel contained 10-12% of silty fines. The parameters used in PYCAP and

ABUTMENT for both dense coarse gravel (3D) tests correspond to the measured soil parameters

Soil TypeLoose Clean Sand 10 - 60Dense Clean Sand 60 - 90 0 - 60Loose Silty SandDense Silty Sand 190 - 380 570 - 650Loose Fine GravelDense Fine Gravel 0 - 79.4Loose Coarse GravelDense Coarse Gravel 150 - 286

PYCAP Cohesion (psf)2D 3D

n/a

n/a 0

60

60

n/an/a

n/a0

Soil TypeLoose Clean SandDense Clean Sand 60 - 130 0 - 100Loose Silty SandDense Silty Sand 50 - 300 500 - 647Loose Fine GravelDense Fine Gravel 15 - 84Loose Coarse GravelDense Coarse Gravel 251 - 286

n/an/a

ABUTMENT Cohesion (psf)2D 3D

n/a

n/an/a

0

0

60

10130

68

obtained from testing in the laboratory. Both the measured parameters and the PYCAP and

ABUTMENT parameters were determined in Rollins and Cole (2006), Shamsabadi (2007), and

Pruett (2009).

The average cohesion of each soil type is shown in Figure 5.13, Figure 5.14, Figure 5.15,

and Figure 5.16. Figure 5.13 and Figure 5.15 show the average PYCAP and ABUTMENT

cohesion values, respectively, of the dense and loose unconfined (3D) soils. Figure 5.14 and

Figure 5.16 show the PYCAP and ABUTMENT cohesion values, respectively, of the confined

and unconfined dense materials.

Figure 5.13: A Comparison of the PYCAP Cohesion Values for the Unconfined (3D) Backfills.

0

100

200

300

400

500

600

700


PYC

AP

Coh

esio

n (p

sf)

Dense Mean

Loose Mean

69

Figure 5.14: A Comparison of the PYCAP Cohesion Values for the Dense Backfills.

Figure 5.15: A Comparison of the ABUTMENT Cohesion Values for the Unconfined (3D) Backfills.

0

100

200

300

400

500

600

700


PYC

AP

Coh

esio

n (p

sf)

2D Mean3D Mean

0

100

200

300

400

500

600

700


AB

UTM

ENT

Coh

esio

n (p

sf) Dense Mean

Loose Mean

70

Figure 5.16: A Comparison of the ABUTMENT Cohesion Values for the Dense Backfills.

5.3 Initial Soil Modulus, Ei

The initial soil modulus is a parameter used in PYCAP to develop the passive force-

displacement relationship of a backfill material. Duncan and Mokwa (2001) provides ranges of

initial soil modulus corresponding to density which are summarized in Table 5.5. The values for

initial soil modulus of the various soil types are shown in Figure 5.17 and summarized in Table

5.6.

0

100

200

300

400

500

600

700


AB

UTM

ENT

Coh

esio

n (p

sf) 2D Mean

3D Mean

71

Table 5.5: Stiffness Ranges for Various Soil Densities (Duncan and Mokwa, 2001)

Figure 5.17: Comparison of the Initial Soil Modulus for All of the Soil Types.

0

200

400

600

800

1000

1200

LooseSiltySand3D

DenseSiltySand2D

DenseSiltySand3D

LooseCleanSand2D

LooseCleanSand3D

DenseCleanSand2D

DenseCleanSand3D

LooseFine

Gravel3D

DenseFine

Gravel3D

LooseCoarseGravel

3D

DenseCoarseGravel

3D

Initi

al S

oil M

odul

us, E

i (ks

f)

72

Table 5.6: Ranges for the Initial Soil Modulus

The results from the initial soil modulus are consistent with those anticipated. The tests in

which the backfill was confined to the width of the wall (2D) resulted in a higher initial soil

modulus than the tests on the same material that were unconfined (3D). Soils under plane strain

conditions typically provide higher stiffness than those in an unconfined condition. In most

cases; the initial soil modulus of the backfill materials in the dense state was higher than those of

the loose state. The higher compactive effort provided a higher relative density as well as a

higher stiffness for the backfill material.

Table 5.7, Table 5.8, Table 5.9, and Table 5.10 summarize the relative density of each

backfill with the initial soil modulus and the corresponding Duncan and Mokwa (2001) ranges.

Table 5.11 shows the range of back-calculated initial soil modulus values and the values

recommended by Duncan and Mokwa (2001). Based on the field load tests, the initial soil

modulus, Ei, in the Duncan and Mokwa hyperbolic equation typically ranges from 450 to 1000

ksf with a mean of 819 ksf for the dense materials, which is a typical fill for bridge approaches.

The range is 150 to 491 ksf with a mean of 275 ksf for the loose sands and gravels, which is

typical for naturally deposited soil bridge abutments.

Soil TypeLoose Clean Sand 201 - 210Dense Clean Sand 680 - 1000 450 - 800Loose Silty SandDense Silty SandLoose Fine GravelDense Fine Gravel 600 - 706Loose Coarse GravelDense Coarse Gravel 600 - 830

Initial Soil Modulus, Ei (ksf)2D 3D

n/a

n/a 491800150

1000

400

n/an/an/a

200

73

Table 5.7: A Comparison of Relative Density with the Initial Soil Modulus of the Silty Sand

Table 5.8: A Comparison of Relative Density with the Initial Soil Modulus of the Clean Sand

Kwon (2007) 40 150 400 - 800

UCLA (Stewart et al., 2007) 92 1000 600 - 1200UCLA Plane Strain 92 1000 600 - 1200

Rollins and Cole (2006) 67 800 500 - 1000Valentine (2007) 80 800 600 - 1200

Duncan & Mokwa Range

Dense Silty Sand 3D

Dense Silty Sand 2D

Loose Silty Sand 3D

Dr Ei

Strassburg (2010) 41 400 400 - 800

Cummins (2009) 44 201 400 - 800Strassburg (2010) 31 210 400 - 800

Bingham (2012) 79 680 600 - 1200Jessee (2012) #1 80 1000 600 - 1200Jessee (2012) #2 80 1000 600 - 1200Jessee (2012) #3 80 1000 600 - 1200

Rollins and Cole (2006) 63 775 500 - 1000Heiner (2010) 80 800 600 - 1200Bingham (2012) 84 450 600 - 1200

Duncan & Mokwa Range (ksf)

Loose Clean Sand 2D

Loose Clean Sand 3D

Dense Clean Sand 2D

Dense Clean Sand 3D

Dr (%) Ei (ksf)

74

Table 5.9: A Comparison of Relative Density with the Initial Soil Modulus of the Loose Gravel

Table 5.10: A Comparison of Relative Density with the Initial Soil Modulus of the Coarse Gravel

Table 5.11: Ranges of Initial Soil Modulus for Different Relative Densities

The values for the initial soil modulus are consistent with the ranges provided by Duncan

and Mokwa (2001). In the preloaded or compacted category, the range for the loose state is 400-

800 ksf and for the dense state the range is 600-1200 ksf. All of the initial soil modulus values of

the dense backfill materials fall within the range given, except dense clean sand (3D) (Bingham,

2012). Three of the five loose materials (loose clean sand (3D), loose silty sand (3D), and loose

Pruett (2009) 35 491 400 - 800

Rollins and Cole (2006) 54 706 500 - 1000Kwon (2007) 85 600 600 - 1200Pruett (2009) 74 670 600 - 1200


Dense Fine Gravel 3D

Loose Fine Gravel 3D

Dr Ei

Pruett (2009) 48 200 400 - 800

Rollins and Cole (2006) 69 600 500 - 1000Pruett (2009) 82 830 600 - 1200


Dr Ei

Dense Coarse Gravel 3D

Loose Coarse Gravel 3D

Density Dr Mean Duncan & MokwaLoose 40% Ei = 150 - 491 275 Ei = 400 - 800Medium 60% Ei = 600 - 800 720 Ei = 500 -1000Dense 80% Ei = 450 - 1000 819 Ei = 600 - 1200

Compacted

75

coarse gravel (3D)) do not fall within the range given by Duncan and Mokwa (2001). For these

materials, the values for initial soil modulus are between 150 and 200 ksf which is about 200 ksf

below the range for compacted material. Due to the majority of the loose materials falling below

the range, it may be necessary to modify the range to be 200-800 ksf.

The plot of the initial soil modulus, Ei, against relative density is shown in Figure 5.18.

The plot includes all of the unconfined (3D) tests performed and shows an upward trend for the

soil modulus as relative density increases. Increasing the density of a soil also increases the

stiffness.

Figure 5.18: A Comparison of Initial Soil Modulus, Ei, against Relative Density.

The average initial soil modulus, Ei, of each soil type is shown in Figure 5.19 and Figure

5.20. Figure 5.19 shows the average initial soil modulus of the dense and loose unconfined (3D)

Ei = 9.4682Dr - 38.648 R² = 0.505

0

100

200

300

400

500

600

700

800

900

30 40 50 60 70 80 90

Initi

al S

oil M

odul

us, E

i (ps

f)


76

soils. Figure 5.20 shows the initial soil modulus of the confined and unconfined dense materials.

The dense materials exhibited higher stiffness than the loose materials and the confined materials

showed higher stiffness than the unconfined values due to plane strain conditions.

Figure 5.19: A Comparison of the Initial Soil Modulus Values for the Unconfined (3D) Backfills.

0

100

200

300

400

500

600

700

800

900


Initi

al S

oil M

odul

us, E

i (ks

f)


77

Figure 5.20: A Comparison of the Initial Soil Modulus Values for the Dense Backfills.

5.4 Strain at 50% of Ultimate Strength, ε50

The strain at 50% of ultimate strength, ε50, is a parameter used in ABUTMENT. The

values for ε50 are shown in Figure 5.21 and the ranges for these values are given in Table 5.12.

The loose materials were expected to exhibit higher strain at 50% of the ultimate strength than

the dense materials because they have lower stiffness. The unconfined silty sands have the same

value for ε50 while the strain of the dense unconfined clean sand is larger than the strain for the

loose clean sand. Heiner (2010) and Bingham (2012) force-displacement curves for the dense

clean sand (3D) category show low stiffness, which might account for the relatively high strain

values.

0

200

400

600

800

1000

1200


Initi

al S

oil M

odul

us, E

i (ks

f)

2D Mean3D Mean

78

Figure 5.21: Comparison of the Strain at 50% of Ultimate Strength for All of the Soil

Types.

Table 5.12: Ranges for the Strain at 50% of Ultimate Strength

The strain at 50% of ultimate strength, as used in ABUTMENT, as a function of the

relative density of the backfill materials and is plotted in Figure 5.22. Only the results of the

unconfined (3D) backfill materials are plotted to remove the influence of plane strain conditions.

The loose materials should have lower stiffness that would allow for more displacement to occur

0

0.002

0.004

0.006

0.008

0.01

0.012

LooseSiltySand3D

DenseSiltySand2D

DenseSiltySand3D

LooseCleanSand2D

LooseCleanSand3D

DenseCleanSand2D

DenseCleanSand3D

LooseFine

Gravel3D

DenseFine

Gravel3D

LooseCoarseGravel

3D

DenseCoarseGravel

3D

Stra

in a

t 50%

of U

ltim

ate

Stre

ngth

, ε50

Soil TypeLoose Clean Sand 0.003 - 0.006Dense Clean Sand 0.004 - 0.008 0.002 - 0.007Loose Silty SandDense Silty SandLoose Fine GravelDense Fine Gravel 0.0015 - 0.004Loose Coarse GravelDense Coarse Gravel 0.0037 - 0.005n/a

2D 3D

n/a

n/an/an/a 0.0074

0.0050.0030.003

0.0036

0.010

Strain at 50% of Ultimate Strength, ε50

79

and therefore a higher strain. This may have been a result of the dense sands that exhibited low

stiffness.

Figure 5.22: A Comparison of the Strain at 50% of Ultimate Strength against Relative Density for the Unconfined Backfills.

The average strain at 50% of the Ultimate Strength, ε50, of each soil type is shown in

Figure 5.23 and Figure 5.24. Figure 5.23 shows the average initial soil modulus of the dense and

loose unconfined (3D) soils. Figure 5.24 shows the initial soil modulus of the confined and

unconfined dense materials. Due to an insufficient amount of test data, other comparisons were

not included. These results are not entirely consistent with the expected results. The dense clean

sand test results showed higher values of strain than the loose sand, which is inaccurate. Also the

confined silty sand exhibited higher strain than the unconfined silty sand. As previously

ε50 = 2E-06Dr + 0.0042 R² = 0.0003

0.0000

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.0070

0.0080

30 40 50 60 70 80 90

Stra

in a

t 50%

of U

ltim

ate

Stre

ngth

, ε50


80

mentioned, the possible reasons for these differences include the low stiffness values of the

dense sand (3D).

Figure 5.23: A Comparison of the Strain at 50% of Ultimate Strength for the Unconfined (3D) Materials.

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008


Stra

in a

t 50%

of U

ltim

ate

Stre

ngth


81

Figure 5.24: A Comparison of the Strain at 50% of Ultimate Strength for the Dense Materials.

5.5 Modified HFD: Fult/Beff

The ratio of the ultimate passive resistance over the effective width of the wall or

abutment is used to calculate the variables C and D according with Equation (2.6). The effective

width of the structure is the actual width multiplied by the Brinch-Hansen 3D correction factor.

The values of Fult/Beff for the soils used during testing are shown in Figure 5.25 and the range of

these values is summarized in Table 5.13. The confined dense clean sand had the highest

measured passive resistance per foot of wall. This is consistent with each of the back-calculated

parameters. The values for Fult/Beff generally increase for the loose condition as soil type moves

from silty sand to the sand and gravels. For the dense conditions, the values of Fult/Beff for all of

the materials are similar except for the coarse gravel, which is higher than the others. As

expected, the dense materials provide higher values of Fult/Beff than the loose materials and the

values for the confined (2D) materials are also higher than those for the unconfined (3D)

materials.

0

0.001

0.002

0.003

0.004

0.005

0.006


Stra

in a

t 50%

of U

ltim

ate

Stre

ngth

2D Mean3D Mean

82

Figure 5.25: Comparison of Fult/Beff for All of the Soil Types.

Table 5.13: Ranges for Fult/Beff for the Modified HFD Equation

The average ultimate resistance normalized by the effective width, Fult/Beff, of each soil

type is shown in Figure 5.26 and Figure 5.27. Figure 5.26 shows the average Fult/Beff of the

dense and loose unconfined (3D) soils. Figure 5.27 shows the Fult/Beff of the confined and

0

10

20

30

40

50

60

70

LooseSiltySand3D

DenseSiltySand2D

DenseSiltySand3D

LooseCleanSand2D

LooseCleanSand3D

DenseCleanSand2D

DenseCleanSand3D

LooseFine

Gravel3D

DenseFine

Gravel3D

LooseCoarseGravel

3D

DenseCoarseGravel

3D

F ult/B

eff(k

ip/ft

)

Soil TypeLoose Clean Sand 8.7 - 16.3Dense Clean Sand 47.8 - 58.9 19.5 - 37.7Loose Silty SandDense Silty Sand 27.5 - 28.5Loose Fine GravelDense Fine Gravel 15.3 - 31.0Loose Coarse GravelDense Coarse Gravel 35.4 - 39.7

30.3n/a 11.5n/an/a 16.4n/a

Fult/Beff (kip/ft)2D 3D

30.0

n/a 8.3

83

unconfined dense materials. The value Fult/Beff is the passive resistance of the backfill and

increases with increasing density. Aside from the fine gravel, the Fult/Beff values increase as soil

type moves from silty sand to sand and then the gravels. The confined conditions also show a

greater value for Fult/Beff over the unconfined conditions.

Figure 5.26: A Comparison of the Fult/Beff Values for the Unconfined (3D) Backfills.

0

5

10

15

20

25

30

35

40


F ult/B

eff (

kip/

ft)


84

Figure 5.27: A Comparison of the Fult/Beff Values for the Dense Backfills.

5.6 Modified HFD: yave

The displacement associated with 50% of the ultimate passive resistance, yave, is used to

calculate the variables C and D according with Equation (2.6). The yave values for the various

soil types are shown in Figure 5.28 and the range of these values is summarized in Table 5.14.

The value of yave for a soil is related to the stiffness of that soil, therefore higher values for yave

are expected for the loose materials than for the dense materials. The results for all of the

material types are consistent with the expected results. The loose gravels had the highest

displacement at 50% of ultimate strength. The confined materials should also have lower

displacement at 50% of ultimate strength than the unconfined materials due to the increase in

strength and stiffness from plane strain conditions. However, the dense silty sand (2D) had a

higher yave than the dense silty sand (3D). This unanticipated result may be a consequence of the

small sample size used in this research.

0

10

20

30

40

50

60


F ult/B

eff (

kip/

ft)

2D Mean3D Mean

85

Figure 5.28: Comparison of yave for all of the Soil Types.

Table 5.14: Ranges of yave for the Modified HFD Equation

The average displacement at 50% of the ultimate strength, yave, of each soil type is shown

in Figure 5.29 and Figure 5.30. Figure 5.29 shows the average yave of the dense and loose

unconfined (3D) soils. Figure 5.30 shows the yave of the confined and unconfined dense

materials. The value yave is the displacement at 50% of the ultimate strength and should decrease

with increasing density and confinement. The results are consistent with the anticipated results

0

0.2

0.4

0.6

0.8

1

1.2

1.4

LooseSiltySand3D

DenseSiltySand2D

DenseSiltySand3D

LooseCleanSand2D

LooseCleanSand3D

DenseCleanSand2D

DenseCleanSand3D

LooseFine

Gravel3D

DenseFine

Gravel3D

LooseCoarseGravel

3D

DenseCoarseGravel

3D

y ave

(in.)


0.3n/a 1.3n/an/a 1.08n/a

Yave (in.)2D 3D0.8

n/a 0.7

86

except in the confined silty sand, which has a higher yave than the unconfined silty sand. This is

consistent with the ε50 results for the confined dense silty sand. (See the Strain at 50% of

Ultimate Strength, ε50 section.) As previously discussed, a possible reason for these

discrepancies is the low stiffness measured in the dense unconfined sand tests.

Figure 5.29: A Comparison of yave for the Unconfined (3D) Backfills.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40


Dis

plac

emen

t at 5

0% o

f Ulti

mat

e St

reng

th, y

ave (

in.)


87

Figure 5.30: A Comparison of yave for the Dense Backfills.

5.7 Passive Earth Pressure Coefficient, Kp

The passive pressure of a backfill material is the resistance of the material to compressive

forces caused by the movement of a structure into the soil. Several methods have been developed

to estimate the ultimate passive pressure of a soil. Some of these methods include the Rankine

theory and the Coulomb theory. The passive earth pressure coefficient, Kp, is calculated using

Equation (5-1) for the Rankine method and Equation (5-2) for the Coulomb method.

𝐾𝑝 = 𝑡𝑎𝑛2 �45 +∅2� (5-1)

𝐾𝑝 =𝑠𝑖𝑛2(𝛽 − ∅)

𝑠𝑖𝑛2 𝛽 𝑠𝑖𝑛(𝛽 + 𝛿) �1 −�𝑠𝑖𝑛(∅ + 𝛿) 𝑠𝑖𝑛(∅ + 𝛼)𝑠𝑖𝑛(𝛽 + 𝛿) 𝑠𝑖𝑛(𝛽 + 𝛼)�

2 (5-2)

0.00

0.10

0.20

0.30

0.40

0.50

0.60


Dis

plac

emen

t at 5

0% o

f Ulti

mat

e St

reng

th, y

ave (

in.)

2D Mean3D Mean

88

where

β = wall angle

φ = soil friction angle

δ = soil-wall interface friction angle

α = angle of the backfill material

For each of the tests, the passive earth pressure coefficients were back-calculated using

Equation (5-3), which accounts for the unit weight and cohesion of the backfill material. The

cohesion was assumed to be negligible for the granular backfill materials; therefore the second

term in Equation (5-3) was not used to calculate Kp, except for the tests on silty sand.

𝑃𝑝 =12𝛾𝐻2𝐾𝑝 + 2𝑐𝐻�𝐾𝑝 (5-3)

where

Pp = passive force per unit length of structure

γ = unit weight of the backfill material

H = height of the structure

Kp = passive earth pressure coefficient

c = cohesion

The passive earth pressure coefficients as back-calculated are shown in Figure 5.31 and

the ranges are summarized in Table 5.15. The results from the comparisons below were

consistent with those anticipated. The tests in which the backfill was confined to the width of the

wall (2D) resulted in a higher value for Kp than the tests on the same material that were

89

unconfined (3D). The soils under plane strain conditions were able to provide more passive

resistance than those in an unconfined condition. For all tests, the passive earth pressure

coefficients of the backfill materials in the dense state were higher than those of the loose state.

The higher compactive effort provided a higher relative density as well as a higher passive

resistance for the backfill material.

The passive resistance of the dense clean sand (2D) was higher than expected. The dense

clean sand (2D) had more than two times the passive resistance of the dense coarse gravel (3D).

Gravels are typically associated with higher resistance to loading than sands. However, the

confinement of the dense clean sand may be the reason for the higher passive resistance. As

shown in the previous sections, the confined (2D) tests resulted in higher strengths and stiffness.

Confined testing on a dense coarse gravel is needed in order to compare the passive resistance of

these tests.

90

Figure 5.31: Comparison of the Passive Earth Pressure Coefficient for All of the Soil Types.

Table 5.15: Ranges for the Measured Passive Earth Pressure Coefficient

The passive earth pressure coefficient for each test with the calculated Rankine and

Coulomb passive earth pressure coefficients are summarized in Table 5.16 through Table 5.19.

The differences from the measured values for both the Rankine and Coulomb methods are also

0

5

10

15

20

25

30

35

40

45

50

LooseSiltySand3D

DenseSiltySand2D

DenseSiltySand3D

LooseCleanSand2D

LooseCleanSand3D

DenseCleanSand2D

DenseCleanSand3D

LooseFine

Gravel3D

DenseFine

Gravel3D

LooseCoarseGravel

3D

DenseCoarseGravel

3D

Pass

ive

Earth

Pre

ssur

e C

oeffi

cien

t, K

p


n/an/a

17.0

Passive Earth Pressure Coefficient, Kp

2D 3D

n/a

n/an/a

8.3

5.9

2.511.3

91

shown. A negative value for the difference denotes an underestimation of the actual value while

a positive value shows an overestimation.

Table 5.16: Comparisons of the Measured Kp Value with the Rankine and Coulomb Methods for the Silty Sands

Table 5.17: Comparisons of the Measured Kp Value with the Rankine and Coulomb

Methods for the Clean Sands

Measured Rankine Coulomb Rankine Coulomb

Kwon (2007) 2.5 3.3 8.7 33% 253%

UCLA (Stewart et al., 2007) 11.3 4.6 24.9 -59% 121%UCLA Plane Strain 11.3 5.7 66.8 -50% 492%

Rollins and Cole (2006) 6.5 2.7 5.2 -59% -20%Valentine (2007) 9.3 2.9 6.1 -69% -35%

Dense Silty Sand 3D

Dense Silty Sand 2D

Loose Silty Sand 3D

Kp Difference


Strassburg (2010) 17.0 3.9 13.5 -77% -21%

Cummins (2009) 3.8 4.0 13.6 5% 254%Strassburg (2010) 9.5 3.9 13.5 -60% 42%

Bingham (2012) 30.1 5.3 36.5 -82% 21%Jessee (2012) #1 46.6 7.2 164 -85% 251%Jessee (2012) #2 46.1 7.2 164 -84% 255%Jessee (2012) #3 46.2 7.2 164 -85% 254%

Rollins and Cole (2006) 13.5 4.4 22.5 -67% 67%Heiner (2010) 15.7 4.7 27.3 -70% 74%Bingham (2012) 18.1 5.3 47.4 -71% 162%

Dense Clean Sand 3D

Dense Clean Sand 2D

Loose Clean Sand 3D

Loose Clean Sand 2D

Kp Difference

92

Table 5.18: Comparisons of the Measured Kp Value with the Rankine and Coulomb Methods for the Fine Gravels

Table 5.19: Comparisons of the Measured Kp Value with the Rankine and Coulomb Methods for the Coarse Gravels

On average, the Rankine method underestimated the measured Kp of the silty sands by

41% and the Coulomb method overestimated by 162%. For the clean sands, the Rankine method

underestimated the measured Kp by 67% while the Coulomb method overestimated by 153%.

The Rankine method underestimated the measured Kp of the fine gravels by 53% and the

Coulomb method overestimated by 195%. The Rankine method underestimated the measured Kp

of the coarse gravels by 64% and the Coulomb method overestimated by 93%.

These results indicate that the Rankine method typically underestimates while the

Coulomb method typically overestimates the passive earth pressure coefficient. In many of the

tests the Coulomb method overestimates the value of Kp by a factor of 2 or 3. The Rankine

method only accounts for the friction angle of the soil and not the geometry whereas the


Pruett (2009) 5.9 4.0 24.2 -31% 314%

Rollins and Cole (2006) 9.1 3.5 10.5 -61% 15%Kwon (2007) 13.2 5.6 59.7 -58% 352%Pruett (2009) 15.0 5.6 30.1 -62% 101%

Dense Fine Gravel 3D

Loose Fine Gravel 3D

Kp Difference


Pruett (2009) 8.3 4.5 23.7 -45% 185%

Rollins and Cole (2006) 19.8 4.6 24.9 -77% 26%Pruett (2009) 16.5 4.7 27.8 -71% 69%

Kp Difference

Dense Coarse Gravel 3D

Loose Coarse Gravel 3D

93

Coulomb method accounts for soil properties as well as geometry. This may explain the

significant differences between the measured and calculated values.

The passive earth pressure coefficients as a function of the relative density is plotted in

Figure 5.32. While the ultimate passive resistance as a function of the relative density is plotted

in Figure 5.33. Only the unconfined (3D) data was used in these comparisons. The ultimate

passive resistance per effective wall area was used and assumes the distribution of Pult to be

uniform across the entire wall. The results show an increase in both Kp and Pult with increasing

relative density for the backfill materials.

Figure 5.32: A Comparison of the Passive Earth Pressure Coefficients against Relative Density for the Unconfined Backfills.

Kp = 0.2013Dr - 1.4545 R² = 0.5194

0.0

5.0

10.0

15.0

20.0

25.0

30 40 50 60 70 80 90

Pass

ive

Earth

Pre

ssur

e C

oeffi

cien

t, K

p


94

Figure 5.33: A Comparison of the Ultimate Passive Resistance per Effective Area against Relative Density for the Unconfined Backfills.

The average passive earth pressure coefficients, Kp, of each soil type are shown in Figure

5.34 and Figure 5.35. Figure 5.34 shows the average Kp of the dense and loose unconfined (3D)

soils. Figure 5.35 shows the Kp of the confined and unconfined dense materials. Due to an

insufficient amount of test data, other comparisons were not included. The passive earth pressure

coefficient, Kp, should increase with increasing density and confinement. The results of the back-

calculated parameters are consistent with this expected result. Also, the passive earth pressure

coefficients generally increase as the soil type moves from silty sand to sand and then to the

gravels.

Pult/Aeff = 0.0746Dr - 0.8999 R² = 0.6089

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

30 40 50 60 70 80 90

Ulti

mat

e Pa

ssiv

e R

esis

tanc

e (k

sf)


95

Figure 5.34: A Comparison of the Passive Earth Pressure Coefficients for the Unconfined (3D) Backfills.

Figure 5.35: A Comparison of the Passive Earth Pressure Coefficients for the Dense Backfills.

0

2

4

6

8

10

12

14

16

18

20


Pass

ive

Earth

Pre

ssur

e C

oeffi

cien

t, K

p


0

5

10

15

20

25

30

35

40

45


Pass

ive

Earth

Pre

ssur

e C

oeffi

cien

t, K

p

2D Mean3D Mean

96

5.8 Caltrans

The results of the dense backfill tests were compared with the bi-linear Caltrans seismic

design approach, as described in the Literature Review. This section also provides comparisons

of the ultimate passive resistance, Pult, and backfill stiffness, K, of the measured data with the

values calculated by the Caltrans approach. The backfill stiffness of the measured data was taken

as the slope of the force-displacement relationship from the first data point until 50% of the

ultimate strength.

Comparisons were made with the Caltrans method for two different wall heights, 3.67 ft

and 5.5 ft. The values of Pult as well as K for a wall height of 3.67 ft are shown in Figure 5.36

and Figure 5.37, respectively. No confined (2D) tests were performed on the pile caps with a

height of 3.67 ft. The Caltrans method was developed for dense materials but the results of tests

on the loose material were included on the plots. The Caltrans approach approximates the

passive resistance as well as the stiffness of the dense materials reasonably well.

97

Figure 5.36: A Comparison of Pult for the Caltrans Method and the Measured Results for a Wall Height of 3.67 ft.

0

100

200

300

400

500

15 17 19 21 23 25 27

Ulti

mat

e Pa

ssiv

e R

esis

tanc

e, P

ult (

kips

)

Effective Width (ft)

Caltrans3D Measured Dense3D Measured Loose

98

Figure 5.37: A Comparison of K for the Caltrans Method and the Measured Results for a Wall Height of 3.67 ft.

The dense material values of Pult as well as K for a wall height of 5.5 ft are shown in

Figure 5.38 and Figure 5.39, respectively. The Caltrans 2004 method provides an accurate

estimation of Pult and K for the unconfined (3D) dense materials with a wall height of 5.5 ft.

However, the estimations for the measured values of Pult for the confined (2D) materials are not

as good. The value for K as calculated by Caltrans 2010 provides a good fit with the confined

data but the passive resistance is underestimated for the confined cases.

0

200

400

600

800

1000

1200

15 17 19 21 23 25 27

Soil

Stiff

ness

, K (

kips

/in.)


3D Measured Dense3D Measured LooseCaltrans 2004Caltrans 2011

99

Figure 5.38: A Comparison of Pult for the Caltrans Method and the Measured Results for a Wall Height of 5.5 ft.

0

100

200

300

400

500

600

700

800

900

10 12 14 16 18 20 22 24

Ulti

mat

e Pa

ssiv

e R

esis

tanc

e, P

ult (

kips

)


Caltrans2D Measured Dense3D Measured Dense

100

Figure 5.39: A Comparison of K for the Caltrans Method and the Measured Results of the Dense Materials with a Wall Height of 5.5 ft.

The values of Pult as well as K for the loose materials with a wall height of 5.5 ft are

shown in Figure 5.40 and Figure 5.41, respectively. The data for the loose backfill materials are

shown despite the Caltrans method being typically used for dense materials. As expected, the

Caltrans method overestimates both Pult and K for the unconfined (3D) loose materials,

especially the the value for K where the Caltrans 2010 method is used. However, the confined

(2D) loose material fits well with the values calculated using the Caltrans 2004 method. More

testing is needed for this case but if the measured point is representative of other confined (2D)

loose backfill material, the Caltrans method may be appropriate for estimating Pult and K for

loose confined materials.

0

200

400

600

800

1000

1200

1400

1600

10 12 14 16 18 20 22 24

Soil

Stiff

ness

, K (

kips

/in.)


2D Measured Dense3D Measured DenseCaltrans 2004Caltrans 2011

101

Figure 5.40: A Comparison of Pult for the Caltrans Method and the Measured Results for Loose Materials with a Wall Height of 5.5 ft.

0

100

200

300

400

500

600

700

800

10 12 14 16 18 20 22 24

Ulti

mat

e Pa

ssiv

e R

esis

tanc

e, P

ult (

kips

)


Caltrans2D Measured Loose3D Measured Loose

102

Figure 5.41: A Comparison of K for the Caltrans Method and the Measured Results for Loose Materials with a Wall Height of 5.5 ft.

0

200

400

600

800

1000

1200

1400

1600

10 12 14 16 18 20 22 24

Soil

Stiff

ness

, K (

kips

/in.)


Caltrans 20042D Measured Loose3D Measured LooseCaltrans 2011

103

6 CONCLUSION

Large-scale as well as small-scale testing has been performed by Dr. Kyle Rollins and

several graduate students at BYU in order to determine the passive force-displacement

relationship of various backfill materials under different conditions. The four backfill materials

used during testing included clean sand, silty sand, fine gravel, and coarse gravel. The backfill

conditions varied from loose to dense and confined (2D) to unconfined (3D).

The results of these tests were collected and compared with common methods used in

developing force-displacement relationships of backfill materials. These methods include

PYCAP (Duncan & Mokwa, 2001), ABUTMENT (Shamsabadi, 2007), and the modified

hyperbolic force-displacement equation as presented by Shamsabadi (2008). Using the common

force-displacement approaches and the measured data, parameters necessary to develop the

passive force-displacement curves without extensive geotechnical testing were back-calculated.

6.1 Conclusions

Based upon the data and analyses presented in this project, the following conclusions and

recommendations are made:

104

6.1.1 Friction Angle

The results from the friction angle comparisons were consistent with those anticipated.

The tests in which the backfill was confined to the width of the wall (2D) resulted in higher

friction angles than the tests on the same material that were unconfined (3D). The 2D failure

geometries produce higher passive force, and therefore higher friction angles, because the soil

fails in a plane strain. In most cases, the friction angles of the backfill materials in the dense state

were higher than those of the loose state. The higher compactive effort provided a higher relative

density as well as a higher strength for the backfill material.

The friction angles of the materials generally increased as soil type moved from the silty

sand up to the sand and gravel. The friction angles of the dense clean sands were higher than the

friction angles of the dense coarse gravels. This may be due to the sand being confined to the

width of the wall and the gravel being unconfined. No testing has been performed on gravels in

confined conditions (2D); therefore further testing on fine and coarse gravels in the confined

condition is needed.

6.1.2 Cohesion

The silty sand materials were expected to have the highest values of cohesion. This was

true for the dense silty sands; however, the loose silty sand needed a much smaller value for

cohesion in order to develop a passive force-displacement curve that matched the measured data.

Despite being a cohesionless soil, most of the clean sands needed some cohesion to obtain good

fits with the measured data. In many cases, this was done to keep the soil friction angle of the

dense sands equal to or less than 50 degrees. The dense coarse gravels contained 10-12% silty

fines and therefore had higher cohesion values than expected for a coarse gravel. The parameters

used in PYCAP and ABUTMENT for both tests correspond to the measured soil parameters

105

obtained from laboratory testing. The measured parameters as well as the PYCAP and

ABUTMENT parameters were determined in Rollins and Cole (2006), Shamsabadi (2007), and

Pruett (2009). Testing on additional cohesive materials, such as a clay backfill, is needed.

6.1.3 Initial Soil Modulus

The results from the initial soil modulus comparisons were consistent with what was

expected. Similar to the friction angle comparisons, tests in which the backfill was confined to

the width of the wall (2D) resulted in a higher initial soil modulus than the tests on the same

material that were unconfined (3D). As expected, soils under higher compactive effort provide

higher relative densities as well as higher values of stiffness.

The values for the initial soil modulus compare reasonably well with the ranges provided

by Duncan and Mokwa (2001). The stiffness of the materials generally increased as soil type

moved from the silty sand up to the sand and gravel except in the dense conditions. For the dense

materials, the stiffness was lowest for the gravels and then increased as soil type moved to silty

sand and then clean sand. All of the values of initial soil modulus for the dense backfill materials

fall within the range given except for one while three of the five loose materials do not fall

within the range provided. For these materials, the values for initial soil modulus are about 200

ksf below the range for pre-loaded or compacted material. Due to the number of loose materials

falling below the range, it is suggested to modify the range to 200-800 ksf. Further testing is

recommended to obtain more data in an effort to determine trends for the various backfill

materials.

106

6.1.4 Strain at 50% of Ultimate Strength, ε50

The strain at 50% of ultimate strength, ε50, is a parameter used in ABUTMENT to

estimate the passive force-displacement relationship of a backfill material. The loose materials

were expected to exhibit higher strain at 50% of the ultimate strength than the dense materials

because they have lower stiffness. This was observed in all of the materials except for the clean

sands, in which the dense sand had higher strains than the loose sand. There may be several

reasons for the higher than expected strains including adjusting other parameters, such as friction

angle or cohesion, to achieve higher stiffness in the force-displacement relationship or the low

stiffness of the measured force-displacement curves for the dense clean sand (3D) category as

measured by Heiner (2010) and Bingham (2012).

6.1.5 Modified HFD: Fult/Beff

The ratio of the ultimate passive resistance over the effective width of the wall or

abutment is used to calculate the variables C and D according with Equation (2.6). The confined

dense clean sand had the highest measured passive resistance per foot of wall. This is consistent

with each of the back-calculated parameters. The values for Fult/Beff generally increase for the

loose condition as soil type moves from silty sand to the sand and gravels. For the dense

conditions, the values of Fult/Beff for all of the materials are close to the same except the coarse

gravel, which is higher than the others. As expected, the dense materials provide higher values of

Fult/Beff than the loose materials and the confined (2D) materials are higher than the unconfined

(3D) materials, due to plane strain conditions.

107

6.1.6 Modified HFD: yave

The displacement associated with 50% of the ultimate passive resistance, yave, is used to

calculate the variables C and D according with Equation (2.6). The value of yave for a soil is

related to the stiffness of that soil, therefore higher values for yave are expected for the loose

materials than for the dense materials. The loose gravels had the highest displacement at 50% of

ultimate strength. The confined materials should also have lower displacement at 50% of

ultimate strength than the unconfined materials due to the increase in strength and stiffness from

plane strain conditions. However, the dense silty sand (2D) had a higher yave than the dense silty

sand (3D). This unanticipated result may be a consequence of the small sample size used in this

research, therefore more testing with these variables is needed.

6.1.7 Passive Earth Pressure Coefficients

The soils under plane strain conditions were able to provide more passive resistance than

those in an unconfined condition, which led to higher values of Kp. Also, the passive earth

pressure coefficients of the backfill material in the dense state were higher than those of the loose

state. The higher compactive effort provided a higher relative density as well as a higher passive

resistance for the backfill material.

On average for all backfill materials, the Rankine method underestimated the passive

earth pressure coefficient by 56% while the Coulomb theory overestimated by 150%. In many of

the tests the Coulomb method overestimated the value of Kp by a factor of 2 or 3. The

differences in the values of Kp are most likely due to the underlying assumptions associated with

each of the methods.

108

6.1.8 Caltrans

The Caltrans approach provides a bi-linear estimation of the passive force-displacement

relationship for dense backfill materials. Caltrans provided a good approximation for Pult and K

of the unconfined (3D) dense measured data but underestimated the confined (2D) dense

materials. The Caltrans method also overestimated the passive resistance and soil stiffness for the

unconfined loose material. However, the Caltrans method provided a good estimation of Pult and

K for the confined loose material. More testing is needed, but the Caltrans method can possibly

be used in approximating the passive resistance of a loose material confined to the width of the

wall. The Caltrans 2010 method provides a good approximation for the stiffness, K, of the

unconfined materials with a wall height of 3.67 ft.

6.2 Recommendations for Future Research

Given the limited amount of data on several of the soil conditions, there is a need for

additional tests to be performed. These test results will provide parameters that are a better

representation of the backfill material populations. In addition, a wider sample of backfill

material conditions, such as including clayey materials or confined (2D) gravels, would be

beneficial.

109

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