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Numerical simulation of soil-geotextile interaction in pullout test

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Title:
Numerical simulation of soil-geotextile interaction in pullout test
Creator:
Helwany, Mohd. Bassam
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Language:
English
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120 leaves : illustrations ; 28 cm

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Subjects / Keywords:
Geotextiles -- Testing ( lcsh )
Geotextiles -- Testing ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 116-120).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Civil Engineering.
Statement of Responsibility:
by Mohd. Bassam Helwany.

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Source Institution:
|University of Colorado Denver
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Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
19783121 ( OCLC )
ocm19783121
Classification:
LD1190.E53 1987m .H44 ( lcc )

Full Text
NUMERICAL SIMULATION OF SOIL-
GEOTEXTILE INTERACTION IN PULLOUT TEST
by
Mohd. Bassam Helwany
B.S., University of Colorado at Denver, 1985
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Civil Engineering
1987


This thesis for the Master of Science degree by
Mohd. Bassam Helwany
has been approved for the
Department of
Civil Engineering
by
Date_ Da*.4., 1981


Helwany, Mohd. Bassam (M.S., Civil Engineering)
Numerical Simulation of Soil-Geotextile Interaction in Pullout
Test
Thesis directed by Associate Professor Tzong H. Wu
Because of the unusually rapid growth of the use of
geotextile in civil and transportation engineering, many of the
design procedures are derived from assumptions of the convention-
al structures and not based on sound engineering research. In
most cases, there is a total lack of understanding of the soil-
geotextile interaction mechanism.
A study was undertaken to establish a reliable analytical
model for analyzing soil-geotextile interaction mechanism of
geotextile-reinforced earth structures (GRES). A finite element
program CANDE was used to simulate large pullout tests conducted
by Su at the University of Colorado at Denver. In the pullout
tests, a large-size geotextile specimen was subjected to in-
cremental pullout forces. The displacement at the end of the
geotextile specimen where the load was applied as well as the
displacements along the length of the geotextile after applica-
tion of each load increment were measured. The large pullout
tests provided excellent controlled test data for validation of
the analytical model.
Convergence problem was encountered in the original CANDE
code which adopted an iterative solution technique for each load
increment. The code was modified to adopt a mid-point one-
iteration technique for solution of material nonlinearity in each


IV
load increment.
The modified CANDE code was used to predict the behavior
of the large pullout tests. The soil parameters used in the
prediction were obtained from triaxial compression tests and from
a uniaxial strain test. The geotextile stress-strain properties
were evaluated from the results of tests performed by confining
the geotextile in the same embedment conditions as those of the
large pullout tests. A "fixed" pullout test was conducted to
obtain the soil-geotextile interface parameters used in the
analysis.
The predicted cumulative displacement along the length of
the geotextile specimen versus applied force were in good
agreement with the tests results except for the region near the
free end of the geotextiie. The predicted failure load was also
in good agreement with the measured value.
The form and content of this abstract are approved. I recommend
its publication.
Signed
Faoiilty iZember in charge of thesis


' ACKNOWLEDGEMENT
I would like to thank Dr. Tzong H. Wu for his guidance,
and encouragement during this study and throughout my graduate
work. Also, I would like to thank Dr. Joseph K. Labuz, who has
been my role model and mentor, Dr. John Mays and Dr. John Trapp,
for serving on my thesis committee. Without their support, as
well as that of many other faculty and fellow graduate students,
I would have been unable to further my education.


CONTENTS
ACKNOWLEDGEMENT................................................... iii
LIST OF TABLES................................................... viii
LIST OF FIGURES.................................................... ix
CHAPTER
1. INTRODUCTION............................................. 1
1.1 PROBLEM STATEMENT................................... 1
1.2 STUDY OBJECTIVE..................................... 6
1.3 METHOD OF INVESTIGATION........................... 6
2. LARGE PULLOUT TEST......................................... 9
2.1 TEST APPARATUS...................................... 9
2.2 TEST MATERIALS................................... 11
2.2.1 The Soil................................... 11
2.2.2 The Geotextile............................. 13
2.3 PULLOUT TEST RESULTS............................... 13
3. NUMERICAL MODEL........................................... 19
3.1 ANALYTICAL FEATURES OF CANDE.................. 19
3.1.1 Soil Models ............................... 22
3.1.2 Structure (Pipe) Model..................... 25
3.1.3 Interface Model............................ 26
3.2 MODIFICATION OF THE NONLINEAR SOLUTION
TECHNIQUE........................................ 29
3.3 VERIFICATION OF THE NEW SOLUTION TECHNIQUE_ 34


CONTENTS (continued)
Vll
CHAPTER
4. MATERIAL PROPERTY TESTS AND MATERIAL PARAMETERS FOR
PREDICTION OF THE LARGE PULLOUT TEST RESULTS....... 41
4.1 SIMULATION OF SOIL BEHAVIOR................... 41
4.1.1 Overburden-Dependent Model.............. 41
4.1.2 Modified Duncan Model................... 47
4.2 SIMULATION OF GEOTEXTILE BEHAVIOR................ 54
4.3 SIMULATION OF INTERFACE BEHAVIOR................. 57
4.3.1 The Fixed Direct Shear Test............ 61
4.3.2 The Free Pullout Test..................... 61
4.3.3 The Fixed Pullout Test.................... 66
4.3.4 Comparison of Soil-Geotextile
Interface Test Results.................. 69
5. FINITE ELEMENT ANALYSIS OF LARGE PULLOUT TESTS.......... 74
5.1 FINITE ELEMENT DISCRETIZATION.................... 75
5.2 MATERIAL PARAMETERS.............................. 75
5.3 PREDICTED RESULTS AND DISCUSSION OF RESULTS... 75
5.3.1 Predictions Using the Modified Duncan
Soil Model with Material Parameters
Obtained from Triaxial Tests............ 78
5.3.2 Predictions Using the Modified Duncan
Soil Model with Material Parameters
Obtained from Confined Compression
Test and Using Overburden Dependent
Soil Model.............................. 94
5.4 PARAMETRIC STUDY................................ 102
5.4.1 Effect of Soil Properties................ 102
5.4.2 Effect of Geotextile Properties.......... 106
5.4.3 Effect of Soil-Geotextile Friction
Angle.................................. 109


CONTENTS (continued)
vi 11
CHAPTER
5.4.4 Effect of Overburden Pressure........... 109
6. SUMMARY AND CONCLUSIONS............................... 112
6.1 SUMMARY........................................... 112
6.2 CONCLUSIONS....................................... 113
BIBLIOGRAPHY.................................................. 116


TABLES
TABLE
2.1 Properties of Trevira 1127 '
(Trevira Catalog, 1984)............................ 14
3.1 Components of the Constructive Matrix for
Isotropic, Linear Elastic Materials under
Plane Strain Condition................................ 23
3.2 Decision Parameters for Various Assumed
Interface States (Wu, 1980)........................... 33
4.1 Relationship Between the Secant Young's Modulus
and Overburden Pressure of the Ottawa Sand.......... 45
4.2 The Modified Duncan Model Parameters for the
Ottawa Sand at 107 pcf Unit Weight.................. 54
5.1 Material Parameters for Finite Element Simulation....
77


FIGURES
FIGURE
1.1 Concept of the Vidal Reinforced Earth Wall............ 2
1.2 Typical Geotextile Reinforced Earth Structures........ 4
2.1 Large Pullout Test Setup (a) Plain View
(b) Side View (after Su, 1986).................... 10
2.2 Grain Size Distribution (Liu, 1985)..................... 12
2.3(a) Applied Load Versus Cumulative Displacements
Along the Length of Geotextile, Test 3
(after Su, 1986)................................................. 15
2.3(b) Applied Load Versus Cumulative Displacements
Along the Length of Geotextile, Test 4
(after Su, 1986)................................................. 16
2.4(a) Deformations Along the Geotextile, Test 3
(after Su, 1986)..................................... 17
2.4(b) Deformations Along the Geotextile, Test 4
(after Su, 1986)..................................... 18
3.1 Schematic Stress-Strain and Load-Displacement
Curves for the Mid-Point One-Iteration
Solution Technique................................... 32
3.2 Mid-Point One-Iteration Solution Technique.............. 33
3.3 Basic Level 2 Mesh Topology with Construction
Increments for Solutions A, B, and C................. 36
3.4 Displacements of the Pipe for the Three
Solution Methods..................................... 37
3.5 Moment Distribution of the Pipe for Three
Solution Methods..................................... 39
3.6 Thrust Distribution of the Pipe for the
Three Solution Methods............................... 40


xi ;
FIGURES (continued)
FIGURE
4.1 Schematic Sketch of Confined Compression
Test Apparatus...................................... 43
4.2 Confined Compression Stress-Strain
Relationship ....................................... 43
4.3 - Secant Constrained Modulus Versus
Overburden Pressure Relationship.................... 44
4.4 Secant Youngs Modulus Versus
Overburden Pressure Relationship.................... 46
4.5 Stress-Strain Curves of Ottawa Sand (Y = 107 pcf)
in Triaxial Compression Test........................' 48
4.6 Volumetric Strain Versus Confining Pressure
Relationship in Isotropic Compression Test
Relationship........................................ 49
4.7 Void Ratio Versus Overburden Pressure
Relationship of the Ottawa Sand (Y = 107 pcf)....... 52
4.8 \/Pa Versus Co/p Relationship from Confined
Compression Test.................................... 53
4.9 Stress-Strain Apparatus (Wu, et al.f 1986)............ 55
4.10 In-Soil Stress-Strain Relationship of the
Geotextile Tested in the Same Conditions
as that of the Large Pullout Tests.................. 56
4.11 Direct Shear Test Methods for Evaluation of
Soil-Geotextile Interface Behavior.................. 58
4.12 Pullout Test Methods for Evaluation of Soil-
Geotextile Interface Behavior....................... 60
4.13 Fixed Direct Shear Test Results....................... 62
4.14 Direct Shear Test on Ottawa Sand
(without Geotextile)................................ 63
4.15(a) Small Pullout Test Apparatus (Plan View)............. 64
4.15(b) Small Pullout Test Apparatus (Side View)............. 65
4.16 Free Pullout Test on Trevira 1127 Geotextile......... 67
4.17 Fixed Pullout Test on Trevira 1127 Geotextile......... 68


Xll
FIGURES (continued)
FIGURE
4.18 Comparison of Soil-Geotextile Interface Tests.......... 70
4.19 Comparison of Test Results: Nonwoven
Material (after Ingold, 1982)......................... 72
5.1 Finite Element Mesh for the Large Pullout
Test Simulation....................................... 76
5.2(a) Applied Force Versus Cumulative Displacement
at Magnet Station No. 1............................. 79
5.2(b) Applied Force Versus Cumulative Displacement
at Magnet Station No. la............................ 80
5.2(c) Applied Force Versus Cumulative Displacement
at Magnet Station No. 2............................. 81.
5.2(d) Applied Force Versus Cumulative Displacement
at Magnet Station No. 2a............................. 82
5.2(e) Applied Force Versus Cumulative Displacement
at Magnet Station No. 3.............................. 83
5.2(f) Applied Force Versus Cumulative Displacement
at Magnet Station No. 4, 4a, 5...................... 84
5.3 Initiation of Movement Along the Length of the
Geotextile Due to Applied Pullout Forces............ 87
5.4 Predicted Interface Shear Stress Distribution
Along the Length of the Geotextile at (a) 180
lb Applied Force and (b) 270 lb Applied Force....... 88
5.4 Predicted Interface Shear Stress Distribution
Along the Length of the Geotextile at (c) 360
lb Applied Force and (d) 525 lb Applied Force
(at Failure).......................................... 89
5.5 Strain Distribution Along the Length of
the Geotextile in Test 3 for 607 lb Applied
Load (at failure)..................................... 90
5.6 Strain Distribution Along the Length of
the Geotextile in Test 4 for 546 lb Applied
Load (at failure).................................... 91
5.7 Force Distribution Along the Length of the
Geotextile in Test 4 for 546 lb Applied
Load (at failure)
92


FIGURES (continued)
Xlll
FIGURE
5.8 The Force Distribution Along the Length of the
Geotextile in Test 4 for 546 lb Applied Load
(at failure).......................................... 93
5.9 Comparison of the Force Distributions Along
the Length of the Geotextile at Failure............. 95
5.10(a) Predicted Applied Force Versus Cumulative
Displacement at Magnet Station No. 1 with
Modified Duncan Model (Confined Compression
Parameters) and Overburden Dependent Model.......... 96
5.10(b) Predicted Applied Force Versus Cumulative
Displacement at Magnet Station No. la with
Modified Duncan Model (Confined Compression
Parameters) and Overburden Dependent Model........... 97
5.10(c) Predicted Applied Force Versus Cumulative
Displacement at Magnet Station No. 2 with
Modified Duncan Model (Confined Compression
Parameters) and Overburden Dependent Model.......... 98
5.10(d) Predicted Applied Force Versus Cumulative
Displacement at Magnet Station No. 2a with
Modified Duncan Model (Confined Compression
Parameters) and Overburden Dependent Model........... 99
5.10(e) Predicted Applied Force Versus Cumulative
Displacement at Magnet Station No. 3 with
Modified. Duncan Model (Confined Compression
Parameters) and Overburden Dependent Model.......... 100
5.10(f) Predicted Applied Force Versus Cumulative
Displacement at Magnet Station No. 4, 4a, 5
with Modified Duncan Model (Confined Compression
.Parameters) and Overburden Dependent Model. 101
5.11 Effect of the Modulus Number (K), and Internal
Angle of Friction ( Pullout Behavior..................................... 103
5.12 Effect of the Bulk Modulus Number (K, ) 0f the
Soil on the Pullout Behavior......................... 104
5.13 Effect of the Unit Weight of the Soil on the
Pullout Behavior................................... 105
5.14 Effect of the Young's Modulus (E) of the
Geotextile on the Pullout Behavior................... 107


FIGURES (continued)
xiv
FIGURE
5.15 Effect of the Poissons Ratio (v) of the
Geotextile on the Pullout Behavior.................. 108
5.16 Effect of the Soil-Geotextile Friction
Angle (6) on the Pullout Behavior................... 110
5.17 Effects of the Overburden Pressure on
the Pullout Behavior................................ Ill


CHAPTER 1
INTRODUCTION
1.1 Problem Statement
The concept of reinforcing an earth fill by incorporating
materials which possess a much higher tensile strength than soil,
and the capacity to bond with soil through friction has been
utilized quite extensively worldwide. Thousands of earth rein-
forcement projects have been completed in the U.S. alone, and
they have repeatedly demonstrated superior structural perfor-
mance, ease and speed of construction, and low costs compared
with alternatives in such applications as embankments over soft
ground, earth retaining walls, bridge abutments contaminants
dikes, foundation mats, and bulk storage and handling facilities.
Raw materials and manufactured products have been used
for earth reinforcement. H. Vidal developed the best-known
earth-reinforcing technique which was primarily applied to
retaining walls. In this technique (known as "Reinforced
Earth"), thin strips of aluminum or steel are placed horizontally
in layers behind a relatively thin concrete or metal "facing",
and then the wall is backfilled in layers with soil, see Figure
1.1. A major problem concerning Vidal technique the long-term
durability of the metallic reinforcement was pointed out by
Symons (1973). The usual practice, at least in the U.S., is to


2
Figure 1.1: Concept of the Vidal Reinforced Earth Wall


3
increase the thickness of metal strips to allow for corrosion.
However, corrosion rates are highly unpredictable in buried
metallic structures, and it is this uncertainty that makes the
Vidal technique less attractive for permanent constructions.
One viable alternative reinforcing technique is to use
woven and non-woven fabric materials (ASTM: "geotextile") as the
reinforcing element. This technique has been applied successful-
ly to embankments over soft foundations (Wager, 1968; Holtz,
1975; Bell, et al., 1977; Maagdenberg, 1977; Fowler and Halibur-
ton, 1980; Fowler, 1981; and Barsvary, et al., 1982; Humphrey,
1986), retaining walls (Bell and Steward, 1977; Douglas, 1982;
Bell, et al., 1983), slope reinforcement (Iwasaki and Watanabi,
1978; Murray, 1981 and 1982), bearing capacity improvement of
shallow foundations (Guido, et al., 1985), and bridge abutments
(Price and Sherman, 1986; Monley, 1987), see Figure 1.2.
In general, geotextiles are more economical, more easily
handled and constructed, and stronger in resisting corrosion and
bacterial action than many traditional materials including
metals. Moreover, geotextiles serve many other functions such as
separation, drainage, and filtration besides serving as reinfor-
cement (Christopher and Holtz, 1986).
Geotextile-reinforced earth structures (GRES), however,
suffer from a major disadvantage there is a total lack of
understanding as to the reinforcing mechanism. As a result, the
design procedures are very empirical and not based on sound
engineering research.


(a) Embankment Over Soft Foundation
(b) Retaining Wall
Figure 1.2 : Typical Geotextile Reinforced Earth
Structures.


5
(c) Bridge Abutment
Figure 1.2 (continued) : Typical Geotextile Reinforced
Earth Structures


6
1.2 Study Objective
The objective of this study was to establish a reliable
analytical model for investigating soil-geotextile interaction
behavior of GRES and to propose methods for obtaining the
material parameters need for the analysis.
The soil-geotextile interaction mechanism of GRES is
complicated. As a general rule when a geotextile reinforced
earth mass deforms under applied loads, the geotextile will be
subjected to tension provided that there is adequate frictional
resistance between the geotextile and soil. As a result, the
stresses in the soil mass will be redistributed into a more
favorable state, and the geotextile will react along the sur-
rounding soil, increasing its confinement and resulting in a
decrease in the lateral expansion of the reinforced soil mass.
The stress redistribution depends on the relative stiffness of
the geotextile and the soil, which are both nonlinear, the soil-
geotextile interface slipping resistance, as well as the loading
geometry of the geotextile-reinforced earth structures. It is of
great importance to develop a numerical model which can realisti-
cally and reliably analyze the soil-geotextile interaction
mechanism of different applications of geotextile reinforcement
under various conditions.
1.3 Method of Investigation
The finite element method was used for this study. The
method is best suited for,investigation of soil-geotextile


7
interaction behavior of GRES, because (1) it is capable of
simulating nonlinear soil behavior and the material characteris-
tics of the geotextile; (2) it permits analysis of practically
any geometric configuration of GRES; (3) it is well suited for
simulating sequential construction operation; (4) it can realis-
tically account for the nonhomogeneity of the GRES.
The finite element program used in this study was CANDE
(Katona, et al., 1976). CANDE code has been applied successfully
to many soil-structure interaction problems (Katona, et al.,
1976; Leonards, et al., 1982; Siel, 1986). The interface model
employed in CANDE which can realistically account for the
behavior at the interface between soil and geotextile, makes
CANDE an excellent candidate for this research.
CANDE code was employed to analyze the behavior of
laboratory pullout test, a test many researchers consider a good
representative of the real phenomenon which actually occurs in
GRES. Large pullout tests conducted by Su (1986) were used for
this investigation. In the tests a large-size nonwoven geotex-
tile specimen (Trevira 1127) embedded in an Ottawa sand was
subjected to incremental pullout forces. The displacement at the
end of the geotextile specimen where the load was applied as well
as the displacements along the geotextile after application of
each load increment were measured. The large pullout test
provided excellent controlled test data for validation of the
analytical procedure.
The soil parameters used in the analysis were obtained


8
from triaxial tests and uniaxial strain tests. The geotextile
stress-strain properties were evaluated from the results of tests
performed by confining the geotextile in the same embedment
conditions as those of the large pullout tests. A "fixed"
pullout test was conducted to obtain the soil-geotextile inter-
face parameters used in the study.


CHAPTER 2
LARGE PULLOUT TEST
Su (1986) conducted four large pullout tests. Four
geotextile specimens of three different length with a constant
width were tested. All tests were conducted until they reached a
failure condition a limiting condition at which significant
movement of geotextile occurred abruptly and continuously. As
the failure load was reached, the load would drop rapidly, and it
would not be possible to maintain the loading level.
The large pullout test apparatus is described herein
briefly along with the test results which were used for verifi-
cation of the analytical procedure. The reader is referred to
the work of Su (1986) for detailed description of the tests.
2.1 Test Apparatus
The large pullout apparatus is depicted in Figure 2.1.
The test bin was 57 inches high with 48 inches by 24 inches in
plane. A hydraulic jack of 10 ton capacity was used for applica-
tion of pullout forces, and a dynamometer was used to measure the
applied pullout forces. A 50 lb load increment was employed for
the tests. The soil was placed at a constant density of 107 pcf
by using a uniform raining device. The soil was subjected to a
constant surcharge pressure of 4.34 psi.


10
(a) Plain View
1986)
Figure 2.1: Large Pullout Test Setup
(b) Side View (after Su,
vrnmxTUTxw


11
Since geotextile must be kept in the confinement of the
soil throughout the test, one end of the geotextile specimen was
glued between a steel sheet metal clamp which was partially
embedded in the soil throughout the test. The use of the metal
clamp prevented unrestrained stretching of the geotextile as it
became exposed to the air and ensured uniform straining along the
width of the geotextile specimen.
An electronic monitoring system including a Hall genera-
tor probe, an X-Y recorder and a digital multimeter was used to
measure displacements along the length of the geotextile speci-
men. This was accomplished by measuring movements of small-size
magnets which were glued at 1.5 inch intervals.along the length
of the geotextile surface. The movements of the magnets were
recorded after each pullout force increment was applied to the
geotextile.
Only the results of tests 3 and 4 will be used for this
investigation as they were judged to be more reliable (Su, 1986).
The geotextile specimens used in the tests were 18 inches wide by
12 inches long.
2.2 Test Materials
2.2.1 The Soil
The soil used in this test was a uniform sand known as
Ottawa No. 30. The grain size distribution curve of the sand is
shown in Figure 2.2. The uniformity coefficient of the sand was
1.43. The sand had subrounded grain shape and the specific


12
Gravel Sand
Coarse to medium Fine Silt Clay-
* 2 U.S. s 2 S >25 Z Z J tandard sie\ s s § l i 6 < : z a ft sizes i
Grain diameter, mm
Figure 2.2 : Grain Size Distribution (Liu, 1985)


13
gravity was 2.65. The minimum and maximum dry density were 97.52
pcf and 112.19 pcf respectively, per Earth Manual (1976). The
soil was prepared at a density of 107 pcf (relative density =
68%). Results of the triaxial compression tests indicated that
the angle of internal friction was 37 degree.
2.2.2 The Geotextile
The geotextile used was a 100% polyester continuous spun
needle punched nonwoven geotextile, call Trevira 1127, manufac-
tured by Hoechst Fiber Industries. Table 2.1 shows the proper-
ties of the geotextile provided by the manufacturer.
2.3 Pullout Test Results
Figure 2.3 shows the cumulative movements along the
length of the geotextile specimens during application of the
pullout forces. The cumulative movements were measured by the
hall-effect probe magnet system at the magnet stations. The
movements represent the compound effect of stretching of the
geotextile itself and sliding against the confining soil. Nine
magnets were used in both tests. The layout of the magnet
stations is also depicted in Figure 2.3.
The deformations along the geotextile for both tests at
different load levels are shown in Figure 2.4. As a general
rule, the deformation along the geotextile reduces toward the
free-end. The rate of the reduction increases as the load level
increases.


14
Table 2.1: Properties of Trevira 1127 (Trevira Catalog, 1984)
Fabric Weight (oz/yd^) 8
Thickness (Mils) (ASTM D-1777) 125
Grab Strength (lb, MD/CD) (ASTM D-1682) 260/225
Grab Elongation (%, MD/CD) (ASTM D-1682) 85/95
Trapezoid Tear Strength (LB, MD/CD)(ASTMD-1117) 100/95
Puncture Strength 5/16" (LB)(ASTMD-751) 125
Mullen Burst Strength (PSI)(ASTMD-3786) 380
Vertical Water Flow (GAL/MIN/FT^)(HFI Test) 280
EOS (CW-02215) 70-100
Std. Roll Widths (FT) 12.5, 14.5 and 16.0
Std. Roll Length (FT) -300 and 1000
MD = Machine Direction
CD = Cross Machine Direction


15
Figure 2.3(a): Applied Load Versus Cumulative
Displacements Along the Length of
Geotextile, Test 3 (after Su, 1986)


16
Figure 2.3(b): Applied Load Versus Cumulative
Displacements Along the Length of
Geotextile, Test 4 (after Su, 1986)
i


Deformation (%)
Magnet Station No.
Figure 2.4(a): Deformations Along the Geotextile,
Test 3 (after Su, 1986)


Deformation (7)
20 -
Applied Load, P (lb)
4 3 2 1
10
0.0
Figure 2.4(b): Deformations Along the Geotextile,
Test 4 (after Su, 1986)


CHAPTER 3
NUMERICAL MODEL
CANDE (Culvert ANalysis and DEsign) code was used in this
study. The code was developed for analysis and design of buried
pipes. In the code, small displacement formulation is adopted;
time-independent response is assumed; the soil-pipe interaction
is treated as a plane strain problem; and sequential construction
technique is simulated. The computer code had been judged to be
the best for analyzing soil-pipe interaction problems (Leonards,
et al., 1982).
3.1 Analytical Features of CANDE
Detailed description of CANDE is given by Katona, et al.
(1976). A brief summary of its features is presented herein.
Element Types. CANDE code incorporated three basic element
types:
(1) straight beam-column element, with three degrees of
freedom (horizontal and vertical displacements and a
rotation) at each node, was used to model the
structure (pipe).
(2) incompatible (nonconforming) quadrilateral element,
defined by four nodes with two degrees of freedom
(horizontal and vertical displacements) at each


20
node, was used to represent the soil. The element,
developed by Hermann (1973), is composed of two
triangles with the complete quadratic shape func-
tions specified within each triangle. Upon applying
appropriate constraints and static condensation
(Felippa and Clough, 1970) the four-node quad-
rilateral element is formed.
(3) constraint element, composed of two nodes with two
degrees of freedom (horizontal and vertical dis-
placements) at each node and an "interior" node
representing normal and tangential interface forces,
was used to simulate interface behavior. In fact,
the element stiffness is a set of constraint
equations with Lagrange multiplier. The constraint
equations impose conditions on normal and tangential
displacements, and the Lagrange multipliers are
interface forces.
Soil Models. There are four soil models available in the CANDE
code:
(1) linear elastic model,
(2) overburden dependent model, in which elastic soil
moduli are dependent upon current overburden
pressure,
(3) extended-Hardin model, which employs a variable
shear modulus and Poisson's ratio whose values are
dependent on the maximum shear strain and the


21
hydrostatic stress level, and
(4) Duncan-Chang model, in which the values of tangent
Youngs modulus and tangent Poissons ratio of a
soil element during each load increment are deter-
mined on the basis of the calculated shear-stress
level (a^-Cg) and confining pressure (02) in the
element.
During the course of this study a fifth soil model was
added into the program. The added soil model is the modified
Duncan model which employs bulk modulus in place of Poisson's
ratio in the Duncan-Chang model.
Interface Model. The constraint elements were used in
CANDE code for simulation of soil-structure interface behavior.
Three possible interface states are defined by using the sub-
scriptors "fixed" and "free" for describing the relative move-
ments of soil-conduit interface in normal and tangential direc-
tions. For a given load increment, the choice of correct
interface state is determined by a trial-and-error process. The
decision parameters involved in the process are: limiting
tensile force in normal direction, limiting shear resistance,
relative tangential movement, and relative normal movement.
Nonlinear Solution Technique. CANDE code adopted an
iterative solution procedure for each construction layer. The
procedure consists of successive corrections of soil and conduit
moduli until equilibrium, under the load from a newly added layer


22
or an externally applied load, is approximated to some acceptable
degree. The nonlinear solution technique in the modified Duncan
model was modified during the course of this study to alleviate
convergence problems associated with soil moduli. The details of
the modification is presented later in this Chapter.
The following describe in some details, the soil models,
the structure (pipe) model, and the interface model used in this
study.
3.1.1 Soil Models
The incrementally elastic stress-strain relationship,
which is governed by the generalized Hookes law of elastic
deformations, may be expressed as follows for conditions of plane
strain:
C11 C12 0 Aex '
Affy Arxy. C12 C22 0 0 0 *-*3 3 . ACy A7xy. Equation 3.1
Subject to the further assumption of material isotropy,
only two independent elastic moduli are needed to completely
define the coefficients Cn> C12, C22 and C33. Any two of the
following elastic moduli may be selected: Young's modulus (E),
Poisson's ratio (v), shear modulus (G), bulk modulus (B),
constrained modulus (M), Lame's parameter (A), and principal
stress ratio in uniaxial strain (Kq). A summary of the relation-
ships between the elastic moduli was given by Baladi (1979).
Table 3.1 lists the components of the constitutive matrix
l
(Equation 3.1) in terms of the elastic moduli pairs commonly used


23
in soil stress-deformation studies.
Table 3.1: Components of the Constitutive Matrix
for Isotropic, Linear Elastic Materials
under Plane Strain Condition
Matrix Component ' (E,i/) (E.B)
E(l-i/) 3B(3B+E)
1 2 2 (Mi/) (1-2!/) 9B-E
c. Ei/ 3B(3B-E)
2 (l+i/)(l-2i/) 9B-E
r E 3BE
,J3 3 2(l+i/) 9B-E
Two soil models were used in this study, namely: (1) an
overburden-dependent incrementally elastic model, wherein the
elastic moduli are dependent on current fill height; and (2)
variable modulus model using the modified Duncan model formula-
tion which employs a variable Youngs modulus and bulk modulus.
Both models are nonlinear and stress-dependent.
The overburden-dependent model is a tabular-form non-
linear elastic model. In this model, a set of soil moduli ex-
pressed as a function of overburden pressure are used as input.
The soil moduli to be used in an element are evaluated by inter-
polation in accordance with the existing overburden pressure of
the element.
The modified Duncan model (Duncan, 1978) is a functional
form nonlinear elastic model. The model involves modification of
the most widely used Duncan-Chang soil model (Duncan and Chang,
1970). In the modified Duncan model the soil properties are


24
characterized by a variable tangent Young's modulus and a
variable bulk modulus. The tangent Young's modulus of a soil was
assumed to be dependent on the shear stress level (a^-cjg) and the
confining pressure (03).
The expression for tangent Young's modulus was given as:
Rf(l-sin^)(or-o2 )
2G cos4> -l- 2t73sin^
Equation 3.2
where, cig = minimum principal stress
= maximum principal stress
P^ = atmospheric pressure
K = modulus number, dimensionless
n = modulus exponent, dimensionless
Pf = failure ratio, dimensionless
C, = the Mohr-Coulomb strength parameters
To account for variation of with confining pressure, the
following equation was used:
= ^0-A^. log10 ^ f2" j Equation 3.3
in which,
t1 = the value of for Og equal to Pg
A = the reduction in for a 10-fold increase in a
3
The model also assumed that the tangent bulk modulus of a
soil was independent of the principal stress difference (a^-g)
and that it varies with confining pressure, Og, in the following


25
form:
Bt
Equation 3.4
where, and m are dimensionless parameters to be determined
experimentally, and P& is atmospheric pressure.
In Equations 3.2 through 3.4 there are a total of eight
parameters to characterize the behavior of a soil. All the
parameters can be determined from the conventional triaxial
tests.
The modified Duncan model was implemented in CANDE for
this study because: (1) There was difficulty in determining
either a constant Poisson's ratio or the variable Poisson's ratio
parameters required for Duncan-Chang model, and (2) the variable
Poisson's ratio formulation in Duncan-Chang model had been found
to behave erratic in some cases (Lee, 1979; Andrawes, et al.,
1982).
3.1.2 Structure (Pipe) Model
Structure model refers to the stress-strain relationship
employed to characterize the material behavior of the structure
geotextile. The behavior of the geotextile in this study was
found to be approximately linear for strains up to the maximum
value encountered in the large pullout test. Therefore, a linear
elastic model with constant Young's modulus and Poisson's ratio
was used to characterize the behavior of the geotextile.


26
3.1.3 Interface- Model
In the context of finite element analysis, there are two
fundamental approaches to simulate the relative movements between
different materials such as soil and geotextile: (1) method of
stiffness, and (2) method of constraints.
(1) Methods of Stiffness
In this method, the stiffness of the elements
representing the interface determine the extent of the
bond between two bodies initially in contact.
Zienkiewicz et al., (1970) advocated the use of
continuous isoparametric elements with nonlinear material
properties for interface normal and shear deformations,
assuming uniform strain in the normal direction.
Numerical difficulties can arise from ill-conditioning of
the stiffness matrix due to very large off-diagonal terms
or very small diagonal terms which are generated by these
elements in certain cases.
Goodman, Taylor and Brekke (1968) developed a
special type of interface element to account for relative
movements between rock joints. The element consists of
two lines each with two nodal joints. The two lines
occupy the same position before deformation and each node
has two degrees-of-freedom (horizontal and vertical
displacements). If, for example, it is desired to
simulate slippage across an interface as the frictional
resistance is exceeded., an arbitrarily large normal


27
stiffness would be specified to enforce near compatibil-
ity in normal direction, while the tangent (shear)
stiffness is set equal to a small value (the residual
interface shear stiffness) to allow independent movement
in the tangent direction.
Clough and Duncan (1969) conducted (direct shear)
interface tests in the laboratory to measure the inter-
face shear stress-relative displacement relation between
concrete and the backfill sand used for the Port Allen
lock, and proposed a hyperbolic functional relationship
for the interface shear stiffness. However, part of the
measured displacements was due to shear strains in the
soil, in addition to those at the interface.
Attempts have been made by a number of investi-
gators to modify the Goodman-Taylor-Brekke interface
model (Ghaboussi et al., 1973; Goodman and St. John,
1977; Wong, 1977). However, there are certain inconsis-
tencies with the elements that are very difficult to
overcome. For example, in order to prevent the two
contacting bodies from penetrating each other when
subjected to compressive force, a very large interface
normal stiffness has to be selected. On the other hand,
penetration is required to recover the normal force at
the interface. Due to the large normal stiffness, the
significant digits of the penetration become truncated,
hence the resulting interface normal force will be in


28
error. On the other hand, if the normal stiffness is not
large enough, significant penetration will occur which is
kinematically inadmissible.
(2) Method of Constraints
The concept of using constraint equations to
represent the interface behavior in finite element
analysis was introduced by Chan and Tuba (1971).
Katona et al. (1976) developed a general theory
for treating constraint equations in the formulation of
interface elements and devised an iterative procedure for
characterizing the interface behavior.
The interface element is defined by a set of
paired nodes joining two bodies. Prior to deformation,
the paired nodes occupy the same location in space but
are assigned to separate bodies (elements). In addition,
a third node is assigned to the interior of the paired
nodes. The spatial location of the interior node is
immaterial; its sole purpose is to provide unique
equation numbers for normal and tangential interface
forces. Each of the paired nodes has two degrees-of-
freedom (horizontal and vertical displacements). The
element stiffness therefore is of the size 6 x 6 in a
mixed formulation.
By using the subscriptors "fixed and "free" to
describe the relative movements of a contact point in
normal and tangential directions, four kinematic states


29
were defined to represent the interface behavior. For a
given load increment, the choice of correct interface
state is determined by a trial-and-error process. A
particular state is first assumed and a set of trial
responses are evaluated. The trial responses are then
used to determine if the assumed state is correct, and if
not, what is the new trial state. The trial responses
which are used as decision parameters of the trial and
error process for different assumed states are given in
Table 3.2. The state which represents separation in the
normal direction while retaining contact in the tangen-
tial direction was discarded because it had no physical
significance in the interface model. Whenever separation
occurs in normal direction, the state representing free
movement in normal and tangential directions is automati-
cally implemented.
The constraint equations corresponding to the
correct interface state are incorporated into the global
stiffness matrix using standard finite element assembly
techniques. In other words, the constraint equations are
treated as interface element stiffness in the analysis.
3.2 Modification of the Nonlinear Solution Technique
The solution of nonlinear problems by the finite element
method is usually obtained by one of three basic techniques:
incremental or stepwise procedures, iterative methods, and step-
iterative or mixed procedures.


Assumed
Interface
State
Table 3.2
Decision Parameters for Various Assumed
Interface States (Wu, 1980)
Fixed in both Normal and
Tangential Directions
(fixed-fixed state)
(1) if the total inter-
face normal force >
tensile breaking force,
try free-free state.
(2) if the total interface
normal force the
tensile breaking force,
and the absolute value
of the total interface
shear force the
frictional resistance,
try fixed-free state;
otherwise, fixed-fixed
state is correct.
Fixed in Normal Direction;
Free in Tangential Direct-
ion (fixed-free state)
(1) if the total interface
normal force > the
tensile breaking force,
try free-free state.
(2) if the total interface
normal force the
tensile breaking force,
and the relative tangent
displacement during the
load increment bears an
opposite sign to the
imposed frictional
resistance, try fixed-
fixed state; otherwise,
fixed-free state is
correct.
Free in both Normal and
Tangential Directions
(free-free state)
if the relative normal
displacement < 0, try
fixed-fixed state; other-
wise, free-free state is
correct.


31
CANDE code adopted an iterative solution technique for
each load increment. The technique consists of successive
corrections of soil and structure moduli until equilibrium is ap-
proximated to some acceptable degree under the load increment.
Convergence problems arose when CANDE code was used with
Duncan-Chang and the modified Duncan models. Consequently, the
nonlinear solution technique in the modified Duncan model was
modified to alleviate the convergence problem. A mid-point one-
iteration technique was adopted in the modification. The
following describes the modified nonlinear solution technique
employed in this study.
Schematic stress-strain curves as obtained from triaxial
tests are depicted in Figure 3.1(a). Also shown in the same
Figure is the corresponding confining pressure versus volumetric
strain curve obtained from an isotropic compression triaxial
test. Figure 3.1(b) depicts a corresponding load-displacement
curve.
The mid-point one-iteration technique is illustrated in
details in the flowchart shown in Figure 3.2.
The algorithm for the modified Duncan soil model which
adopted the mid-point one-iteration solution procedure was
implemented in a subroutine called Duncan in CANDE code. The
behavioral characteristics and limitations of the modified Duncan
model (Equations 3.2 through 3.4) are enumerated below:
(1) As ag (such as confining pressure in a triaxial
test) increases, E and Bt become larger, hence the soil


32
Displacement Curves for the Mid-Point
One-Iteration Solution Technique.


33
Figure 3.2: Mid-Point One-Iteration Solution Technique
V


34
becomes stiffer. As maximum shear stress ((a^-cjg)/2),
increases, E becomes smaller, but Bt remains unaffected.
(2) Shear failure is said to occur when ap-
proaches zero. That is, the bracketed term in Equation 3.2
approaches zero as increases. If a significant
portion of the soil mass fails in shear, the results may no
longer be reliable because the model does not simulate
accurately the behavior of real soils at and after failure.
To avoid the numerical problem, the CANDE algorithm arbi-
trarily limits the minimum value of the bracketed term in
Equation 3.2 to 0.01. Thus, E^. does not actually become
zero in shear failure.
(3) The CANDE algorithm sets limits on B as
calculated from Equation 3.4 dependent on the value of E
from Equation 3.2. Specifically, the calculated Poisson's
ratio which corresponds to Et and Bfc (v = -((3Bt-Et)/6Bt))
is maintained in the range 0.01 to 0.48.
3.3 Verification of the New Solution Technique
To verify the new solution technique, i.e., the mid-point
one-iteration technique, a soil-pipe interaction problem was
analyzed to compare solutions of the original technique (itera-
tion to convergence) and the new technique.
CANDE code's Level-2 solution (with automated mesh
generation) was used to analyze the performance of a circular
corrugated steel pipe. The pipe had the following parameters:
diameter = 8.25 feet, yield stress = 40 ksi, E = 30 x 10^ psi,


35
v= 0.3, A = 0.3433 in.2/in., I = 0.1658 in.Vin., and S = 0.1458
in. Vin.
The pipe was buried in a silty.clay with 16.5 feet of the
soil above its springline. The soil had the following parameters
(Wong and Duncan, 1974, soil CL-30E): unit weight = 113 pcf, C =
7.1 psi, o = 33 degrees, A(j> = 0 degree, K = 150, n = 0.62, Rf =
0.61, G = 0.58, F = 0.33, and D = 2.3.
The Standard Level-2 solution utilizes a preprogrammed
finite element mesh with five construction increments. With the
one-iteration solution technique, however, it is desirable to use
as many construction increments as possible in order to obtain
the best possible accuracy. Consequently, the problem was
analyzed in three different manners: the first used the original
technique with five construction increments (Solution A), the
second used the new technique with ten Construction increments
(Solution B), and the third used the new technique with five
construction increments (Solution C). Figure 3.3 illustrates the
mesh used with construction increments for the three solutions.
The displacements of the pipe at the end of construction
for the three solutions are shown in Figure 3.4. It is seen that
Solutions A and C are significantly different while solutions A
and B are fairly close, indicating the importance of using a
large number of load increments when the new solution technique
is to be employed.
The largest disagreement between Solutions A and B
occurred at the invert of the pipe (approximately 30% dif-


36
= R2 = 8.25'
Sol. Sol.
B A,C
10
5
9
8
1
1

Figure 3.3 : Basic Level 2 Mesh Topology with Construction
Increments for Solutions A, B, and C


37
Displacement Scale
i___:________i
0.1 inch
Soil: CL-30E, 16.5'above
Springline. Pipe: Corrugated
Steel of 8.25' dia.
A'
--A
o---------o
A------,A
Iterative to Convergence Solution, 5 construction
layers (Solution A)
Mid-Point One-Iteration Solution, 10 construction
layers (Solution B)
Mid-Point One-Iteration Solution, 5 construction
layers (Solution C)
Figure 3.4 : Displacements of the Pipe for the Three
Solution Methods


38
ference). It was found that the difference mainly arose in the
first construction increment used in Solution B which had a large
thickness and was tedious to discretize into increments of
similar sizes as other increments.
The distribution of bending moment in the pipe at end of
construction of the three solutions is shown in Figure 3.5. Very
good agreement is observed between Solutions A and C while the
deviation of Solution B from Solution A is somewhat larger. The
discrepancy can be again attributed to the extraordinarily large
first increment'(compared to the rest of the increments) used in
Solution B. It is thought herein that the large thickness of the
first construction increment (see Figure 3.3) compared with other
increments in Solution B caused the discrepancies between
Solutions A and B. However, in Solution C the large thickness of
the first construction increment did not cause any discrepancies
since the thickness of the first construction increment was not
much larger than the thickness of other increments in Solution C.
Thrust distribution in the pipe was found to be nearly
identical for all three solutions (see Figure 3.6).
In summary, use of the mid-point one-iteration solution
technique will alleviate possible convergence problems without
introducing significant errors. It is important, however, to
adopt a large number of load increments in order to obtain
satisfactory results.


Moment Scale
39
*_____________i
400 (lb. inch/inch)
o-----o
A-.....A
Iterative to Convergence Solution, 5
Construction Layers (Solution A)
Mid-Point One-Iteration Solution, 10
Construction layers (Solution B)
Mid-Point One-Iteration Solution
Construction Layers
Figure 3.5 : Ibment Distribution of the Pipe for
the Three Solution Methods


L
Thrust Scale
j

\
__Soil: CL-30E, 16.5' above Springline
Pipe: Corrugated steel of 8.25' dia.
__Iterative to Convergence Solution, 5
Construction Layers (Solution A)
- Mid-Point One-Iteration Solution, 10
Construction Layers (Solution B)
-A Mid-Point One-Iteration Solution, 5
Construction Layers (Solution C)
Figure 3.6 : Thrust Distribution of the Pipe for
the Three Solution Methods


CHAPTER 4
MATERIAL PROPERTY TESTS AND MATERIAL PARAMETERS
FOR PREDICTION OF THE LARGE PULLOUT TEST RESULTS
In this chapter, the material parameters required to
predict the large pullout test behavior described in Chapter 2
and the tests performed to obtain the material parameters are
presented. The material parameters include those of the soil,
the geotextile, and the soil-geotextile interface.
4.1 Simulation of Soil Behavior
Two soil models were used to simulate the soil behavior.
They were an overburden-dependent model and the modified Duncan
model.
4.1.1 Overburden-Dependent Model
The overburden-dependent model is an incrementally
elastic model. The model assumes that the soil stiffness in-
creases with the overburden pressure. It should be noted that
soil stiffness does increase with the overburden pressure if the
soil is essentially in a state of confined compression (uniaxial
straining). However, if the soil is subjected to a different
stress path, such as that of the triaxial compression test, then
increased overburden (axial stress) will not stiffen the soil,
but, on the contrary, the stiffness will be reduced due to shear
straining.


42
In the large pullout test, the soil is predominantly in a
state of confined compression wherein the overburden-dependent
model is applicable; however, for the soil immediately above and
below the geotextile, applicability of overburden-dependent model
may be questionable.
Material Property Test and Test Results
The overburden-dependent model requires results of a
confined compression test to determine the increase of soil
stiffness due to increase of overburden pressure. A confined
compression test was conducted using the apparatus shown in
Figure 4.1. The apparatus consists of a stiff box made of
aluminum with a base of 6.5 inch by 4.75 inch and a height of 1
inch. The small height of 1 inch was used to minimize the soil-
wall friction. Thin polyester sheets were used to line the box
interior in order to further reduce soil-wall friction.
The Ottawa sand prepared at a density of 107 pcf, same as
that used in the large pullout test, was used in this test.
Vertical load was applied using an Instron machine with loading
rate of 0.005 inch per minute.
Figure 4.2 shows the relationship of overburden pressure
versus axial strain of the soil. The shape of the curve shows
increased stiffness with increasing overburden pressure.
Figure 4.3 depicts the secant constrained modulus, M
for various values of overburden pressure a m a /e
y, s y1 y*
In order to use the overburden-dependent model in CANDE
the soil stiffness should be expressed in terms of Young's


Overburden Pressure
43
Applied
Load
Displacement
Dial
4.75
Polyester Sheet
Figure 4.1: Schematic Sketch of Confined Compression
Test Apparatus
Figure 4.2: Confined Compression Stress-Strain Relationship


Secant Modulus Mg (psi)
44
Figure 4.3 : Secant Contrained Modulus Versus
Overburden Pressure Relationship


45
modulus and Poisson's ratio. It is generally recognized that
Poissons ratio remains practically constant in the environment
of confined compression (Katona, 1976). Therefore, a constant
Poisson's ratio was assigned when using the overburden-dependent
model. The Young's moduli of the soil were calculated from the
constrained moduli and the Poisson's ratio as:
E = (l+v)(l m Equation 4.1
S (1-v)
Using a Poisson's ratio of 0.35, the Young's moduli were
calculated and plotted versus the overburden pressure as shown in
Figure 4.4. Table 4.1 shows the tabular-form relationship
between the secant Young's modulus and overburden pressure. This
Table was used as input for this study.
Table 4.1
Relationship Between Secant Young's Modulus
and Overburden Pressure of the Ottawa Sand
Overburden
Pressure (psi)
1
2
3
4
5
7
9
11
13
15
Secant Young's
Modulus (psi)
288.
360.
425.
488.
544.
645.
733.
806.
875.
935.


Secant Young's Fbdulus, E (psi)
Figure 4.4 : Secant Young's Modulus Versus Overburden
Pressure Relationship


47
4.1.2 Modified Duncan Model
Evaluation of the material parameters required in the
modified Duncan model requires results of triaxial compression
tests. Detailed description of the procedure for obtaining the
material parameters from the test results were given by Wong and
Duncan (1974) and Duncan, et al., (1978).
Drained triaxial tests were conducted on the Ottawa sand
prepared at 107 pcf. The stress-strain curves obtained from the
triaxial tests are shown in Figure 4.5. For the tests, confining
pressures of 5 psi, 10 psi, and 15 psi were used. The material
parameters that define the tangent Young's modulus, E were
determined as: K = 2700, n = 1.05, _ 0.96, C = 0, = 37,
= 2. Using these parameters, the stress-strain curves of the
soil were back-calculated and plotted in Figure 4.5 as dashed
lines. It is seen that the parameters provide a good simulation
of the soil behavior.
To evaluate the parameters that define the tangent bulk
modulus, an isotropic compression test was conducted using the
Ottawa sand prepared at a density of 107 pcf. Conventional
triaxial cell was used, and the changes in volume corresponding
to increase of confining pressures were measured. Figure 4.6
shows the volumetric strain versus confining pressure relation-
ship. The volume change measurements initiated at = 5 pSi
which was applied during sample preparation, i.e., the volumetric
strain at (j = 5 psi was set to zero. The curve shown is a
straight line which implies that the bulk modulus is independent


48
- Triaxial Test
- Back-calculated
el
Figure 4.5 : Stress-Strain Curves of Ottawa Sand (r=107pcf)
in Triaxial Compression Test


49
Confining Pressure (psi)
Figure 4.6 : Volumetric Strain Versus Confining Pressure
Relationship in Isotropic Compression Test


50
f ac. The material parameters for the tangent bulk modulus, Bt,
were determined as: in = 0, _ 200.
Alternatively, the parameters K and n can be deduced from
the confined compression test, using the following equation
derived by Clough and Duncan (1969):
Ap(Ue0) I 2K70 1
Ae
1
:____________p(i-k0)re_________________
K0p(tan2(A5+^'/2)-1) + 2C' tan(45 ('/2)
2 Equation 4.2
In which = initial tangent modulus
Ap = increment of pressure in consolidation test
Ae = decrease in void ratio due. to Ap
e0 = void ratio at beginning of increment
= coefficient of earth pressure at rest
p = average pressure during increment
c' = effective cohesion intercept
= failure ratio as defined in Section 3.1.1
When values of E^ have been determined (from Equation
4.2) for several load increments, they can be plotted against the
corresponding value of a^ to determine the values of K and n for
the soil using the following equation:
Equation 4.3


51
The average value of cr^ during each increment can be
calculated using the equation:
Cg = KqP Equation 4.4
The value of Kq may be estimated from the test results of
Brooker and Ireland (1965) or it may be calculated from the
Poisson's ratio of the soil (Kq = v/l-v). In this study, Kq was
calculated by employing an empirical relation suggested by Jaky
(1948), K 1-sin
The void ratio versus overburden pressure relationship
for the Ottawa sand at a density of 107 pcf is shown in Figure
4.7. This curve was deduced from results of confined compression
test (Figure 4.2). By dividing the curve into 10 increments,
values of E. for each load increment were calculated. From
l
Figure 4.8, K = 1700, and n = 0.63 were determined.
Table 4.2 summarizes modified Duncan parameters obtained
from both triaxial and confined compression tests. Values of K
and n obtained from triaxial tests were found to be higher than
those obtained from the confined compression test. It is
believed that the values of K and n obtained from the triaxial
tests may be more reliable than those obtained from the confined
compression test; since the latter is subject to soil-wall
friction of undetermined degree.


Void Ratio
52
Figure 4.7 : Void Ratio versus Overburden Pressure Relationship of
the Ottawa Sand (Y = 107pcf)


Ei/Pa
53
3/%
Figure 4.8 : /Pa Versus a3 /Pa Relationship from confined
Compression Test


54
Table 4.2
The Modified Duncan Model Parameters
for the Ottawa Sand at 107 pcf Unit Weight
Parameters Value
c 0
o 37
A 2
K 2700 (1700*)
n 1.05 (0.63*)
Rf 0.96
200
b m 0
* determined from the confined compression test.
4.2 Simulation of Geotextile Behavior
The stress-strain behavior of the geotextile used in the
large pullout test has to be obtained by testing the geotextile
under the same conditions as those of the large pullout tests,
i.e., the geotextile should be tested in the same direction, with
approximately the same strain rate, in the confinement of the
same soil prepared at the same density, subject to the same
overburden pressure as those used in the large pullout tests.
This is important in order to be consistent with the formulation
of CANDE code.
Using an apparatus developed at the University of
Colorado at Denver (Wu, et al, 1986), as illustrated in Figure
4.9, the stress-strain relationship of the geotextile under the
same test conditions as the large pullout test was obtained (see
Figure 4,10). The friction between the soil and the sheet metal
clamp was subtracted using a friction angle of 18. The in-soil


55
Normal Load ,
0.3" 4.75" 0.3"
(b) Plan View
Figure 4.9 : Stress-Strain Apparatus C'/u, et al., 1986)


56
Strain (%)
Figure 4.10 : In-Soil Stress-Strain Relationship of the Geotextile
Tested in the Same Conditions as that of the
Large Pullout Tests
L


57
stress-strain relationship of the geotextile is found to be
linear for strains up to 20% which was the maximum value measured
in the large pullout test. The elastic modulus of the geotextile
was determined to be 1030 psi. The Poisson's ratio of the
geotextile was assumed as 0.3. A parametric study was presented
in Chapter 5 to.illustrate the effect of the Poissons ratio on
the predicted pullout test behavior.
4.3 Simulation of Interface Behavior
The behavior of the interface between soil and geotextile
is commonly evaluated by either direct shear tests or pullout
tests. Since in the large pullout tests (and under operational
conditions of geotextile-reinforced structures) the geotextile is
subjected to tensile forces, it is apparent that soil-geotextile
interface behavior can best be determined with pullout tests.
However, as might be expected, such tests often result in a very
nonuniform strain distribution, and it has been argued that
direct shear tests should be more appropriate for evaluation of
the interface behavior.
When soil-geotextile interface behavior is evaluated by
direct shear test, three different test methods have been used:
(1) fixed direct shear test (Figure 4.11(a)), in which the
geotextile specimen is glued to a wooden block (Ingold, 1982, and
Christie and El Hadi, 1977) or clamped to a steel or Perspex
former (McGown, et al., 1978), (2) free direct shear test (Figure
4.11(b)), in which the reinforcement is clamped at one end of the


58
Overburden Pressure
Shear Force
(a) Fixed Direct Shear Test
Overburden Pressure
Shear Force
Normal Force
Figure 4.11 : Direct Shear Test Methods for evaluation of
Soil-Geotextile Interface Behavior


59
shear box and free at the other end. In this test, the rein-
forcement is in contact with a support soil in the lower half of
the shear box and a cover soil in the upper half of the shear box
(Ingold, 1982), and (3) constant-area direct shear test (Figure
4.11(c)), in which the lower half of the shear box is replaced by
a layer of the reinforcement glued to a large wooden block so
that the contact area between the soil and geotextile remains
constant throughout the test (Al-Hussaini and Perry, 1978).
In the past when pullout tests were used to evaluate
soil-geotextile interface behavior, the geotextile specimen had
always been allowed to deform freely, termed free pullout tests,
as shown in Figure 4.12. In this study, however, a new test
method fixed pullout tests was used (Figure 4.12). In the
tests, the geotextile specimen was glued to both the top and
bottom surfaces of a thin metal plate, therefore during applica-
tion of the.pullout forces geotextile straining was suppressed.
The friction coefficient evaluated from the fixed pullout tests
represents a "point-to-point" friction behavior between the soil
and the geotextile a parameter required for characterizing
interface behavior for the constraint element formulation in
CANDE code.
For purposes of comparison, three types of soil-
geotextile interface tests were conducted, including (1) .the
fixed direct shear test, (2) the free pullout test, and (3) the
fixed pullout test.


60
(a) Free Pullout Test
(b) Fixed Pullout Test
Figure 4.12 : Pullout Test Methods for Evaluation of Soil-
Geotextile Interface Behavior


61
4.3.1 The Fixed Direct Shear Test
In. this test, a geotextile specimen was glued to a wooden
block at the lower half of a direct shear box. The upper half of
the box was filled with the Ottawa sand prepared at 107 pcf. The
test was conducted under three different overburden pressures:
2.17 psi, 4.34 psi, and 6.52 psi. Test results are shown in
Figure 4.13. Comparing to Figure 4.14 which depicts the results
of direct shear test on the Ottawa sand, it is seen that the
displacement required to mobilize the strength in the fixed
direct shear test between the geotextile and the sand was ap-
proximately 0.11 inch whereas about 0.03 inch was enough to
mobilize the shear strength in the direct shear test of the sand.
The friction angle between sand and geotextile (6) was
found to be 35 (from Figure 4.13) which is almost the same as
the internal angle of friction ( (from Figure 4.14).
4.3.2 The Free Pullout Test
Free pullout tests were conducted with an aluminum box
2.5 inch in height and with a base of 6.5 inch by 4.75 inch. The
pullout forces were applied horizontally by a pulley-dead weight
system as shown in Figure 4.15. The box has two slots of size
3.5 inch by 0.3 inch at the front and the back through which a
geotextile specimen of 3.5 inch in width was allowed to move in
and out of the test box. A sheet metal clamp was used to keep
the geotextile in the confinement of the soil during the test.


Shear Stress (psi) Toad (ib)
at failure
(b)
Figure 4.13 : Fixed Direct Shear Test Results


Displacement (x 103 inch)
(a)
Figure 4.14 : Direct Shear Test on Ottawa Sand (without
63
an = 6.51 psi
cn = 4.34 psi
on= 2.17 psi
Geotextile)


£
Figure A.15 (a) : Small Pullout Test Apparatus (Plan View)


Normal Load
Figure 4.15(b):: Small Pullout Test Apparatus (Side View)
Ln


66
The pullout forces were applied in 1 lb load increments
until a failure condition was reached. Failure is defined herein
as the limiting condition at which significant movement of
geotextile occurs abruptly and continuously. The displacements
of the geotextile were measured by a dial gauge. Three different
overburden pressures (2.17 psi, 4.34 psi, and 6.51 psi) were
used.
Figure 4.16 depicts results of the free pullout tests
conducted under the three overburden pressures. The friction
between the sand and the sheet metal clamp was subtracted using a
friction angle of 18. It is seen from Figure 4.16(a) that the
pullout forces required to mobilize displacements are higher at
higher overburden pressures up to approximately 0.15 inches
displacement beyond that the reverse is true.
Figure 4.16(b) shows that the friction angle is dependent
on the overburden pressure. The friction angle decreases as the
overburden pressure increases. The soil-geotextile friction
angle was found to be 10 at 4.34 psi overburden pressure.
4.3.3 The Fixed Pullout Test
Using the same apparatus described in the free pullout
test, three fixed pullout tests were conducted. Two layers of
geotextile were glued to the top and bottom surfaces of a thin
metallic sheet of 3.5 inch in width. A clamp was not used in
this test. Instead, the thin metallic sheet was attached
directly to the loading mechanism.
Figure 4.17(a) depicts the pullout force-displacement


Shear Stress (psi)
at failure .. Pullout Force (lb)
67
= 6.51 psi
(a)
Normal Stress (psi)
(b)
Figure A.16 : Free Pullout Test on Trevira 1127 Geotextile


Shear Stress (psi)
at failure Pullout Force (lb)
68
Displacement x 103 inch
(a)
Normal Stress (psi)
(b)
Figure 4.17 : Fixed Pullout Test on Trevira 1127 Geotextile


69
relationship at three different overburden pressures: 2.17 psi,
4.34 psi, and 6.51 psi. Failure occurred at relatively smaller
displacement (approximately 0.05 inch). The soil-geotextile
friction angel was found to be higher (6 = 15) than that of the
free pullout test (s = 10) at an overburden pressure of 4.34
psi.
From Figure 4.17(b) it is seen that the friction angle
decreases as the overburden pressure increases. Similar behavior
with steel strip reinforcement was observed by Schlosser and
Elias (1978).
4.3.4 Comparison of Soil-Geotextile Interface Test Results
Figure 4.18 shows a comparison of the test results of the
fixed direct shear test, the free pullout test, and the fixed
pullout test. It is seen that the results from the pullout tests
(free and fixed) are totally different from the fixed direct
shear test results, with the former indicating a much lower
frictional resistance. This is attributed to the different shear
stress distribution in the tests.
The fixed pullout test results show the same tendency as
the free pullout test results, i.e., decrease in frictional
resistance with increase in normal pressure). However, the
effect of geotextile extensibility becomes significant in the
free pullout test for overburden pressures higher than ap-
proximately 2 psi.
The findings of the soil-geotextile interface tests are


Shear Stress (psi)
Ottawa Sand: Density = 107 pcf
A---------A Fixed Direct Shear Test
O--------o Fixed Pullout Test
--------- Free Pullout Test
Normal Stress (psi)
Figure 4.18 : Comparison of Soil-Geotextile Interface Tests


71
in agreement with the tests conducted by Ingold (1979 and 1980)
using a number of metallic and geotextile reinforcements. His
general conclusion was that the pullout test gave higher values
of soil-reinforcement bond for metallic and inextensible "geo-
grid" reinforcements and lower values for the more extensible
geotextiles and geogrids. These low values were related not only
to extensibility but also to failure in the structure of the
geotextile embedded in the soil. In 1982 his earlier investiga-
tion was extended to embrace four test methods: (1) the 60-by-60
mm fixed shear box tests in which the geotextile is fixed to a
rigid spacer block inserted in the lower half of the shear box
with soil in the upper half of the box; (2) the 300-by-300 mm
fixed sheaf box test with the geotextile fixed as in Test Method
1; (3) the 300-by-300 mm free shear box test in which the
geotextile is clamped at one end of the shear box and free at the
other end. The geotextile is in contact with a support soil in
the lower half of the shear box and a cover soil in the upper
half of the shear box; and (4) the 285-by-500 mm pullout test.
As shown by Figure 4.19, the results from the pullout
test are totally different from the shear box results, with the
former indicating a much lower frictional resistance. The reason
for this was not fully understood; however, it was thought that
because of the low geotextile modulus of approximately 50 kN/m
the bond stress in the pullout test was only mobilized over a
comparatively short section of the sample close to the point of
application of the pullout load. For an extensible geotextile


t(KM/m
72
200
150 .
60 x 60 nm fixed shear
300 x 300 nm.fixed shear
300 x 300 irm free shear
Pullout
joo -
50 -
"n (KN/nr)
Figure 4.19 : Comparison of Test Results:
Material (after Ingold 1982)
250
Nonwoven


73
subject to pullout most of the relative soil geotextile strain,
and hence mobilized'bond stress, occurred at the point of load
application with little or no relative strain occurring at the
free end of the sample. Assuming that this phenomenon became
more pronounced as the normal stress level increased, then
pullout resistance was generated over progressively shorter
sections of the geotextile.
With the state of the art in testing expanding rapidly it
would be premature to draw any firm conclusions. Despite this,
it is evident from the limited test data presented herein that
there is a significant difference between results from shear box
tests and pullout tests. Although there is consistency in the
shear box tests, this does not indicate any supremacy but may
merely reflect the consistent inapplicability of such testing.
There is general agreement that the often large disparity between
shear box and pullout test results arises from the extensibility
of the geotextile.


CHAPTER 5
FINITE ELEMENT ANALYSIS OF LARGE PULLOUT TESTS
The large pullout tests 3 and 4 conducted by Su (1986)
and described in Chapter 2 will be analyzed herein using the
modified finite element program CANDE. Pullout tests 3 and 4
were conducted with presumably identical conditions, whereas a
difference in the test results of approximately 50 lb load was
measured. This difference was attributed primarily to the dif-
ficulty in lining up the pulling mechanism with the geotextile
specimen on a level plane at the beginning of the test (Su,
1986).
In this chapter, the modified CANDE code was used to
predict the behavior of the pullout tests, in particular the
cumulative displacements along the length of the geotextile
versus the applied forces for all load increments and the
distribution of tensile forces along the geotextile specimen at
failure. In addition, a parametric study was performed to
investigate the effect of the material parameters involved in the
analysis (including the soil parameters, geotextile parameters,
and soil-geotextile interface parameters) as well as the effect
of the overburden pressure on the pullout behavior.


75
5.1 Finite Element Discretization
Figure 5.1 depicts the finite element mesh used for
simulation of the large pullout test. The soil is discretized
into 112 rectangular elements, and the geotextile is represented
by 8 beam elements. A total of 16 interface elements were used
along the top and bottom of the geotextile. The rigid walls of
the large pullout box were simulated by suppressing the horizon-
tal displacement at the corresponding nodal points as shown in
the figure. In the finite elements simulation, the soil and the
geotextile were placed in the soil bin before application of the
pullout forces. The pullout forces were applied in 18 lb
increments at the clamped-end of the geotextile.
5.2 Material Parameters
The material parameters required for predicting the
behavior of the pullout tests were described in Chapter 4. The
values of the parameters are summarized in Table 5.1.
5.3 Predicted Results and Discussion of Results
The behavior of the large pullout tests were first
predicted by using the modified Duncan model parameters deduced
from the triaxial test for simulation of the soil behavior, using
the fixed pullout test results with the constraint elements for
simulation of the soil-geotextile interface behavior, and using
the uniaxial tension in-soil geotextile properties for simulation
of geotextile behavior. A constant pullout force increment of 1
lb per inch width (18 lb increment for the geotextile specimen of


76
S^i.l
Figure 5.1 : Finite Element Mesh for the Large Pullout
- Test Simulation


77
Table 5.1
Material Parameters for Finite Element Simulation
(a) Soil Parameters
Overburden-Dependent Model Parameters
Modified Duncan Model Parameters Overburden Pressure (psi) Secant Young's Modulus (psi)
C = 0 1 228
$ = 37 degrees 2 360
A = 2 degrees 3 425
K = 2700 (1700*) 4 488
n = 1.05 (0.65*) 5 544
Rf = 0.96 7 645
' Kb = 200 9 733
m = 0 11 806
13 875
15 935
* Deduced from confined compression test
(b) In-Soil Stress-Strain Parameters of the Geotextile
Young's modulus, E = 1030 psi
Poissons ratio, v = 0.3
(c) Soil-Geotextile Interface Parameters
Tensile breaking force, & = 0.
Friction angle,

78
18 inch width) was used in the analysis until a failure condition
developed.
5.3.1 Predictions Using the Modified Duncan Soil Model with
Material Parameters Obtained from Triaxial Tests
Cumulative Displacements versus Applied Forces
The predicted cumulative displacements along the length
of the geotextile (at magnet sections 1, la, 2, 2a, 3, 4, and 5)
versus the applied forces are shown in Figure 5.2. In the
figure, the results of both large pullout tests are also depict-
ed. It can be seen that the predicted cumulative displacement
versus applied force relations are in good agreement with the
test results except for the region near the free-end of the
geotextile specimen. The prediction agreed somewhat better with
the results of Test 4.
The predicted failure load was 525 lb, compared with the
measured failure loads of 607 lb and 545 lb in Tests 3 and 4,
respectively. The discrepancy between the predicted failure load
and the measured values in Tests 3 and 4 were 13.5% and 3.7%,
respectively.
The difference between the predicted cumulative dis-
placement versus applied force at the region near the free-end of
the geotextile may be attributed to the shear induced dilatancy
effect in the soil located immediately above and below the
geotextile specimen as explained in the following.
Geotextile is a ,rdeformable" material. When a tensile
force increment is applied to one end of an embedded geotextile


79
- Test 3
* Test 4
Figure 5.2(a) : Applied Force Versus Cumulative Displacement
at Magnet Station No. 1


Displacement (in)
80
- Test 3
- Test 4
- Prediction
Figure 5.2(b) : Applied Force Versus Cumulative Displacement
at Magnet Station No. la


Displacement (in)
Test 3
Test 4
Figure 5.2(c) : Applied Force Versus Cumulative
at Magnet Station No. 2


Displacement (in)
82
Figure 5.2(d) : Applied Force Versus Cumulative Displacement
at Magnet Station No. 2a


Displacement fin)
83
Figure 5.2(e) : Applied Force Versus Cumulative Displacement
at Magnet Station No. 3


Displacement (in)
84

Figure 5.2(f) : Applied Force Versus Cumulative Displacement
at Magnet Station No. 4, 4a, 5


85
specimen, the movement of the geotextile is due entirely to
stretching of the geotextile itself until a large enough load is
reached so that sliding (rigid body movement) of the entire
specimen against the soil begins to take place. As sliding
against the soil occurs, the soil particles surrounding the
geotextile rearrange their structure (dilation if dense") and
increase the confining effect, thus increase the pullout resis-
tance of the geotextile. If the applied force is not large
enough (i.e., less than the failure load), this increase in
pullout resistance may be adequate to prevent a complete slippage
(pullout) from occurring and allow the entire geotextile specimen
to move over a short distance without reaching the failure
condition.
Upon examining the results of large pullout Test 3
(Figure 2.3), it is seen that the magnet stations at the region
near the free end of the- geotextile (magnet stations 4 and 5)
moves 0.04 inch at 284 lb applied force with no change in their
relative positions; for an applied force of 394 lb, magnet
stations 4 and 5 move again without straining in between them for
an amount of 0.09 inch. Failure was reached at 607 lb applied
force causing magnet stations 4 and 5 to slip 0.34 inch without
deformation. On the other hand, the finite element analysis
results shows no slippage at magnet stations 4 and 5 at applied
forces of 285 lb and 394 lb, whereas it shows complete slippage
(failure) at applied force of 525 lb. In the present analytical
model, once all the interface elements reach the fixed-free


86
state, the entire specimen will slip, accompanied with very large
displacements, and a failure condition is said to have occurred.
Consequently, the dilatancy induced partial slippage of the
entire specimen cannot be accounted for in the analytical model
and result in unsatisfactory prediction of the pullout behavior
near ;the free-end of the specimen.
Figure 5.3 depicts the initiation of movement along the
length of the geotextile due to applied pullout forces. It is
seen that all magnet stations in the Large Pullout Test 3 started
to slip (Fixed-Free State) at lower applied forces than the
prediction. Figure 5.4 depicts the predicted interface shear
stress distribution along the length of the geotextile at applied
forces: 180 lb, 270 lb, 360 lb, and 525 lb. Shown in this
Figure is the state of interface along the length of the geotex-
tile.
Force Distribution Along the Geotextile
Figures 5.5 and 5.6 show the strain distribution along
the geotextile specimen for Tests 3 and 4 at their respective
failure load. The strains were obtained by dividing the relative
movement between two magnet stations by their initial distance.
Combining the in-soil stress-strain relationship of the geotex-
tile shown in Figure 4.10 with Figures 5.3 and 5.4, the force
distribution in the large pullout tests 3 and 4 at failure can be
determined as shown, respectively, in Figures 5.7 and 5.8.
A comparison between the force distribution at failure in