Citation |

- Permanent Link:
- http://digital.auraria.edu/AA00003269/00001
## Material Information- Title:
- Numerical simulation of soil-geotextile interaction in pullout test
- Creator:
- Helwany, Mohd. Bassam
- Publication Date:
- 1987
- Language:
- English
- Physical Description:
- 120 leaves : illustrations ; 28 cm
## Subjects- Subjects / Keywords:
- Geotextiles -- Testing ( lcsh )
Geotextiles -- Testing ( fast ) - Genre:
- 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.
## Record Information- Source Institution:
- |University of Colorado Denver
- Holding Location:
- Auraria Library
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 19783121 ( OCLC )
ocm19783121 - Classification:
- LD1190.E53 1987m .H44 ( lcc )
## Auraria Membership |

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 ( 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 Â§ 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, To account for variation of following equation was used: in which, t1 = the value of for Og equal to Pg 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, 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 |