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GEOSYNTHETIC REINFORCED PILE SUPPORTED EMBANKMENTS By RUTUGANDHA GANGAKHEDKAR A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2004 Copyright 2004 by Rutugandha Gangakhedkar ACKNOWLEDGMENTS I am indebted to Dr. Townsend, as the chairman of my committee for providing me great guidance in the research proj ect. He has made this experience at U.F. a very pleasurable one. I would like to thank Dr. Davidson and Dr. Bloomquist for serving on my committee. Working with Dr. Davidson, as a teaching assistant, has been a very enj oyable learning experience. I would like to express my gratitude to all the faculty members in the Geotechnical Department for making the master's program a pleasant experience. I am grateful to my family back home for always standing by my side. I am thankful to all my friends back home and here who always have supported and encouraged me. TABLE OF CONTENTS page ACKNOWLEDGMENT S ................. ................. iii........ .... LI ST OF T ABLE S ................. ................. vii........ .... LIST OF FIGURES ................. ..............viii............... AB STRAC T ................ .............. xi CHAPTER 1. INTRODUCTION ................. ...............1.......... ...... 1.1. Background................ ...............1 1.2. Statement of the Problem............... ...............4. 2. LITERATURE REVIEW ................. ...............5................ 2. 1. Theory of Soil Arching ................. ...............5............ .. 2. 1.1. Load Transfer Mechanism ................. ...............8............. 2. 1.2. Stress Concentration Ratio .............. ...............9..... 2.2. Design of Geosynthetic Reinforcement ................. ...............................10 2.2. 1. Stress Reduction Factor ................. ...............11............... 2.2. 1.1. BS8006(1995) .........._.... ...............11..._._._ ... 2.2.1.2. Terzaghi Method .............. ...............13.... 2.2.1.3. Hewlett and Randolph Theory .............. ...............13.... 2.2.1.4. Guido's Theory .............. ...............14.... 2.2.2. Tension in Reinforcement .............. ...............15.... 2.2.3. Soil Resistance.................. .. ... .. ...................1 2.2.4. Tension in Reinforcement due to Lateral Sliding............... ................1 2.2.5. Reinforcement Strain ................. ...............19................ 2.3. Plate Model Tests .............. ...............20.... 2.4. Pile Design ................... .......... ...............22..... 2.4.1. Pile Group Extent ............... ..... .......... ...............2 2.4.2. Lateral Movement of Pile and Bending Moment in the Pile ................... ..23 2.4.3. Pile Cap Punching Capacity .............. ...............27.... 2.4.4. Efficiency of the Piles ................. ...............27........... ... 2.5. Lateral Movement............... ...............29 2.5.1. Empirical Methods .............. ...............31.... 2.5.2. Theoretical Methods ................. ...............35........... ... 2.6. Slope Stability ................. ...............35................ 2.6.1. BS8006 .............. ....... ............ .........3 2.6.2. Modified Boundary Element Method ................. ......... ................37 2.6.2. 1. Homogenous Slopes ................. ...............37........... . 2.6.2.2. Two Layer Soil Slope............... ...............40. 2.6.3. Friction Circle Method .............. ...............42.... 2.7. Settlem ents............... .. .. ......................4 2.7. 1. Public Work Research Center Method ................ .......... ...............47 2.7.2. Ogisako's M ethod .............. ...............49.... 3. MODELLING INT PLAXIS .............. ...............53.... 3.1. Axisymmetric Model ................. ...............53.............. 3.2. Plane Strain M odel .............. ...............60.... 4. CASE HISTORIES, COMPARISON OF VARIOUS METHODS ...........................65 4.1. Axisymmetric Model Analysis............... ...............65 4. 1.1. Maximum Settlements ................. ...............65........... .. 4. 1.2. Differential Settlements ................. ...............67........... ... 4.1.3. Tensile Strength of the Geogrid .............. ...............69.... 4. 1.4. Stress Concentration Ratio .............. ...............71.... 4. 1.5. Position of the Geotextile ......_......_.._.. ......._._. ..........7 4.2. Case Histories ................. .. .... .... .. ..............7 4.2. 1. Timber Pile inSitu Soil Reinforcement ................ ................ ...._..74 4.2.2. Route 403 Niitsu Bypass Japan .............. ... ...... .... .. .. ........7 4.2.3. Yono City, Japan Geogrid Reinforced Low Height Embankment on Deep Mixed Columns .............. ...... ...............79 4.2.4. Stansted Airport Piled Embankment ..................... .. ...............8 4.2.5. AuGeo Piled Embankment for Double Track Railway RawangBidor ....82 4.3. Comparisons .............. ...............83... 4.3.1. Lateral Movements ................. ...............83........... .. 4.3.2. Geogrid Strength ............... ...............84.... 4.3.3. Bending Moment in the Piles .............. ...............87.... 4.3.4. Pile Efficiency .............. ...............88.... 4.3.5. Slope Stability .................. ....... .. ..............8 4.3.6. Maximum and Differential Settlements .............. ...............90.... 5. CONCLUSIONS AND RECOMMENDATIONS ................... ...............9 5.1.Conclusions............... ............9 5.2. Recommendations............... ............9 APPENDIX SAMPLE CALCULATIONS INT MATHCAD............... .................9 LI ST OF REFERENCE S ................. ...............107................ BIOGRAPHICAL SKETCH ................. ...............109......... ...... LIST OF TABLES Table pg 1: Recommended values for design parameters ................. ....._.._.............. ......2 2: Soil properties for axisymmetric model............... ...............57. 3: Soil properties for the embankment fill .............. ...............60.... 4: The effect of position of the geogrid ................. ...............73.............. 5: Effect of support of underlying soil ................. ...............74.............. 6: Comparison between maximum lateral movements ................. .......... ...............84 7: The lateral movements in Case 4.5 in various conditions ............. .....................8 8: Comparison between the tensile strength of the geosynthetic reinforcement for the case of no void below geogrid .......................... .................. ................86 9: Comparison between observed and predicted values for tensile strength of the geogrid along the length of the embankment ................. ...............86............... 10: Comparison between observed and predicted values for tensile strength of the geogrid along the width of the embankment .....__.___ ............. ....___ ...........8 11:. Prediction of maximum bending moment in piles near the toe of the embankment ...88 12: Prediction of maximum bending moment in piles near the toe of the embankment ...88 13: Efficiency of the piles .......................... ............_.......8 14: The predicted maximum and differential settlements at the top of the embankment..91 15: The predicted maximum and differential settlements at the top of the pile ................91 LIST OF FIGURES Figure pg 1: Conventional pilesupported system ....__ ......_____ .......___ ...........2 2: Piled embankments with concrete slab ....__ ......_____ .......___ ..........2 3: Geosynthetic reinforced piled supported embankments ................. ................ ...._.3 4: The soil mass overlying a potential void ............. ...............6..... 5: The formation of a true arch (Void under soil mass). ......___ .... ... ._ ........._......6 6: Soil mass collapses to form an inverted arch .....__.___ .... ....___ ....._._ ........ 7: Load Transfer Mechanism ........._.__ ......._._ ...............8... 8: Unit Cell Utilization. ........._.__ ..... ._ ...............11... 9: Hemispherical domes model ........._.__ ......._._ ...............14... 10: Tensile force in the reinforcement under embankment of medium dense soil............17 1 1: Lateral sliding stability at the interface of fill and reinforcement .............. .... .........._.19 12: Plot of M* versus q/co............... ...............26.. 13: Values of h and P derived from regression analysis............... ...............26 14: Relation between the maximum stability and maximum lateral movement. ...............32 1 5: Impact of soil stiffness and emb ankment geometry on lateral movements .................3 3 16: Relation between the depth of maximum lateral movement to minimum shear strength ................ ...............34....... ...... 17: Relation between depth of maximum lateral movement and the embankment width.34 18: Variables required for the stability analysis of GRPS embankments ........................36 19: Effect of pile position on the homogenous slope.. ......___ .......__ ...............38 20: Effect of pile diameter on the homogenous slope................... ..........................38 21: Effect of pile spacing on homogenous slope ................. .........._......._.........39 22: Effect of pilesoil limiting pressure on homogenous slope .............. .....................3 23: Effect of pile position on twolayer slope ................. ....__. ............. ......4 24: Effect of pile diameter on a twolayer slope ....._.__._ .... ... .___ ............... ....4 25: Effect of pile spacing on the twolayer slope ................. ........._. ....__. .......41 26: Effect of pilesoil limiting pressure multiplier on the twolayer slope.............._._. .....42 27: Forces on slopes without piles ................. ...............44......__._... 28: Forces acting on a slope reinforced with piles............... ...............45. 29: Settlement and differential settlement of soil embankment on deep mixed columns. 47 30: Determination of the influence factor ......__................. ............... 49. ... 31: Coefficient C1 versus the improvement ratio, as ................. ................ ......... .51 32: Relation between the coefficient C2 and improvement ratio as .............. ..................52 33: Yield surfaces of soft soil model in p' q plane .....__.___ .... ... .___ .................5 34: Axisymmetric model............... ...............57. 35: Initial Stresses are developed............... ...............5 36: Stages of construction ................. ...............59............ 3 7: Plane strain model for Polk County proj ect ................. ....___ .....__ .......6 3 8: Mesh generated for the Polk County Proj ect. ................. ....___ ............... ..6 3 9: Stability analysis s using Plaxi s Phic reduction method ................. ............ .........64 40: Influence of pile modulus on the maximum settlements at pile head..............._.._.. .....66 41: Influence of tensile stiffness on the maximum settlements at pile head. ........._..._.......66 42: Influence of height of embankment on maximum settlements at pile head ...............67 43: Influence of pile modulus on differential settlement at pile head.. ............_. ..............68 44: Influence of tensile stiffness on differential settlement at pile head. ................... ........68 45: Influence of height of embankment on the differential settlement at pile head ..........69 46: Influence of pile modulus on tensile strength of geogrid ................. .....................70 47: Influence of tensile stiffness of geogrid on tensile strength of geogrid ................... ....70 48: Influence of height of embankment on tensile strength of geogrid ................... ..........71 49: Influence of pile modulus on stress concentration ratio ................ ............ .........72 50: Influence of tensile stiffness of geogrid on stress concentration ratio. ......................72 51: Influence of height of the embankment on stress concentration ratio.............._..._.......73 52: Model for Polk Parkway Timber pile insitu soil reinforcement ............... .... ...........76 53: Model for Niitsu Bypass, Japan ................. ...............77........... .. 54: Results of Geotechnical monitoring on the NiitsuBypass site. ............. ..................78 55: The model for street in Japan, Yono city ................. ...............80........... 56: Embankment from Stansted airport terminal to CambridgeLondon mainline ...........81 57: The model of AuGeo piled embankment for double track railway Rawang Bidor...83 58: Evaluation of factor of safety for the embankment slope of AuGeo Piled Embankment Rawang Bidor .............. ...............90.... Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering GEOSYNTHETIC REINFORCED PILE SUPPORTED EMBANKMENTS By Rutugandha Gangakhedkar May 2004 Chair: Frank Townsend Maj or Department: Civil and Coastal Engineering The design of embankments on weak foundation soils is a challenge to the geotechnical engineer. There are several issues related to bearing capacity failures, intolerable settlements and slope instability that need to be addressed. The piled embankments with the inclusion of a geosynthetic layer have proved to be one of the economic and effective techniques to handle such problems. The inclusion of the geosynthetic reinforcement eliminates the need for inclined piles used in conventional piled embankments for resisting large lateral pressures. The geosynthetic layer enhances the load transfer mechanism and considerably minimizes the differential and maximum settlements. This study attempts to analyze the various methods available today for the design of these structures. A numerical study is carried out. The effects of certain factors like pile modulus, stiffness of the geosynthetic reinforcement, height of the embankment, effect of the soil layer directly below the geogrid which are not considered by other available methods are studied using a finite element program Plaxis 2D. Plane strain models of five case studies found in the literature are developed. The results from various methods are evaluated and compared with the results from Plaxis. It is found that numerical analysis was able to address many factors that were neglected by all the other available methods. It was also found to be more reliable than currently used methods. CHAPTER 1 INTTRODUCTION 1.1. Background Weak foundation soils have always been a challenge to Geotechnical Engineers. When designing embankments over weak foundations, bearing capacity, slope stability, lateral pressures and movements and differential settlement are some of the maj or concerns. A variety of techniques are available to address these issues. They include preloading, deep mixing columns, stone columns, use of light weight fill, and soil replacement. Steel and concrete piles have also been used. Geosynthetic reinforced pile supported (GRPS) embankments, the subj ect of this thesis have also been very successful . The conventional pilesupported (CPS) system (Figure 1) requires large pile caps and very closely spaced piles. This is essential to transfer the large embankment loads to the piles and to avoid surface deformations due to large differential settlement between the caps. The CPS requires inclined piles at the edges of the embankment to resist large lateral pressures. The Piled embankments with a concrete slab (Figure 2) are successful in transferring all the load, however they require a large amount of steel as reinforcement or very thick concrete slabs. This makes them very uneconomical and hence they are rarely used in practice. Conventional pile embor ent Figurel: Conventional pilesupported system Inclned pllps Smott size pile caps Continuous concrete slab Verti;al piles~ III embankment with a continuous concrete slab Figure 2: Piled embankments with concrete slab Geosynthetics have a very high tensile strength which the soil lacks. Geosynthetics reduce the differential settlement, increase the bearing capacity, and the slope stability when used in soft soils. The GRPS system (Figure 3) has a geosynthetic reinforced platform or mat which increases the efficiency of transferring the load from the soil to the piles without giving rise to deflections between the pile caps. The geosynthetic layers provide a resistance to the lateral thrust at the edges of the embankments. GRPS embankments can be more rapidly constructed than CPS embankments. :;,~ .. reinforced platform ledI embankment w th a geogrid .li forced p otfform Figure 3: Geosynthetic reinforced piled supported embankments From a survey of various proj ects (Han, 1999), it was found that in conventional piled embankments the percent coverage of the pile caps over the total foundation area is 6070% whereas, in the GRPS system the percent coverage is reduced to about 1020%. In this system, the pile size can also be reduced and larger pile caps can be used. This illustrates that this technique has technical and economical advantages over others. Vibroconcrete columns, deep mixed columns, stone columns or any other columnar system used in ground improvement can be used to support the embankment. Such columns, commonly have larger diameters than the piles. The column heads act as pile caps and help in transferring the load. The deformation of the soil between the pile caps induces negative skin friction in the piles. This is eliminated in the columnar system. The columnar systems have a range of stiffness and their stiffness is less than the piles. The columnar system can be installed in various patterns, grid, block, wall as per the specific requirements. The columnar system and soil act as a composite foundation and carry the load from the embankment. Hence, they can act as end bearing or a floating system unlike the piles which have to be seated on a firm strata. GRPS embankments have several applications: * Embankments over soft soils, * Embankments approaching a bridge supported by deep foundations, * To prevent differential settlement between a new embankment near existing structures or existing embankment where settlement has ceased. * Subgrade improvement 1.2. Statement of the Problem A number of methods are available for the design of GRPS embankment systems. Limited guidelines are also available for columnar systems. This report addresses design issues and compares the various methods available. A Einite element model is developed for the case studies in Plaxis Einite element software. The design issues of lateral movement, geosynthetic mattress design, pile design, slope stability and settlement will be handled here. The case studies will be discussed and comparison of various methods and the finite element model will be presented. CHAPTER 2 LITERATURE REVIEW 2.1. Theory of Soil Arching Arching is defined by McNulty (1965) (cited in Han, 1999) as "the ability of a material to transfer loads from one location to another in response to a relative displacement between the locations. A system of shear stresses is the mechanism by which the loads are transferred." Figure 4,5 and 6 illustrate this concept. Consider soil on a rigid base, there is no tendency for differential movement and hence no soil arching. The stress acting at a point a in Figure 4 is the overburden stress yH, where y is the unit weight of the soil and H is the height of the soil prism. When one of the local supports at the point a is removed, the point a is in tension and a roof tension arch is formed. The true arch collapses as the soil is not in equilibrium. The soil settles in an inverted arch, the adj acent soil develops the required shear strength and the soil reaches equilibrium state. The transfer of pressure from the yielding portion to the stationary portion is called arching. iii : +: rr " 6 i: I _ ___ ____ II II II I, CI Il II II I II Ci *. I* II II IIIILI131 1. t IC I I* r I~ II ~ 11 II II II II II IC I*l~lili II II el I I I I I I 1* r* ~~ ;~~;~;~~ %r Ir Ir i"'ll I *. I. *. *. .b I II .  " " " o~~p~ nr I/ III111 311 rl C .Jt I I ~~=1~. ~. ~~ B ~" :: ~: i: :1 : :: :: :I :: j: ::: ii : I~II~~' iilii :~r3 1 ." .* '. *. *. . : .* 1 : . : . & ;~ir~n;~~in~Jbcts~Jc~ Figure 4: The soil mass overlying a potential void (McKelvey, 1994 cited in Li et al., 2002) Figure 5: The formation of a true arch (Void under soil mass) (McKelvey, 1994 cited in Li et al., 2002) Figure 6: Soil mass collapses to form an inverted arch (McKelvey, 1994 cited in Li et al., 2002) Different methods have been proposed to model the soil arching effect. Terzaghi (1936) (cited in Han and Gabr, 2002) considered the shear strength along the soil prism which is mobilized to a certain height, at which the plane of equal settlement exists. Giroud et al. (1990) (cited in Han and Gabr, 2002) applied McNulty's model to deal with soil layergeosynthetic systems overlying voids. Hewlett and Randolph (1988) (cited in Li et al., 2002) considered limit equilibrium in a domed region for the sand between the two piles. Most of the load above the crown was transferred onto the support through the crown. Schmertmann (1991) (cited in Han and Gabr, 2002) proposed that all the load within the triangular prism(plane strain) or conical prism(axisymmetric) is transferred directly onto the adj oining support. In all the above cases, it is assumed that all the pressure is to be carried by the geosynthetic; i.e., there is a cavity below the geosynthetic layer as shown in Figure 7. 2.1.1. Load Transfer Mechanism Stes cncnrato rai n_ Go > The gosynteticlayerand he emankmet fil for a s iffe yned fipafomta supports load transfer mechanism. High quality fill is used for better interaction between the soil and pile. The weight of the fill tends to move downward due to the presence of soft soil below the geosynthetic layer. This downward motion is resisted by the shear resistance provided by the fill on the pile caps. The shear resistance reduces the pressure acting on the geosynthetic but increases the load acting on the caps. The inclusion of the geosynthetic layer is expected to reduce the differential settlement between two pile caps. The reduction of the displacement reduces the shear stresses induced by soil arching. Hence, the load transfer by soil arching is reduced. This also reduces the load transferred to the pile caps. The vertical component of the tension forces in the reinforcements) is however, transferred to the pile caps. A single geosynthetic layer acts as a tension membrane while a multilayer system can interlock better with the surrounding soil and act as a stiffened "beam" or "plate". The shear resistance from the reinforced mass is considered as apparent cohesion. In the case, where the geosynthetic reinforced platform is perfectly rigid there is no differential settlement, tension in reinforcement, nor relative movement between the soil and reinforcement. Here, the mechanism of soil arching, tensioned membrane or apparent cohesion cannot be developed. This leads to the stress concentration on the pile caps which is due to the stiffness difference between the pile caps and soil. 2. 1.2. Stress Concentration Ratio The stress concentration ratio is a parameter that is used to quantify load transfer. It is defined as the ratio of the stress on the pile(caps) to the soil between the pile(caps). The stress concentration is a global index which incorporates the mechanism of soil arching, tension membrane or apparent cohesion effect and pilesoil stiffness difference. Ooi et al. (1987) (cited in Han, 1999) indicated that the value of n for conventional pile embankments ranged between 1.0 to 8.0. This ratio increased with the increase in the ratio of the embankment height to the net spacing between the two near edges of the caps on the piles. Based on studies by Reid et al. (1993) and Maddison et al. (1996) (cited in Han, 1999), the n values for the GRPS systems on vibro concrete columns and concrete piles ranged from 8 to 25, which is much higher than the conventional piled embankments. This increase in n is due to the inclusion of the geosynthetic layer. The n value depends on the stiffness or rigidity of the foundation. The stress concentration for a fully flexible foundation resting on a pilesoil composite foundation without soil arching is said to have a n value equal to one. The concentration ratio for a rigid foundation is very high. The GRPS system can be considered as an intermediate state between flexible and rigid foundations. 2.2. Design of Geosynthetic Reinforcement In geosynthetic reinforced pile rafted embankments, the conventional rigid concrete mat resting on the piles is replaced by a layer of soil along with a geosynthetic reinforcement to provide the required tensile resistance. This layer is more flexible. Due to the flexibility of the geosynthetic layer, load transfer due to soil arching is seen. The degree of soil arching and hence the vertical stress on the reinforcement and pile(caps) needs to be evaluated. The design of the reinforcement should consider: * Vertical stress on the reinforcement after soil arching effect between the adjacent piles has taken place * The tensile force developed in the reinforcement due to the vertical pressure of the embankment * The tensile force in the reinforcement due to lateral spreading of the embankment. The design methods that will be discussed here are: BS 8006, Terzaghi's theory, Helwett and Randolph theory and Guido's theory. The finite element method using Plaxisfinite element program will be discussed in Chapter 3. Most of the current design methods ignore the soil resistance below the geosynthetic layer; i.e., a void is considered below the geosynthetic layer. This makes the design conservative. Here we are considering piles arranged in a rectangular pattern. ~~~~I Figure 8: Unit Cell Utilization (Russell and Pierpoint, 1997 cited in Li et al., 2002) A unit cell supported at four ends on piles is considered (Russell and Pierpoint, 1997 cited in Li et al., 2002). The area of the cell is s2 and the area not supported by the pile is (s2 a2). A quarter of the load is assumed to be transferred to the reinforcement. 2.2.1. Stress Reduction Factor In order to compare the various methods a stress reduction ratio denoted as S3D is defined. It is defined as the ratio of the average vertical stress acting on the reinforcement to the overburden pressure due to the embankment fill. 2 W, (s a) S3D =H(Ia Eqn.2.1 2.2.1.1. BS8006(1995) BS8006, (cited in British Standard 8006, 1995) is the British Standard method used for design of embankments with reinforced soil foundations on poor ground. This is the ' 14 of thB verlical loa~d Carried b he hpile i .. ssurned to be transferred to the geogrid between SpiLes most widely used method and is very conservative. The distributed vertical load acting on the reinforcement between the pile caps is WT For H>1.4x(sa) W 1.4sffsy(sa) X 2 c qn2. s2 v For 0.7(sa) < H <1.4(sa) sx(frsTH+f~ws) (_2 c Eqn.2.3 W, = s2 s2 but W,= 0 if <;'Eqn.2.4 a oV where s the spacing between the piles a the size of the pile caps ws the uniformly distributed surcharge loading p', the vertical stress on pile caps o'v the factored average vertical stress at the base of the embankment v, =fesH+f~w fes the partial load factor for soil unit weight f, the partial load factor for applied external loads Y the unit weight of the soil H the height of the embankment fill This method considers the piles as buried rigid conduits. The vertical stress is given using Marston' s formula for positive proj ecting conduits. p,= va Eqn.2.5 BS8006 gives empirical equations for arching coefficient as follows C, =1.95 H0. 18 for endbearing piles(unyielding) Eqn.2.6 C, =1.5 H 0.07 for friction and other piles Eqn.2.7 Based on the above equations the stress reduction ratio is given by 2.8s ap S (s+a):H THjEq.. 2.2. 1.2. Terzaghi Method Terzaghi's (1943) (cited in Li et al., 2002) method was based on results from trap door tests at large displacement. Terzaghi considered the problem as three dimensional. He considered the shear strength along a soil prism which is mobilized to a certain height where there exists a plane of equal settlement. The stress reduction ratio is given as (S2 a2) X 4aHK tan( ~ q.. 3D4HaK ta@95 ) K is the ratio of the horizontal to vertical pressure. Terzaghi has taken K=1. 2.2.1.3. Hewlett and Randolph Theory Hewlett and Randolph (1988) (cited in Li et al., 2002) found a theoretical solution for a granular, free draining soil based on model tests. It assumes the soil arching as a series of vaulted domes of hemispherical shape supported by the pile caps. In this case, the critical locations for failure would be at the crown of the domes or at the pile caps. The stress reduction factor is evaluated using limiting plastic equilibrium. To top at embankment Figure 9: Hemispherical domes model (Hewlett & Randolph, 1988 cited in Li et al., 2002) The stress reduction ratio at the crown is given by S, = 1 + xEqn.2.10 D S 2K <3)) JH (2K ~3) The stress reduction ratio on the pile caps is given by S,, Eqn.2.11 D K a 1KJ as 1(+ aKs +~ 1 Here, K, is the passive earth pressure. The higher of the two stress reduction ratios is used for the calculations. Hence, it considers the worst case scenario. 2.2.1.4. Guido's Theory Guido et al.(1987) (cited in Li et al., 2002) considered the effect of lateral spreading of the embankment. The reinforcement carries load from only a rectangular pyramid, that is not carried by the piles. The stress concentration ratio is given by (sa) SD Eqn.2.12 3D3JH Schmertmann (1999) (cited in Han and Gabr, 2002), proposed a triangular load transfer model for soil arching. It was assumed that all the load above the triangle will be transferred onto the adj oining support. This was confirmed by finite element analysis by Gabr and Hunter(1994) (cited in Han and Gabr, 2002) However, all the above models have neglected the effects of the difference in the stiffness of the geosynthetic layer and elastic modulus of the pile caps. The maximum tension in the geosynthetic is said to occur at the edge of the pile. 2.2.2. Tension in Reinforcement The British Standard BS8006 (1995) suggests the following formula for an extensible reinforcement. The tensile load T, per metre "run" generated in the reinforcement resulting from the distributed load WT is given by W, (s a a) 1 T, = 1I+ Eqn.2.13 2a 6E where T, the tension in the reinforcement a the strain in the reinforcement. The tension in the reinforcement is calculated taking into consideration the maximum allowable strain in the reinforcement. Six percent strain is considered the upper limit for transferring the load to the piles. The load/strain curve should be studied at different load levels. The upper limit should be reduced for shallow embankments to prevent differential movements on the surface of the embankment. To avoid long term localized deformations at the surface of the embankment, the long term strain should be kept to a minimum. A maximum creep strain of 2% is permitted for permanent construction. This tensile load is developed as the reinforcement deforms during embankment construction. If it does not deform during construction, the tensile force is not developed; i.e., the load is not carried by the reinforcement till the foundation settles. Alternative equations should be used to determine the tensile strength of inextensible reinforcement. Giroud et al. (1990) (cited in Li et al., 2002) proposed a membrane theory for a geosynthetic layer overlying an infinitely long void. This was also used to determine the tension in the reinforcement. The formula can be stated as T, =o,(sa)O Eqn.2.14 where as the stress placed on the geosynthetic reinforcement R a dimensionless factor relating the geosynthetic strain to the geosynthetic deflection. O can be defined as R=4ez +(sa2 Eqn.2.15 where y the geosynthetic deflection. Many geosynthetics are anisotropic in nature. They have more strength in the machine or crossmachine direction. Giroud et al.(1990) (cited in Li et al., 2002) has two theories for the strength of the geosynthetic layer that is to be used. In the first approach the strength of the geosynthetic in the weak direction is assumed for the strength in all directions. The second approach is to limit the applied tension to half of the strength in the strong direction. The more conservative approach is generally used in all designs. The actual value is generally close to the less conservative approach. 2.2.3. Soil Resistance All the design methods stated above consider a void below the geosynthetic layer. The resistance from the soil below the GRPS platform is ignored. This leads to a conservative design. In practice, there will be some support provided by the soil below. This will considerably reduce the tension in the reinforcement. Reid and Buchman (1984) (cited in Han, 2003) found from their study that the resistance from the soil below the GRPS platform is 0. 18yH where y is the unit weight of the embankment fill and H is the height of the embankment. John (1987) (cited in Han, 2003) found the soil resistance to be 0. 15yH. Later, a finite element model by Jones et al. (1990) (cited in Han, 1999) proved that partial support from the reinforcement reduced the tensile force in the reinforcement significantly (Figure 10). This can be seen in the Plaxis model developed in Chapter 3. 1400  Heig~hl of No conlinbution from foundation soil emb~ankment (m) 1200 E I ~ earnal support frorn foundation soil softh day) 10i 'j 2 00 . D I I I M 1 K .5 Center to center spacing of piles, Yrim Figure 10: Tensile force in the reinforcement under embankment of medium dense soil (Jones et al. (1990) cited in Han, 1999) However, it seems to be reasonable to consider a cavity under the GRPS platform if the settlement below the platform is caused by factors other than the embankment loads. The settlement can be due to consolidation or underconsolidation of the soil, liquefaction, lowering of ground water, etc. 2.2.4. Tension in Reinforcement due to Lateral Sliding The reinforcement should resist the horizontal force due to lateral sliding. This tensile load should be generated at a strain compatible with allowable lateral pile movements. The need for raking of the piles is eliminated. The reinforcement tensile load needed to resist the outward thrust on the embankment in accordance to BS8006 (1995) is Tds =0.5K a (ffs H+2fq ws )H Eqn.2.16 where Ka the active earth pressure coefficient (Ka=tan2(45O/2)). ws the uniformly distributed surcharge loading fes the partial load factor for soil unit weight f, the partial load factor for applied external loads Y the unit weight of the soil H the height of the embankment fill. To generate this tensile load the embankment fi11 should not slide outwards over the reinforcement. The reinforcement bond length should be 0.5KaH(ffsTH+2f ws>fsfn Le Eqn.2.17 a tan@ ) c TH f171 where fs the partial factor for reinforcement sliding resistance fn the partial factor governing the economic ramifications of failure h the average height of the embankment fill above the reinforcement length ns the par ot' bond angle to t stress condition fms the interaction coefficient relating the embankment fill/reinforcement ;an@' cy the large strain angle of friction of the embankment fill under effective tial material factor applied to tan $'cv Surcharge, we 1 u I Reinforement Sorftfcldation Figure 1 1: Lateral sliding stability at the interface of fill and reinforcement (BS8006, 1995) 2.2.5. Reinforcement Strain According to BS 8006, the maximum allowable strain in the reinforcement should be limited to ensure that no differential settlement occurs at the surface of the embankment. In shallow embankments, however it might happen that the full soil arch cannot be formed within the embankment fill. Emb~ankme~nt An initial tensile strain is required for transfer of load to the piles. An upper limit of about 6% is imposed to ensure that all the load is transferred to the piles. This upper limit can be reduced for shallow embankments to prevent differential movements. In order to ensure that long term localized movements do not occur at the surface of the embankment, the long term strain should be kept to a minimum. A maximum creep strain of 2% is generally allowed over the design life of the reinforcement. 2.3. Plate Model Tests Reinforced foundations have four possible modes of failure (Wayne et al., 1998, cited in Li et al., 2002). Variation in soil conditions and configuration of reinforcement result in these different modes. The failure modes are * When soil beneath the reinforced soil is very soft. * Dimension punching failure failure above the uppermost reinforcement it can occur when the topmost reinforcement layer is not placed close enough to the bottom of the reinforcement. * Failure between the reinforcements it can occur due to large spacing between two reinforcement layers. * Deep punching failure it occurs when the underlying soil is very soft and the reinforced mass is very strong but the reinforced mass does not have sufficient width or thickness to reduce the stress at the base of the reinforcement. The actual failure of the foundation is controlled by the critical mode. The ultimate bearing capacity in the critical mode is less than that in any other types of failure. Many model tests were performed by Wayne et al.(1998), Krishnaswamy et al.(2000) and Guido et al.(1997) (cited in Li et al., 2002) on reinforced foundation. These tests were performed to determine the influence of various factors on the bearing capacity of the foundation. Wayne Model Test Bearing capacity ratio(BCR) is used for convenience in comparing the test: BCR= q,/qo Eqn.2.18 where qo the ultimate bearing pressure for the unreinforced sand qr the bearing pressure of the geogridreinforced sand at a settlement corresponding to the settlement at the ultimate bearing pressure for the unreinforced sand. Wayne recommended typical design parameters in order to keep the bearing capacity ratio in the range of 1.5 to 2.5. Generally a 0.1m thickness is placed below the lowest geogrid in order to have good interaction. Table 1: Recommended values for design parameters Typical Values Recommended (not greater than) u 0.15B to0.3B 0.5B s 0.15B to 0.3B 0.5B z 0.5B to 1.0B 2.0B b 2.0B to 3.0B 4.0B a 0 1B to 0.2B 0.3B Al 0.5B to 1.0B 2.0B N 2 to 4 5 Note : u = distance from the uppermost geogrid to the footing base s = spacing between the geogrid layers z = thickness of the reinforced fill b = width of the reinforced fill a = distance from the lowest geogrid to the bottom of the reinforced fill Al = length of the geogrid beyond each of the strip footing N = number of geogrid layers 2.4 Pile Design The pile reinforces the underlying subsoil. The piles give direct support to the embankment through soil arching. The embankment imposes a lateral thrust on the piles. In conventional pile supported embankments, inclined piles are included at the toe of the embankment. In GRPS, the geosynthetic membrane is laid on the pile caps. The tension provided by the membrane provides support and prevents lateral sliding of the embankment. In geosynthetic reinforced pile supported embankments, the term pile is used not only for conventional piles but also for other soil improvement columns like stone columns, vibro concrete columns, soilcement columns, etc. The pile design incorporates * lateral movement of the pile * bending moment developed in the pile due to lateral movement * axial bearing capacity of the pile * settlement of the pile The load carrying capacity of the pile or any other column used in soil improvement should be evaluated according to the methods developed for that type of soil improvement. The effect of group action should be considered. The spacing of the piles is maximized for economical reasons. An upper limit on the spacing of the piles is imposed (BS 8006) when the piles are installed in a square grid pattern. Q, s = Eqn.2.19 es TH+f ws) where Q, allowable load carrying capacity of each pile/column in pile group fes partial factor for soil unit weight g unit weight of the soil H height of the embankment f, the partial load factor for external applied loads ws the external surcharge loading 2.4.1. Pile Group Extent According to BS 8006(1995), the piled area should extend beyond the edge of the shoulder of the embankment. This is to ensure that any differential movement/settlement or instability outside the piled area does not affect the crest of the embankment. The outer edge limit for the outer pile cap can be given as L,=H ntane,) Eqn.2.20 where L, the horizontal distance between the outer edge of the outer pile cap H the height of the embankment n the side slope of the embankment 6, the angle to the vertical between the shoulder of the embankment and the outer edge of the outer pile cap 6 =45 90 where Avdescribes the embankment fill 2.4.2. Lateral Movement of Pile and Bendinn Moment in the Pile The pile prevents the ground soil from moving with the soil mass. This develops a lot of horizontal stresses on the pile. This horizontal stress is relieved partially when the pile deflects from its original position. Hence, the soil experiences some earth pressure. This can be related to the difference between the movement of the pile and that of the soil. The deformed shape of the soil depends on various factors like, the stiffness of the pile, the restraint provided by the embankment, the fixity provided by the lower stiff/firm layers, the depth of the deforming layer and the strength of the moving soil. The load applied on the pile will produce a lateral deflection and rotation at the level of the pile cap. Hence, horizontal displacement of the pile and the bending moment produced are of interest in this situation. The behavior of the piles can be attributed to * Strength of soil * Relation of soil stiffness and strain * Pile diameter * Pile length * Pile stiffness * Pile group layout and spacing * Lateral restraint provided by the deeper layers * Relationship between the earth pressure on the pile and the soil strength * Rate of movement of the soil The pilesoil interaction is very complex in nature. There are various methods used for the determination of the lateral deflection of the piles * Empirical relations * Finite element analysis * Displacement based methods * Pressure based methods * Centrifuge testing and large scale prototype testing Goh et al.(1997) (cited in Li et al., 2002) used numerical methods to study the behavior of the lateral movement of a single pile. The piles are represented by beams to study the bending moments and the lateral movement. Hyperbolic soil springs are used to denote the soilpile interaction. All the properties or input data for the soil are attained from experimental data. Initially, the lateral displacement due to the applied construction load of the embankment is analyzed. This "freefield" soil movement is applied in the second case, to an existing pile and its effect is studied. BCPILE was used to study this effect. According to Goh et al. (1997) (cited in Li et al., 2002) the difference between predicted and measured values was very small. Goh et al. (1997) (cited in Li et al., 2002) developed some charts from experimental data. The empirical relations developed can be used for preliminary estimation of the bending moment induced in the piles located near the toe of the embankment and restrained from rotating at the pile head. A dimensionless quantity M* is calculated from the following equations: M* M*=he[p"q eg] Eqn.2.21 c dhs The values for h and P can be obtained from the charts Figure 13 1=1.88 KR) P=0.18 KR 0 1 Eqn.2.22  4 nr .~~mm ~ r~~ ( ~I I _I I _ 0.003~2 10.4 Qz ~ 4 5 6 0 1 2 3 Figure 12: Plot of M* versus q/co (Goh et al., 1997 cited in Li et al., 2002) 0.08 3e0.06 0.04 0.02 0 0.44 0.4 0.38 0.32  0.28 0.004 0.002 Figure 13: Values of h and P derived from regression analysis (Goh et al., Li et al., 2002) 1997 cited in where El E5h~ KR relative pilesoil stiffness ratio; EI, bending stiffness of the pile co undrained shear strength of the soil d width of the pile hs thickness of the soft clay layer E5o secant modulus at half ultimate stress in undrained test of soil q applied embankment pressure Mmax maximum bending moment in the pile Lee et al. (1991) (cited in Li et al., 2002) used a modified nonlinear boundary element approach to study the response of offshore piles subj ected to external soil movements. Finite element programs like PLAXIS can be used to analyze the response of piles to this type of system. The results from some PLAXIS models are presented in Chapter 4. 2.4.3. Pile Cap Punching Capacity The pile caps can punch through the embankment fill if there is a concentration of stresses on the pile caps and if the embankment height is very low. The inclusion of a geosynthetic layer decreases the stress concentration on the pile caps (cited in Han and Gabr, 2000). This reduction of the stress on the pile cap can result in a smaller probability of punching failure of the pile caps. There is currently no design available for designing the punching failure of the pile caps. However, it can be simulated numerically. 2.4.4. Efficiency of the Piles The efficiency of the pile support is the ratio of the weight of the embankment that the piles can carry. E=16 1 is )K Eqn.2.23 where 3=b H height of the embankment s c/c spacing between the piles b width of the pile caps K, Rankine passive earth pressure If the weight of the soil is considered then the crown will not be the only weakest position where failure will occur. The limited area on the pile cap is also prone to bearing failure at those points. The efficiency for this case can be expressed as E Eqn.2.24 1+P where 2K 1 (K +1) (1+6)2 (~)i (+K) In normal conditions, K, is assumed to be 3. The efficiency of the pile caps increases as the height of the embankment increases. When the embankment height, pile spacing and K, are fixed then the efficiency of the piles depends on the width of the pile caps. When all other factors are kept constant, the efficiency of the piles depend on the angle of internal friction. Piles in GRPS embankments need not be conventional piles. Vibroconcrete columns, stone columns, deep mixed columns are also considered here. Deep mixing columns initially popular in Asia and Europe are becoming more popular in America. The application of these deep mixed columns requires a thorough subsoil investigation. Undrained shear strength of the soil and stiffness of the surrounding soil are very important properties. These columns can be made using a continuous flight displacement auger. They can be made up of dry or wet cement columns or lime. The degree of improvement of the soil depends on densification and pressurization. Load transfer depends on the soil conditions. Deep mixed columns can be installed in grid, wall, block or column type. The load transfer to the deep mixed columns occurs due to the difference in the stiffness of the columns and the surrounding soil. Hence, there is more load concentration on the columns. This load transfer is controlled by * Length of the column and its stiffness * Ratio of the area covered by the columns to the total area * Ratio of column stiffness to the stiffness of the surrounding soil * The effects of the load spreading bearing layer or bearing layer on the top of the columns. A detailed report of construction and analysis of the deep mixed columns in soft soil is found in a report of Coastal Caisson Corporation. Coastal Caisson installed five deep mixed columns in Jacksonville, Florida. There is much literature found on deep mixed columns written by Porbaha et al. (1998, 2000), Bruce et al.(2001) and Terashi et al.(2003) cited in Interim Report by Han (2003). 2.5. Lateral Movement Large lateral movements are seen when an embankment load is applied. This large lateral deflection is dangerous for the piles in the GRPS system. This causes excessive settlements in the system and can prove to be more dangerous than vertical settlements. The foundations or structures in the adj acent areas can be greatly affected by the lateral movements caused. There are no methods available to estimate the lateral movements of geosynthetic reinforced pile supported embankments. It is however essential to get an initial estimate of the lateral movements. This can be done by prototype testing. However, this is very uneconomical. Initial predictive methods should be used to determine lateral ground movements. The design method used will depend on the sensitivity of the structure to the soil movements. Seaman(1994) (cited in Li et al., 2002) investigated the effects of various factors on lateral movements. The increase in certain factors that tend to increase the lateral movements are: * Vertical stress applied on the soil due to the embankment fill * Length of the embankment * Width of the embankment * Embankment slope * Poisson' s ratio of the soil The increase in certain factors that tend to decrease the lateral movements are * Thickness and stiffness of the fill * The distance from the embankment toe * Stiffness of the soil * Strength of the soil * Adhesion between the soil and the fill The lateral movements caused by application of the embankment load can be estimated using * Empirical relations with the soil properties and the observed behavior of the soil on the site. * Theoretical Analysis * Prototype Testing All three methods listed above do not consider the effect of piles and geosynthetic reinforcement. The prototype testing method is one of the best and most reliable methods. However, it is not an economical method for initial estimation. Empirical methods seem to be the simplest for estimation for the lateral movements. 2.5.1. Empirical Methods The maximum lateral deflection was related to the thickness of the deforming layer by Bourges and Mieussens(1979) (cited in Li et al., 2002) 1_ ma Eqn.2.25 This value of h is related to the stability factor F= (SI+2)c" Eqn.2.26 where co average undrained shear strength along failure surface of the soil q average overburden pressure applied by the embankment load Figure 14 shows Bourges and Mieussens results. The data points indicate the distance from the crest of the embankment. The results show that greater displacements are found with an increase in the width of the embankment. 1 2 3 4 5 1 2 3 4 5 Starbility Number F Stability Number F Figure 14: Relation between the maximum stability and maximum lateral movement (Bourges and Mieussens, 1979 cited in Li et al., 2002) Marche and Chapuis(1974) (cited in Li et al., 2002) compared displacement factor, qB with a D/B ratio (Figure 15). This method considers the relation of the undrained modulus of the soil, the width of the embankment and the depth of the deforming soil. Eu is generally found from empirical relations with the undrained shear strength. F f IR + 2)IE; 5~,h I P .41 D t I ~OIBrOd p ~sz 0.5 Lb a 1 j OXI~~1 II. X/L~2 01 2~X1L  U _ __ __ __ I ~ 1 4,, Influence of distance from embankment crest T 51 5 4 3 .h r; 8 2 B ur 1 Y ha I ~ ~ 30$ O,5 1.0 1,S 2.0 O/B Q.20 Figure 15: Impact of soil stiffness and embankment geometry on lateral movements (Marche and Chapuis, 1974 cited in Li et al., 2002) The magnitude of lateral movement with depth varies with the stiffness and the strength of the soil. The ratio of the deforming soil layer to the embankment width also influences the lateral movements. Tavenas et al. (1979) (cited in Li et al., 2002) determined that the maximum lateral movements occur at a depth of minimum shear strength of the weak soil (Figure 16). However, Suzuki(1988) (cited in Li et al., 2002) concluded that the maximum lateral movements occur at a distance of 23m below the depth of minimum shear strength (Figure 17). Suzuki concluded that the width of the embankment had a very strong effect on this value. These conclusions were drawn for the weak clay overlain by a stronger soil. Zm~D LOBTr ~irmlo' OM D Icoani~eiatsr st ollrrr~tion c 0.8f] I I d  *'I k I ~ Figure 16: Relation between the depth of maximum lateral movement to minimum shear strength (Tavenas et al., 1979 cited in Li et al., 2002) Figure 17: Relation between depth of maximum lateral movement and the embankment width (Suzuki, 1988 cited in Li et al., 2002) O,8 0.6 0.1 02 6.~ Zr~miraO 0.5 O.Es 4.4 2.5.2. Theoretical Methods The most commonly used theoretical methods to predict the lateral movement of the soil are * Volume conservation method * Elastic continuum methods These methods give results which are more reliable than the empirical methods. The lateral movements can be predicted using finite element methods. The prediction of lateral movements using PlaxisFinite element program will be dealt with in the Chapter 3. 2.6. Slope Stability 2.6.1. BS8006 The stability of GRPS embankments can be carried out by using conventional slip circle methods. However, the presence of piles and basal reinforcement should be taken into consideration (Figure 18). According to BS8006, the analysis can be performed using effective stress parameters taking account for the pore water pressures. An analysis for short term stability should assume undrained conditions. To ensure stability the following relationship should be satisfied at all locations along the base of the embankment: MD MD the factored distributing moment at all locations along the base of the embankment MRs the factored restoring moment due to the soil at all locations along the base of the embankment MRP the resisting moment due to the axial load in the piles along the base of the embankment MRR the restoring moment due to the reinforcement at all locations along the base of the embankment Ship circle cone~r c Surcharge, ~ein orcernent MD~~~F 6 b4 i aR Restol~srf~eingc moment duetopies Restodlng moment due to reil enforcement: MD'[ 9 I~V + T 4 7sna~ BSn 8006, 195 2.6.2. Modified Boundary Element Method Lee et al. (1995) (cited in Li et al., 2002) studied the effect of piles on slope stability. The Bishop circle method was used to Eind the stability of the slope. The effect of the piles was studied separately by a modified boundary element method. Lee et al. defined the improvement ratio as N s Eqn.2.28 psFs where F, factor of safety of the pilesloped problem Fs minimum factor of safety of the problem without piles Lee et al. presented charts for the behavior of castinsitu reinforced concrete piles in homogenous (Figure 19 to 22) and layered slopes (Figure 23 to 26). 2.6.2.1. Homogenous Slopes * The most effective position of the piles is near the crest or near the toe. If the pile is close to middle of the slope the improvement ratio is reduced to 1.0. If the pile head is Eixed against rotation it has no effect on the stability of the slope. * As the pile spacing increases the improvement ratio reduces. * The larger the diameter of the pile, the greater is the improvement ratio. In this case, when d/ds is greater than 1.0 toe piles are more effective. * The soil modulus and the pile stiffness have little or no effect on the stability of the slope. * The piledslope improvement ratio increases linearly with increase in pile soil limiting pressure  r L  __________ __ _~_ __ 1.16 1.04X P Free":III;( Hea leC *Fi xed Headc Pile  Figure 19: Effect of pile position on the homogenous slope (Lee et al., 1995 cited in Li et al., 2002) 1.20 1.16 1.12 1.038 1,OO L O.S I.0) L5 2.0) Figure 20: Effect of pile diameter on the homogenous slope (Lee et al., 1995 cited in Li et al., 2002) o Toe Pile 1.16 Cet l Figure 21: Effect of pile spacing on homogenous slope (Lee et al., 1995 cited in Li et al., 2002) 1.16 11)11 1).3 Il.g KFY~K ms 1,2 l.J Figure 22: Effect of pilesoil limiting pressure on homogenous slope (Lee et al., 1995  cited in Li et al., 2002) 2.6.2.2. Two Laver Soil Slope CASE 1: An upper soft layer is underlain by a stiff layer CASE 2: A lower soft layer is overlain by a stiff layer It is generally preferred to have the pile embedded through the soft layer into the firm lower layers. * The most effective position of the piles for Casel is between the crest and the middle of the slope. For Case 2, the most effective position is at the toe or at the crest. * The larger the diameter, the greater the pile improvement ratio. This effect is seen more vividly in Casel. * The greater the spacing, the smaller the pile improvement ratio. This effect is more evident in Case 1 than Case 2. * The improvement ratio increases with increase in the pilesoil limiting pressure. This ratio is higher in Casel than in Case 2. Figure 23: Effect of pile position on two layer slope (Lee et al., 2002) 1995 cited in Li et al., 1.0 L O.5 f.0 1.5 2.0 Figure 24: Effect of pile diameter on a twolayer slope (Lee et al., 1995 cited in Li et al., 2002) 152.0) 15 3.0. 3.5 410 4.5 1 Figure 25: Effect of pile spacing on the twolayer slope (Lee et al., 1995 cited in Li et al., 2002) 42 1.4 Figure 26: Effect of pilesoil limiting pressure multiplier on the twolayer slope (Lee et al., 1995 cited in Li et al., 2002) 2.6.3. Friction Circle Method The Friction Circle method is very useful for homogenous slopes. This method is found to be very convenient for pile reinforced slopes. The method is generally used when both cohesive and frictional components are to be used. Using the Mohr Coulomb criterion, the factor of safety can be defined as the available shear strength to the required shear strength. Factor of safety with respect to friction F, and cohesion Fe are as follows: c tanga Fe F ~ Eqn.2.29 c, V~tang The forces that maintain the equilibrium of the system are weight of the mass, cohesion force Cr required to maintain equilibrium and the resultant of the normal and frictional component of strength mobilized along the failure surface (Figure 27). The direction of the resultant corresponds to the line that forms a tangent to the friction circle, with a radius, R'=E iG Taylor(1937) (cited in Li et al., 2002) derived two expressions for the stability number For toe failure: c(1/2) cosec2X (ycosec'yCOty) +cotxcoti a Eqn.2.30 Fe TH 2cotxcotv+2 For base failure: c(1/2) cosec2X (ycosec'yCOty) +cotxcoti2p a Eqn.2.31 FeTH 2cotxcotv+2 In this method, a value for F, is assumed and a surface is defined by angles x and y. The angle v is obtained from its relation with cpr. A number of iterations are carried out using the above equations, until Fe is obtained equal to F,. The critical surface is the one which has a minimum factor of safety. When a number of piles are introduced into the system, the critical surface and the factor of safety will change. The forces acting in this system are similar to those above with the exception of the force acting on the slope due to the piles, F, (Figure 28). This resulting force F, can be incorporated into the system. This results in two new expressions for toe failure and base failure. slopes without piles (Taylor, 1937 cited in Li et al., 2002) 12FT cos(CEO) H 6oE~ cscxsi 7[H~ coexcosecyxsin +OG X Figure 27: Forces on a  FcTH Eqn.2.32 Eqn.2.33 (E+61126plsinrpxcosecxxcosecy) A2 6cosec xxcosecyxiipCsXinv +cosecvcosxv where E= 1 2 (cot~i +3 coti x cotx3 coti x coty+3 cotx x coty) Eqn.2.34 where CEO is the angle formed by F, and horizontal, OG is the moment of F,. The above equations can be used for calculation of factor of safety of the slope. 00" = R~dk A6 Figure 28: Forces acting on a slope reinforced with piles (Taylor, 1937 cited in Li et al., 2002) 2.7. Settlements Soft clay and other compressible soils have a tendency to settle under heavy loading. There are various soil improvement techniques used to prevent these settlements. The technique used in any particular case depends on soil conditions, the availability of equipment and the cost required for improvement. Piles, stone columns, vibroconcrete columns, deep mixed columns are some of the commonly used techniques. The GRPS system is gaining popularity in embankment construction over such soils. Settlement is greatly reduced with the inclusion of a geosynthetic layer. The greater the stiffness of the geosynthetic reinforcement, the smaller the settlement. The settlement also decreases with an increase in the stiffness of the piles. Due to the complex nature of the system, no analytical method has been developed to determine the settlement of GRPS embankments. The settlement analysis is carried out as for the unreinforced case. In the case of rigid piles, it is assumed that the entire load of the embankment is taken by the piles. Settlement calculations are carried out by available methods. In the case of other ground improvement techniques, settlement calculations are carried out on the basis of methods available for those techniques. BS8006(1995) states that a plane of equal settlement exists at a height of 1.4(sa) from the top of the pile caps in which s is spacing of the pile caps and a is the width of the pile cap. Terzaghi(1943) (cited in Han, 1999) carried out laboratory tests and found that the plane of equal settlements exists at 1.52.5 times the width of the void. If the height of the embankment is greater than this height then there is no problem of local depressions. However, if the height is less than 1.4(sa) the method for estimating the surface depression due to the existence of a void can be used. When two or more geogrids are used in the system, the differential settlement is effectively reduced. The strain in the upper reinforcement is 30% of the strain in the lower geogrid (Jenner et al., 1998 cited in Han, 1999) although the upper geogrid is weaker than the lower one. The height of the equal settlement plane is reduced significantly by soil resistance. Soil resistance when increased to a certain limit can result in the equal settlement plane being lowered to the top of the upper geosynthetic layer in a multi layer system. PWRC (2000) and Ogisako (2002) (cited in Han, 2003) have developed methods to determine the settlement of geosynthetic reinforced embankments on deep mixed columns. Finite element or finite difference methods provide a measure of the settlement expected in a GRPS embankment. This can be seen in the Plaxis models developed and discussed in Chapter 3. 2.7.1. Public Work Research Center Method The PWRCGeosynthetic reinforced Earth Committee (2000) (cited in Han, 2003) has come up with a design method for reinforced embankments on deep mixed columns. Geos onthrele I Embankment fill Figure 29: Settlement and differential settlement of soil embankment on deep mixed columns. The settlement of the deep mixed columns is given as Eqn.2.35 where So settlement of the deep mixed column o, stress on the deep mixed columns L length of the deep mixed columns E, modulus of deformation of the deep mixed columns The modulus of deformation is given as Ec=100q, Eqn.2.36 where qu unconfined compression strength of the deep mixed columns The settlement of the untreated soil is given by Ss = So O Eqn.2.37 where Ss settlement of the untreated soil subj ected to reduced pressure as So settlement of the untreated soil subj ected to the actual load of the embankment p as reduced pressure on the untreated soil due to the embankment p total applied pressure of the embankment The differential settlement between the soil and the columns in the absence of geosynthetic reinforcement is given by AS= SsS, When there is a inclusion of geosynthetic layer present, the differential settlement can be given taking into account an influence factor due to the inclusion of the reinforcement. AS= Eqn.2.38 1+2a where AS, differential settlement between the columns and the untreated soil oc influence factor due to the presence of geosynthetic reinforcement layer This influence factor is related to the tensile stiffness of the geosynthetic reinforcement. The relation between the two factors can be seen in the Figure 30. 49 10000 b = 2m 1000oo 100 S b = center to center sapcing of column ns 100 1000 10000 1~00000 Tensile stiflfness of geosynthetics, J (I 2.7.2. Ogisako's Method Ogisako (2000) (cited in Han, 2003) used the finite element method to study the relation between tensile stiffness, improvement ratio, stress concentration ratio and the ratio of the volumetric compression modulus of the untreated soil to the columns. He developed a 2D problem considering the deep mixed columns as a continuous wall. In the absence of the geosynthetic reinforcement, the settlements can be estimated as follows. The settlement of the untreated soil between the deep mixed columns is given by S, =m lcLac Eqn.2.39 where mys volumetric compression modulus of the untreated soil L length of the deep mixed column os average vertical stress acting on the untreated soil The settlement of the deep mixed column is given by S, =mveLee =Ss Eqn.2.40 where mve volumetric compression modulus of the deep mixed columns L length of the deep mixed column n n stress concentration ratio Os Rm ratio of the volumetric compression modulus of the untreated soil mv to the deep mixed columns m m oc stress acting on the deep mixed column The differential settlement is given as AS= s ,=! 1 myso Eqn.2.41 The inclusion of the geosynthetic reinforcement can be taken care of by using the stress concentration ratio calculated in the presence of the geosynthetic reinforcement. AS=1 n yLos Eqn.2.42 The average stress acting on the untreated soil between the columns is given by as= Eqn.2.43 1+as (n1) This can be included into the above equation, and the differential settlement is given as Ogisako found the relation between the stress concentration with and without the reinforcement. This can be related to the tensile stiffness of the reinforcement. n J _ +1 Eqn.2 n C, +C,J where nr stress concentration ratio in the presence of the geosynthetic reinforcemr n stress concentration ratio without the inclusion of geosynthetic reinforcement J tensile stiffness of the geosynthetic reinforcement C1 and C2 COefficients which can be determined from the following charts !.45 lent 450 400 350 E Rm 150 50 0 0.1 0.2 0.3 0.4 ImproveJment ratio, as Figure 31: Coefficient C1 versus the improvement ratio, as 52 4 "*"" 0 F Improvemlent Ratio, a, Figure 32: Relation between the coefficient C2 and improvement ratio as Much research has been carried out on determining of the settlements in situations involving deep mixed columns. No direct methods have been developed for settlements for other type of soil improvement techniques. However, conventional settlement methods give approximately close estimates of settlement. CHAPTER 3 MODELLING IN PLAXIS Numerical modeling of the geosynthetic reinforced pile supported embankments was performed in PLAXIS 7.2 finite element software. Numerical modeling enables the designer to study the effects of embankment loading, the soil behavior in various conditions without resorting to simplified assumptions. An attempt was made to design the system in Plaxis 3D. However, Plaxis 3D was unable to simulate the field conditions.3D cannot simulate the condition of a void below the geogrid. Updated mesh analysis is required for this analysis. This is not available in Plaxis 3D. Hence, the experimentation was then carried out in Plaxis 2D. The study comprised two parts. The axisymmetric unit cell was used to determine the strength of the geogrid, considering an infinitely long embankment. This axisymmetric model was utilized to show the effect of the soil support below the geosynthetic layer. A parametric study was performed on this model. Large plane strain models were built. These comprised of all the elements which had an influence on the behavior of the system. The various aspects like lateral movements, tensile strength of geogrid, bending moment in the piles and the total settlements were studied. 3.1. Axisvmmetric Model The piles in the GRPS embankments were arranged in a rectangular or triangular pattern. A rectangular arrangement of the piles was taken into consideration. For this analysis, one pile was considered. In order to simplify the analysis, each pile was assumed to have its own zone of influence. A pile with a diameter of 0.7m was used for the analysis. A review of constructed GRPS embankments indicated that the typical spacing used in many proj ects is 1.5 to 4.5m (Han, 1999). An average spacing of 3m was used for this study. The geogrid was placed on the top of the pile. This model was used to perform parametric study. The four important materials involved in this complex system are the piles, the geogrids, the foundation soil and the embankment soil. A drained condition was considered for the analysis. Simplified constitutive models were used to model these complex components. The "Soft soil model" in Plaxis was used to represent the weak foundation soil. This model is a Cam Clay type model used to simulate the behavior of normally consolidated clay or peat. The most important characteristic of the soft soil model is the stress dependent stiffness, which corresponds to the soft soil behavior. A logarithmic relation between the volumetric strain ev and mean effective stress, p' is assumed. As the model uses volumetric strain instead of void ratio, modified compression index h* is used in place of h (Burland, 1965) (cited in Brinkgreve & Vermeer, 1998). For virgin isotropic compression it yields E, E" = Ajl n Eqn.3.1 For isotropic loading/reloading the elastic volume strain is formulated as s"e eO = K ln Eqn.3.2 These modified compression index and modified swelling index can be related to Cam clay parameters and internationally normalized parameters as below: Relation to Cam clay parameters A*" = = Eqn.3.3 1+e 1+e Relation to normalized parameters C, 1 ?, C, A*= K *= 1.3 Eqn.3.4 2.3(1+e) 1+v, 1+e Other input parameters for the soft soil model are c,# and ty. The yield function can be described by an ellipse in p' q plane. The Mline is referred to as the critical state line. The tops of all ellipses pass through this line which is inclined at slope M. The failure is described by the Mohr Coulomb criterion with $' can c' parameters. Both the M line and the failure line are given at a shift of c' cot)'(Brinkgreve & Vermeer, 1998). The total yield contour is the boundary of the elastic area (Figure 33). The failure line is fixed. However, the cap may increase due to primary compression. c~ cot ( Figure 33: Yield surfaces of soft soil model in p' q plane The "MohrCoulomb Model" was used for the embankment fill. The geogrid was represented by a geotextile element in Plaxis. These are flexible elastic elements that represent sheet of fabric in out of plane direction. They can sustain tensile forces but not compression. A linear elastic model was applied to the pile. It is important to model the interface between the geosyntheticsoil and the pilesoil. The influence of the interface is reduced when the deformations are very small. For this study, a fully bonded interface between the soilpile and soilgeogrid was assumed. The factors that were varied in the parametric study were geosynthetic stiffness, height of the embankment, position of the geosynthetic layer and modulus of elasticity of the pile. All the analytical methods used for the determination of tensile strength in the geogrid assume that there is a void below the geogrid. The axisymmetric model is used to prove the importance of the supporting behavior of the underlying soil. The tension in the reinforcement in the presence of the underlying soft soil is noted. Later, the soil below the geogrid was removed to represent the existence of a void. The change in the tension of the reinforcement was studied. The elastic normal stiffness of the geogrid was varied to study its impact on the system. The geogrid undergoes creep which result in an increase in the strains. This will cause a reduction in the tensile strength to a certain extent. For simplicity, it was also assumed that the geogrid had identical properties in all horizontal directions. The finite element model for the above described model can be seen in Figure 34. ;~'~'I LI1 rl1l1111 rl~l lillllll~~lj 8 00 *** ** ** 000 200. 4.00 ~~ ~1 0 00 8 00 Pitnumber and coordinates [ Figure 34: Axisymmetric model Table 2: Soil properties for axisymmetric model Material Unit Modulus of Angle of Cohesion Poisson s weight elasticity internal ratio (kN/m ) (kN/m ) friction (deres Embankment 19 20000 30 10.3 fill Foundation soil 22 5 1) soft soil parameters are lambda*=0.2, kappa*=0.05, nuar=0.15 Once the geometry of the model was developed, initial situation and initial stress state should be stated. This was done in the initial conditions part of the input program. The elements that are not active in the initial situation can be deselected. Initial stresses are developed by the Koprocedure. The water conditions can also be specified in the Geometry configuration mode (Figure 35). l ~ ~ ~ ~~~ ~~3.00 12,00 Pitnumber and coordinates . Figure 35: Initial Stresses are developed The generation of the finite element model was followed by the calculations phase. An updated mesh analysis was applied. In the finite element analysis it is generally assumed that the change in the geometry of the mesh does not significantly affect the equilibrium conditions. However, in cases of reinforced soil structures and the cases where the soft soils cause large deformations the influence of change in the geometry of the model has to be taken into consideration. Updated mesh analysis was used in such cases (Figure 36). A staged construction procedure was used for simulation of realistic process of construction. This option enabled activating and deactivating of elements, changing geometry configuration, changing properties of materials and changing water pressures. The phases of construction can be given as * Soil in place prior to construction * Installation of pile + geogrid I~ ~Rs4ulml~ ~I~T~ Il~rlltil Illllllllliillll I I 1:11 1 * Application of embankment load * Removal of soil below the geogrid if the void below the geogrid is to be represented In the parametric study, the last phase is not considered. Updated mesh F3 J*e.te I Phase 3> ILoad adv. ultimate level is jlol re.:....~l p i 2 Prescribed ultimate state fully reached Initial phase 0 0 N/A N/A 0 0 0 1 0 Llpdated mesh Staged construction 1 2 0 