FE-Analysis of piled and piled raft foundations Jean-SØbastien LEBEAU April - August 2008 Abstract In the last few years the number of piled raft foundations especially those with few piles, has increased. Unlike the conventional piled foundation design in which the piles are designed to carry the majority of the load, the design of a piled raft foundation allows the load to be shared between theraftandpilesanditisnecessarytotakethecomplexsoil-strutureinteractione(cid:27)ectsintoaccount. The aim of this paper is to describe a (cid:28)nite element analysis of deep foundations: piled and mainly piled raft foundations. A basic parametric study is (cid:28)rstly presented to determine the in(cid:29)uence of mesh discretisation, of materials - loose or dense sand -, of dilatancy and interface elements. Then the behavior of piled raft foundations is analysed in more details using partial axisymmetric models of one pile-raft. We continue by preparing a more sophisticated 3D study to take into account the complex pile- pile interaction which occured when the pile spacing is (cid:17)small(cid:17). So the possibilies of employing the embedded pile concept as implemented into Plaxis 3D foundations is investigated. Finally, some clues about the group e(cid:27)ect are indicated. Key words: Piled raft foundation, piles, embedded pile, volume pile, hardening soil model 1 Acknowledgements First of all I would like to express my gratefulness to Professor Helmut F. Schweiger for giving me the opportunity to work on geotechnical issues at the Institute for Soil Mechanics and Foundation Engineering of Graz University of Technology. This paper was made possible by the great contribution of my supervisor Dipl.-Ing Franz Tschuch- nigg. I am indebted to him for his friendly supervision and guidance throughout the period of my traineeship. I deeply thank him because he conveyed me a better understanding of (cid:28)nite element modeling and analyses. IalsowouldliketothankmyFrenchprofessor, Yvon Riou forgettingmeintouchwiththeInstitute. Finally,IwouldliketoexpressmyappreciationtoallthepeopleImetherewhomademy(cid:28)vemonths stay in Austria very enjoyable. 2 Contents 1 Introduction 6 2 Preliminary studies 7 2.1 Single pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Presentation of calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1.2 Boundaries conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1.3 Material properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1.4 Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.1.5 Load control and calculation steps . . . . . . . . . . . . . . . . . . . 10 2.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.2.1 Mesh dependency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.2.2 Comparison between distributed loads and prescribed displacement 14 2.1.2.3 In(cid:29)uence of the interface coe(cid:30)cient R . . . . . . . . . . . . . . . 16 inter 2.1.2.4 In(cid:29)uence of the dilatancy . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Pile-raft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.1 Presentation of calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.1.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.1.2 Boundaries conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1.3 Materials properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1.4 Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1.5 Load control and calculation steps . . . . . . . . . . . . . . . . . . . 20 2.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 CONTENTS CONTENTS 2.2.2.1 Mesh dependency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.2.2 In(cid:29)uence of the interface coe(cid:30)cient R . . . . . . . . . . . . . . . 21 inter 2.2.2.3 In(cid:29)uence of the dilatancy . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Analysis of 2D models 24 3.1 Single-pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 Pile-Raft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.1 Load-displacement curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.2 Variations of Skin friction and Normal Stresses along the pile . . . . . . . . . 29 3.2.3 Analysis of the α factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Kpp 3.2.3.1 De(cid:28)nition of α . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Kpp 3.2.3.2 Methodology to calculate α . . . . . . . . . . . . . . . . . . . . . 37 Kpp 3.2.3.3 Comparison and evolution of α for di(cid:27)erent geometries: . . . . . 39 Kpp 3.2.3.4 Evolution of α for di(cid:27)erent materials and dilatancy . . . . . . . . 41 Kpp 3.2.3.5 Evolution of α for di(cid:27)erent values of R . . . . . . . . . . . . 42 Kpp inter 3.2.4 E(cid:30)ciency of a piled-raft foundation in comparison with a raft foundation . . 44 3.2.5 Analysis of the pile behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2.5.1 Base resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2.5.2 Skin resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2.5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4 Preliminary studies of 3D models 49 4.1 Volume pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.1.1 Finite element models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.1.2.1 Load-displacement curves . . . . . . . . . . . . . . . . . . . . . . . . 52 4.1.2.2 Variations of skin friction . . . . . . . . . . . . . . . . . . . . . . . . 54 4.1.2.3 Some remarks about parameters . . . . . . . . . . . . . . . . . . . . 58 4.2 Embedded pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2.1 Embedded pile-raft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2.1.1 Finite element models . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4 CONTENTS CONTENTS 4.2.1.2 Embedded pile with linear skin friction distribution . . . . . . . . 63 4.2.1.3 Embedded pile with multilinear skin friction distribution . . . . . 69 4.2.1.4 Embedded pile with layer dependent skin friction distribution . 73 4.2.1.5 Comparison of the three options: Linear, multilinear and layer de- pendent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5 Group e(cid:27)ect 82 5.1 Presentation of calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.1.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.1.2 Finite element model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2.1 Vocabulary details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2.2 Load-displacement curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.2.3 Displacement pro(cid:28)les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2.4 More precise analysis of group 5 . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6 Conclusion 98 5 Chapter 1 Introduction In traditional foundation design, it is customary to consider (cid:28)rst the use of shallow foundation such as a raft (possibly after some ground-improvement methodology performed). If it is not adequate, deepfoundationsuchasafullypiledfoundationisusedinstead. Inthelastfewdecade,analternative solutionhasbeendesigned: piledraftfoundation. Unliketheconventionalpiledfoundationdesignin which the piles are designed to carry the majority of the load, the design of a piled raft foundation allows the load to be shared between the raft and piles and it is necessary to take the complex soil-struture interaction e(cid:27)ects into account. The concept of piled raft foundation was (cid:28)rstly proposed by Davis and Poulos in 1972 and is now used extensively in Europe, particularly for supporting the load of high buildings or towers. The favorable application of piled raft occurs when the raft has adequate loading capacities, but the settlement or di(cid:27)erential settlement exceed allowable values. In this case, the primary purpose of the pile is to act as settlement reducer. The aim of this paper is to describe a (cid:28)nite element analysis of deep foundations: piled and mainly piled raft foundations. A basic parametric study is (cid:28)rstly presented to determine the in(cid:29)uence of mesh discretisation, of materials - loose or dense sand -, of dilatancy and interface elements. Then the behavior of piled raft foundations is analysed in more details using partial axisymmetric models of one pile-raft. We continue by preparing a more sophisticated 3D study to take into account the complex pile- pile interaction which occured when the pile spacing is (cid:17)small(cid:17). So the possibilies of employing the embedded pile concept as implemented into Plaxis 3D foundations is investigated. Finally, some clues about the group e(cid:27)ect are indicated. 6 Chapter 2 Preliminary studies - 2D axisymmetric models - In order to prepare a more sophisticated analysis a large number of calculations have been per- formed in axisymmetric conditions. This approach o(cid:27)ered the possibility to study with reasonable calculation times the in(cid:29)uence of mesh discretisation, dilatancy and interface elements for a single pile and a pile-raft. The di(cid:27)erent models and conclusions are presented in this part. 2.1 Single pile 2.1.1 Presentation of calculations 2.1.1.1 Geometry In order to analyze the behavior of the single pile, a model has been made in PLAXIS V8 using an axisymmetric model. A working area of 20 m width and 40 m depth has been used. At the axis of symmetry the pile has been modeled with a length of 15 m and a diameter of 0,8 m. The soil is modeled as a single layer of sand with properties are described in 2.1.1.3). The ground water is located at 40 m below the soil surface. In this way we did not take into account the water in(cid:29)uence. Along the length of the pile an interface has been modeled. We extended this interface 1 to 0,5 m below the pile inside the soil body to prevent stress oscillation in this sti(cid:27) corner area. We added two clusters close to the pile to enrich easily the mesh in this more moving area. 1This (cid:16)longer(cid:17) interface will enhance the (cid:29)exibility of the (cid:28)nite element mesh in this area and will thus prevent non-physicalstressresults. However,theseelementsshouldnotintroduceanunrealisticweaknessinthesoilaccording to PLAXIS V8 manual. 7 2.1. SINGLE PILE CHAPTER 2. PRELIMINARY STUDIES 2.1.1.2 Boundaries conditions We used the standard (cid:28)xities PLAXIS tool to de(cid:28)ne the boundaries conditions. Thus these bound- aries conditions are generated according to the following rules: (cid:136) Verticalgeometrylinesforwhichthex-coordinateisequaltothelowestorhighestx-coordinate in the model obtain a horizontal (cid:28)xity (u = 0). x (cid:136) Horizontal geometry lines for which the y-coordinate is equal to the lowest y-coordinate in the model obtain a full (cid:28)xity (u = u = 0). x y Figure 2.1: Global geometry of the axisymmetric model of the single pile 2.1.1.3 Material properties Theconstitutivemodelusedforthesoil-sand-istheHardening soil model. Themainadvantage of this constitutive law is its ability to consider the stress path and its e(cid:27)ect on the soil sti(cid:27)ness and its behavior. We used two di(cid:27)erent types of sand: one loose and the other dense. We also varied the dilatancy value. 8 2.1. SINGLE PILE CHAPTER 2. PRELIMINARY STUDIES For the concrete pile, a linear elastic material set was applied. The parameters of all this materials are summarized in the following table: Parameter Symbol Loose sand Dense sand Concrete (pile) Unit Material model Model Hardening Soil Hardening Soil Linear Elastic - Unsaturated weigth γ 17 19 25 kN/m3 unsat Saturated weigth γ 20 21 25 kN/m3 sat Permeability k 1 1 0 m/day Eref 20 000 60 000 kN/m3 50 Sti(cid:27)ness Eref 20 000 60 000 3E7 kN/m3 oed Eref 1E5 1,8E5 kN/m3 ur Power m 0,65 0,55 Poisson ratio ν 0,2 0,2 0,2 - ur (cid:176) Dilatancy y 2/0 8/0 (cid:176) Friction angle f 32 38 Cohesion c 0,1 0,1 kN/m2 ref Lateral pressure coe(cid:27). K 1-sinf 1-sinf - 0 Failure ratio Rf 0,9 0,9 - Table 2.1: Materials parameters 2.1.1.4 Meshes To study the mesh dependency 3 analyses were performed: one with a coarse, one with a medium and one with a very (cid:28)ne mesh. For each one we considered 6 models varying the interface elements. 2 Thus we played around the R coe(cid:30)cient from 0,1 to 1. inter 2This factor relates the interface strength (wall friction and adhesion) to the soil strength (friction angle and cohesion) 9