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FE-Analysis of piled and piled raft foundations

Jean-Sébastien 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

the raft and piles and it is necessary to take the complex soil-struture interaction e�ects into account.

The aim of this paper is to describe a �nite element analysis of deep foundations: piled and mainly

piled raft foundations. A basic parametric study is �rstly presented to determine the in�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 �small�. So the possibilies of employing the

embedded pile concept as implemented into Plaxis 3D foundations is investigated. Finally, some

clues about the group e�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 �nite element

modeling and analyses.

I also would like to thank my French professor, Yvon Riou for getting me in touch with the Institute.

Finally, I would like to express my appreciation to all the people I met here who made my �ve months

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�uence of the interface coe�cient Rinter . . . . . . . . . . . . . . . 16

2.1.2.4 In�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�uence of the interface coe�cient Rinter . . . . . . . . . . . . . . . 21

2.2.2.3 In�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 αKpp factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.3.1 De�nition of αKpp . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.3.2 Methodology to calculate αKpp . . . . . . . . . . . . . . . . . . . . . 37

3.2.3.3 Comparison and evolution of αKpp for di�erent geometries: . . . . . 39

3.2.3.4 Evolution of αKpp for di�erent materials and dilatancy . . . . . . . . 41

3.2.3.5 Evolution of αKpp for di�erent values of Rinter . . . . . . . . . . . . 42

3.2.4 E�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�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�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 �rst the use of shallow foundation such

as a raft (possibly after some ground-improvement methodology performed). If it is not adequate,

deep foundation such as a fully piled foundation is used instead. In the last few decade, an alternative

solution has been designed: piled raft foundation. 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 the raft and piles and it is necessary to take the complex

soil-struture interaction e�ects into account.

The concept of piled raft foundation was �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�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 �nite element analysis of deep foundations: piled and mainly

piled raft foundations. A basic parametric study is �rstly presented to determine the in�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 �small�. So the possibilies of employing the

embedded pile concept as implemented into Plaxis 3D foundations is investigated. Finally, some

clues about the group e�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�ered the possibility to study with reasonable

calculation times the in�uence of mesh discretisation, dilatancy and interface elements for a single

pile and a pile-raft. The di�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�uence. Along the length of the pile an interface has been modeled. We extended this interface

to 0,5 m below the pile inside the soil body to prevent stress oscillation in this sti� corner area.1

We added two clusters close to the pile to enrich easily the mesh in this more moving area.

1This �longer� interface will enhance the �exibility of the �nite element mesh in this area and will thus preventnon-physical stress results. However, these elements should not introduce an unrealistic weakness in the soil accordingto PLAXIS V8 manual.

7

2.1. SINGLE PILE CHAPTER 2. PRELIMINARY STUDIES

2.1.1.2 Boundaries conditions

We used the standard �xities PLAXIS tool to de�ne the boundaries conditions. Thus these bound-

aries conditions are generated according to the following rules:

� Vertical geometry lines for which the x-coordinate is equal to the lowest or highest x-coordinate

in the model obtain a horizontal �xity (ux = 0).

� Horizontal geometry lines for which the y-coordinate is equal to the lowest y-coordinate in the

model obtain a full �xity (ux = uy = 0).

Figure 2.1: Global geometry of the axisymmetric model of the single pile

2.1.1.3 Material properties

The constitutive model used for the soil - sand - is theHardening soil model. The main advantage

of this constitutive law is its ability to consider the stress path and its e�ect on the soil sti�ness and

its behavior. We used two di�erent types of sand : one loose and the other dense. We also varied

the dilatancy value.

8


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 γunsat 17 19 25 kN/m3

Saturated weigth γsat 20 21 25 kN/m3

Permeability k 1 1 0 m/day

Eref50 20 000 60 000 kN/m3

Sti�ness Erefoed 20 000 60 000 3E7 kN/m3

Erefur 1E5 1,8E5 kN/m3

Power m 0,65 0,55

Poisson ratio νur 0,2 0,2 0,2 -

Dilatancy y 2/0 8/0 °

Friction angle f 32 38 °

Cohesion cref 0,1 0,1 kN/m2

Lateral pressure coe�. K0 1-sinf 1-sinf -

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 �ne mesh. For each one we considered 6 models varying the interface elements.

Thus we played around the Rinter coe�cient2 from 0,1 to 1.

2This factor relates the interface strength (wall friction and adhesion) to the soil strength (friction angle andcohesion)

9


Figure 2.2: A very �ne mesh for calculations with interface elements

Coarse Medium Very �ne

Number of elements 611 1848 4365

Number of nodes 5215 15 389 36 019

Elements 15-node

Table 2.2: Information on the generated meshes

2.1.1.5 Load control and calculation steps

To assign a load at the top of the pile we considered two approaches: one with prescribed displace-

ment, one with distributed loads.

With prescribed displacement we impose a certain displacement at the top of the pile whereas with

distributed loads we impose a force; results should be the same.

2.1.2 Results

Remark: All the following curves are plotted for the node point located at the top right side of

the pile.

10


Figure 2.3: Node point selected for load-displacement curves

2.1.2.1 Mesh dependency

By analysing all the calculations made, we can conclude that for each material - loose or dense sand

- the curves have the same shapes for calculations performed with coarse, medium and

very �ne mesh. Nevertheless, we can observe that with �ner meshes, we have unphysical premature

soil body collapsing. The following �gure illustrates this conclusion with some examples.

11


Figure 2.4: Mesh dependency for the loose sand - ψ=2° - and di�erent values for Rinter

�les : Geo2Load_Mesh 1/2/3_Rinter0,1/0,7/1_Psi2_HS.plx

To avoid this premature failure we decided to restart the medium and very �ne calculations switching

o� the arc length control procedure. But we now observed convergence problems with more or less

important oscillations.

These oscillations occurred for important displacements (from 20 cm) whatever the material, mesh

or Rinter value. However, the global shape of the load-displacement curve seems to stay realistic

even if there are these �stairs�.

12


Figure 2.5: Mesh dependency for the loose sand - ψ=2° - and di�erent values for Rinter

�les : Geo2Load_Mesh 2_Loose_Rinter0,1/0,7_Psi2_HS(_alc=OFF).plx

Figure 2.6: In�uence of arc length control for the loose sand - ψ=2° - and Rinter=0,7/0,1parameters: mesh1= coarse, arc length=ON; mesh2= medium, arc length=OFF; mesh3= Very �ne, arc

length=OFF;

13


The �gure 2.6 enables us to con�rm that the mesh dependency is negligible for this model.

2.1.2.2 Comparison between distributed loads and prescribed displacement

The previous paragraph was based on �les with the load approach. We did the same calculations with

the displacement approach. By comparing these two approaches we can conclude that the shape

of the load-settlement curves is exactly the same in each case . Moreover, there are less

oscillations with prescribed displacement than with distributed loads. There are no �stairs' ' even

with an important displacement. So because it limits this problem of big oscillations, prescribed

displacement seems to be better to study a single pile. The following picture illustrates

these conclusions.

Figure 2.7: Distributed loads and prescribed displacement, comparison for the loose sand - ψ=0°- and Rinter=0,1/0,4/0,7

�les : Geo2Disp/Load_Mesh 2_Rinter0,1/0,4/0,7_Psi0_HS(_alc=OFF).plx

14


Remark: The �gure 2.7 shows us the settlement with the load [kN] whereas in the previous section

we plotted the settlement with the distributed load [kN/m2]. To compare the two approaches we have

to:

� Distributed load: Multiply the distributed load [kN/m2] by the area of the pile to get the totalforce (Rtot) [kN].

� Prescribed displacement: Read out the �force� value in Plaxis output [kN/rad] and multiply itby 2 π to get the total force (Rtot) [kN]

Now we can try to interpret the �stairs� of the load approach by comparing with the same calculations

done with the prescribed displacements.

Figure 2.8: Comparison Displ and Load approaches for the loose sand � ψ=0° - No interface �medium mesh

�les : Geo2Disp/Load_Mesh 2_Loose_RinterNo_Psi=0_HS(_alc=OFF).plx

15


Figure 2.9: Comparison Displ and Load approaches for the loose sand � ψ=0° - R=1 � medium mesh

�les : Geo2Disp/Load_Loose_Mesh 2_Rinter1_Psi=0_HS(_alc=OFF).plx

As we can see on �gures 2.8 and 2.9, it is impossible to deduce correctly the normal shape from the

�distributed load� curves by interpreting the oscillations. Sometimes, the �prescribed displacement�

curve is under the �distributed load� one, sometimes it is in the middle. So we have to interpret

with caution the shape of the �stairs� part of the distributed load curves.

2.1.2.3 In�uence of the interface coe�cient Rinter

We varied the way to model the pile to sand interface by changing the Rintervalue and doing a model

without interface. We also performed one calculation by drawing an interface in Plaxis input and

unselected it in Plaxis calculation.

We can conclude that the choice of the value for Rinter is not negligible when you model

a single pile. As we can see in the table, for the same load, the settlements increase by more than

40 % between R=0,4 and 0,1, 80% between R=0,7 and 0,4 and 600 % between R=1 and 0,7 for

loose sand.

Load=2000 kN Settlement [cm]

Rinter=0,1 22,5

Rinter=0,4 15,7

Rinter=0,7 8,6

Rinter=1 1,2

Table 2.3: Settlements of the single pile for loose sand, ψ=2° and Rtot=2000 kN

16


As we could expect the load-displacement curves have almost the same shape for models with R=1

and without interface. We also noticed that unselecting the interface lead to false results with

premature failure (see red following curve) or an unrealistic behavior. So the interface drawn in

the Plaxis input must be selected in the calculations steps. The following curves sum up all these

conclusions.

Figure 2.10: Load-settlement curves for Loose sand, ψ=2° and coarse mesh

�les : Geo2Load_Mesh1_Loose_Rinter0,1/0,4/0,7/1/Unselected/No_Psi=2_HS.plx

2.1.2.4 In�uence of the dilatancy

We tested two values of dilatancy ψ for both materials: (ϕ− 30) and 0°. As expected, we have less

displacement with a high ψ value than without dilatancy.

17

2.2. PILE-RAFT CHAPTER 2. PRELIMINARY STUDIES

Figure 2.11: In�uence of dilatancy for dense sand, mesh medium

�les : Geo2Load_Mesh2_Dense_Rinter0,4/0,7_Psi8/0_HS_ALCo�.plx

2.2 Pile-raft

2.2.1 Presentation of calculations

2.2.1.1 Geometry

We performed the same calculations as we have done with the �single pile model� using an axisym-

metric model of a pile-raft foundation.

As we did for the single pile, the pile has been modeled with a length of 15 m and a diameter of

0,8 m at the axis of symmetry. We added a slab in concrete with a thickness of 0,5 m. The soil is

also modeled as a single layer of sand with the same properties as the single pile. The ground water

is located at 40 m below the soil surface. In this way we did not take into account the water

in�uence. Along the length of the pile an interface has been modeled. We extended this interface

to 0,5 m below the pile inside the soil body to prevent stress oscillation in this sti� corner area.

18


2.2.1.2 Boundaries conditions

We also used for this study the standard �xities PLAXIS tool (see 2.1.1.2).

2.2.1.3 Materials properties

The parameters of all the materials are recalled in the following table:

Parameter Symbol Loose sand Dense sand Concrete Unit

Material model Model Hardening Soil Hardening Soil Linear Elastic -

Unsaturated weigth γunsat 17 19 25 kN/m3

Saturated weigth γsat 20 21 25 kN/m3

Permeability k 1 1 0 m/day

Eref50 20 000 60 000 kN/m3

Sti�ness Erefoed 20 000 60 000 3E7 kN/m3

Erefur 1E5 1,8E5 kN/m3

Power m 0,65 0,55

Poisson ratio νur 0,2 0,2 0,2 -

Dilatancy y 2/0 8/0 °

Friction angle f 32 38 °

Cohesion cref 0,1 0,1 kN/m2

Lateral pressure coe�. K0 1-sinf 1-sinf -

Failure ratio Rf 0,9 0,9 -


2.2.1.4 Meshes

To study the mesh dependency 3 analysis were also performed: one with a coarse, one with a medium

and one with a very �ne mesh. For each one we considered 6 models varying the interface elements.

Thus we varied the Rinter coe�cient from 0,1 to 1. We also performed one batch of calculation with

6-nodes instead of 15 nodes.

Coarse Medium Very �ne Coarse

Number of elements 459 1417 3012 903

Number of nodes 4246 12 578 25 708 2211

Elements 15-node 6-node


19


2.2.1.5 Load control and calculation steps

To assign a load at the top of the slab we considered in this case only a distributed load

Figure 2.12: Details about a pile-raft geometry with the axisymmetric model, Very �ne mesh

2.2.2 Results

Remark: All the following curves are plotted for the node point A, situated at the top right side

of the pile, under the slab (see �gure 2.12).

2.2.2.1 Mesh dependency

By analysing all the calculations made, we can conclude that for each material - loose or dense

sand - the curves have exactly the same shapes for calculations performed with coarse,

medium and very �ne mesh.

20


Figure 2.13: Example, Mesh dependency for the pile raft model with loose sand, ψ=2°, Rinter=0,7

�les : Geo1_Mesh1/2/3_loose_Rinter0,7_Psi2_HS.plx

2.2.2.2 In�uence of the interface coe�cient Rinter

We varied the way to model the pile to sand interface by changing the Rintervalue and doing a model

without interface.

As we can see in the table and on the following curve the way you model the interface has a

negligible in�uence on the settlements.

Sand Mesh ψ Rinter=0,4 Rinter=0,7 Rinter=1

Loose Coarse 2° -34,3 cm -33,0 cm -32,4 cm

Dense Coarse 8° -13,6 cm -13,2 cm -13,0 cm

Table 2.6: Settlements with di�erent values of Rinter for load=1000 kN/m2

21


Table 2.7: Load-settlement curves for Loose sand, ψ=2° and coarse mesh

�les : Geo1_Mesh1_loose_Rinter0,1/0,4/0,7/1/NO_Psi2_HS.plx

2.2.2.3 In�uence of the dilatancy

We tested two values of dilatancy (ψ) for both materials: 2° and 0° for the loose sand, 8° and 0° for

the dense sand. We can conclude that the in�uence of the dilatancy is negligible for this

model even for the dense sand.

Sand Mesh ψ Rinter=0,4 Rinter=0,7 Rinter=1



Dense Coarse 8° -13,6 -13,2 -13,0

Dense Coarse 0° -13,7 -13,2 -13,1

Table 2.8: Settlements with di�erent values of Rinter for load=1000 kN/m2

22


Figure 2.14: In�uence of dilatancy for dense sand, mesh coarse

�les : Geo1_Mesh1_dense_Rinter0,4/0,7_Psi8/0_HS.plx

23

Chapter 3

Analysis of 2D models

- Behavior of a pile and a pile-raft -

In chapter 2 we made conclusions about how to de�ne e�ciently and correctly an axisymmetric

model of a single pile and a pile-raft. Now we present other calculations performed by taking these

preliminary practical conclusions into account.

In design of piled rafts, design engineers have to understand the mechanism of load transfer from

the raft to the piles and to the soil. It requires to take complex interactions into account such as:

pile-soil interaction, raft-soil interaction, pile-raft interaction and pile-pile interaction.

The aim of this chapter is to have a better understanding of the pile and raft behavior and to check

the ability of the software to model such complex interactions. In this part, we only modeled a single

pile with a raft so we did not take into account the pile-pile interaction.

3.1 Single-pile

In the previous calculations we simulated an axial load test on a bored pile. We get the following

load-displacement curve:

24

3.1. SINGLE-PILE CHAPTER 3. ANALYSIS OF 2D MODELS

Figure 3.1: Axial load curve for a single-pile

�le : Geo2Disp_Mesh2_loose_R=0,7_Psi2_HS.plx

Now we observe the mobilisation of the skin friction (qs) with di�erent loads.

Figure 3.2: Evolution of the Skin friction with the load (Rtot)


25

3.2. PILE-RAFT CHAPTER 3. ANALYSIS OF 2D MODELS

s = 1cm s = 8cm s = 15cmRb[kN ] 140 906 1380

Rs[kN ] 1050 1044 1040RsRb

7,5 1,15 0,75

Table 3.1: Evolution of the skin and base resistance with settlements


That shows that the maximum skin friction is already reacted when 1,0 cm settlements occur (see

�gure 3.1). Further, the skin resistance stays the same.

3.2 Pile-Raft

Key questions that arise in the design of piled rafts concern the relative proportion of load carried

by raft and piles. It depends on the geometric parameters of the pile and of the raft.

We performed four new models based on the �rst geometry described in chapter 2 to interpret the

raft and pile in�uence1.

Figure 3.3: Some geometric parameters

1The �Pile-Raft I � is the geometry described in details in the chapter 2

26


Paramater Symbol Pile-Raft I Pile-Raft II

Diameter of the pile dpile 0,8 m 0,8 m

Length of the pile Lpile 15 m 15 m

Width of the raft Lraft 2 m 5 m

Depth of the model Hmodel 40 m 40 m

Thickness of the slab traft 0,5 m 0,5 mLraft

dpile2,5 6,25

Table 3.2: Parameters of the �rst set of calculations

Figure 3.4: Details of Pile-Raft I and II

27


Paramater Symbol Pile-Raft V Pile-Raft III Pile-Raft IV

Diameter of the pile dpile 1,5 m 1,5 m 1,5 m

Length of the pile Lpile 30 m 30 m 30 m

Width of the raft Lraft 4,5 m 9 m 18 m

Depth of the model Hmodel 60 m 60 m 60 m

Thickness of the slab traft 1 m 1 m 1 mLraft

dpile3 6 12

Table 3.3: Parameters of the second set of calculations

Figure 3.5: Details of Pile-Raft V, III and IV

We tested all these geometries with the materials loose and dense sand2, with and without dilatancy

and varying the value of Rinter. The outcome was that the in�uence of dilatancy and of

Rinter is very limited. We also performed these calculations with 3 di�erent meshes to con�rm

that there is no mesh dependency. We tryed to have next the pile the same mesh coarseness in

2See table n°2.4

28


each model in order to compare precisely the di�erent models. The load is a distributed load applied

on the slab and the boundaries conditions are those described in chapter 2. In this study we did

not take into account the ground water.

Remark: As we did in chapter 2, all the load-displacement curves are plotted for the node point

A, situated at the top right side of the pile, under the slab (see �gure 2.12).

3.2.1 Load-displacement curve

As we see on the following �gure, the load-displacement curve for a pile-raft and a single pile is

completely di�erent.

Figure 3.6: Load settlement curve for pile and pile-raft foundation

�les : Geo1/1Bis/2load_Mesh1_loose_R=0,7_Psi2_HS.plx

3.2.2 Variations of Skin friction and Normal Stresses along the pile

For each model we plotted the skin friction and the normal stresses along the pile. This procedure

gave us the possibility to illustrate how the load transfer works when the load increases. All the

following curves concern dense sand with ψ=8° and Rinter = 0, 73.3According to Plaxis manual this Rinter value is the most common to model standard situations

29


Remark: All these �gures are plotted by selecting the interface in the Plaxis output. In order toget something comparable from one model to an other, we subtracted the �rst phase with the �pile-activation� for each load steps plotted. Thus the Skin friction or Normal Stresses that we presenthere are only due to the load and the weight of slab.

Figure 3.7: Evolution of the skin friction with the load for the Pile-raft I (dpile

lraft= 2, 5)

�le : Geo1_Mesh1_Dense_R=0,7_Psi2_HS.plx

30


Figure 3.8: Evolution of the skin friction with the load for the Pile-raft II (dpile

lraft= 6, 25)

�le : Geo1Bis_Mesh1_Dense_R=0,7_Psi2_HS.plx

On the previous �gures we can easily see that the mobilization of skin friction of a pile in a piled-raft

foundation is completely di�erent from the one of with a single pile. For the model Pile-Raft II with

a big spacing ( dpile

lraft= 6, 25), the slab has a strong in�uence on the shear stress distribution along the

pile. We notice an increase of shear stresses at the top of the pile, just under the slab. In this case,

the slab increases locally the normal stress, so the shear stresses increase in this area provoking this

peak in the top area of the pile.

For the model Pile-Raft I, the slab does not participate to the load transmission because we do not

see such a �peak� in the distribution: The spacing ( dpile

lraft= 2, 5) is too small and almost all the load

goes to the pile. Nevertheless, the slab has an in�uence too because the distribution is di�erent from

the one for the single pile. There is an important mobilization of skin friction in the lower part of

the pile and no mobilization in the top part.

As we can see on the following curves the shape of the normal stresses is in compliance with these

observations about the shear stresses.

31


Figure 3.9: Evolution of the normal stresses with the load for the Pile-raft I (dpile

lraft= 2, 5)

�le : Geo1_Mesh1_Dense_R=0,7_Psi2_HS.plx

Figure 3.10: Evolution of the normal stresses with the load for the Pile-raft II (dpile

lraft= 6, 25)

�le : Geo1Bis_Mesh1_Dense_R=0,7_Psi2_HS.plx

32


We now plotted the Skin friction for the second set of calculation.

These curves plotted for the geometries with a 30 m length pile and a 1,5 m diameter con�rme theses

comments.

Figure 3.11: Evolution of the skin friction with the load for the Pile-raft V (dpile

lraft= 3)

�le : Geo1Cinq_Mesh1_Dense_R=0,7_Psi2_HS.plx

33


Figure 3.12: Evolution of the skin friction with the load for the Pile-raft III (dpile

lraft= 6)

�le : Geo1Ter_Mesh1_Dense_R=0,7_Psi2_HS.plx

Figure 3.13: Evolution of the skin friction with the load for the Pile-raft IV (dpile

lraft= 12)

�le : Geo1Quater_Mesh1_Dense_R=0,7_Psi2_HS.plx

34


For the model Pile-raft IV - biggest spacing - with a 1000 kN/m2 loading (�gure 3-12), there is

positive shear stresses on some centimeters in the top part of the pile . This e�ect should be studied

in further research.

By plotting the same curves for the di�erent materials -loose and dense sand- and di�erent values

for ψ we can conclude both dilatancy and materials have very few in�uence on the normal stresses

and the skin friction distribution.

Figure 3.14: Evolution of the skin friction with dilatancy

�les : Geo1Bis_Mesh1_Dense_R=0,7_Psi0/8_HS.plx

35


Figure 3.15: Evolution of the skin friction with dense or loose sand

�les : Geo1Bis_Mesh1_Dense/Loose_R=0,7_Psi0_HS.plx

3.2.3 Analysis of the αKpp factor

The previous curves in the last section let us understood some aspects of the behaviour of a piled-

raft foundation. We easily saw that the bigger the spacing is the more the raft acts in the load

transmission. We are now going to describe these observations in a more precise way by calculating

the pile/raft stress repartition.

In Austria and Germany a common approach consists in calculating the αKpp4 factor.

3.2.3.1 De�nition of αKpp

The αKpp factor is the ratio between the load carried by the pile and the total load applied on the

piled raft foundation.Thus it gives us a precise idea of the proportion of load carried by the pile and

by the raft.

αKpp=

Rpile

Rtot

with:

4In English, Kpp (Kombinierte-Pfahl-Plattengründung) means piled-raft-foundation

36


� Rpile = Rb +Rs = Load carried by the pile 5 [kN]

� Rtot =Total load =Distributed load on the slab + weigth of the slab = Rraft +Rpile6 [kN]

So it means that:

� If αKpp = 1 , all the load is carried by the pile

� If αKpp = 0 , all the load is carried by the raft

We will also use the (1-αKpp) coe�cient which represents the proportion of load carried by the raft.

(1-αKpp)=

Rraft

Rtot

Remark: Again the weight of the pile is not taken into account.

3.2.3.2 Methodology to calculate αKpp

The simplest way to calculate αKpp with Plaxis 2D consists in realizing a cross section under the

slab and reading out the normal stresses on this cross section. Then we just have to sort the normal

stresses which are into the pile and into the soil.

Remarks:

In order to get an accurate value for αKpp we need to take care of:

� Making a cross section which crosses as much stress points as possible because the value is

obtained from extrapolation.

� Making a cross section not too close to the slab because the junction Slab/pile is a high stress

variation area and singularities could occur (take 10 cm to 20 cm under the slab usually leads

to accurate values).

The following example explains in detail this methodology.

5Rb =Base resistance of the pile [kN]; Rs =Skin resistance of the pile [kN]6Rraft =Load carried by the raft [kN]

37


Example: calculation of αKppfor Pile-Raft I, Load=1000 kN/m2, Dense sand, mesh medium,Ψ=8°:

In this case, we have Rtot = 1000.area + weigth of the slab = 3180 kN/m2

Figure 3.16: Cross sections for Pile-raft I

We �rst made the cross section n°1 just under the slab. We get the normal stresses as we can see

on the pro�le � normal stresses for cross section n°1�.

Figure 3.17: Normal stresses for cross section n°1

38


From the values of this pro�le we calculated Rpile and Rtot. We found: Rpile = 3687 kN and

Rtot = 3704kN , thus there is an error of 16 % for Rtot. In this way we overestimate Rpile and Rtot

because of the unrealistic high normal stress value at the interface.

So we started again with the cross section n°2. This one is not directly under the slab, thus we

avoid the �singular� area. Moreover the soil weigth added is negligible in comparison with the load.

Now we have the following distribution:

Figure 3.18: Normal stresses for cross section n°2

Here we calculate: Rpile = 3127 kN and Rtot = 3151kN. There is an error of only 1 % for Rtot.

Thus crossing the section in this way is more accurate.

We �nally �nd for this example αKpp= 0,99.

3.2.3.3 Comparison and evolution of αKpp for di�erent geometries:

With a small spacing (Widthraft

Diameterpile=2,5 or 3) it seems that the raft takes a small part of the load. In

these cases, we calculated an αKppequal to 0,99 for all load.

With a bigger spacing (Widthraft

Diameterpile=6; 6,25 or 12), we can notice that:

� The stress repartition between the raft and the pile evolves with the loading. The higher the

loading is, the more the stress is shared. With a load between 0 and 200 kN/m2 everything

goes mostly to the pile (1 <αKpp< 0,8). From 200 kN/m2the raft has a stronger in�uence.

39


� The bigger the spacing is, the more load the raft takes.

� In each case the curves converge to an equilibrium state, around αKpp=0,65 for Pile-Raft III,

αKpp= 0,5 for Pile-Raft II and αKpp= 0,2 for Pile-Raft V.

� The pile obviously carries more load by increasing the length of the pile (compare the geome-

tries Pile-Raft II and III).

Figure 3.19: In�uence of geometry on αKpp for loose sand, ψ=2°, R=0,7, mesh medium.

Name Lengthpile Diameterpile WidthraftWidthraft

Diameterpile

Pile-Raft I 15 m 0,8 m 2 m 2,5

Pile-Raft II 15 m 0,8 m 5 m 6,25

Pile-Raft V 30 m 1,5 m 4,5 m 3

Pile-Raft III 30 m 1,5 m 9 m 6

Pile-Raft IV 30 m 1,5 m 18 m 12

Table 3.4: Reminder, basic parameters of each geometry

40


Rtot [kN/m2] 25 + Slab 250 + Slab 500 + Slab 1000 + Slab

Pile-Raft I 0,99 0,99 0,99 0,99

Pile-Raft II 0,95 0,65 0,57 0,52

Pile-Raft V 0,99 0,99 0,99 0,99

Pile-Raft III 0,96 0,85 0,71 0,62

Pile-Raft IV 0,66 0,29 0,22 0,19

Table 3.5: Few values of αKpp for loose sand, ψ=2°, R=0,7

3.2.3.4 Evolution of αKpp for di�erent materials and dilatancy

As we can see on the following curves, the material - loose or dense dand - and the dilatancy have

a negligible in�uence on the stress repartition in the piled-raft foundation.

Figure 3.20: In�uence of material on αKpp , Pile-raft II, R=0,7

41


Figure 3.21: In�uence of the dilatancy on αKpp , Pile-raft II, R=0,7

3.2.3.5 Evolution of αKpp for di�erent values of Rinter

In this sub-section we present the evolution of αKpp with the load (�gure 3.19) and the displacement

(�gure 3.20) for di�erent Rinter values. In both cases, the tendency is exactly the same. We only

added �with the displacement� because it is also a common presentation in the literature.

Concerning the in�uence of Rinter on αKpp we can conclude that the part of the load carried by

the pile decreases when we reduce the interface strength factor. It is an expected behavior because

by reducing the Rinter value we decrease the maximum amount of mobilization of the skin friction

along the pile7.

7On the interface, τ≤ Rinter.(σn.tanφsoil+csoil)

42


Figure 3.22: In�uence of Rinter on the evolution of αKpp with the load, Pile-raft II, R=0,7

Figure 3.23: In�uence of Rinter on the evolution of αKpp with the displacement, Pile-raft II, R=0,7

43


3.2.4 E�ciency of a piled-raft foundation in comparison with a raft foundation

To evaluate the e�ciency of a piled-raft foundation in comparison with a raft foundation it is inter-

resting to compare the settlements with and without a pile. So, we performed one new calculation

for each geometry putting just the raft without the pile. Then we calculated the β coe�cient.

De�nition

β is the ratio between the settlements which occured without pile (Uraft) and with the settlements

which occured with a pile (Upile+raft):

β=Uraft

Upile+raft

Thus, we necessarily have β≥1 and if βw1 the pile is useless.

As expected, the evolution of β with the load has the same tendency as αKpp . When we have a

high value for αKpp the pile carries most of the load and thus acts a lot against displacements. So

the value of β is high.

On the contrary, when the raft carries a big part of the load - for example with Pile-Raft IV - the

settlements are very close to those observed with a raft only.

For the model Pile-Raft II in which we have a good sharing of the load, we have a β value from 1,15

to 2,1.

Figure 3.24: Evolution of β with the load, Loose sand � Ψ=2° - Mesh Medium � Rinter=0,7

44


Rtot [kN/m2] 25 200 500 1000

Pile-Raft I 2,4 2,15 2,0 1,8

Pile-Raft II 2,1 1,3 1,2 1,15

Pile-Raft V 3,1 2,5 2,5 2,2

Pile-Raft III 2,6 1,65 1,4 1,3

Pile-Raft IV 1,5 1,15 1,1 1,0

Table 3.6: Few values of β for loose sand, ψ=2°, R=0,7

Figure 3.25: Comparison between the evolution of β and α for Pile-Raft II, loose, ψ=2°, R=0,7

3.2.5 Analysis of the pile behavior

The bearing capacity of a pile consists of the base resistance (Rb) and the skin resistance (Rs). Now

we study in detail these two forces in order to have a better idea of the pile behavior for di�erent

geometries.

3.2.5.1 Base resistance

The method to calculate Rb is the same as for Rtot. We made a cross section under the pile. In this

part, we considered only the contribution of the distributed load by subtracting the two

�rst phase with the pile and raft activation.

On the next �gure, we can see the evolution of the base resistance with the load for the model

Pile-Raft I and II. The curves are both approximatively linear. It means that in our cases the part

of the total load (Rtot) carried by the base of the pile is approximatly constant.

45


Figure 3.26: Evolution of Rbwith the load for Pile-Raft I and II, dense sand, ψ=8°

Now we compare the Rbase for the pile-raft I and the single-pile.

Figure 3.27: Comparison of Pile-Raft I and Single Pile, evolution of Rbwith the load for Pile-Raft Iand II, dense sand, ψ=8°

3.2.5.2 Skin resistance

The skin friction pro�les presented previously give us the possibility to work out the skin resistance

Rs. As we did for Rb we only considered in this section the contribution of the distributed load by

46


subtracting the constribution of the pile and of the raft.

Figure 3.28: Evolution of Rswith the load for Pile-Raft I and II, dense sand, ψ=8°

3.2.5.3 Conclusions

The following curves sum up the Rbase, Rskin and Rraft proportions for various models.

Figure 3.29: Repartition of the forces into the single-pile, dense sand, ψ=8°

47


Figure 3.30: Repartition of the forces into pile for Pile-Raft I, dense sand, ψ=8°

Figure 3.31: Repartition of the forces into pile for Pile-Raft II, dense sand, ψ=8°

48

Chapter 4

Preliminary studies of 3D models

- From 2D axisymmetric models to 3D models -

We previously studied the behavior of one pile-raft foundation. Nevertheless the load settlement

behavior of piles in a pile group is usually observed to be totally di�erent from the behavior of

a corresponding single pile. This group e�ect cannot be studied with axisymmetric models and

consequently it requires performing calculations with Plaxis 3D foundation.

In order to prepare the group e�ect analysis, we �rstly tested the di�erent Plaxis 3D foundation

tools to model a pile: the volume pile and a new feature, the embedded pile. These comparisons are

presented in this chapter.

Remark about the mesh dependency:

The previous calculations with axisymmetric models showed a negligible mesh dependency. We also

checked that 6-node coarse meshes lead to the same load-displacement behavior as 15-node �ne

meshes.

Due to the bigger size of working areas in 3D models we cannot use e�ciently �ne meshes. Thus,

we will perform calculations from coarse to medium meshes. The results should be realistic because

of the low sensitivity of the mesh re�nement observed in 2D.

Remark about the mesh generation:

To create a mesh with Plaxis 3D foundation we �rstly generate a 2D mesh on a horizontal work

plane. When the 2D mesh is satisfactory, the 3D mesh is generated from the 2D mesh. Since

there is no vertical re�nement option, badly shaped elements with a higher vertical than horizontal

dimension could occur. To get a satisfactory vertical re�nement, we added multiple work planes in

the input, then when the 3D mesh is generated from the 2D one, these additional planes are taken

into account and the vertical size of the elements is adapted from their spacing. In this way we get a

good medium 3D mesh with a local 3D re�nement under the slab and at the pile bottom (see �gure

4.1).

49

4.1. VOLUME PILE CHAPTER 4. PRELIMINARY STUDIES OF 3D MODELS

4.1 Volume pile

The volume pile is a common Plaxis 3D foundation option to model a pile.

4.1.1 Finite element models

To start this study, all the previous geometries (Pile-Raft I, II, III, IV, V) were modeled using Plaxis

3D foundation. The working area was adapted in each case to have the same raft area with 3D and

with axisymmetric models.

Actually the raft area with axisymmetric models is circular whereas it is a square raft in 3D. Thus

in 2D, the raft area is given by the following formula:

Araft2D= π × (

Lraft2D2 )2 [m2]

The 3D width raft is obtained by taking the square root of 2D area raft as followed:

Lraft3D=

√Araft2D

=√π × (

Lraft2D2 )2 [m]

In this way, the area of the 3D raft is equal to the one in 2D: Araft3D= Araft2D

[m2]

Figure 4.1: Comparison between the axisymmetric and 3D raft shapes

The pile is modeled as a volume pile and we selected the massive circular pile type. Interfaces are

modeled along the pile with a Rinter = 0, 7. The soil consists of a single layer of dense sand with

the same properties as the sand we used previously. The load is modeled as a distributed load on the

slab. Two di�erent meshes with di�erent levels of re�nement were applied to the �rst two geometries.

Only a medium one was used for the remaining geometries. The following tables and �gures sum

up the most important parameters used.

Name Thicknessslab Depthmodel Lengthpile Diameterpile WidthraftWidthraft

Diameterpile

Pile-Raft I 0,5 m 40 m 15 m 0,8 m 1,8 m 2,25

Pile-Raft II 0,5 m 40 m 15 m 0,8 m 4,4 m 5,5

Pile-Raft V 1 m 60 m 30 m 1,5 m 4 m 2,7

Pile-Raft III 1 m 60 m 30 m 1,5 m 8 m 5,3

Pile-Raft IV 1 m 60 m 30 m 1,5 m 16 m 10,6

Table 4.1: Basic parameters of each geometry

50


Parameter Symbol Dense sand Concrete Unit

Material model Model Hardening Soil Linear Elastic -

Unsaturated weigth γunsat 19 25 kN/m3

Saturated weigth γsat 21 25 kN/m3

Permeability k 1 0 m/day

Eref50 60 000 kN/m3

Sti�ness Erefoed 60 000 3E7 kN/m3

Erefur 1,8E5 kN/m3

Power m 0,55

Poisson ratio νur 0,2 0,2 -

Dilatancy y 8 °

Friction angle f 38 °

Cohesion cref 0,1 kN/m2

Lateral pressure coe�. K0 1-sinf -

Failure ratio Rf 0,9 -


Figure 4.2: Details about a pile-raft geometry in 3D, medium mesh (Pile-raft IV)

51


Number of 15-noded elements

Medium Fine

Pile-Raft I 12 610 31 290

Pile-Raft II 22 230 31 464

Pile-Raft V 17 574 /

Pile-Raft III 22 134 /

Pile-Raft IV 24 186 /


4.1.2 Results

Remark: As we did for axisymmetric models all the following load-settlement curves are plotted

for the node point located at the top right side of the pile, under the slab.

Figure 4.3: Position of the node point A

4.1.2.1 Load-displacement curves

We plotted the load-displacement curve for each geometry. Then we compared these curves with

the associated axisymmetric curves. In each case, we noticed a good match with the 3D volume

pile-raft and the associated axisymmetric models.

Moreover the �gures 4.3, 4.4 and 4.5 con�rm that the mesh dependency is negligible.

52


Figure 4.4: Load-displacement curves comparison for Pile-Raft I, dense sand, ψ=8°

Figure 4.5: Load-displacement curves comparison for Pile-Raft II, dense sand, ψ=8°

53


Figure 4.6: Load-displacement curves comparison for Pile-Raft IV, dense sand, ψ=8°

4.1.2.2 Variations of skin friction

Remarks:

� All the following �gures are plotted by selecting the interface in Plaxis output. For Pile-Raft I

and II (respectively for Pile-Raft V and IV) we plotted the interface along the line - X = 0, 4(resp. 0, 75); Y ∈ [−15;0] (respec. [−30; 0]); Z = 0 (resp. Z = 0 ) -. In order to get something

comparable from one model to an other, we subtracted the �rst phase from the pile for each

load steps plotted. Thus the skin friction presented in this part are only due to the load and

the weight of the slab.

� Then, we compared the 3D volume pile pro�les with the axisymmetric ones. They are not

strictly comparable because the shape of the raft area is not the same. Nevertheless a com-

parison stays relevant as we choose the same area for every models.

Results of 3D volume pile models are in a very good aggreement with those we got with axisymmetric

calculations. We observed almost the same shape of skin friction for each Pile-Raft �le.

54


Figure 4.7: Axisymmetric and 3D volume pile skin friction curves, Pile-Raft I, Dense, ψ = 8,Rinter = 0, 7

Figure 4.8: Axisymmetric and 3D volume pile skin friction curves, Pile-Raft II, Dense, ψ = 8,Rinter = 0, 7

55


Figure 4.9: Axisymmetric and 3D volume pile skin friction curves, Pile-Raft V, Dense, ψ = 8,Rinter = 0, 7

Figure 4.10: Axisymmetric and 3D volume pile skin friction curves, Pile-Raft III, Dense, ψ = 8,Rinter = 0, 7

We can also notice that there are more oscillations in the lowest part of pile with the 3D volume

pile models than with 2D axisymmetric models. These non-physical stress oscillations are due to

56


the high peaks in stresses at the bottom of the pile. As we can see on �gure 4.11, we can reduce

these numerical inaccuracies by lengthening the interface at the bottom of the pile (+0,5 m).

Figure 4.11: Reduction of oscillations by lengthening the interface, Pile-raft III, Dense, ψ = 8,Rinter = 0, 7

By analysing in more details the load repartion for each model we can conclude that not only the

skin friction but also the base resistance �ts well.

Axisymmetric Pile-Raft II 250 kN/m2 500 kN/m2 1000 kN/m2

Rskin [kN] 2270 3513 6026

Rbase [kN] 1671 3094 5720Rskin

Rbase1,36 1,13 1,05

Volume Pile-Raft II 250 kN/m2 500 kN/m2 1000 kN/m2

Rskin [kN] 2058 3288 5745

Rbase [kN] 1858 3491 6520Rskin

Rbase1,1 0,94 0,88

Table 4.4: Comparison between volume and axisymmetric pile raft II

57


Remarks: The following values have been calculated without subtracting the weight of the pile

and of the raft. For the volume pile, we estimated Rbase and Rskin by reading in Plaxis output the

normal force values N at the top and at the bottom of the pile. Then we considered that: Rbase=

Nbottom and Rskin= Ntop-Nbottom.

4.1.2.3 Some remarks about parameters

We also varied the value of Rinter and ψ with some 3D volume pile models. We can conclude that

both dilatancy and Rinter have little in�uence on results.

Figure 4.12: Load-displacement curves for Pile-Raft I for di�erent values of Rinter, dense sand, ψ=8°

58


Figure 4.13: Load-displacement curves for Pile-Raft III for di�erent values of ψ, dense sand, Rinter =0, 7

Figure 4.14: Skin friction with the load for ψ = 8 and 0°, Pile-Raft III, Dense sand, Rinter = 0, 7

59

4.2. EMBEDDED PILE CHAPTER 4. PRELIMINARY STUDIES OF 3D MODELS

4.2 Embedded pile

An embedded pile is a pile composed of beam elements that can be placed in arbitrary direction

in the sub-soil (irrespective from the alignment of soil volume elements) and that interacts with

the sub-soil by means of special interface elements. The interaction may involve a skin resistance

as well as a foot resistance. Although an embedded pile does not occupy volume, a particular

volume around the pile (elastic zone) is assumed in which plastic soil behaviour is excluded. The

size of this zone is based on the (equivalent) pile diameter according to the corresponding embedded

pile material data set. This makes the pile almost behave like a volume pile. Nevertheless, when

creating embedded piles no corresponding geometry points are created. Thus, contrary to volume

pile, embedded piles do not in�uence the �nite element mesh as generated from the geometry model.

So the mesh re�nement is lower and we save calculation time. 1

In contrast to what is common in the Finite Element Method, the bearing capacity of an embedded

pile is considered to be an input parameter rather than the result of the �nite element calculation.

Plaxis gives us the possibility to enter the skin resistance pro�le in three ways:

� Linear: The user enters the skin resistance at the pile top and the skin resistance at the pile

bottom. The skin resistance is de�ned as linear along the pile. This way of de�ning the pile

skin resistance is mostly applicable to piles in a homogeneous soil layer.

� Multi-linear: The skin resistance is de�ned in a table at di�erent positions along the pile.

Multi-linear can be used to take into account inhomogeneous or multiple soil layers with

di�erent properties and, as a result, di�erent resistances.

� Layer dependent, can be used to relate the local skin resistance to the strength properties of

the soil layer in which the pile is located, and the interface strength reduction factor Rinter,

as de�ned in the material data set on the corresponding soil layer. Using this approach the

pile bearing capacity is based on the stress state in the soil, and thus unknown at the start of

a calculation. Nevertheless an overall maximum resistance can be speci�ed before to avoid an

undesired too high value at the end.

We performed another set of calculations by modeling the previous geometries using embedded

piles. This study gave us the possibility to test the reliability of this new feature to model pile-raft

structures.

4.2.1 Embedded pile-raft

For this study, we focused our calculations on the two �rst geometries named Pile-Raft I and Pile-

Raft II. We took exactly the same geometries by using embedded piles instead of volume piles. We

1See Plaxis manual for more details about embedded piles

60


considered the pile to raft connection as rigid. As mentioned previously the capacity of the pile is an

input parameter for an embedded pile so we had to de�ne the most relevant skin friction distribution

and base resistance. This is the reason why we tested each possibility o�ered by Plaxis to try to

con�gure in a proper way this new tool.

4.2.1.1 Finite element models

The parameters we examined for the embedded pile are the same as those desribed previously for

the volume pile. We performed calculations for only one material, the dense sand with Rinter = 0, 7.The load is modeled as a distributed load on the slab. Two di�erent meshes with di�erent levels of

re�nement had been used. The following tables sum up the most important parameters.

Name Thicknessslab Depthmodel Lengthpile Diameterpile WidthraftWidthraft

Diameterpile

Pile-Raft I 0,5 m 40 m 15 m 0,8 m 1,8 m 2,25

Pile-Raft II 0,5 m 40 m 15 m 0,8 m 4,4 m 5,5

Table 4.5: Basic parameters of each geometry

Parameter Symbol Dense sand Concrete (slab) Unit





Eref50 60 000 kN/m3


Erefur 1,8E5 kN/m3

Power m 0,55


Dilatancy y 8 °





Table 4.6: Soil parameters

61


Parameter Name Value Unit

Young´s modulus E 3.107 kN/m3

Weight γ 5 kN/m3

Properties type Type Massive circular pile -

Diameter dpile 0,8 m

Length Lpile 15 m

Table 4.7: Material properties of the embedded pile

Number of 15-noded elements

Medium Fine

Pile-Raft I 16 048 36 120

Pile-Raft II 14 300 36 800

Table 4.8: Information on generated meshes

Figure 4.15: Details about an embedded pile-raft geometry in 3D, �ne mesh, pile-raft II

62


Remark:

� As we did previously all the following load-settlement curves are plotted for the same node

point A located at the top right side of the pile, under the slab.

� Concerning the skin friction pro�les, we read out the Tskin2 value [kN/m] by selecting the

embedded pile in Plaxis output. Then we divided Tskin by the perimeter of the pile to get the

skin friction qs [kN/m2]. In order to get something comparable from one model to an other,

we subtracted the �rst phase from the pile for each load step plotted. Thus the skin friction

that we present here are only due to the load and the weight of the slab.

� We also read out the pile foot force Ffoot3 [kN] by selecting the embedded pile in the Plaxis

output. Thus we compared this value with the base resistance values found with axisymmetric

models.

4.2.1.2 Embedded pile with linear skin friction distribution

For this �rst set of calculations we de�ned linear skin friction distribution using unrealistic high

values (see �gures bellow).

Skin friction distribution linear [-]

Ttop,max 2000 [kN/m]

Tbot,max 2000 [kN/m]

Fmax 10 000 [kN]

Table 4.9: Linear skin friction distribution n°1 for Pile-Raft I and II

2The Skin force Tskin, expressed in the unit of force per unit of pile length, is the force related to the relativedisplacement in the pile´s �rst direction (axial direction)

3The pile foot force Ffoot, expressed in the unit of force, is obtained from the relative displacement in the axialpile direction between the foot of the pile and the surrounding soil.

63


Thus we got the following results:

Figure 4.16: Load-displacement curves for Pile-raft I, dense sand, ψ=8°, Rinter = 0, 7

Figure 4.17: Load-displacement curves for Pile-raft II, dense sand, ψ=8°, Rinter = 0, 7

64


Load=1000 kN/m2 Settlement [cm]

axisymmetric Pile-Raft I -13,2

Embedded Pile-Raft I_Medium -14,8

Embedded Pile-Raft I_Fine -15,8

axisymmetric Pile-Raft II -19,1

Embedded Pile-Raft II_Medium -19,6

Embedded Pile-Raft II_Fine -19,9

Table 4.10: Settlements for the di�erent models for 1000 kN/m2, Dense sand, ψ=8°, Rinter = 0, 7

We can conclude that the mesh in�uence seems to be still quite negligible.

We also notice that axisymmetric curves are not in a very good agreement with embedded pile curves.

Thus, we note a di�erence of around 15% in the settlements for axisymmetric and embedded �ne

Pile-Raft I (with Load=1000 kN/m2).

Now we observe the skin friction pro�le for these models:

Figure 4.18: Skin friction with the load for ψ = 8, Pile-Raft I, Dense sand, Rinter = 0, 7

65


Figure 4.19: Skin friction with the load for ψ = 8, Pile-Raft II, Dense sand, Rinter = 0, 7

When we compared these embedded pile skin friction pro�les with the axisymetric ones we notice

that they are very di�erent. We cannot observe the increase under the slab we described previously

in the 2D analysis. Thus the mobilization of such a de�ned embedded pile is di�erent.

So we decided to change our linear skin friction distribution using more realistic values. We de�ned

these values from the axisymetric skin friction pro�les. Thus we performed new calculations by

specifying this new input information:

66



Ttop,max 620 [kN/m]

Tbot,max 620 [kN/m]

Fmax 2260 [kN]

Table 4.11: Linear skin friction distribution n°2 for Pile-Raft I


Ttop,max 1110 [kN/m]

Tbot,max 1110 [kN/m]

Fmax 8300 [kN]

Table 4.12: Linear skin friction distribution n°2 for Pile-Raft II

67


The load-displacement curves we got with these new parameters are almost strictly the same as

those we had with the �linear skin friction n°1�. However, we can observe some di�erences in the

skin friction pro�les:

Figure 4.20: Skin friction with the load for Pile-Raft I, Dense sand,ψ = 8, Rinter = 0, 7

Figure 4.21: Skin friction with the load for Pile-Raft II, Dense sand,ψ = 8, Rinter = 0, 7

68


For the lowest load, the pro�les are exactly the same for the distribution -n°1 or n°2- . Nevertheless,

with the highest load and the input � linear skin friction distribution n°2 �, the skin friction reaches

the input value and stops growing.

To conclude we can say that neither � linear skin friction distribution n°2 � nor � linear skin friction

distribution n°1� leads to a skin friction pro�le in aggrement with the realistic one.

4.2.1.3 Embedded pile with multilinear skin friction distribution

For this second set of calculations we tested three di�erent multilinear skin friction distributions.

Input:

The multilinear skin friction distribution n°1 is a quite simple but realistic multilinear distribution:

Skin friction distribution : Multilinear

Depth [m] Tmax [kN/m]

0 565

-14,75 565

-15 1

Fmax [kN ] 2260



0 800

-14 800

-15 1

Fmax [kN ] 8300

Table 4.13: Multilinear skin friction distribution n°1 for Pile-Raft I (left) and II (right)

69


The multilinear skin friction distribution n°2 is the same as multilinear skin friction distribution

n°1 with Tmax=0 kN/m instead of 1 in the depth equal to 15m. Finally the multilinear skin

friction distribution n°3 is a more complex multilinear distribution designed from the axisymetric

skin friction pro�le as followed:



0 0

-8 15

-10,5 156

-13,5 302

-14,6 515

-15 0

Fmax [kN ] 8300



0 0

-1,2 315

-2,15 290

-10,2 430

-12,1 553

-14 804

-15 0

Fmax [kN ] 8300

Table 4.14: Multilinear skin friction distribution n°3 for Pile-Raft I (left) and II (right)

Output:

We noticed that the behaviors observed with distributions n°1 and 2 are exactly the sames. More

precisely, the load-displacement curves and the shear stresses distributions we got with �n°1� and

�n°2� are completly equal.

70


When we compare the n°1&2 load-displacement curve with the axisymmetric one, we see that they

do not �t very well. There is a di�erence of 12,5% (Pile-Raft I) and 7% (Pile-Raft II) in settlements.

Figure 4.22: Load-displacement curves for multilinear n°1/2 embedded and axisymmetric pile-raft I

Figure 4.23: Load-displacement curves for multilinear n°1/2 embedded and axisymmetric pile-raftII

Concerning �distribution n°3�, the load-settlement curve is almost the same as for �distribution

n°1/2�.

71


Load=25 kN/m2 Load=500 kN/m2 Load=1000 kN/m2

Axisymmetric Pile-Raft II -5,4 mm -110 mm -191 mm

Multilinear n°1/2 Emb Pile-Raft II -5,6 mm -112 mm -204 mm

Multilinear n°3 Emb Pile-Raft II -5,6 mm -115 mm -210 mm

Table 4.15: Comparison Load/Settlements for di�erent Pile-Raft II inputs

Finally by plotting the shear stresses distributions for each case, no multilinear skin resistance input

yields to the realistic skin friction mobilization we calculated with the axisymmetric models.

72


Figure 4.24: Evolution of skin friction for di�erent models and loadings

4.2.1.4 Embedded pile with layer dependent skin friction distribution

For this third set of calculations we tested the layer dependent option. According to a recent

update on plaxis website, �when using the layer dependant skin resistance for the embedded

piles, while leaving the linear skin resistance values to their defaults, the calculation kernel will show

a "severe divergence" error message. This severe divergence is caused by the zero values for the

linear skin resistance, though they do not have any in�uence on the layer dependant skin resistance.

To overcome this error, users are advised to set the linear skin resistance values to some values not

equal to zero, and then activate the layer dependant option. These linear skin resistance values

will not have an in�uence on the layer dependant values for the skin resistance.�4

We perfomed some tries.

Input:

For the layer dependent distribution n°1 we let the default values suggested by Plaxis.

Skin friction distribution: Layer dependent

Tmax [kN/m] 100 000

Fmax [kN] 10 000

Table 4.16: Layer dependent distribution n°1, parameters

4Plaxis website, Known issues 3D Foundation 2.1, 26-03-2008

73


As we explained in the introduction of this section, we did not let the default values for the linear

skin resistance. We input 1.

For the layer dependent distribution n°1bis we used the values as described in the previous table,

but we input 2000 for the linear skin resistance.

We tested with dense sand, Rinter = 0, 7.

Output:

The �layer dependent distribution n°1� and the �layer dependent distribution n°1bis� perfectly match.

It con�rmed that these linear skin resistance values do not have an in�uence on the layer

dependent results. We just need to write a value not equal to zero in linear to use correctly the

layer dependant option.

Figure 4.25: Comparison of load-displacement curves

Moreover, the skin distribution pro�le is in a perfect agreement for the �layer dependent distribution

n°1� and �n°1Bis�. We also have a quite good match with the axisymmetric pro�le.

If we calculate the di�erence of skin friction at half a pile between the axisymmetric and layer

dependent results : ∆7,5m = qs2D(−7, 5m) - qs3D(−7, 5m)

74


We get for a load equal to 500 kN/m2, ∆7,5m ' 25kN/m2.

Figure 4.26: Evolution of skin friction, Pile-raft II

We performed another calculation with the parameters of the so called �layer dependent distribution

n°1�. We just changed the Rinter value from 0,7 to 1.

We compare the load-displacement behavior on the following �gures.

75


Figure 4.27: Comparison of load-displacement curves

The load-displacement curves we got for the layer dependent distribution n°1 with Rinter = 1 is close

to one with Rinter = 0, 7 but not exactly equal. In each case, they are not in good aggrement with

the axisymmetric results. We have a di�erence of around 12,5 % (Pile-Raft II) in the settlements

for a distributed load equal to 1000 kN/m2.


Axisymmetric Pile-Raft II -5,4 mm -110 mm -191 mm

Layer dependent 1 - Rinter = 0, 7 -5,6 mm -126 mm -215 mm

Layer dependent 2 - Rinter = 1 -5,6 mm -123 mm -213 mm

Table 4.17: Comparison Load/Settlements for di�erent Pile-Raft II inputs

For each input distributions we also plotted the skin friction distributions. In each case, the skin

distribution pro�le is in quite good agreement with the axisymmetric pro�le, particularly with the

layer dependent distribution n°1 with Rinter = 1.

76


Figure 4.28: Evolution of skin friction for di�erent inputs, Pile-raft II

We get for a load equal to 1000 kN/m2, ∆7,5m ' 77kN/m2 with Rinter = 0, 7 and ∆7,5m '16kN/m2with Rinter = 1.

The layer dependent distribution option seems to be the best way for embedded piles to get skin

friction distributions with realistic shapes. Nevertheless further tests must be done to really determine

the in�uence of the virtual value we need to input in linear skin resistance when we use the layer

dependant option.

4.2.1.5 Comparison of the three options: Linear, multilinear and layer dependent

We now compare the three approaches in order to determine which approach is the best for analysing

piled raft foundations.

Load-displacement behavior:

Concerning the load-displacement behavior, the linear embedded pile raft is the closest to the ax-

isymmetric model. However for common geotechnical displacements (max. 10 cm), whatever the

input option for the embedded pile is, the load displacement curve stays quite reasonably close to

the axisymmetric one with a di�erence of around more or less 1 cm.

77



Axisymmetric -5,4 mm -110 mm -191 mm

Linear embedded +3,7 % +0,9% +3,7%

Multilinear embedded +3,7 % +4,5% +12%

Layer dependent embedded +3,7 % +14,5% +12,6%

Table 4.18: Displacement with the load, for Pile-Raft II

Figure 4.29: Load-displacement curves for Pile-Raft II

Pile-raft behavior:

According to the skin friction distributions presented previously, we saw that the mobilization of the

embedded pile-raft foundation and the axisymetric pile-raft foundation is di�erent. So we analysed

in more details the load repartion for each model. The following values have been calculated by

subtracting the weight of the pile and of the raft .

78


Axisymmetric Pile-Raft II 25 kN/m2 250 kN/m2 500 kN/m2 1000 kN/m2

Rskin [kN] 386 2038 3281 5794

Rbase [kN] 82 1482 2905 5531

αKpp 0,95 0,72 0,63 0,57Rskin

Rbase4,73 1,38 1,13 1,05

Linear n°2 Emb. Pile-Raft II 25 kN/m2 250 kN/m2 500 kN/m2 1000 kN/m2

Rskin [kN] 430 3638 6218 10 074

Rbase [kN] 12,7 95,3 230 631

αKpp 0,9 0,76 0,66 0,55Rskin

Rbase33,9 38,2 27 16

Multilinear n°1 Emb. Pile-Raft II 25 kN/m2 250 kN/m2 500 kN/m2 1000 kN/m2

Rskin [kN] 411 3471 6232 8585

Rbase [kN] 23 211 414 848

αKpp 0,88 0,75 0,66 0,48Rskin

Rbase18,1 16,4 15 10,1

Layer dependent n°2 Rinter = 0, 7 Emb. Pile-Raft II 25 kN/m2 / 500 kN/m2 1000 kN/m2

Rskin [kN] 438,3 / 2760,9 3756,7

Rbase [kN] 16,9 / 570,4 967,6

αKpp 0,99 / 0,34 0,24Rskin

Rbase25,9 / 4,84 3,88

Layer dependent n°2 Rinter = 1 Emb. Pile-Raft II / 500 kN/m2 1000 kN/m2

Rskin [kN] / 3930,8 5729,2

Rbase [kN] / 526,6 935,8

αKpp / 0,45 0,33Rskin

Rbase/ 7,46 6,12

Table 4.19: Rraft,Rskin,and Rbase repartition for di�erent models of Pile-Raft II (Dense sand, ψ=8°)

79


Figure 4.30: Evolution of skin friction, Load=500 kN/m2

Figure 4.31: Evolution of skin friction, Load=1000 kN/m2

Remark

For these previous �gures we substracted the weight of the pile and of the raft .

80


Axisymmetric Pile-Raft I 25 kN/m2 250 kN/m2 500 kN/m2 1000 kN/m2

Rskin [kN] 50,3 451,5 812,5 1426

Rbase [kN] 35,8 335,1 783 1768

αKpp 0,99 0,99 0,99 0,99Rskin

Rbase1,41 1,35 1,04 0,81

Linear n°2 Emb. Pile-Raft I 25 kN/m2 250 kN/m2 500 kN/m2 1000 kN/m2

Rskin [kN] 74 747 1463 2863

Rbase [kN] 4,6 35 85,1 203

αKpp 1 1 0,99 0,98Rskin

Rbase16 21,4 17,2 14,1

Multilinear n°1 Emb. Pile-Raft I 25 kN/m2 250 kN/m2 500 kN/m2 1000 kN/m2

Rskin [kN] 67 697 1400 2792

Rbase [kN] 9 65,2 123,5 252

αKpp 0,97 0,97 0,97 0,97Rskin

Rbase7,6 10,7 11,3 11,1

Table 4.20: Rraft,Rskin,and Rbase repartition for di�erent models of Pile-Raft I (Dense sand, ψ=8°)

The linear and multilinear embedded pile models seem to lead to realistic values of αKpp . Actually

we calculated values of αKpp very close to the axisymmetric ones. The main problem remains

the mobilization of the base resistance because whatever the input is, we underestimate Rbase

with embedded piles in comparison with 2D models.

Moreover, the skin friction of embedded piles seems to be overestimated in comparison with chapter 2

except the calculations with the layer dependent skin resistance. But with this approach we always

got too much settlements.

To conclude we can say that with embedded pile option we did not manage to calculate

the pile raft behavior we observed with volume piles or axisymmetric models.

81

Chapter 5

Group e�ect

- Analysis of the group e�ects in piled raft foundations -

The previous models gave us a �rst idea of a piled raft foundation behavior. These models took

into account the pile-soil interaction, the raft-soil interaction and the pile-raft interaction but not

the pile-pile interaction. Yet when the piles spacing is small, a partial geometry with a single pile

and one section of the raft is not accurate enough. We must consider the pile-pile interaction and

design more complex models with a group of piles.

In this chapter, we present some observations about the group e�ect in a piled raft foundation.

5.1 Presentation of calculations

We studied a piled raft foundations with 6×6 piles. Thus by using symetries we modeled only 9

piles. To study the in�uence of pile length and diameter as well as spacing between piles we designed

�ve di�erent geometries.

82

5.1. PRESENTATION OF CALCULATIONS CHAPTER 5. GROUP EFFECT

Figure 5.1: 6×6 piled raft foundation, we model the red delimited quarter only

5.1.1 Geometry

The following pictures present the global geometry of our models.

83


Figure 5.2: Model of one quarter of one piled raft foundation (6×6 piles)

84


The main geometric paramaters of this study are presented in this �gure:

Figure 5.3: Some geometric parameters

From this scheme, we designed �ve di�erent geometries:

Paramater Symbol Group 1 Group 2 Group 3

Diameter of the pile dpile 0,8 m 0,8 m 0,8 m

Length of the pile Lpile 15 m 15 m 30 m

-Lpile

dpile18,75 18,75 37,5

Length of the pile group Lg 8,75 m 16,8 m 16,8 m

Depth of the model Hmodel 50 m 50 m 80 m

Thickness of the slab traft 1,5 m 1,5 m 1,5 m

Spacing between piles a 2,5 m ('3×dpile) 4,8 m (6×dpile) 4,8 m (6×dpile)

Paramater Symbol Group 4 Group 5



-Lpile

dpile45 45

Length of the pile group Lg 15,75 m 31,5 m

Depth of the model Hmodel 80 m 80 m

Thickness of the slab traft 1,5 m 1,5 m

Spacing between piles a 4,5 m (3×dpile) 9 m (6×dpile)

Table 5.1: Geometric parameters for each model

85

5.2. RESULTS CHAPTER 5. GROUP EFFECT

For each group we also performed the same calculations without the piles in order to evaluate the

piled raft e�ciency in comparison with a raft foundation (β-factor).

5.1.2 Finite element model

We modeled the piles with the volume pile option. Moreover, we generated for each model a medium

mesh with around 50 000 elements (see �gure 5.2). Finally, the load is a distributed load applied on

the slab.

We tested only the dense sand material, with Rinter=0,7 and ψ=8°.

Parameter Symbol Dense sand Concrete Unit





Eref50 60 000 kN/m3


Erefur 1,8E5 kN/m3

Power m 0,55


Dilatancy y 8 °





Table 5.2: Material properties

5.2 Results

5.2.1 Vocabulary details

Please note that in the following sections we will distinguish four types of pile depending on their

position in the group:

� the center pile is pile A

� the middle piles are piles B, D, E

86


� the corner pile is pile I

� the edge piles are piles C and G

Figure 5.4: Name of each pile

Remark: To plot the load displacement curves we selected the node point located in the center of

the upper face of each pile.

5.2.2 Load-displacement curves

For the so called center pile, edge piles and corner pile of the group 1 and 2 we read out the Rpilevalue

and the corresponding pile settlements for each load steps. We got the following curves:

Figure 5.5: Displacement of the pile with Rpile, group 1

87


Figure 5.6: Displacement of the pile with Rpile, group 2

These curves are in agreement with the shape described in books.

For the other models, we plotted the load-settlement curves for the raft. We also compared the

behavior with the �closest� single pile-raft model. As these partial geometries have not exactly the

same geometric parameters (see previous chapter) they are not entirely comparable but give us some

clues to interpret the group behavior.

Figure 5.7: Load-displacement curves for Group 4

88


Figure 5.8: Load-displacement curves for Group 5

Whatever group we examine the settlement behavior of each pile is not really di�erent from one pile

to another. The whole behavior is very sti� and we could propably improve our models by varying

the parameters of the raft in order to have a less sti� behavior.

5.2.3 Displacement pro�les

A cross section has been performed as described in the following �gure. It gives us the possibility

to observe vertical displacements (uy) around center, middle and edge piles. All these cross sections

are performed for a distributed load equal to 1000 kN/m2.

89


Figure 5.9: A, B, C piles cross section

Figure 5.10: Group 1 (left) and Group 2 (right) cross sections

90


Figure 5.11: Single pile-raft II cross section

Figure 5.12: Group 4 (left) and Group 5 (right) cross sections

91


Figure 5.13: Single pile-raft III

We notice that the displacement behavior around middle and center piles for groups with a large

spacing (group 2 and 5) is quite comparable and in good agreement with the associated single pile-

raft model. On the other hand, with the small spacing groups (group 1 and 4) the settlements are

di�erent from one pile to another.

In each case the behavior of the edge pile cannot be compared with the one of the associated single

pile-raft model because the raft is larger in the area of the edge pile.

5.2.4 More precise analysis of group 5

We estimated Rbase and Rskin by reading out in Plaxis output the normal force values N at the top

and at the bottom of the pile. Then we considered that: Rbase= Nbottom and Rskin= Ntop-Nbottom.

The value from Nbottom are not the highest value of the normal force along the pile but this value

normally occurs a bit above the pile toe (around -29,5 m).

These values give us an idea of the real base and skin resistance.

92


Group 5 Center pile Middle piles edge piles corner pile Single pile-raft III

Rskin [kN] 12 281 12 732 13 060 13 092 24 268

Rbase [kN] 23 400 22 526 23 318 22 228 21 500

Rskin+ Rbase 35 681 35 258 36 378 35 320 45 768Rskin

Rbase0,52 0,57 0,56 0,59 1,12

Table 5.3: Base and skin resistance for di�erent piles

Remark:

Paramater Symbol Group 5 Pile-Raft III



-Lpile

dpile45 45

Thickness of the slab traft 1,5 m 1 m

Spacing between piles a 9 m (6×dpile) 8 m (5,3×dpile)

Table 5.4: Main geometric parameters

We noticed that each pile of the group seems to be mobilizated in the same way (around the same

values of Rskin and Rbase ). But the mobilization of skin resistance appears to be lower than for a

single pile-raft. The skin friction pro�les we see in the following pictures con�rm these observations.

This low skin friction mobilization is due to pile-pile interaction.

We represented the skin friction pro�le in four directions for the center, middle and corner piles of

group 5. We added the skin friction pro�les for the single pile-raft III (in blue).

93


Figure 5.14: Skin friction pro�le for the center pile, Load=1000 kN/m2

94


Figure 5.15: Skin friction pro�le for a middle pile, Load=1000 kN/m2

95


Figure 5.16: Skin friction pro�le for the corner pile, Load=1000 kN/m2

96


5.2.5 Conclusion

So, we can notice that the behavior of a pile in a pile raft foundation is di�erent from the single pile

raft. The pile-pile interaction seems not to be negligible even with a quite big spacing

(6 × draft).

Nevertheless, we did not have enough time to perform a more precise study. Our models seem to be

too sti� and we can easily improve this studies by modifying the raft parameters for instance. This

section only give some clues to start a more relevant work about the pile-pile interaction.

Remark:

A last calculation has been perfomed with Group 2. We reduced the raft sti�ness from Eref = 3.107

kN/m2 to Eref = 1.106 kN/m2. We get the following load displacement curves:

Figure 5.17: Load-settlements curves group 2 with Eref = 1.106 kN/m2

97

Chapter 6

Conclusion

This work led us to both practical and more general conclusions.

In chapter 2 a parametric study has been performed. Some remarks about how to design axisym-

metric single pile or pile-raft models with Plaxis can be done.

For a single pile:

� The importance of interface elements was shown. The input value for Rinter changes the load

settlement curves

� The mesh dependency is negligible

� Prescribed displacement seems to be better than load control to study a single pile

� By using load control, premature failures can occur. We can prevent this problem switching

arc-length control o�. But without arc-length control, oscillations can appear. We observed

we have to interpret with caution the shape of these �numerical inacuracies�.

For a single pile-raft:

� The mesh dependency is negligible

� The input value for Rinter do not have an important in�uence

� Dilatancy do not have an important in�uence

In chapter 4 we tested some 3D Plaxis tools to model piles: volume pile and embedded pile. The

results observed with volume piles are in a very good agreement with the ones of axisymmetric

models. On the other hand, the use of embedded pile to model piled-raft foundations was more

di�cult. We did not manage to calculate the pile raft behavior we had observed with

98

CHAPTER 6. CONCLUSION

volume piles or axisymmetric models. The main problem remains the mobilization of

the base resistance because whatever the input is, we underestimate Rbase with embedded piles

in comparison with 2D models.

Chapter 3 and 5 were focused on the analysis of the load repartition in piled-raft foundations. The

ability of Plaxis to model the complex pile-raft-soil interaction was con�rmed. We observed the

main aspects of the pile-raft behavior that are usually described in books. We noticed

that:

� The stress repartition between the raft and the pile evolves with the loading. The higher the

loading is, the more the stress is shared. With a load between 0 and 200 kN/m2 everything

goes mostly to the pile (1 <αKpp< 0,8). From 200 kN/m2the raft has a stronger in�uence.

� The bigger the spacing is, the more load takes the raft.

� In each case the raft and pile load sharing converges to an equilibrium state

� The pile obviously carries more load by increasing the length of the pile

We started a more sophisticated analysis of the total structure with a three dimensional model to

take the pile-pile interactions into account. We noticed that the behavior of a pile in a piled raft

foundation is di�erent from the single pile raft model. There is a reduction of the skin friction

mobilization due to a group e�ect. We did not have enougth time left to pursue in more details

the improvement of these models. This �nal chapter gives some basic clues to perform a deeper

analysis of pile-pile interactions in piled-raft foundations. This e�ect should be studied in further

researches.

99

Bibliography

[1] Brinkgreve R.B.J (2006). Plaxis, Finite Element Code for Soil and Rock Analyses, user

manual. Delft University of Technology & Plaxis b.v, The Nederlands. Balkema, Rotterdam.

[2] Y. El-Mossalany. Single pile and pile group in overconsolidated clay, Plaxis 3D foundation /

validation Version 2. Ain shams University

[3] Y. El-Mossalany. Pile raft foundation in frankfurter clay, Plaxis 3D foundation / validation

Version 2. Ain Shams University

[4] H. K Engin. Validation of embedded piles, the Azley Bridge pile load test, Plaxis 3D foundation

/ validation Version 2. Middle-East Technical University

[5] F. Tschuchnigg and H. Schweiger. Application of the ground anchor facility, Plaxis 3D

foundation / validation Version 2. Graz University of Technology

[6] M. Wehnert and P.A. Vermeer. Numerical Analyses of Load Tests on Bored Piles. University

of Stuttgart

100

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