BEHAVIOUR OF GEOTECHNICAL STRUCTURES

2012 - 2013

Fabrice EMERIAULT

GENERAL OUTLINE

� Introduction

� Shallow foundations

� Retaining structures: gravity walls

� Retaining structures: flexible walls

Deep foundations� Deep foundations

� Soil improvement

FLEXIBLE WALLS

OUTLINE

� Introduction

� Different types of flexible walls

� Failure mechanisms

� Specific aspects of the behaviour

� Active and passive pressures on a flexible wall� Active and passive pressures on a flexible wall

� Arching effect

� Incidence of construction phases

� Design methods

� Simplified

� Empirical

� Subgrade reaction method

� FE calculations

� Design of the anchors

INTRODUCTION

INTRODUCTION

� Retaining walls

� What are they used for ?

� What are the main mechanisms involved ?

� Gravity walls� Gravity walls

� Flexible walls

� Temporary or definitive walls

� Installed in the native soil

� Generally:

� Water tight

� Use structural elements to equilibrate a part of the � Use structural elements to equilibrate a part of the

horizontal efforts

THE DIFFERENT TYPES OF

FLEXIBLE WALLS

SHEET PILE WALLS

Continuous wall made of steel profiles assembled during installation in the soil

CIRCULAR EXCAVATION WITH SHEET PILES

Cofferdam

Sheet pile wall with 4 levels of anchors

Quay walls

Installation by:- hammering- vibrations- jacking

DIAPHRAGM WALLS

PRE-CAST WALLS

SECANT PILE WALLS

SOLDIER PILE WALLS

SLURRY WALLS

FLEXIBLE WALLS

OUTLINE

� Introduction

� Different types of flexible walls

� Failure mechanisms

� Specific aspects of the behaviour

� Active and passive pressures on a flexible wall� Active and passive pressures on a flexible wall

� Arching effect

� Incidence of construction phases

� Design methods

� Simplified

� Empirical

� Subgrade reaction method

� FE calculations

� Design of the anchors

� Temporary or definitive walls

� Installed in the native soil

� Generally:

� Water tight

� Use structural elements to equilibrate a part of the � Use structural elements to equilibrate a part of the

horizontal efforts

HORIZONTAL STRUCTURAL ELEMENTS

� Struts inside the excavation

� Anchors in the ground

� Elements of the future structure installed top-down

Slabs� Slabs

� Beams

Temporary steel struts

Anchors: temporary action (long term efforts transmitted to the floors)

Reinforced concrete beams constructed top-down (beams will support the final floors)

Horizontal support brought by (partial) floors

FAILURE MECHANISMS

NON ANCHORED WALL

Failure by overturning

Embedment depth is not suffisant

Under-designed wall

Failure by excessive bending

ANCHORED WALL

Fiche insuffisante

Failure by wall toe excessive

displacement

Passive force is not suffisant

Embedment depth is not suffisant

suffisant

Internal failure of the anchor

Or failure of the grout-soil interface

Strut buckling

Failure by overturning due to lack of

horizontal resistance of anchor or strut

Failure by excessive bending (strength of the material is reached)material is reached)

Example of Nicholl Highway - Singapore

NICOLL HIGHWAY EXCAVATION – 3 DAYS BEFORE THE COLLAPSE

SOUTH NORTH

NICOLL HIGHWAYGROUND LEVEL

6VERY SOFT MARINE CLAY

10m

20m

1

2

3

4

5

7

89am waler starts to fail at

SECTION S335

OLD ALLUVIUM

30m

99am waler starts to fail at

9th level

20th APRIL 2004

increased wall movements

Length of the anchor is not suffisant

Soft soil

Inclinaison of anchor too large

Wall too thin

Global failure

Failure by lack of bearing capacity at the toe

Case of a wall in a general slope

Overall failure = slope stability problemstability problem

Main concern in urban site

« failure » by excessive deformation

Failure of the bottom of the excavation

Occurs when the hydraulic gradient at the bottom of the excavation

reaches the critical value

Possible with a very soft soil

ic = -γ’/γw

Occurs when the pore pressure under the least permeable soil layer is larger

than the total vertical stress

SPECIFIC ASPECTS OF THE

BEHAVIOUR

Depend on the wall kinematics

ACTIVE AND PASSIVE PRESSURE

DISTRIBUTIONS FOR FLEXIBLE WALLS

Terzaghi’s trapdoor experiment (1936)

ARCHING EFFECT

trappe

Stress concentration on the boundaries of the fixed zone

Stress decrease within the moving zone

Illustration of the arching effects in

the case of flexible vertical walls

EFFECT OF THE CONSTRUCTION SEQUENCES

DESIGN METHODS

OUTLINE

� Design methods

� Simplified

� Empirical

� Subgrade reaction method

FE calculations� FE calculations

�Complex soil—structure interaction problem

linked to:�The geometry of the problem

�The soil properties

The presence of supports (struts, anchors)

INTRODUCTION

�The presence of supports (struts, anchors)

�But also and essentially to:�The initial state of the soil

�The stiffness of the wall

�The effect of water

�The sequences of construction

�Different levels of design approaches:�Empirical approach

�Simplified theoretical mechanisms

�Sub-grade reaction method

Finite element method calculation or equivalent�Finite element method calculation or equivalent

�Due to the complexity of the problem, the

different approaches are complementary

SIMPLIFIED THEORETICAL APPROACHES

� Based on theoretical active and passive pressure distributions

� Different methods depending on the type of wall (non anchored,

anchored, passive anchor, rigid wall or flexible wall)

� Consider separately the horizontal and vertical components of

efforts acting on the wall

�Actually the vertical component is generally neglected

Non anchored wall

H

Correspond to the overturning failure mechanism and therefore to a lack of embedment depth:

A safety coefficient is applied to the passive forces B and CB (F is generally taken equal to 1.5 or 2)

For simplification, the passive force CB is replaced by a concentrated force at the point

of rotation

f0f

P

CB

B/F

H

� f0 is obtained through the moment equilibrium MO(P) = MO(B)

� CB is obtained through the horizontal force equilibrium

� f calculated in order to mobilize CB*

� or approx. f= 1,2. f0

f0

P

CB

B/Ff

O

* CB = [1/F].(K pγ.γγγγ/2).[(H+f)² - (H+f 0)²].cos δ

Anchored « rigid » wall

H

a A

Bending moment

A

fP

B/F

Unknowns : f;A

Corresponds to a rotational failure due to the lack of embedment depth:

A safety coefficient must be applied to the passive force

(generally 1.5 or 2)

H

a A

� Determination of f:

� Moment equilibrium

written in A

Anchor force:

A

fP

B/F

� Anchor force:

� Equilibrium of

horizontal forces

Anchored « flexible » wall

H

a A For simplification, the passive force CB is replaced by a concentrated force at the point

of rotation

f0f

P

CB

B

H

a A

Bending moment

�Hyperstatic problem:

�Determination of the

3 unknowns: A, f, CB

f0f

P

CBB

d

Assumptions on the position of this point:

- d = point where pressure is null (σσσσp=σσσσa)- or d~0,1.H (after Blum)

�Determination of the

point where bending

moment is null

H

a A

P

a A

f0f

P

CB

B

d

d

The wall is divided in 2 isostatic beams

T

H

a A

P

a A

f0f

P

CB

B

d

d

f0

CB

B P

T

T

The wall is divided in 2 isostatic beams

H

a A

� Determination of T:

� Moment equilibrium

A

P

d

T

� Moment equilibrium

written in A

� Determination of the anchor

force A:

� Equilibrium of horizontal

forces

Upper beam

f0 B P

T

� Determination of f0:

� Moment equilibrium written in O (where CB is applied)

� Determination of CB (not necessary):

� Equilibrium of horizontal forces

� Determination of f

� Required height for mobilization of CB

f

CBmobilization of CB

� Or approx.: f= d+1.2 f0

Lower beam

Choice of the method

L’hypothèse sur l’encastrement pilote de façon importante la forme et l’amplitude du diagramme des moments

� Observations by Rowe

� From small scale model tests, Rowe has shown that the behaviour of the wall depends mainly on its bending stiffness

� The maximum bending moment and the anchor force decrease drastically when the flexibility of the wall increases

� The bending flexibility can be defined by the coefficient ρρρρ

ρρρρ = H4 / E.I

Correction on the maximum bending moment proposed by Rowe

Wall flexibility:

ρρρρ = H4 / E.I

Summary of the simplified methods

� Accurate estimation of:

� The embedment depth,

� The bending moments,

� The anchor force

� Limits:

� Do not account for the construction sequences

� The deformation of the wall can not be determined

� Not applicable for « complex » walls: several rows of anchors, possibly active anchors

Be careful !

� Results strongly depend on the soil properties, in particular the cohesion

� Whatever the method !

EMPIRICAL METHODS

� Based on the observation of the behaviour of real walls

� Can propose a simple design method for simple or very

complex cases

for example several rows of struts or anchors� for example several rows of struts or anchors

� Application limited to the types of soil and wall

considered in the calibration of the empirical method

� Complexity of the

problem due to the

numerous

redistributions of

Excavation with several levels of struts

redistributions of

effort at each phase

of excavation

The deformation is strongly limited in the upper part.

Redistributions of active pressures are induced with a concentration at the top of the wall

Terzaghi and Peck have monitored a large number of real walls in order to determine the efforts induced in the struts. The proposed diagrams represent the envelop of the measured efforts.

It does not correspond to the real pressure distribution but is an empirical approach for the design of struts !

Diagrams proposed in the EAB german code

SUBGRADE REACTION METHOD

� Based on Winkler’s approach

� Account for the active and passive limits to pressure

Presents a certain number of advantages compared to � Presents a certain number of advantages compared to

the empirical methods

� But has its own limitations

� Analogy with a beam resting on independant elastic

springs σ = k w

� Gives the possibility to determine the efforts and moments

in the beam (necessary for concrete design)

� Simplified approach: stress in one point only depends on

the movement of this point

Winkler’s approach

P1P2

W

y(x)

extérieur (e)

Even tough the very crude assumption of independant springs is considered,

The extension of the approach to walls requires the determination of more complex contact laws such as:

σσσσ(e) = K0. σσσσv - kh. y(x)

Application to vertical walls

Intérieur (i)

σσσσ(e) = K0. σσσσv - kh. y(x)

σσσσ(i) = K0. σσσσv + kh. y(x)

These laws must be complex, non linear and present hysteresis

Developpement of softwares at the end of the 60s

Largely used by consultants (Rido, K-Rea, …)

� Based on active/passive pressure tests

σσσσh

kpσσσσv

Subgrade reaction law

y

k0σσσσv

kaσσσσv

Experimental curve

Approximation by a tri-linear law with a limitation on the active and passive pressure

σσσσh

σσσσv

σσσσh

kpσσσσv

� General case

y

k0σσσσv

kaσσσσv

� Cohesive soil

σσσσh

Passive pressure

For cohesive soil, the theoretical active

pressure can locally be negative, thus inducing traction between the soil

yk0σσσσv

traction between the soil and the wall

In this case, the stress is considered equal to 0

Active pressure

σσσσh

Passive pressure

When the soil reaches the active or passive limit, an irreversible behaviour is

observed

Induces a shift of the

A B

� Irreversible behaviour

yk0σσσσv

Induces a shift of the reaction curve (path ABC)

poussée théorique

C

Illustration in the case of passive pressure

σσσσh

Passive pressure

yk0σσσσv

poussée théorique

A

C

B

Illustration in the case of active pressure

σσσσhk0σσσσv

� Unloading behaviour

y

Different rules can be proposed for the position of the new reaction curve

New passive pressure

New active pressure

1st step:Define the initial conditions,

i.e. the initial force in each spring:

σσσσ(e) = K0. σσσσv

σσσσ(i) = K0. σσσσv

It can also account for a surcharge at ground

Subgrade reaction method

Intérieur (i)

extérieur (e)

It can also account for a surcharge at ground surface, the presence of the water table…

At that point, no bending moment or shear force in the wall.

2nd step (for example):

A first excavation is defined

The corresponding springs are deleted

The wall will move and deform in order to reach a new equilibrium state

y(x)

Intérieur (i)

extérieur (e)

reach a new equilibrium state

2nd step (for example):The equilibrium must satisfy:

The equation of beams

yIV(x) = σσσσi(x) –σσσσe(x)

The equilibrium of horizontal forces

y(x)

Intérieur (i)

extérieur (e)

The equilibrium of horizontal forces

(Σ Σ Σ Σ horizontal forces =0;

Σ Σ Σ Σ Moment of horizontal forces = 0)

The reaction law

σσσσ(e) = K0. σσσσv - kh. y(x)

σσσσ(i) = K0. σσσσv + kh. y(x)

The boundary conditions (at the top and toe of the wall)

yIII (x) =yIV(x) = 0 (for example)

3rd step (for example):It can include:

- the installation of a strut

- a new excavation step

This will induce:

y(x)

A

Intérieur (i)

extérieur (e)

- a new deformation of the wall

- and a force A in the strut

� It is not a intrinsec property of the soil (can not be

considered as a collection of independant springs)

� It can not be measured (the result depend on the testing

method!)

� It can only be estimated

Several approaches:

Determination of the Subgrade reaction coefficient

� Several approaches:

� Based on the pressumeter modulus EM (Balay)

� Based on φ and c (Chadeisson)

� Empirical values proposed by different authors

� Values resulting from back-analysis

� Account for the displacement and deformation of the wall in the pressure diagram

� Gives an estimate of the shape and values of the displacements

Account for the different excavation sequences in the

Advantages of the method

� Account for the different excavation sequences in the loading of the wall

� Allows to analyse complex cases (different levels of struts or anchors, with or without preloading)

� kh can not be measured

� Arching effect can not be reproduced

� One illustration

Limits of the method

Association of rigid struts and preloaded anchors

Canal du Midi Station – Toulouse subway:

Association of 2 levels of steel struts and 2 levels of preloaded anchors

Argileuse

Molasse

REMBLAIS

STATION

buton 133 NGF

du canalposition définitive

tête de P.M.

136,20

StrutMade Ground

Clayey Molasses

Canal du Midi Station – Toulouse subway:

Association of 2 levels of steel struts and 2 levels of preloaded anchors

Sableuse

Argileuse

Molasse

Molassebuton 120 NGFStrut Sandy Molasses

Clayey Molasses

120

125

130

135

cote

NG

F

exc 123

tirant 123.5

exc 119.5

buton 120 +exc 115.55

NG

F le

vel

Excav. 123 NGF

Anchor 123.5 NGF

Excav. 119.5 NGF

Excav. 115.5 NGFStrut 120 NGF

RIDO predictions

120

125

130

135

cote

NG

F

exc 123

tirant 123.5

exc 119.5

buton 120 +exc 115.55

NG

F le

vel

Excav. 123 NGF

Anchor 123.5 NGF

Excav. 119.5 NGF

Excav. 115.5 NGFStrut 120 NGF

RIDO predictions

120

125

130

135-5 0 5 10 15 20

déplacement (mm)

cote

NG

FN

GF

leve

l

Displacement (mm)

Experimental results

120

125

130

135-5 0 5 10 15 20

déplacement (mm)

cote

NG

FN

GF

leve

l

Displacement (mm)

Experimental results

SGRM calculations under-estimate the displacements and deformations of the wall (ratio of 2)

110

115

-1 0 1 2 3 4 5 6 7 8 déplacement (mm)Displacement (mm)

110

115

-1 0 1 2 3 4 5 6 7 8 déplacement (mm)Displacement (mm)105

110

115

18/09/02

27/09/02 - exc 123NGF

18/10/02 - mise en tensiontirants 123.5NGF25/11/2002 - exc 119.5NGF

04/02/2003 - exc 115.5NGF

pied de laparoi moulée

Excav. 123 NGF

Anchor 123.5 NGF

Excav. 119.5 NGF

Excav. 115.5 NGF

Bottom of thediaphragm wall

105

110

115

18/09/02

27/09/02 - exc 123NGF

18/10/02 - mise en tensiontirants 123.5NGF25/11/2002 - exc 119.5NGF

04/02/2003 - exc 115.5NGF

pied de laparoi moulée

Excav. 123 NGF

Anchor 123.5 NGF

Excav. 119.5 NGF

Excav. 115.5 NGF

Bottom of thediaphragm wall

120

125

130

135-5 0 5 10 15 20

déplacement (mm)

cote

NG

FN

GF

leve

l

Displacement (mm)

Experimental results

120

125

130

135-5 0 5 10 15 20

déplacement (mm)

cote

NG

FN

GF

leve

l

Displacement (mm)

Experimental results

120

125

130

135

cote

NG

F

exc 123

exc 119.5

exc 115.5

NG

F le

vel

Excav. 123 NGF

Excav. 119.5 NGF

Excav. 115.5 NGF

Plaxis back-analysis

120

125

130

135

cote

NG

F

exc 123

exc 119.5

exc 115.5

NG

F le

vel

Excav. 123 NGF

Excav. 119.5 NGF

Excav. 115.5 NGF

Plaxis back-analysis

FEM calculations (Plaxis) give a good description of the observed displacements

105

110

115

18/09/02

27/09/02 - exc 123NGF

18/10/02 - mise en tensiontirants 123.5NGF25/11/2002 - exc 119.5NGF

04/02/2003 - exc 115.5NGF

pied de laparoi moulée

Excav. 123 NGF

Anchor 123.5 NGF

Excav. 119.5 NGF

Excav. 115.5 NGF

Bottom of thediaphragm wall

105

110

115

18/09/02

27/09/02 - exc 123NGF

18/10/02 - mise en tensiontirants 123.5NGF25/11/2002 - exc 119.5NGF

04/02/2003 - exc 115.5NGF

pied de laparoi moulée

Excav. 123 NGF

Anchor 123.5 NGF

Excav. 119.5 NGF

Excav. 115.5 NGF

Bottom of thediaphragm wall

110

115

0 5 10 15 20

déplacements (mm)Displacement (mm)

110

115

0 5 10 15 20

déplacements (mm)Displacement (mm)

Excavationlevel (NGF)

Force measuredin the strut

(kN)

Force predictedby SGRM (kN)

Force predictedby FEM

(kN)

129 750 850 640

126 1250 570 1000

123 1400 640 1500

121 1600 670 1900

119 1600 600 2300

116 1900 600 2500

120

125

130

135Différence des pressionsappliquées surla paroi

120

125

130

135Différence des pressions appliquées sur la paroi

RIDO FEM

Strut 133 NGF

Strut 120 NGF

Anchor 128.5 NGF

Anchor 123.5 NGF

Better description of the distribution (and re-distribution) of pressures

110

115

-300 -100 100 300110

115

-300 -100 100 300

Strut 120 NGF

FEM APPROACH

� More and more used by consultants for complex

excavations:

� Complex geometry (for example non symmetric problem)

� Use of struts and/or anchors of various types, stiffness, …

� Presence of other structures close to the excavation� Presence of other structures close to the excavation

� Possible local soil treatment

� Coupled analysis in case of water flow (dewatering, pumping,

…)

� The main concern can be the displacements and not the

failure (urban sites)

� Definition of the geometry

� Definition of the mesh

� Definition of the boundary conditions

� Definition of the initial conditions

� Choice of the soil model

� Simulation of the different phases of excavation

� Illustration on an example

DESIGN OF THE ANCHORS

PA

A

Cδ

Global stabilité – Kranz method

P

F

C

Φ

δ

Efforts on the failure wedge

P active force at the soil – wall interface

PA Rankine active force [Kaγ=tg(π/4−π/2)]

C effort due to cohesion on the failure ligne (= c . BC)

F friction force on the failure line

A anchor force

P

PA

A’

Cδ

W

W

PA

C

F

A’

P

FΦ

P

A’ is the anchor force that would lead to global failure

A’ must be greater than the actual anchor force A required for the wall stability

P active force at the soil – wall interface

PA Rankine active force [Kaγ=tg(π/4−π/2)]

C effort due to cohesion on the failure ligne (= c . BC)

F friction force on the failure line

A anchor force