The Effect of Surcharge Loading Adjacent to Piles, TRL

d

The effect of surcharge loading adjacent to piles

by S M Springman and M D Bolton (Cambridge University)

Contractor Report 196

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TRANSPORT AND ROAD RESEARCH LABORATORY Department of Transport

Contractor Report 196

~


I by S M Springman and M D Bolton (Cambridge University)

Th work reported herein was carried out under a

6""

mtract placed on Cambridge University by the Trans- port and Road Research Laboratoiy. The research customer for this work is Bridges Engineering Division, DTp.

This report, like others in the series, is reproduced with the authors' own text and illustrations. No attempt has been made to prepare a standardised format or style of presentation.

copyright &mller of HMSO 1990. Reproduced by permission of the Controller of HMSO. The views expressed in this publication are not necessarily those of the Department of Transport. The Transport Research Laboratory is no longer an Executive Agency of the Department of Transport as ownership was transferred to a subsidiary of the Transport Research Foundation on 1 st April 1996.

Ground Engineering Division Structures Group Transport and Road Research Laboratory Old Wokingham Road Crowthorne, Berkshire RG11 6AU

1 990

ISSN 0266-7045

CONTENTS

ABSTRACT

SYMBOLS AND ABBREVIATIONS

1 INTRODUCTION

1.1 The problem 1.2 Types of bridge support 1.3 1.4 Loading cases

Structural idealisation for analysis of lateral loading effect

2 SMPLEIED MECHANISM OF BEHAVIOUR

2.1 Introduction 2.2 Pile response 2.3 Lateral pressure exerted on a pile in the soft stratum

2.3.1 Working load case 2.3.2 Ultimate lateral pile capacity 2.3.3 2.3.4 2.3.5

Upper bound mechanism for bearing capacity failure Elasto-plastic interaction diagram for lateral pressure Adjusting the lateral pressure profile 2.3.5.1 Top of soft layer 2.3.5.2 Base of soft layer 2.3.5.3 Pile cap effects 2.3.5.4 Refined lateral pressure profile Net effect of lateral pressure

Interaction effects on pile movement

2.3.6 Behaviour of the pile in the st i f f substratum 2.4.1 Theory 2.4.2

2.5 Deepstifflayer

PILE BENDING MOMENTS AND DEFORMATION PROFILES

2.4

3

3.1 Bending moment 3.2 Deformation 3.3 Comparison with centrifuge model tests

3.3.1 Scaling factors 3.3.2 Working load case 3.3.3 Ultimate load case

4 PILE GROUP ANALYSIS

4.1 Introduction 4.2 Comparison with centrifuge model tests

4.2.1 Working load case 4.2.2 Ultimate load case

1

1 2 2 2

3

3 3 4 4 6 6 7 9 9 10

' . 11 13 13 13 13

17 15

18

18 18 19 19 19 20

21

.2 1 21 22 22

5 DESIGNPROCEDURE

5.1 5.2

5.3 5.4

5.5

5.6 5.7

5.8

5.9

Introduction Foundation characteristics 5.2.1 Clay 5.2.2 Pile geometry Embankment 5.4.1 Equivalent surcharge load 5.4.2 Embankment stability Lateral pressure on a pile in the soft layer 5.5.1 5.5.2 5.5.3 5.5.4 Input for SIMPLE 5.5.5 Behaviour of stiff substratum Results of the analysis 5.7.1 5.7.2 Improving the design Example 5.8.1 5.8.2 5.8.3 5.8.4 5.8.5 Equivalent pile group Other design aspects and concluding remarks

Determination of shear modulus in the stiffer substratum

Preparation of the elasto-plastic interaction diagram Ideal design zone: working load case Plastic failure: ultimate pile pressure

Design charts for free headed piles

Calculation of pile bending moment, rotation and deflection

Problem geometry and foundation properties Working load case: parabolic distribution Ultimate load case: linear distribution Calculation of pile bending moment, rotation and deflection

6 ACKNOWLEDGEMENTS

7 REFERFiNW

23

23 ~

24 24 1

i 25 26 26 26 26 27 27 28 28 29 29 31 31 31 33 33 34 34 35 35 38 39

39

40

1 1 1

~

~

~

~

,

,

APPENDIX 1: DETERMINATION OF SHEAR MODULUS IN THE STIFFER SUBSTRATUM

42 42 42 43 44

A.1 Introduction A.2 A.3 Laboratory determination A.4 Self boring pressuremeter A S Empirical considerations

Choice of shear modulus profile

TABLES

FIG=

@ CROWN COPYRIGHT 1990 Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.

I The Gect of surcharge loading adjacent to piles

S.M. Springman & M.D. Bolton

ABSTRArn.

The objective of this report is to present an approach to designing pile foundations, embedded at I

I

I

depth in a stiff substratum and influenced by adjacent loads applied on the surface of soft

superficial soils. The effect of lateral thrust on the piles in an upper soft clay layer due to

simulated embankment construction is examined, and soil-pile interaction mechanisms are

identified herein for behaviour both at working load and at ultimate lateral capacity.

I I

l -

I A combination of cenmfuge model testing and three dimensional finite element analysis was used

to investigate the performance of a row of free headed piles and of a pile group, for different pile

and foundation geometries, in terms of changes of bending moment, deflection and lateral

pressure due to a uniform surcharge. An approximate formula for lateral thrust in the soft clay

layer is developed, based on the differential movement between the piles and the surroundin,o

soil, which accounts for pile spacing, relative pile-soil stiffness and the degree of soil strength

mobilisation. This loading function has been incorporated in a computer program, SIMPLE,

which calculates the pile bending moment and deflection profiles for long piles and pile groups.

The algorithm has been calibrated against the experimental and numerical results, and design

charts are produced for the free headed pile case.

A design procedure is recommended, and illustrated by a worked example, for piled full-height

bridge abutments and other facilities which feature passive lateral loading of piles by a nearby

surcharge.

Keywords: piles, surcharge loading, lateral thrust, bridge abutment, soil-pile interaction, soft clay

SYMBOLS AND ABBREVIATIONS

English

'mob C

U

'U0

d

E

EP e

P F

G

GC

Gm

GO

Gm

Gr G*

PO9295 G

H

Hh

HPC

HS

h

he

hS

hU

I

k

e

: mobilised value of undrained shear strength

: undrained shear strength

: undrained shear strength at surface of clay layer, y = 0 I I

I : external pile diameter ~

I

I 1 : Young's Modulus of pile material

: equivalent Young's Modulus of pile

: freestanding length of pile above mudline

: ratio of lateral pressure acting on front and rear piles in a group

: shear modulus at depth, y

: characteristic shear modulus of stiff layer where, G,= f (Go, m, v, e,) : shear modulus at y = N2

: shear modulus at top of stiff layer

: shear modulus at top of clay layer

: shear modulus via self boring pressuremeter tests at 0, 2, 5% volumemc strain

: reduced shear modulus in the annulus around the pile

: shear modulus adapted to account for Poisson's ratio, G( 1 + 3/4v)

: total shear force distribution in pile

: shear force at y = h

: additional shear force applied to pile at pile cap level

: shear force in pile at top of stiff layer

: depth of lateral pressure applied to pile in the soft layer

: height of embankment

: depth of soft layer

: unloaded length of pile in soft layer, hU = hs - h

: second moment of area of a single pile, diameter d

: stiffness

: length of pile in stiffer substratum

eC

M

Mh

MP

MS

m

n P

"r OCR

P

P'

Pa

P C

Pci

Pf

Pm, Pm'

Pr

P U PI

q

9c qmax r

S

sX

U

U'

U. 1

0 U

critical length of pile in stiffer substratum for lateral loading, $= f (G,, r, EP)

equivalent length of unsupported pile below soft-stiff interface, le = f (t,, p,)

bending moment distribution

bending moment at y = h

plastic pile bending moment

bending moment at top of stiff layer

gradient of shear modulus with depth, m = dG/dy

number of piles

number of rows of piles

overconsolidation ratio

net lateral pressure acting on pile

mean effective smss

atmospheric pressure

characteristic lateral pressure acting on a pile

component of lateral pressure due to the i'th load

lateral pressure on the front pile in a group

average and maximum (parabolic) values of applied lateral pressure

lateral pressure on the rear pile in a group

ultimate lateral pile pressure

plasticity index

equivalent vertical uniform load for embankment simulation

measured cone resistance

maximum simulated embankment load

external radius of pile

pile spacing

spacing between front and rear rows of piles

lateral deflection

corrected value of U after pile group interaction effects accounted for

component i, of deflection

deflection at ground surface, y = 0

PC U

S U

X

Y

zP Z

Greek

a. - 9

ao' "s

"UH

aX8H

"0M

%f

P C

"m

P 6U

6uS

: deflection at pile cap level

: deflection at the top of the stiff layer

: coordinate defining longitudinal horizontal geometry

: depth measured vertically downwards from top surface of the soil

: plastic section modulus of pile

: coordinate defining transverse horizontal geometry

: pile group interaction factors between i'th and j'th piles

: adhesion factors along soil boundaries

: pile group interaction factor for increase in deflection due to

neighbouring piles for a free headed pile under lateral load


neighbouring piles for a free headed pile under moment loading

: pile group interaction factor for increase in rotation due to

neighbouring piles for a free headed pile under lateral load

: pile group interaction factor for increase in rotation due to

neighbouring piles for a free headed pile under moment loading


neighbouring piles for a fixed headed pile due to lateral load

: load description factor

: vertical stress increment at any appropriate depth

: additional pile rotation in soft layer due to integration of bending moment

: additional pile rotation in 'unloaded' section of soft layer due to integration of M

: additional pile displacement in soft layer due to double integration of M

: additional pile displacement in 'unloaded' section of soft layer due to double

integration of bending moment

: additional pile displacement in soft layer due to rigid body rotation at the y = hs

: lateral pile displacement

: lateral soil displacement at centreline of piles with no pile present

f

h

i, j

m, M

max

min

0

P

PC

r

S

U

e

angle of departure of pile loading from orientation to neighbouring pile

shear strain

bulk unit weight of embankment

Poisson's ratio

rotation profile

corrected value of 8 after pile group interaction effects accounted for

rotation of pile due to component i, of the loading in the soft layer

rotation of pile at ground surface, y = 0

rotation of pile at pile cap level

rotation of pile at the top of the stiff layer

factor relating homogeneity of stiffer substratum shear modulus

total and effective horizontal stress

total and effective vertical stress

maximum past effective vertical stress

yield strength of pile material

(applicable when abbreviations have not been defined elsewhere)

front

value at depth y = h or factor due to shear force

i'th or j'th variables

factor due to bending moment

maximum

minimum

a ty=O

pile

at pile cap

rear

soil or interface between soft and stiff layer

unloaded section of pile at base of clay layer or factor due to deflection

. factor due to rotation

The effect of surcharge loading adjacent to piles page: 1

1 INTRODUCIION

The construction of approach embankments to bridges on compressible subsoil can induce lateral

loading on the piled foundations, which causes bending and shear in the piles together with

rotations and translations of the abutments. This problem is compounded where the piles pass

through a soft layer and are founded within a stiffer substratum. At present, the approaches to the

design of piled abutments under these conditions are largely empirical (De Beer 8c Wallays, 1972;

Frank, 1981) and there is a need for a straightforward design procedure based on a fundamental

understanding of soil-pile interaction.

A programme of research on this topic comprising centrifuge model tests and numerical analyses

has been carried out by the Engineering Department of Cambridge University for the Transport

and Road Research Laboratory. Centrifuge model tests were conducted on both a single row of

free headed piles and a pile group, which were pre-driven through a soft layer of clay into a

stiffer substratum and loaded by lateral thrust due to an adjacent surcharge. Finite element

analyses of the model configuration were also carried out and the results verified by the

experimental data. The findings from the research are fully described by Springman (1989).

This report recommends a design approach for full-height piled abutments, based on these

studies. Both ultimate and working load conditions are considered. The form of the soil-pile

interaction is described briefly, leading to an introduction to an interactive computer program,

SIMPLE, which calculates pile bending moments and deflections for a single free headed pile and

a simple pile group. Alternative design charts are also given for the single pile case.

I

1.1 The m b l e m

Generally, the piles are installed before the embankment loading is applied. In consequence, the

soft soil deforms further than the piles, causing passive lateral thrust on them, which is resisted by

the lower section of pile embedded in the stiff substratum. The magnitude of this thrust is largely

dependent upon the differential soil-pile displacements and the stiffness of the soft soil.

The eflect of surcharge loading adjacent to piles page: 2 I

1.2 Tvpes of bridge suDprt

The analyses were designed to model the performance of a piled full-height bridge abutment.

Three different configurations were considered:

i)

ii)

iii)

single row of piles (Fig: 1. la)

full-height abutment wall founded on two rows of vemcal piles in a group (Fig: 1.1 b)

full-height abutment wall founded on a raked pile group (Fig: 1. lc).

1.3 Structural idealisation for analvsis of lateral loadin~ effect

These were simplified in plane idealisations as follows: ~

i)

ii)

a row of free headed piles (Fig: 1.2a),

two rows of vertical piles, fully fixed into a rigid pile cap, which is free to displace

I

I

horizontally with zero rotation and equal deflection of each pile at the cap (Fig: 1.2b),

two rows of vertical piles, fully fixed into a rigid pile cap, which is not permitted

either to move horizontally or rotate at pile cap level (Fig: 1.2~).

iii)

I

In all cases the embankment was replaced by an equivalent normal load, to simplify the analysis.

In cases (ii) and (iii), the lateral thrust of the embankment can be carried by the abutment wall, so

there need be no shear stress applied to the surface of the soft clay. In case (i) there would be

additional outward shear stress at the junction of the fill and the clay, which would tend to cause

additional soil displacements unless the embankment were reinforced (Jewell, 1987). The raking

pile was represented by a vertical one because the rake was not expected to alter the soil

displacement field signrficantly, so the lateral thrust/unit depth of soft clay would be the same.

1.4 Loadinpcases

It is considered an advantage to be able to analyse soil constructions either at collapse under

extraordinary load conditions with the development of ultimate soil strengths, or in operation

under projected design loadings, mobilising permissible deformations and stresses. These two

cases are therefore considered explicitly below, so that the engineer can not only predict pile

bending moments and soil and structural displacements from an interaction analysis, but can also

form a judgement on the margin of safety against complete shear failure in the soft clay.

I

I


2 SIMPLIFIEDMECHANI SM OF BEHAVIOUR I

I 2.1 Introduction I I

Design guidelines are set out which allow prediction of the bending moments and deflections of

piles subjected to passive lateral loading by soil. Initially, a single vertical pile is considered,

driven through a soft layer of soil and embedded in a stiffer substratum so that the essentials of

soil-pile interaction can be appreciated.

I Vertical loading on the abutment structure is not dealt with. This is consistent with most analyses

of pile behaviour, which treat the lateral and axial loading cases for a vertical pile separately, and

superimpose the results to give the complete picture. This approach was followed here and so it

was only necessary to predict lateral deformations in response to vertical soil loading.

2.2 Pile respo nse

When a soft soil foundation is surcharged by an embankment, noticeable horizontal displacements

are observed under the edge of the load. If there are any piles in the vicinity, these will also tend

to deflect horizontally, but less than the soil, causing a lateral thrust to be applied to them. From

a prediction of these lateral pressures, the designer will evaluate the magnitude of the pile

bending moments and deflections.

The pile response is considered, initially, in two complementary parts:

i) The upper section (AB in Fig: 2.la) of the pile in the soft soil is

assumed to cantilever out of the soft-stiff soil interface at depth

y = hs, while receiving horizontal thrust from the clay, which

has a greater lateral deformation than the pile,

The lower section (BC in Fig: 2.la) of the pile embedded in the

stiff substratum resists the lateral loading from the upper layer

and deflects further than the surrounding soil.

ii)


Where there is no sharp and obvious demarcation between "soft" and "stiff' strata, the initial

decision on the location of an interface will be somewhat arbitrary. The intention is that any soil

which comes to plastic failure due either to embankment loading or pile displacement should be

treated as in the upper "soft" layer, so that the lower "stiff' layer can be treated as a quasi-lastic

material described solely in terms of its shear modulus profile. Essentially, the method set out

below treats the upper layer as a loading system which generates pile bending moments and shear

forces at the soft-stiff interface, below which the piles can be analysed by conventional methods.

page: 4

2.3 Lateral pressure exerted on a pile in the soft stratum

2.3.1 Working load case

Springman (1989) describes a method by which the lateral pressure acting on the pile in the soft

layer may be predicted for undrained conditions. In this, the soil displacement field &us

(Fig: 2.lb) is represented by a simplified geo-structural mechanism in which boundaries are rigid

and frictionless and the soil is isotropic and homogeneous with constant shear strain .y. Pile

deflection 6u (Fig: 2 .1~) and 6us are calculated and compared and the thrust on the pile, with

diameter d, is taken to be proportional to the relative soil-pile displacement (Fig: 2.ld) multiplied

by the local shear modulus G (Baguelin er al, 1977; Fleming et al, 1985). For the pseudo-lastic

working load case under plane strain Conditions, the pressure on the pile at any depth is then

given by (see Fig: 2.le):

P

p = 5.33G(6us - 6Up)/d

Assume, initially that the pressure profile is constant, p, over some depth h, and that h is equal

to the total depth of soft layer hs (Fig: 2.10. For a surcharge load q, pile spacing s, pile bending

rigidity EI, this mean pressure will be, (following Bolton, Springman & Sun, 1990):

9 +0.71G dh3 -1 E1

The efect of surcharge loading adjacent to piles page: 5 I

where allowance has been made for the increased shear strain in the region around the pile where

the secant shear modulus Gr, will be lower than that for the remainder of the soft layer Gm, with

both values taken at the mid-depth of the loaded section, y = h/2. The first term in the

denominator may be thought of as representing relative soil stiffness, the second covers the

pile-soil spacing and the third refers to pile-soil bending rigidity.

I

The shear modulus chosen for the area close to the pile is subject to two effects. The action of

pile driving causes displacement of the surrounding soil, locally increased pore pressures and

subsequent consolidation resulting in an increase in undrained shear strength. Randolph, Carter &

Wroth (1979) predict this to be in excess of 33% for an annulus of 1 pile radius (1 I OCR I 32)

based on the modified Cam Clay constitutive model. On the other hand, larger shear strains are

then induced in the annulus up to 1 pile diameter wide around the pile. Both X-ray photographs

(Fig: 2.2) and results from finite element analyses confirm this finding. In a typical analysis, the

shear strains were up to 5 times greater in this annulus when the soil was taken to be linear

elastic. An even greater disparity in strains would have been observed if the soil had been

represented as elasto-plastic. Therefore, the secant shear modulus chosen to represent the

stiffness of the clay in this region will be lower. These two effects will offset each other to some

extent but each case should be examined carefully. Values for Gm/Gr may be taken to lie

between 1.5 and 2 for driven piles and around 2.5 to 3 for bored piles (Springman, 1989).

The G d G r term in the denominator of Eqn: 2.1 is typically that which has the greatest effect on

p, for piles which are rigid with respect to the clay. Therefore, allowance for a zone of reduced

modulus will also have a noticeable impact on p,.

An alternative design approach is to replace the soil around the pile by an annulus of bentonite

mixed with cement. This is described by hlsfort (1989) as the buttonhole method. Clearly, the

ultimate lateral pressure on the pile will be markedly reduced, provided that the lateral

displacement of the soft cement-bentonite mixture around the pile does not bring the natural soil

foundation into contact with the pile.


2.32 Ultimate lateral pile capacity

The ultimate lateral pile pressure should be considered since this defines the absolute upper

bound to the pile bending moments and deflections. As the surcharge loading increases with

construction of the embankment, so will the lateral pressures approach the level at which yielding

commences around the pile (p -2xcu, Springman, 1989), when it is no longer adequate to

describe the foundation behaviour as pseudo-elastic. The plastic domain extends upwards and

downwards from that critical depth as more embankment loading is applied. During this

development, elastic analysis becomes increasingly invalid.

I

At even greater surcharges, the soil will move plastically past the pile over the entire depth of the 1 I

I soft layer, and the pile will receive the maximum possible lateral thrust. If the pile is capable of

sustaining such moments and shear forces, it will be invulnerable to any possible superimposed

surcharge. I

Randolph & Houlsby (1984) calculated the limiting load on cylindrical piles of differing

roughness, moving through an infinite medium of homogeneous, perfectly plastic soil, using

classical plasticity theory. At an intermediate roughness, the ultimate pressure agrees well with

that quoted by Broms (1964) and Poulos & Davis (1980):

pu = 1 0 . 5 ~ ~ (2.2)

i 2.33 Upper bound mechanism for bearing capacity failure

Considering the maximum embankment load qmax, required to create a bearing capacity failure, ~

an upper bound calculation was made for a local undrained failure of a soil foundation with

uniform cu, which allowed for some reinforcement by the piles due to the energy dissipated by

the soil shearing past the pile. Fig: 2.3a shows the active and passive zones marked by two 45'

isosceles mangles, with a radial fan in between. For conservation of energy per unit width, with

p/cU = 10.5:

I I


= (2 + x)cU + 1 0 . 5 ~ ~ d - S qmax

2 ( 2 + x ) c u ( l + - ) 2d S qmax

page: 7

(2.3)

For bearing capacity failure of the embankment with .no piles present, then p/cu = 0 and

q/cu = (2 + x) . The line joining these two points may be thought of as the maximum bearing

capacity of the embankment-pile-foundation system and is given by:

Q = (2 + x ) +- d P

cU cu (2.4)

2.3.4 Elasto-plastic interaction diagram for lateral pressure

Fig: 2.4a, with ordinate pm/cu and abscissa q/cu displays the whole elasto-plastic interaction

between mean lateral pressure pm and surcharge q. The elastic loading behaviour described by

Eqn: 2.1 is shown for h/d values of approximately 4 and 10. As the line for low values of h/d

approaches the intersection with Eqn: 2.4, the soil foundation begins to yield prior to bearing

capacity failure. As displacements increase, further loading will induce fully plastic pressures on

the piles. For larger values of Wd, as the embankment load is increased, the soil tends to yield

around the pile before general yield of the soil mass. This local yielding has no major drawbacks

as far as safety and serviceability of the facility is concerned, it merely marks the onset of

non-linearity of the soil-pile interaction. Completely plastic flow around the pile occurs when

= 1 0 . 5 ~ ~ (Eqn: 2.2) when the maximum embankment load, qmax (Eqn: 2.3) has been reached. Pm In every case, the loading line will eventually progress towards this intersection at F, when there

will be ultimate plastic failure of the soil mass and the soil around the pile.

It is difficult to quantify the effect of the curved loading line as it veers towards point F'in

Fig: 2.4% at which the lateral pressure reaches 1 0 . 5 ~ ~ over the entire depth of the soft stratum. In

I some cases, the whole of the soft layer would not be involved in an embankment collapse, and it I

I will be appropriate to restrict the effective depth of lateral loading on the pile (Fig: 2.lg).

The efect of surcharge loading adjacent to piles page: 8

In general, the design values of pm/cu, q/cu describing the loading system should be prevented

from approaching too closely to the boundaries of the plastic zone, in view of the excessive

deformations that would then result. The pre-requisite for any serviceability calculation is to

restrict the state of the soft clay foundation, and hence the lateral pressures imposed on the pile,

to a pseudo-elastic region. The limit to Eqn: 2.1 may be thought of as a serviceable bearing line

at which the maximum bearing capacity defined by Eqn: 2.4 is factored by 1.5 (Fig: 2.4a). This

will imply that the mobilised shear strength cmodcu = 0.67, which from Fig: 2.3b for kaolin

suggests that the shear strain wil l be between 1 - 3 % for a range of overconsolidation ratios.

Since the shear strain can be shown to be 26us/hs (Fig: 2.lb), for hs = 6 m, the vertical and

horizontal displacements are then expected to lie between 30 - 90 mm.

Figs: 2.4b & c show the elasto-plastic interaction plot for pm/cu and q/cu together with the

experimental data derived for specific surcharge loads between q = 53 to 189 kPa for model test

SMS7 conducted in the centrifuge. Two interpretations of the data are shown. Initially, @e value

assumed to represent the strength of the soil while loading was applied, cu, was taken as the best

fit to the data obtained from vane shear testing outside the area of influence of the surcharge.

The values of pm and q were divided by this initial cu. From Fig: 2.4b, this implies that both the

bearing capacity criterion and the ultimate pile pressure were exceeded. However, the effective

stress had increased under the surcharge load as testing progressed, due to the observed

dissipation of pore pressure, during an equivalent test period of 1.1 years. In conjunction, soil

strength must have increased throughout the test, and so revised values of pm/cu and q/cu have

been suggested based on an expression relating cu, 0; max and OCR, and are plotted in Fig: 2 .4~.

Skempton (1957) quoted a relationship cu/ov' = 0.11 + 0.37PI for normally consolidated clays,

where PI (as a ratio) is the plasticity index. The application of this correction would have led to a

,

similar improvement in matching the data to theory.

The ultimate pressure on the piles was not reached, and this was borne out by inspection of the

X-rays (Fig: 2.2) which showed soil bulging between rather than shearing past the piles. This

The efect of surcharge loading djacent to piles page: 9

meant that the fully plastic point F was not reached. Observation of test SMS7 suggested a small

reserve of safety against complete soil collapse.

2-35 Adjusting the lateral pressure p f d e

Remembering that lateral pressure is a linear function of both shear modulus and differential

soil-pile displacement, the initial assumption that the lateral pressure, p,, is constant with depth

(Fig: 2.5a) is clearly unreasonable for many cases. Adaptations may be made for several reasons:

i)

ii)

lower soil stiffness at the top of the soft layer,

in a deep soft layer, the pile may displace further than the soil below

some level, restricting the effective depth of lateral loading,

restraint on the soil from the pile cap will tend to reduce relative

soil-pile displacement at the top of the soft layer.

iii)

Data obtained from centrifuge model tests and the results of finite element computations, have

indicated that the lateral pressure profde is approximately parabolic. Comparisons sugsest that

while the average value of pressure may be taken as p, from Eqn: 2.1, the shape of the pressure

profile should be adjusted as follows (Fig: 2.5).

235.1 Top of sofr @er

Since the lateral pressure acting on the pile is proportional to the product of differential pile-soil

displacement and the soil stiffness, a reduction in either of these values will likewise induce

lower lateral pressures. For a free headed pile, some differential displacement would be expected

at ground level and so the lateral pressure should be reduced simply by the ratio Goc/Gm, where

G, is the shear modulus at this horizon (Fig: 2.5d). However, both the model tests and the finite

element analyses suggest that the lateral pressure at the surface is even smaller, possibly due to

the freedom of the soil to squeeze upwards rather than around the pile at the ground surface. For

pile p u p s with a pile cap in contact with the ground surface, which is free to move at ground

level (Fig: 1.2b), differential displacement could be prevented by friction on the underside of the

pile cap, and in this case, the pressure would then be reduced to zero (Fig: 2.5b).


2356 Base of soft @er

Where the lateral extent of the embankment is less than the depth of the soft layer, it may be too

conservative to assume that the increment in vertical stress is constant with depth. Elastic stress

dismbutions (Poulos & Davis, 1974) may be used to derive a reduced value of pm by replacing q

with AoV at the mid-depth of the layer before substitution.into Eqn: 2.1.

In any event, forces and moments on the pile at the interface between soft and stiff layers will

tend to drag the pile forwards through the stiffer soil. Since the soft soil of depth h, will tend to

be prevented from moving by friction at the soft-stiff interface, there will be some zone of depth

hU at the base of the soft layer within which the pile displaces forwards relative to the soil, and

within which the pile can conservatively be treated as unloaded (Fig: 2.5b). An iterative

approach which allows for a reduction in the lateral pressure is described.

Consider the section of pile below y = hs. Select an equivalent length of pile, le, (Fig: 2.6~)

which can be treated as unsupported by the soil in the stiffer substratum. This encastre beam

must give approximately the same value of rotation and deflection at y = hs under moment and

force loading as the "long" pile which would be supported by the stiffer soil (Fig: 2.6b) over the

critical length for lateral loading, tC (Fig: 2.6a) (Randolph, 1981). It can be shown that

1, = 0.341/(,/pc) where pc and lC are fully defined in Section 2.4. Thus for constant shear

modulus with depth in the stiffer substratum, (p, = l.O), le z O.34lc; while for shear modulus

increasing linearly with depth from zero (pc = 0.5), le N 0.5tc.

By equating expressions for pile deflection and soil displacement in the soft layer at a depth of

y = h = hs - hU, the following relation can be derived in terms of hu and hs:

d d

The effect of surcharge loading aa'jacent to piles page: 11

where Gm is taken as the shear modulus at mid-depth, y = W2. This is charted for specific

values of the non-dimensional groups s/d, E /G , hdd, c$d in Figs: 2.7a, b & c to give values of

hJhs , obviating the need for iteration. P m

I

Double differentiation of pile bending moments obtained from centrifuge model tests for a 6 m

I

t

depth of soft clay and with s/d = 3.15, E d G, 2 28000 (Fig: 2.7d) show that hU increases from

0.2 to 1 m as surcharge load increases. Calculations yield h id = 6/1.27 = 4.724,

le/d = (0.34 x 8.4)/(&.523 x 1.27) = 3.11, which from Fig: 2.7a give hu/hs = 0.16 so that hU 2 1

m, which agrees quite well with the experimental data. I

I

If hu/hs e 0.2 then the additional work entailed in refining the calculation for a new value of h is

not justified by the cost savings that would result from a more tailored design and h should be I I

I taken as equal to h,. However if hu/hs > 0.2 then pm should be re-calculated for the new value

of h and the value of G, adjusted likewise. I

2353 Pile cap e$ects

For undrained, constant volume behaviour of the soft layer, and a pile cap which is resting on the

soil, then the pressure on both front and rear rows of piles may be assumed to be identical

because the same volume of soil will flow past the rear piles as the front piles.

The elasto-plastic interaction diagram should be adapted to give an increased bearing capacity of

the foundation. At failure (Fig: 2.8a) Eqn: 2.3 becomes: I

= cu(2 + x + 10.5 nr d ;) + E 'x (ao + as)cu qmax

where sx is the spacing between the front and rear rows of piles, nr is the number of rows of piles

and cu is assumed to be constant with depth while the factors a. and as define the pile cap-soft


soil and soft-stiff soil adhesion. For the limit to the

1.5 as before to give an effective Cmob = 0 . 6 7 ~ ~ .

The procedure detailed in section 2.3.1 is followec

iesign zone, the 1

page: 12

dues of cu are factored by

in detennining tile lateral pressure profile,

with the following adjustment to the equation defining p, (Eqn: 2.1) according to the pile ,group

configuration and the fixity condition at the pile cap. For a lateral deflection at pile cap level

Pm =

equal to half that of an equivalent free headed pile under identical loading conditions:

(2.7a) 4

1 3Gmd(4h + sXX) n,d + 0.1354Gmdh2 (4h + sxX) +- 4G,h2 S E1

where X = (nr- l)(ao + as). For zero lateral deflection at pile cap level:

9 3Gmd( 4h + s,X) n,d 0.0104Grndh2 (4h + s,X) +-+ ” = [ 4G,h2 S E1

(2.7b)

Both cases assume p, constant with depth, zero rotation and full fixity at tlle pile cap. If t1e

spacing between the rows of piles is less than 3d, then take nr = 1 because it is less likely that

full resistance has been developed at the soil-pile cap interface. These equations also assume

that there is friction along the interface between the soft and stiff layers between the rows of piles

and also between the pile cap and the soft soil. A total pile cap shear load of aocusxs should be

applied per double row of piles, (i.e. for nr = 2, additional shear load = aocusxs for each set of

one front row and one rear row pile) together with the shear load imposed by the lateral earth

pressure on the retaining wall. These loads, together with p, calculated from Eqn: 2.7, can be

used to design adequately reinforced sections. Note that the shear force on the piles due to the

pile cap should ideally have been permitted to increase the bending deflection of the pile

represented as the third term in the denominator of Eqn: 2.7. Neglect of these additional

deflections leads to a small, safe, over-prediction of p,, so iteration is usually not necessary.

I The eflect of surcharge loading djacent to piles page: 13

I 2.3 5.4 Refined lateral pressure profile

I The lateral pressure may be adjusted by reducing the rectangular profile as follows (Fig: 2.5b): ~

0

ii)

reduce the value of lateral pressure at the top of the soft layer (section 2.3J.I),

reduce to zero the value of lateral pressure at the depth of either the base of the

I

I

layer if hu 2 0 or at y = h, (section 2.352),

plot a new value of pm, pm' = 1 . 5 ~ ~ at the mid-depth of loading, y = h/2 and draw a

parabola through these three points.

I

I

iii)

For example, for the centrifuge test with s/d = 3.15, d = 1.27 m, h = 6 m, E1 = 5.13 106 him2,

= 1400 kPa, G,/G, = 1.8, Eqn: 2.1 gives p,/q = 0.66. Assuming that there is no differential Gm displacement between pile and soil at ground level, and calculating that hu/hs 2 0.16 c 0.2, the

pressure may be reduced to zero at ground level and at the soft-stiff interface while pressure at

the mid-depth is increased by 1.5 to pm'/q = 0.99. The adapted profile is shown in Fig: 2.8b and

this will be compared with the appropriate centrifuge model test results in section 3.3. I I

2.3.6 Net effect of lateral pressure

I Once the profile of the lateral pressure acting on the pile has been determined, the net effect on

the pile section in the sti f fer substratum may be calculated. By integrating the lateral pressure to

I give the shear forces, which are in turn integrated to yield the moment diagram for the upper I

section of the pile, the net bending moment Ms, and shear force Hs, which will be applied to the

lower section of pile at the soft-stiff interface, may be determined.

2.4 Behaviour of the &le in the stiff substratum i 1. I 2.4.1 Theay ~

The Randolph (1981) solutions for the deflection and rotation at the head of a pile, and pile

bending moment and deflection due to either a head force or moment loading, are used to predict

the behaviour of the lower section of the pile in the stiffer substratum, where the pile length is

greater than the critical length, tc over which lateral loading effects are relevant.

1

~

~

I

I

I I I

The effect of surcharge loading adjacent to piles page: I4

Several parameters are defined, based on the shear modulus of the stiff layer, which was taken as ~

Go at the top (y = hs), increasing by m per metre with depth. Thus for y > hs: I

I and the shear modulus is then adjusted to include the effects of Poisson's ratio so that:

G*= G (1 + 3 ~ / 4 ) 0

and so a characteristic shear modulus is described as (Fig: 2.6b):

(2.9)

(2.10) . ~

and a soil homogeneity factor, which lies between 0.5 and 1, as: I

The critical slenderness ratio of the pile is determined from:

(2.1 1)

After iteration between Eqns: 2.10 & 2.12 to obtain consistent values of Gc and tC, values of us

and 8, can be determined at the soft-stiff interface, y = hs, of the soil, from the relations:

(E G )1'7 U = &b.27H S (.$/2)l+ 0.3Ms(!J2)7]

pc c


The first of these equations has been incorporated into curves which showed non-dimensionalised

deflection (Figs: 2.9a & 2.10a) versus depth, normalised by the critical pile length, for either a

lateral force Hs, or a moment Ms, acting at the top of the stiff substratum, y = h,, and for

different values of soil homogeneity pc = 0.5, 0.75, 1.0 (Randolph, 1981). Figs: 2.9b & 2.10b

give corresponding distributions for determining bending moments.

This approach gives a simple elastic solution for the behaviour of the pile in the suffer

substratum, which is sufficiently accurate for the majority of engineering problems where soil

working stresses are much lower than the ultimate load condition and an appropriate secant

modulus can be selected. The main source of emor lies in allotting values to Go, m and v.

However, the bending moment prome is far more sensitive to changes in the choice of lateral

loading in the soft layer, and hence the values of Hs and Ms at the top of this stiffer layer, than to

variations in the shear modulus for the lower layer.

2.4.2 Interaction effects on pile movement

The interaction between adjacent piles, either as a row of free headed piles or as a pile group will

have a cumulative effect on deformation and rotation and this should be added to results obtained

from the algorithm. Poulos (1971) pioneered the use of appropriate factors, and m t e the

expression for deflection within a group of n piles: P

(2.15)

where a was the interaction between the i'th and j'th piles, k was the stiffness of a single isolated

pile, and H was the lateral load. Thus, interaction factors were defined depending on the spacing,

angle and type of loading, and pile head fixity (Fig: 2.1 1).

In this case, the factors will be applied to the section of pile in the stiff layer, which will behave

as a free headed pile subjected to a lateral head load H, or moment M. The factors are auH and

auM for deflection and aeH and aXBM for rotation.


Randolph (1981) conducted finite element analyses on laterally loaded fixed headed piles, which I

were prevented from rotating, and concluded that auf was the only relevant factor and could be '

approximated by:

ad = 0.6pc@dGc)1'7(r/s)( 1 + cos2@

unless ad exceeded 0.33 at close pile spacings, when the value was replaced by:

I

auf = 1 - 2/(27a,)1'2

(2.16)

(2.17)

Poulos (1971) proposed that interaction factors for fixed headed piles were larger than for free

headed piles. Randolph (1983) suggested that for free headed piles, 0.6 should be replaced by 0.4

in Eqn: 2.16:

~ U H = 0.4pc@dGc)1'7(r/s)( 1 + cos2q) ' (2.18)

For axuH > 0.33, Eqn: 2.17 was adopted with the subscript 'uf replaced by 'U". The other ~

interaction factors were considerably smaller than auH and were taken as (Randolph, 1983): I

auM = aeH N auH 2

aOM N aUH3

I

Thus, the individual values of the interaction factors are deterrnined for each pile in relation to its 1 neighbours, and summed to give the total effect on the pile displacements. For plane strain cases

in which load, H and stiffness, k are also nominally equal, the deflections can simply be factored ~

up to account for the interaction between the group or row of piles. I

I

I

~

The eflect of surcharge loading adjacent to piles page: 17

2.5 Deep stifflaver

There will be some situations for which it is difficult to define the interface between a notional

soft layer and a stiff substratum. For deep deposits of London Clay, with shear strength

increasing with depth, passive thrust will be experienced by the piles when a surcharge load is

placed adjacent to them. However, the stiffer nature of this clay will mean that there is less

relative displacement between the soil and the pile. The point at which the soil ceases to apply

passive thrust to the pile will occur when the pile and soil displacements are equal and this would

be shallower than might be expected for a softer clay.

Under these conditions, the suggested approach is to select an arbitrary value of hs and then

calculate values of pc, Gc, tc and le for the stiff clay from below this depth. Using Figs: 2.7,

calculate the ratio hJhs and hence h = hs - hU. If hubs is greater than 0.2, set the next estimate

of hs = h, and repeat the calculation until hJhs is less than 0.2 then make the final adjustment to

hs and define the soft-stiff interface at this depth. The remainder of the analysis follows the

same format as described above. Although there is no experimental data to support this approach,

it will provide some guidance. Clearly, for such s t i f f layers it will be unlikely that the ultimate

lateral load will be reached for typical embankment heights.

The effect of surcharge loading adjacent to piles page: I8

3 PILE BENDING MOMENTS AND DEFORMATION PROFILES

3.2 Deformation

3.1 Bendinv moment

The bending moment profile can now be determined for both sections of the pile (Fig: 3.la). For

the lower section in the stiff substratum, values obtained from Figs: 2.9b & 2.10b will be

superimposed and summed for the appropriate 'head load, Hs, and moment, Ms at y = hs. For

the upper section in the soft layer, double integration of the lateral pressure profile acting on the

pile diameter will complete the bending moment diagram for the pile.

0 I I

dem=( M/EIdy hS 0

Aum = (( M/EI dy dy hS

(3.1) i

(3.2)

Thus at the top of the pile, the critical design values of deflection and rotation are obtained from: I

eo = e, + Aem (3.3) I I

= U +Au +Aum (3.4) ~

~

uo s e

The maximum bending moment will occur at 1-3 pile diameters below the interface between the

The egect of surcharge loading adjacent to piles page: 19

soft and stiff layers. This value may be obtained by summation of the separate components of

bending moment due to head load (Fig: 2.9b) and moment (Fig: 2.10b) at the interface.

The original calculation.of the effect of the pile displacement on the mean lateral pressure, p,

was based on the conservative assumption that us and 8, were zero. This section has shown how

to use pm to calculate a safe estimate of pile displacement, taking us and 8, into account. It was

found to be unnecessary to iterate on the initial value of pm.

3.3 Comparison with centrifuge model tests

The results of the centrifuge model tests were compared against predictions obtained from this

analysis for .both working and ultimate load cases. The general arrangement for test SMS7 is

given in Fig: 3.2 for a row of five free headed piles at a spacing/diameter ratio of 3.15. The

instrumentation and site investigation details are also shown. The upper section of the clay layer

was slightly overconsolidated with an initial cu at ground surface of about 10 kPa. Loading was

applied over a period of 1.1 years, which included some loading at reasonably short intervals

interspersed with longer periods to allow for consolidation.

3.3.1 Scaling factors

Scaling factors should be applied to the experimental data shown in the figures to convert the

values to prototype equivalent:

Bending moment

Lateral pressure

Deflection

Scale factor

1003

1

100

3.32 working load case

Consider the bending moments, lateral pressure and deflections derived from the pile strain gauge


data for surcharge loads q = 53, 72 & 93 kPa (Figs: 3.3a4). The predicted values of pm were

calculated to give a corrected value of pm'/q = 0.99 reducing to zero at the ground surface and 3t ~

the soft-stiff interface. These pressure distributions were input into the analysis and the bending

moment and deflection profiles were deduced. Interaction effects on pile deflection between

adjacent piles were added, as described in section 2.4.2. In each case the predicted pressure and

bending moments overestimated the values derived from experimental data. However the general

form of agreement was good, with the exception of the pile deflection where pile tip rotations had

increased these beyond predicted values.

page: 20 ~

I

3.3.3 Ultimate load case

Similarly, calculation of the ultimate pressure of 1 0 . 5 ~ ~ has given the maximum pressure exerted

on the pile. The choice of a value of cu will depend on the judgement of the engineer. Two

factors are relevant. Firstly the method of pile installation will affect the soil strength in the

annulus around the pile before the embanlanent load is applied. Thereafter, the undrained shear

strength will increase with time as drainage occurs and effective stresses become greater. An

estimate of this value prior to the application of the last loading step will be appropriate for the

calculation of ultimate pressure. It has been observed (Springman, 1989) that there is little

change in pile bending moment with time as a particular loading increment has been maintained,

implying that the analysis conducted for undrained soil conditions may be taken as the ultimate

load case.

The predicted ultimate pressure, pile bending moments and deflections were compared with the

data of test SMS7 as failure approached due to a surcharge of 189 kPa. Fig: 3.4 shows that

although the pressure derived from the experimental data falls off over the bottom part of the soft

layer, the bending moment profiles are in quite good agreement. Calculation of the pile

deflection assumed zero pile rotation at the base of the pile. If the tip rotation, back figured from

integration of the experimental bending moment data combined with the head displacement

measured by linear variable differential transfomers, is superimposed on the calculated profile,

agreement would be excellent.

The effect of surcharge loading djacent to piles

4 PILE GROUP ANALYSIS

page: 21 I

4.1 Introduction

The analysis described above may be adapted to deal with a pile group containing two rows of

long vertical piles which penetrate a soft soil layer overlying a stiffer substratum, and are fully

fixed into a stiff pile cap, which is positioned at, or any height above, ground level. The single

pile solution is used to solve the problem for two independent free headed piles, for appropriate

values of lateral pressure on the front and rear piles, and the rotation and deflection at the top of

both of the piles are calculated (Fig: 4.la). It is also possible to apply an additional horizontal

shearing force at the pile cap. Finally, a stiffness matrix is constructed, relating moment and

lateral load to rotation and deflection at pile cap level, for the piles embedded in the sand layer,

with the following end conditions imposed by the pile cap (Fig: 4.lb & c):

i) deflection equal,

ii) zero rotation,

iii) equal and opposite shear forces.

This process is numerically complicated and it is recommended that the computer solution

described in the next chapter is used. The algorithm is described in Springman (1989).

4.2 ComDarison with centrifuge model tests

A comparison was made between the cenmfuge model test results and predictions based on this

analysis. The soil applied loading over the full depth of the soft clay layer, 6 m, and the other

parameters were identical to those quoted in earlier sections.

By continuity for an undrained soil the same lateral movement would be anticipated for each pile,

and the same lateral pressure would be expected to act on both the front and rear rows of piles

(Fig: l.lb) so that if

Pr = Fp Pf (4.1)

The eflect of surcharge loading adjacent to piles page: 22 I

then F = 1. In practice, this will not happen, but it will give the worst possible loading case for

the pile group and it is this case which is considered. If the soil is permitted either to move

vertically or to consolidate as was the case in these tests, then F < 1. Looking at the X-ray of

the deformed lead threads taken following the test (Fig: 4.2), this shows that the rear row of piles

experienced 20-3096 of the differential displacement of the front row, so F =0.3 could be

adopted for the fully drained case with a pile cap raised above ground level.

P

P

P

4.2.1 Working load case

Figs: 4.3 & 4.4 show the results of the analysis on the pile group under working load conditions.

Predictions of the lateral pressure, bending moment and deflection were quite good for both the

front and rear piles for q = 100 kPa (Figs: 4.3a & b), although the lateral pressure is smaller and

the mean thrust at a shallower depth for the rear pile. For q = 50 kPa (Figs: 4.4a & b) similar

observations hold m e except that the predicted deflections were considerably larger than those

measured in test SMS8.

The pressure distribution on the rear pile was of a different shape and magnitude to that assumed

for F = 1, because the soil was permitted to move vertically up between the piles, concentrating

the main lateral thrust nearer to the surface. In view of this, it was expected that the rear pile

bending moments would be overpredicted by the analysis, but in the event the moments ageed 1 very well (Fig: 4.3b & 4.4b).

'

P

~

4.2.2 Ultimateloadcase

The lateral pressure distribution slightly exceeds the 1 0 . 5 ~ ~ limit at the mid-section of the soft

layer for the front pile (Fig: 4.5a), whereas the freedom of movement in the vertical direction has

affected the experimental pressure distribution for the rear pile (Fig: 4.5b). Nonetheless, the

bending moments predicted as the ultimate values exceed the experimental measurements. If the

implied drift at the pile tip was subtracted from the experimental deflection profile, the net

displacements would be similar to those predicted


5 DESIGN PROCEDURE

5.1 Introduction

The engineer will design the sub/superstructure for a piled full-height bridge abutment as an

integrated assembly. Following site investigation and field trials, geotechnical analyses will be

implemented to consider bearing capacity and stability of the approach embankment, pile and pile

group design including axial and lateral loading, long term total and differential settlement, lateral

earth pressures, horizontal movements above and below ground level and retaining wall design.

This report is solely concerned with the prediction of bending moments in, and deflections of,

either a row of free headed piles or a pile group when an embankment is consuucted adjacent to

the piles. These piles are considered to be embedded in a stiff substratum overlain by a soft clay

layer. Clearly the sequence of construction will affect the behaviour of the abutment. In most

cases the piles will be installed first, followed by the abutment wall, bridge deck and finally the

embankment.

A computer program, SIMPLE, has been written to assist with this analysis for both free headed

piles and a pile group which is permitted to move laterally at pile cap level (Figs: l.la & b).

Alternatively, design charts are presented for calculation of the performance of a free headed pile.

Once the preliminary abutment design is completed, the effect on the bridge superstructure may

be evaluated. Total and differential settlements, horizontal translation and differential

movements, tilting, longitudinal and transverse distortion, and displacements due to dynamic

loading are considered. If these are within acceptable limits then the costs will be determined

and the design refined only if a cheaper, serviceable alternative can be found. If the design is not

within the sewiceability criteria, then the foundation system, structural design or foundation will

be adapted, and the optimising process continues.

The efSect of surcharge loading adjacent to piles page: 24

Undrained behaviour of the foundation is generally more critical for the analyses described herein

than when drainage is permitted. In the cenmfuge model tests on long flexible piles, the bending

moments induced by undrained loading reduced only slightly during consolidation. For tests with

short stiff piles, rotation about the tip allowed the pile displacement to increase marginally with

time, decreasing the differential pile-soil movement and significantly reducing the measured

bending moments. However the long tern foundation consolidation will affect the displacement

of the abutment and may cause tilting. Drained conditions should therefore be considered in

relation to tolerable movements and the serviceability of the abutment and bridge deck.

5.2 Foundation characteristics

The first step is to investigate the ground conditions.

accompanying foundation strength parameters will be determined.

A profile of the strata and the

5.2.1 Clay

In the soft upper stratum it is necessary to idealise the profile of cu with depth as linear:

(5.1) I

Many factors influence the measured values of shear strength. Installation disturbance may

combine with variability of the upper, weaker and more friable soil which lies in the critical zone

for lateral resistance near the ground surface. Weathering, seasonal changes in moisture content

and scour are common occurrences. In this instance, there is a requirement for two values of cu: l

i) a lower bound strength, cu -, for bearing capacity calculations, for estimating

the embankment load at which it is inappropriate to describe the foundation

I

I I

behaviour as pseudo-elastic, and for examining the lateral pressure at which

soil starts to yield around the pile

an upper bound, cu max’ to estimate the maximum lateral pressure which may be

applied to the pile by the soft soil.

I

I

I ii)


A secant shear modulus, G, must be chosen, which permits the foundation behaviour at or below

working loads, to be described as elastic (Fig: 5.1). For situations when the soil is

overconsolidated, this assumption is quite acceptable. The stiffness of the soft clay, although

required in the calculation of the lateral pressure acting on the pile, does not greatly affect the

result since the Gmdh3/EI term in Eqn: 2.1 is much smaller than the others. In consequence, the

selection of G may be made by the usual empirical methods. For very soft clays, 75cu < G <

100cu and for soft clays, 100cu G c 200cu. Far more influence is shown by the ratio of shear

modulus in the soil mass under the surcharge to the shear modulus in the area of high strain

around the pile, Gm/Gr, where the method of pile installation is also crucial. For driven piles

Gm/Gr may be approximately 1.5 to 2, whereas for bored piles the ratio lies between 2.5 and 3.

5.22 Determination of shear modulus in the stiffer substratum

The stiffness of the sand layer has been modelled using a linear profile of shear modulus which

has been considered acceptable for engineering design (Randolph, 1981). Knowledge, of the

variation of G with shear strain, y, will enable the designer to choose appropriate values of G for

the deformations expected in the region around the pile. A conservatively small value of G will

lead to a reduced value of maximum pile bending moment occurring at a greater depth in the

stiffer substratum. Generally it is the choice of lateral pressure distribution in the soft layer

which is the controlling factor. However, pile installation methods will be critical to the choice

of stiffness in the substratum.

Determining the magnitude of G with depth is discussed in Appendix: 1, considering:

i) laboratory determination,

ii)

iii) empirical relationships.

in-situ testing using a pressuremeter,

In stiff clay or soft rock, the effects of softening or weathering at the surface of the layer should

also be considered. Generally, G/p' N 200 for overconsolidated clays (Fleming et al, 1985) where


p' is the mean effective stress.

5.3 Pilegeometry

Once the pile material and shape have been chosen, a first estimate of pile size and stiffness may

be made. Pile stiffness, E is calculated for an equivalent solid circular pile of either the same

diameter, d, (circular pile) or with d = b, (rectangular pile with b = width, c = breadth and P

I = bc3112) so:

E = 64EU(xd4) (5.2) P

The total length of pile required to ensure flexible behaviour under lateral loading may be

decided once the critical pile length in the Stiffer substratum has been determined from Eqn: 2.12.

The spacing between the rows of piles in a group has been ignored because the lateral pressure

profiles, pf and pr, for the front and rear piles are assumed to be equal. Since the pile cap is

assumed to be sufficiently rigid to prevent bending, the pile cap rigidity and geometry are not

required.

5.4 Embankment

5.4.1 Equivalent surcharge load

To represent the embankment loading, an equivalent surcharge must be determined. Although the

geometry and characteristics of each embankment are different (Figs: l.la & b), it is acceptable

to assume plane strain conditions across the width of the embankment, and that the vertical stress

due to the unit weight of the N1 for the height of the embankment describes the surcharge load.

5.42 Embankment stability

It is well known that inclining the resultant load on a foundation by 15' from the vertical is^ enough to reduce the ultimate bearing capacity by 50% (Bolton, 1979). This effect can, similarly,

reduce the bearing capacity of embankments. It may be necessary, therefore, to build

I


the embankment on a geotextile mat or to place some reinforcement at the base, to carry the

outward shear forces which could otherwise destabilise the underlying soil. It is possible that the

embankment material or construction method may cause arching within the fill, either

longitudinally or transversely. This will affect the magnitude and distribution of load carried by

the foundation.

The stability and resistance to bearing capacity failure of the embankment structure should be

considered separately, without allowing for additional strengthening resulting from the row of

piles, which will only tend to prevent longitudinal, but not lateral movement. In this way, the

embankment and foundation will be designed to avoid failure during their working life, whilst

limiting lateral deformations to tolerable levels.

5.5 Lateral uressure on a uile in the soft laver

Clear recommendations are made on the choice of lateral pressure dismbution:

i) parabolic profile for the pseudo-elastic working load case, such that

the initial assumption that p, is constant with depth is adapted so

that the parabolic pressure dismbution has a peak value 1 . 5 ~ ~ at the

mid-depth of the soft stratum,

linear pfile for the plastic ultimate load case. ii)

These will be calculated and adapted as described in section 2.3.

5.5.1 Reparation of the elasto-plastic i n t d o n diagram

The first stage considers the boundaries of pseudo-elastic and plastic behaviour, by preparing an

elasto-plastic interaction diagram (Section 2.3.4, Fig: 2.4a). Plotting p/cu (ordinate) against q/cu

(abscissa), the following lines and zones may be distinguished:

i) the pseudo4asic performance line (Eqn: 2.1) which relates the average

pressure, pm, acting on the pile in the soft layer to the surcharge load, q,

for the particular value of h/d.

The effect of surcharge loading aa'jacent to piles page: 28

ii) the elasto-plastic zone, which lies underneath the ultimate pile pressure

defined by p/cu max = 10.5 and to the left of the complete bearing capacity

failure line, (Eqn: 2.4) which defines the conditions for local failure

underneath the abutment wall in the direction of the road centreline,

iii) the fully plastic failure intersection point at which the soil shears

plastically past the pile simultaneously as the soil mass fails under

the embankment (Eqn: 2.3).

The local yield of the soil around the pile, which occurs above p N 2xcU does not detract from the

safety or performance of the system provided that the serviceable bearing capacity is not I

exceeded. With these considerations in mind, it is possible to evaluate the lateral pressures acting

on the pile in the soft clay layer due to the differential movement between the pile and the soil.

5.52 Ideal design zone: wurking load case

Once the surcharge load has been decided, and the position of pm has been added to the

interaction diagram, it will be clear whether this surcharge-soil-pile configuration may be

described as falling in the ideal design zone. The shape of the lateral pressure profile in the soft ~

layer, which was initially assumed constant with depth under plane strain conditions should then 1 be adjusted (section 2.3.5) to allow for three dimensional effects and to give a Darabolic Dressure 1

I

distribution.

5.5.3 Plastic fail=: ultimate pile pressure

, The ultimate lateral pressure which could act on the pile must also be considered. Defined as

1 0 . 5 ~ ~ over the entire depth of soft soil, a linear pressure distribution is usually adopted to give ~

I I an absolute upper bound in cases where accidental overloads are possible.

In the case of a stiffer soil deposit, in which the projected surcharge loading wil l be unable to

generate sufficient lateral pressure to reach the ultimate loading case, pu = 1 0 . 5 ~ ~ over any of the

The effect of surcharge loading djacent to piles page: 29

depth of the "soft" layer, then this upper bound need not be considered. Reference ta the elastic

loading line on the elasto-plastic interaction chart will help to indicate the safety margins.

5.5.4 Input for SIMPLE

The computer program allows the lateral pressure distribution to be either linear, parabolic or a

cubic spline fitted to data points of lateral pressure versus depth. SIMPLE allows the input to be

made using E3M GDDM graphics, an existing datafiile or interactive format. Figs: 5.2, 5.3, 5.4

show the screens displayed for the graphics input.

5.55 Design charts for free headed piles

An alternative to the use of the computer program for fiee headed piles is the use of design charts

given in Fig: 5.5 & 5.6. The lateral pressure profile can then be represented by any combination

of the following:

i) constant pressure with depth,

ii)

iii)

pressure increasing or decreasing linearly with depth,

parabolic loading, with zero pressure at the top and bottom

of the layer and the maximum value at the mid-depth,

any combination of the above loadings over depth, h, which

reduce to zero at hU above the soft-stiff interface, y = hs.

iv)

It is possible to fit a large number of likely lateral pressure profiles using these design charts, by

combining and superimposing the distributions above.

When using the design charts with linear distributions of pressure with depth, the value of a

characteristic pressure, pc, and a load distribution factor, pc, must be determined (Fig: 5.5a).

These are obtained from:

(5.3)


The charts are prepared for values of 0.5 5 pc 2 1.5. Parabolic loading cases are also included.

Non-dimensional p u p s are defined for the behaviour of the piles in the soft upper soil layer

such that lateral pressure p, force H, moment M, rotation 8, and deflection U, and are presented as

(Figs: 5.5a-c, 5.6a & b):

M 8EI uEI Y Y 9 versus -

h

P H - - - - - Pc PC* P c r h 2 Pcrh3 Pcrh4

for different values of pc. Having established the values of pc and p,, the pressure applied, the

bending moment dismbution and in particular Hs and Ms at the soft-stiff soil interface, y = h,

may be determined from the charts (Figs: 5.5b & c) and summed for the components of pressure

(section 5.5.5 i-iv) to give the total values of Hs and Ms. These can then be applied to the

bottom part of the pile which is embedded in the stiffer substratum. If, however, the pressure I I I

dismbution reduces to zero above the interface (loading case (iv), Fig: 5.7), then simple structural

analysis will determine the values of Hs and Ms at the top of the stiff layer based on moment,

Mh, and shear force, Hh, at a depth y = h:

Hs = Hh

Lateral forces H may be imposed on the pile cap because of the earth pressure on the abutment

wall. These will tend to enhance the pile movements and reduce the differential pile-soil

displacement. It is therefore conservative to ignore this effect while calculating the lateral

pressures in the soft layer, and to directly superimpose the pile head forces on M, and Hs so that

Eqns: 5.5 & 5.6 become:

Pc’

The d e c t of surcharge loading adjacent to piles

2.10b, 5%). By reference to the charts of normalised moment versus depth for the stiffer

page: 31

5.6 Behaviour of st i f f substratum

These are the steps in the analysis for the elastic behaviour of the lower section of the pile:

i) assume the pile is flexible if it exceeds a critical length { .tc = f (Gc, r, Ep)),

which is dependent on relative pile-soil stiffness (Eqn: 2.12),

calculate a characteristic shear modulus {Gc = f (Go, m, v, e,)) (Eqns: 2.8-2.10),

iterate between i) and ii) (Eqns: 2.10, 2.12) to determine values of critical

pile length, lc, and equivalent shear modulus, Gc; find pc, (Eqn: 2.1 l),

substitute these values into the algebraic expressions which relate deflection

ii)

iii)

iv)

and rotation of the pile in response to a force or moment applied at the head

of the pile (Eqns: 2.13,2.14), or apply them to the charts which give normalised

profiles of deflection and moment against depth (Figs: 2.10), remembering to

include the appropriate interaction factor from Eqns: 2.18-2.20.

5.7 Results of the analvsis

5.7.1 Calculation of pile bending moment, rotation and deflection

substratum, (Figs: 2.9b, 2.1Ob), the maximum value can be assessed, together with the

deformation profile (Figs: 2.9% 2.10a) and the rotation of the pile at the soft-stiff soil interface

can be determined from Eqn: 2.14. The rotation and deflection components due to the loading in

the top part of the pile may be found from Figs: 5.6a & b respectively. Furthermore, allowance

can be made for a freestanding section of pile above ground level of length e, and also for

loading case (iv) when the pile is loaded over less than the full depth of soft clay (Fig: 5.7, 5.8). I

I I

In this latter case, the increments of rotation and deflection over length hU are given by:

h A9, = ME1 dy N, (Mh + Ms)hu/2EI

hS h

AuU = (( M/(EI) dy dy N, (Mh + Ms)h;/4EI hS

(5.9) I (5.10)


pile head and the maximum bending moment carried by the pile, which generally occurs just

and:

page: 32 ~

(5.1 1) 1

If there is no 'unloaded section, hU = 0, and Auu = 0, A€),, = 0 and e h = os. These effects can be 1 added to the values from the lower part of the pile such that (Fig: 5.8):

4 -

PC U = us + hutanes + Auu + htaneh + 2 ui + etan0

PC y=h

V=O

(5.12)

(5.13)

I

below the soft-stiff soil interface. The design charts may be used to find this information quite I

efficiently for simple distributions of lateral pressure in the soft layer. From the program I

SIMPLE, output is given in plot format (Fig: 5.9) or in numerical format (Table: 5.1), the mode I

depending on the hardware available.

I

I

I Increased pile deflection and rotation due to the proximity of other piles have been allowed for in

the stiff layer. However, the interaction caused by the passive thrust of the soil in the soft layer

has not been considered and further research is required in this area. The additional movement

due to lateral thrust from the soft soil on a row of piles is likely to be only a fraction of that

caused by the rotation and deflection in the stiff layer.

The egect of surcharge loading adjacent to piles page: 33

5.72 Improving the design

If it is not possible to design the piles and abutment to fulfil1 safety and serviceability criteria,

additional measures will have to be taken. These could include:

i) ground improvement techniques pre-loading, embankment piling, excavation of

selected soft material, installation of stone columns or wick drains, reinforcement,

ii) embankment load reduction: reduce embankment height, use lightweight fill,

minimise earth pressure on abutment wall and hence pile head load,

redesign of pile foundation: alter pile spacing, material, size, shape or use

buttonhole construction method.

iii)

It is preferable to keep the design solution within the pseudo-elastic region to minimise yielding

of either the soil mass or the soil around the pile, to ensure that the structure remains serviceable.

It is also necessary to check that the plastic moment of the pile:

M = Z O P P Y

is greater than the maximum design moment imposed either by the ultimate loading case or by

some reduction of this, where o is the yield strength of the pile material, 2 is the section Y P

modulus. A different failure criterion is required for a reinforced concrete pile.

5.8 Exam~le

It may be helpful to work through an example which illustrates the use of the design charts and

procedures to predict ground level pile deflections and maximum pile bending moments.

Consider an idealisation of Fig: 1.1% in which a rectangular block of fill, 8 m high, is placed

adjacent to a row of five free headed piles which penetrate a 6 m layer of soft clay and are

embedded in a stiffer sand substratum. These piles may be, as a preliminary choice, of minimum

length 16 m below ground, 1.27 m diameter reinforced concrete, with E = 40. 106 kPa,

I = 0.1277 m4, installed at a spacing of 4.0 m, with s/d = 3.15. There will be no freestanding

length of pile above ground level, y = 0 m. Assume also that the piles are to be driven.

The erect of surcharge loading adjacent to piles page: 34

5.8.1 Problem geometry and foundation properties

Embankment:

Soft clay:

(0 I y I 6 rn)

specify lightweight fill, ye = 15.4 kN/m3, he= 8 m, q = 123 @a.

take cu min = 22 kPa (for bearing capacity calculations),

take max if G/cu N 75, Gm = 2100 kPa at y = 3 m, Grn/Gr = 1.5 (driven piles),

Ep/G,

= 22 + 2y kPa (for calculation of p,, Eqns: 2.2, 5.1),

2 19O00, hs/d = 4.72

Take G = 2 + 10 (y - 6) MPa (Eqn: 2.8)

with v = 0.3, G = (1 + 0.3 x 0.75) G = 1.225 G (Eqn: 2.9),

assume lc = 10 m, Gc = 1.225 x 52 = 63.7 MPa (Eqn: 2.10),

lc = 1.27 (40. 1@/63.7)2/7 = 8 m (Eqn: 2.12),

iterate so that lc = 8.4 m, Gc = 53.9 MPa,

*

= (1.225 x 23)/(1.225 x 44) = 0.523 (Eqn: 2.11), PC

le = 0.34 x 8.4/(Jo.523) = 3.95 (section 2.3.5.2), e,ld = 3.1 1.

Then, determine the lateral pressures acting on the pile in the clay layer, assuming that the pile

will be laterally loaded over the entire 6 m depth of clay.

5.82 Working load case: parabolic distribution

Assume that the soil is loaded over the entire depth of soft layer so hU = 0 and h = hs. From

Eqn: 2.1:

123 = 93.0 kPa I 3 x 1.5 x 1.27.1.27 +0.458 x 2100 x 63 x 1.27 - 6 4 40 106 x 0.1277

192

I L J = 93.0 kPa I 3 x 1.5 x 1.27.1.27 +0.458 x 2100 x 63 x 1.27 - 6 4 40 106 x 0.1277

where the first term in the denominator reflects the relative soil stiffness, the second term refers

to the pile-soil spacing and the third to the pile-soil bending rigidity.


Check the elasto-plastic interaction diagram (Fig: 2.4a), to ensure that this loading case will

plot inside the ideal design area with pm/cu min = 93/22 = 4.22, and q/cu = 123/22 = 5.59. For

s/d = 3.15, h = 6 m, (Fig: 2.4b), this working load case will plot outside the boundary of the

ideal design zone for which cmo,.jcu = 0.67, and will have a cmo,.jcu N 0.85. However, if an

allowance is made for the increase in cu during construction of the embankment to this height,

this reduced factor of safety may be acceptable. Although this loading case is perhaps too

severe for a single row of piles, a pile group would be able to support the lateral pressures

applied due to this embankment load.

Failure under the abutment end wall at the complete plastic failure intersection point (Eqn: 2.3)

will occur at q/cu N 8.4, so the lowest possible value of qmax N 185 kPa, which is >> 123 Wa.

Out of plane bearing capacity collapse would also require investigation.

I Checking to see whether the loading can be reduced due to the depth of the soft layer, hu/hs

may be obtained from Fig: 2.7a. For E Gm N 19O00, hdd = 4.72, le/d = 3.1 1, hu/hs 2 0.18.

Since this is less than 0.2 then this may be ignored and hU taken to be zero with h = hs = 6 m.

Now the parabolic distribution is redefined to be zero at y = 0 and 6 m, with

Pm

d ~

' = 1.5 x 93.0 = 139.5 kPa at y = 3 m.

5.8.3 Ultimate load case: hear distribution

From Eqns: 2.2 and 5.1:

= 1 0 . 5 ~ ~ = 231 + 21y (Wa) PU

5.8.4 Calculation of pile bending moment, mtation and deflection

Using the design charts (Figs: 5.5 & 5.6) and the equations defined above, the example follows

overleaf. Firstly, establish characteristic lateral pressure and load description factor:

I

8,' = 8, (1 + a) 2.78 107rads 8.426 107rads

I

I


U, 8 in the soft layer:

I

I

page: 36

Working load case Ultimate load case

pc (Eqn: 5.3, Fig: 5.5a) 139.5 294.0 kPa

Pc (Eqn: 5.4) - 262.51294.0 = 0.892

Refer to design charts to find shear force and moment at the top of the sand layer:

Hs/<pcrh) (Fig: 5.5b) 1.333 2

Ms/(PC rh2) (Fig: 5 3 ) 0.667

0.71 MN HS

MS 2.13 MNm

Establish the deflection at the top of the sand layer:

0.5 1

0.575

0.93

2.24 MN

6.25 MNm

0.5 1

0.575

The rotation at the top of the sand layer must also be determined from Eqn: 2.14. Allowance

must be made for the interaction between piles (Section 2.4.2). Factors for increasing calculated

rotations and deflections are listed in Table: 5.2 for a row of 5 piles at s/d = 3.15, with the

pile-soil stiffness (E Gc) for the centrifuge model tests which are identical to E /G from this

example. The loading was assumed to be applied equally at the top of each free headed pile by

means of a shear force, H, or a moment, M. For the most critical (middle) pile, aUH = 0.32,

= 0.102, aeM = 0.033. Therefore, corrected deflections and rotations for this pile auM = a8H in the stiffer layer:

p/ P C


Working load case

ABEU(pcrh3) (Fig: 5.6a) 0.2

AuEV(pcrh4) (Fig: 5.6b) 0.156

A0 7.469 10-4rads

Au 3.5 mm

and due to the rotation, Os, at the base of the soft layer (Fig: 5.8):

h tanes 16.68 mm

so rotation and deflection at the ground surface will be:

e 0 = e,'+ A0 eqn: 5.13)

uo = us' + Au + h tane,

3.527 107rads

29.26 mm

uo/d 2.3%

Ultimate load case

0.30

0.23

2.37 103rads

10.89 mm

50.56 mm

1.08 l07ads

89.28 mm

7.0%

Therefore the total lateral displacements for a free headed pile exceed a 25 mm serviceability

criterion for differential lateral displacement, assuming that up to 100 mm vertical displacement

may also be tolerated (US Department of Transportation, 1985). But, since the pile

configurations used for a bridge abutment generally have a fixed pile cap, this would reduce the

deflections. By inspection (Figs: 2.9b, 2.10b), to find the maximum bending moment:

Working load case Ultimate load case

(Y -hs)/$ 0.25 0.25

Y 8.1 m 8.1 m

Mh/HslC (Fig: 2.9b) 0.17 0.17

M e s (Fig: 2.10b) 0.84 0.84

Mmax = Mm + Mh 2.80 MNm 8.45 MNm

Check Mmax is less than the plastic moment for the pile. If not, redesign reinforcement,

increase concrete strength, or increase size of pile since it is unlikely that s/d c 3 will be used in

practice. Table: 5.3 summarises the calculation at working load.


5.8.5 Equivalent pile group

The analysis was repeated using the SIMPLE program for a group of two rows of piles with the

same atmbutes, and spacing between the rows sx = 5 m, with an identical parabolic working

load case pm' = 139.5 kPa, acting on both front and rear piles. The intention was to investigate

the effect of pile cap fixity on the displacements, to see whether the pile group displaced

roughly half as much as a single pile, and it was found that uo was reduced by 52%. after

interaction between piles (Table: 5.2) was allowed for, to 2 14 mm (uo/d = l.l%), with 8, = 0

(which is a pre-condition of the program). While the effect of the pile cap had been to limit the

pile movement to about 10 mm, the proximity of a second row of piles had increased the

additional displacement due to interaction. This magnitude of displacement is acceptable under

US DOT criteria, and it would seem that analysis of the problem using the single pile algorithm

and halving the displacement will give reasonable results.

page: 38

Similar values of pile displacement were obtained when an additional working load analysis was

conducted for a pile group for which the pile cap was permitted to deflect horizontally, for

identical embankment load and foundation conditions to those described above for the single

free headed pile example. Eqn: 2.7a would be used to define the pressure on each pile, giving

' = 89.9 Wa, 64% of the original value of the single pile. In this instance, a pile cap load Pm equal to aocusxs (= 22 x 5 x 4 = 440 lcN) per pair of piles or 44O/s = 110 kN/m length, would

be applied at pile cap level, where a. and as have been taken as unity.

The maximum moments for the working load, pm' = 89.9 kPa, were -2.18 MNm at y = 0 m,

and +1.27 MNm at y = 8.01 m which are 78% and 45% of IMmaxI for the single free headed

I pile at working load respectively. Similar reductions obtain for the ultimate load case when the

maximum moments were -6.34 MNm at y = 0, and +4.15 MNm at y = 9.01 m. These

improvements in lateral pile performance, under both serviceability and collapse conditions,

demonstrate the advantages of using a pile group with a fixed pile cap.

~

I

The effect of surchurge loading djacent to piles page: 39 I

5.9 Otherdesien aspec ts and concludinP remarks

Analysis of the behaviour of piles and pile groups subjected to passive lateral thrust has been

introduced. Design methods accounting for both serviceability and ultimate collapse were

considered with appropriate recommendations, and a computer program, SIMPLE, was

developed to carry out the numerical analysis.

In parallel, other local considerations such as axial loading capacity, total or differential

settlement, must be investigated together with the impact on the rest of the structure of the pile

behaviour. US Department of Transportation (1985) comment that horizontal differential

movements are far more damaging to abutments and bridge decks than differential vertical

settlements. They recommend that the combined tolerable movement criteria are 100 mm

vertical and 25 mm lateral movement.

Short rigid piles driven through a deep soft layer into a stiffer substratum will rotate abqut the

tip as the surrounding soil consolidates under a constant load. The pile bending moments will

then reduce significantly and be accompanied by a slight increase in pile displacement. For

long flexible piles such as those considered in this report, only minimal changes in either pile

bending moment or displacement with time were observed in the centrifuge model tests.

Retaining wall and pile cap design, settlement, embankment bearing capacity and stability must

also be examined. A complete breakdown of costs, availability of materials, site conditions and

location, transportation and environmental impact will all be factors in the final design choice.

6 ACKNOWLEDGEMENTS

The work described in this report forms part of the research programme of the Ground

Engineering Division (Division Head Dr M.P. OReilly) of the Structures Group of TRRL. The

Project Officer at TRRL was Mr I.F. Symons and the Report is published by permission of the

Director.


7 REFERENCES

Baguelin, F.J., Frank, R.A., Said, Y., (1977). Theoretical study of lateral reaction mechanism of piles. Geotechnique 27, No. 3, pp. 405434.

Baguelin, F.J., Bustamante, M.G., Frank, R.A., (1986). The pressuremeter for foundations: French Experience. Proc. In Situ '86, GT Div., ASCE.

Bolton, M.D., (1979). A Guide to Soil Mechanics. Macmillan.

Bolton, M.D., SpMgman, S.M., Sun, H.W., (1990). The behavior of bridge abutments on clay. Design and perfomance of earth retaining structures. Geotech. Eng. Div. of ASCE Specialty Conference, Cornell University, Ithaca, USA.

Broms, B., (1964). Lateral resistance of piles in cohesive soils. JSMFD, ASCE, Vol. 90, No. S M 2 , pp. 27-63.

De Beer, E.E., Wallays, M., (1972). Forces induced in piles by unsymmemcal surcharges on the soil around the piles. Proc. V European Conf. on SMFE, Madrid, Vol. 1, pp. 325-332.

I

Duncan, J.M., Chang, C.Y., (1970). Non-linear analysis of stress and strain in soils. JSMFD, ASCE, Vol. 96, NO. S M , pp. 1629-1653.

Fleming, W.G.K., Weltman, A.J., Randolph, M.F., Elson, W.K., (1985). Piling Engineering. Surrey University Press.

Frank, R.A., (1981). Design of piles subjected to lateral pressures in soft soils. Colloquy of Jablonna, Gdansk, Poland.

Frank, R.A., (1988). Private communication: Pressuremeter test results for sites at Provins and Plancoet, France.

Frydman, S., (1970). Discussion. Geotechnique 20, No.4, pp. 454 & 455.

Jewell, R.A., (1987). The mechanics of reinforced embankments on soft soils. Report OUEL/1694/87.

Mair, R.J., Wood, D.M., (1987). pressuremeter testing. CIRIA/Butterworths.

Marchetti, S., (1980). In-situ test by flat dilatorneter. Proc. ASCE, JGED, Vol. 106, No. GT3, pp. 299-321.

I Meigh, A.C., (1987). Cone penetration testing. CIRIA/Buttenvorth. I

Meyerhof, G.G., (1976). Terzaghi Lecture, Pile Foundations, GT3, pp. 197-227.

Poulos, H.G., (1971). Behaviour of laterally loaded piles: I - single piles, and II - pile

Poulos, H.G., Davis, E.H., (1974). Elastic solutions for soil and rock mechanics. John Wiley & Sons.

Bearing capacity and settlement of pile foundations. 11th I

! groups. JSMFD, ASCE 97, NO. SM5, pp. 711-731,733-751.

I

I

The efect of surcharge loading djacent to piles page: 41

Poulos, H.G., Davis, EH, (1980). Pile foundation analysis and design. John Wiley & Sons.

Powie, W., (1986). The behaviour of diaphragm walls in clay. PhD. thesis. Cambridge University.

Price, G., Wardle, LF., Frank, R, Jezequel, J.F., (1987). Monitoring the below ground performance of laterally loaded piles. Ground Engineering, Vol. 20, No. 5, pp. 11-15.

Pulsfort, M., Walz, B., Steinhoff, J., (1989). Slightly stabilised bentonite suspension sheltering piles against lateral passive earth pressure in soft cohesive soils. IC Piles and Foundations, London

Randolph, M.F., Carter, J.P., Wroth, C.P., (1979). Driven piles in clay - the effects of installation and subsequent consolidation. Geotechnique 29, No. 4, pp. 361-393.

Randolph, MF., (1981). The response of flexible piles to lateral loads. Geotechnique 31,

Randolph, M.F., (1983). PIGLET - A computer program for the analysis and design of pile groups under general loading conditions.

Randolph, M.F., Houlsby, G.T., (1984). The limiting pressure on a circular pile loaded laterally in cohesive soil. Geotechnique 34, No. 4, pp. 613-623.

Robertson, P.K., Campanella, R.G., (1983). Interpretation of cone penetration tests: Pan i and 2. Canadian Geotech. J. 20, pp. 718-745.

Seed, H.B, Tokimatsu, K., Harder, L.F., Chung, R.M., (1985). Influence of SPT procedures in soil liquefaction resistance evaluations. Proc. ASCE, JGED, Vol. III(GT12),

NO. 2, pp. 247-259.

pp. 1425-1445.

Skempton, A.W., (1957). Discussion on planning and design of the new Hong Kong airport. Proc. ICE, Vol. 7, pp. 305-307.

Springman, S.M., (1989). construction. PhD. thesis, Cambridge University.

Lateral loading on piles due to simulated embankment

U.S. Department of Transportation, (1985). Tolerable movement criteria for highway bridges. Final Report FHWA/RD-85/107, Federal Highway Administration, USA.

Wroth, C.P., Hughes, J.M.O., (1973). An instrument for the in-situ measurement of the properties of soft clays. Rot. 8th ICSMFE, Moscow, Vol. 1.2, pp. 487494.

Wroth, C.P., Randolph, M.F., Houlsby, G.T., Fahey, M., (1979). A review of the engineering properties of soils with particular reference to the shear modulus. Cambridge University Engineering Department Technical Report, CUEDD TR 75.


APPENDIX: 1

Detemination of shear modulus in the stiffer substratum

A1 Introduction

Most granular soil deposits will have experienced sufficient cycles of loading to have reached a

stable hysteretic state, although this process takes longer for increasing amplitudes of stress and

for looser soils (Bolton, 1988). However for completely virgin soil, the initial loading cycle will

show plastic shear strains and a lower value of shear modulus. Duncan & Chang (1970), Bolton

(1988) estimate that this reduction is of the order of 2 for dense and 5 for loose deposits.

A2 Choice of shear modulus prome

Two options are available for the analysis described in earlier chapters. If soil homogeneity

factor, pc = 0.5 then there will be a linear variation of G with depth and for pc = 1.0, G will be I

constant with depth. Large lateral strains are expected in the soil at the ground surface around a , 1

laterally loaded pile, and a smaller secant shear modulus is appropriate at this horizon. Lareral

strains wil l decrease to zero at depths below the critical pile length, where a higher value of

shear modulus should be selected, and some interpolation between 0.5 e p, e 1.0 is realistic.

1

A.3 Laboratory determination

In the past, it was common practice to measure the G-y relationship from small scale laboratory

tests in the triaxial or simple shear apparatuses after restoring the sample to the presumed

in-situ stress state. However, there are inherent problems in ensuring that the sample remains

undisturbed during insertion of the sampling tube, transportation and subsequent storage, and I i 1 finally during extrusion and preparation for testing. Choosing a small volume of soil to depict

the behaviour of the whole mass, once outside the confines of controlled sample preparation for

centrifugal modelling, may also lead to misinterpretation of properties if the presence of fissures

in stiffer clays, larger fragments and soil anisotropy are ignored.


Nowadays, laboratory determination of parameters may be combined with in-situ testing, which

has become more popular through the development of the self boring pressuremeter (Wroth &

Hughes, 1973; Mair 8z Wood, 1987), other types of cone penetrometer (Meigh, 1987) and flat

plate dilatometers (Marchem, 1980). Of these options, the self boring pressuremeter is thought

to offer the least disturbance to the soil fabric and the in-situ stress state (Wroth & Hughes,

1973), and it is used to measure G = f(y) directly without recourse to empirical correlations.

A.4 Self boring pressuremeter

In-situ testing using a self boring pressuremeter offers horizontal pressure-defonnation

characteristics from which the appropriate secant shear modulus may be evaluated, at a variety

of depths, and for the range of stresses and strains that will be experienced during the life of the

foundation. French research was summarised by Baguelin, Bustamante & Frank (1986), who

defied values of shear modulus at 0,2% and 5% volumetric strain as G G and G PO’ P2 PS‘

Lateral loading effects are likely to dissipate over the critical pile length, with zero lateral strain

below this, so G would be an appropriate value at y = $. At the surface, where larger strains

are expected, a smaller modulus, perhaps G would be applicable. However, the disturbance Ps’

caused by pile installation may indicate that G is a better choice at y = e,. Results from a P2

French full scale laterally loaded pile test with nearby self boring pressuremeter tests were

analysed.

PO

A combination of extensometers (E-Ls) and strain gauges (ERS) were used to provide data

from which pile bending moments were determined (Fig: A.lb) for the site arrangement at

Plancoet (Price, Wardle, Frank & Jezequel, 1987) (Fig: A.la). Using Eqn: 2.8 to define G,

values of Go and m were applied to the analysis from section 2.4 to give best fit data to these

profiles of bending moment and deflection (Fig: A.lc). predicted and experimental data agreed

well for Go = 0 MPa, m = 0.8 MPa/m. This prome is plotted on results from a pressuremeter

test which was conducted near the pile (Fig: A.2, Frank, 1988).


With greater strains expected at the surface than at depth, it was not surprising that Go was

closer to the value of G and G at depth. Fleming

et a1 (1985) recommended that Go was either half the value taken for axial loading at ground

level, or zero, increasing to the full value taken for axial loading, at the critical depth.

and the shear modulus was between G P5 PO P2

A5 Empirical considerations

Robertson & Campanella (1983) obtained correlations between dynamic shear modulus, cone

resistance and vertical effective stress for uncemented, normally consolidated sands under small

strains for standard cone penetration tests Fig: A.3). For the mid-depth of the 10 m sand layer

in the centrifuge model tests, where a lower bound 9~ = 3 MPa, their estimate of

N, 50 MPa compared with the assumed value of 52 MPa based on Eqns: A.1 8z A.2 below

(Table: A.l).

Wroth er a1 (1979) conducted a literature survey investigating ways of estimating G. Often G

may be proportional to p', and it is usually realistic to allow a linear dismbution of G with depth

for sands under high strains. However, the following expression based on curve fitting dynamic

laboratory test data on sands accounted for the effect of strain:

(0.765433 exp 3000Y)

0.9 + - 1 .23 [ 5:J G - - 710

Pa (A. 1)

These equations were valid for a range of 10-6 < y > 107; 0.25 < p'/pa > 2; 20 < Dr > 100, and

imply that 300 c G/p' > 600, which is generally applicable for lateral loading at working levels.

Relationships between standard penetration test (SPT) data and G for sands were also reviewed

by Wroth et aZ(1979) who recommended:

The eflect of surcharge loading adjacent to piles'

based on data between 60 N

page: 45

c Gm Jpa > 300 N O'*. For 9~ = 3 MPa, a loose deposit with I

i N 2 7 is indicated leading to an estimate of Gmax = 54 MPa. However, the value of blow

count, N determined by SPT depends on the type of hammer and method of initiating its fall.

Frydman (1970) conducted field trials which showed variations in N of up to 40%. More recent

work by Seed et a1 (1985) compared international testing methods and recommended correction

factors to align these with a standard

I Tables

'otal C z ' i e C t i T ? +ytb of p i l e for la teral Loadin; (:I = Zotal 1304th o f p r l e (a) - 17.020 iac1.d in.:. . .

> a p t 5 a

-1 ,000 0.009 o.ao3 3.803 1.200 1.603 2.000 2.oOJ

3.200 3.600

2.aoo

a.ooo 0.100

, a . i o o 5.200 5.600 i, 000 6.900 6.300 7.200 7.603

9.000 10.090 11.000 12.000 13.300

15.000 1 6 o O O O 16.000

a.ooo

ia.ooo

3andinq Eoacn t 3ef lee :Lan kYa

0.030 3.003 0 . x 2.182 7 . i ~ ?

16.3'32 3l.Jt3 52.9;9 90.:21

116.963 160.j16

273.130 3 0 7 . 2 2

5OO.SS6 s 96. E as 6 95.0f8 798.929 9 07.096

10 in.3 i a 1131,105 1295.111 1 2 9 1 . 7 ~ ~ 1 I17.:51

a 09 .a an 556.317 300.a63 1 16.308

212.3ar

a 19.575

0.000 0.000

Rotation a t to? o f p i l e

a

0.02033 0.3 i a 13 0.0 113s J. 0 16Sf 3.01590 0.0 1502 0. o 1a2a 0.0 1196 0.0 1269 3-01191 0.01115 0.0 1038 0.00962 0.00589 0.00810 0.0070 i

0.0351a 0.00a7o o.ooao9 0.001s0 9.0 0 2 a 2 9.031a8

' 3.00075 0.00521 ~.OOO02 . 0 00 0 6

-3.0 3003 0.00300 0.00000

3 006 70 0.40601

. .

3.001 987 r r d i m s

page T.I

TABLE: 5.1

17.033

l3000. JS 3

Tables page T:

TABLE? 5.2

Interaction factors for a single row of piles

No. of piles in row: 5 (s/d = 3.15)

Designation: middle offside outer

“L lH 0.320 0.302 0.222

“uM = a8H 0.102 0.09 1 0.049

“8M 0.033 0.028 0.01 1

Interaction factors for a pile group

Pile group containing 2 rows of 5 piles at s/d = 3.15:

Designation: middle offside outer

“UH 0.657 0.598 0.499

“uM = “OH 0.432 0.358 0.249

“8M 0.284 0.214 0.062

Loading is normal to the front and rear row of piles

Tables

stiff Unloaded soft Loaded soft Freestanding At pile cap

page T.3

Y (m) U (mm) 8 (rads) h, ui= 5.42 U&= 3.66 :U = 9.08 0.00278

20.18 :A9 = By& 0.00075 0 :A8 = 0 0

0 A u = h t a n e S + Z

S h Au = hu tang, = 0 0 :A8 = 0 0

+ A U = le l tane =

-e !$= 2226 q- - o.00353

Y=o=

TABLE: 5.9

Determination of pile maximum bending moment, rotation & deflection

Case: Test example: Working load Ref No: 21/1 Date: 1/2/88

Pile Prouexties Stiff Swbsadtun: Radius, r = 0.635 m G at top of layer Go =3MPa

Young’s modulus, E = 40 l@ MPa Shearmodulusgdt m =lOMPa/m 2nd moment of area I = 0.1277 m4 Homogeneityconstant p, = 0.523 Freestanding length e = 0 m Critical pile length lc = 8.4 m

soft uoprr soil Lavcr, Poisson‘s ratio, v = 0.3 Equivalent modulus,

Depth of layer, h, = 6.0 m Characteristic G, G, =53.9 W a

= 40 l@ h4Pa Total pile length, e+hs+$ = 14.4 rn EP

Establish us & 8, by taking Hs & M,, & using charts (Figs: 2.9 & 2.10) or equations (adapting to U; and e; for pile interaction by multiplying appropriate components by (1 + a)):

= -+- [027 H,(t$?)l+ 0.3 Ms(t$?)l] , 8, = ~ 4 k . 3 Hs(t‘$?)7 + 0.8 4iC Ms(lp)7] (E G )1’7 (E G

us pc c pc c umr2G, EpIGc#’ 2 0.575, us = uh+ urn

MS pI

’hr Gc For lateral force. H,, (E Gc)d7 IL 0.51, moment, M,, HS

Then, using charts (Figs: 5.63 & b), calculate rotation & deflection:

Determination of maximum moment by inspection, M e 2 0.84 Mm;o(Hslc 2 0.17 so Y=hs

2 2.8 MNa at depth, y = Ic (yllc) + h, = 8.4 (.25) + 6 = Saan

Tables page T.4

TABLE: A.1

Determination of shear modulus in the sand substratum

Depth

m Assumed

0 5 8 10

2 52 82 102

G (mal N = 7 Dr=50%

75 (reduce to nearly 0) 54

126

Y

U e,

3

2 9 M

!L a ta

Y

U e, M U

3

t%

.-

.. W k .II

c) L

a m P 1 rl

L P cr 0

a 2

b

c) L 0 n n a m Q) W U L P cr 0 m aJ p1 h

aJ

*I 0 5: 0

a

.I

c)

5

.I c)

m .I I

3

E a a f;

= .-. I

c) U

L

CT

h 1 .- s 8 U

a 9 - n cn .I

U

E a

n ep v

r

-

a c

c L

m 00

m c

i- . - - I I

Fig: 2.2 Photograph from X-ray (taken vertically downwards through sample) showing post-flight deformation of lead threads around five piles at s/d = 3.15. The sample was loaded on the right hand side of the piles

Stiff layer

Pile

Maximum embankment load, qmau

Fig: 2.3a Increase in bearing capacity allowing for reinforcement by a single pile

L I 1 1 1 I I

0 2 L 6 8 10 shear strain v o l e

Fig: 2.3b Mobilisation of undrained shear strength of kaolin (Powrie, 1986)

" I : I

c) 0 I

n

40

0 0 1. I I

0 0 F'

E a

I * - E c

a

Q) .- a n

m In c

I I - c c"

II A

h / h u s

0 2 4 6 8 1 0 1 2

I Id e

h /h u s

h / h u s

Determination of 'unloaded' length of pile, h,

Fig: 2.7a

1 .o

0.8

0.6

0.4

0.2

0.0 0 2 4 6 8 1 0 1 2

I Id e

dd=4;h i d = 5 s

1.0 -I

Fig: 2.7b

Fig: 27c

* Ep/G,= 5000 * E P m = loo00 + E/G =2oooO * EIG = 50000 P m

* E ~ G ~ = I C I O O O O P-m -

0 2 4 6 8 10 12

I Id e

+- . - -cs € ?

o! U’ - I

4 c U,

- 1 n 1 . l ).c 0.2 0.4 0.6 0.8 1.0 1.2 1.6 - - - -

.-A’,=

/

:j 4

w c A U

A

9 < v)

I

a10 -’ 2 Q c

8 0 z W c3 W J

L 1

c) ?I * = \ + O h

I

t

. 0 z W m

Maximum embankment load,

qmax S

Stiff layer

Pile R Fig: 2.8a Increase in bearing capacity allowing for reinforcement by two piles

h Soft layer s

h = O U

Fig: 2.8b Adjusted profile of lateral pressure

F31'

0 0.1 0.2 0.a 0.4 " 8 0.8 0.a

0.2

0.4

0.0

01

0 0

0.4

0.0

oa

9 1

Fig: 2.9 Generalized w e s of lamal deflection and bending moment profile for force loading

4.2 0 0.2 0.4 0.0 0 ) 0 0.0 0 ) 1 0

0.4

0.8

01 y 1

02

0.4

0 1

01

Ag: 2.10 Gtnaalized cunm d law deflection and knding moment profile for moment

OIRECTIGN OF

-- LATERAL L O A D I N G 0

0 PlLE. O . O l l t V . 0

Fig: 2.11 Pile group interaction

Aum A u B U s Ae+e L& .I-4

m , s i I T '

4 soft

. soil h s

Stiffer substratum

Fig: 3.la Pile bending moment diagram

water table

Fig: 3.lb Pile deflection

12.7mrn. dia.instrumented pile r

Legend. Dimensions in millimetres Lead thread oPore pressure m Vane test

transducer xStrain gauge % Penetrometer test 4 LVDT

Fig: 3.2 Centrifuge model test general arrangement, Test 7

M

UTERAL P R E S w l i CPA

w m n

OEFLECTION m do

I -

i !

I I !

I ,

i i i

i I

i

!

!

!

I !

CENTRIFUGE TEST KPISMS 7 I

BENDING MOMENT, LATERAL PRESSURE 8 DEFLECTION [Xi

CENTRIFUGE TEST KP/SMS 7 BENDING MOMENT, LATERAL PRESSURE 8 DEFLECTION I=

I

LEGENO

0.051 0.02) 6

oomn . OOln n

w

TIC 10* 3.4 I . BENDING MOMENT, LATERAL PRESSURE 8 DEFLECTION

Equiva lent Moments d fo rces

f r e e headed opplled t o ~ l v e

pi les equal 6 oppos i te

r o t o t Ions

(01 (b)

P I le gr,oup

behov i our

d oorometers

( C )

Fig: 4.1 Parameters used in the analysis of pile group behaviour

Fig: 4.2 Photograph from X-ray (taken vertically downwards through sample) showing post-flight deformation of lead threads around a pile group with 2 rows of three piles, sdd = 3.94 apart, and at s/d = 5.25 within each row. The sample was loaded on right hand side of the piles

I

I

CENTRIFUGE TEST KP/SMS 8 P I L E AF BENDING MOMENT, LATERAL PRESSURE 8 DEFLECTION

f / 1

CENTRIFUGE TEST KP/SMS 8 P I L E AR BENDING MOMENT, LATERAL PRESSURE 8 DEFLECTION I Z

.

I ! BDOtrCiumT lm

1 . l . t -1.0 -0.1 4.6 4.9 a + C o a.¶ 0.4 0.4 0.8 1.0 , , . . * -

I YrQ - 0 b

m m n

LEGEND L l l r n l u U a Lolo s.0 50.0 L l l C 4- - - - /- 1- 0 m 0.017 0.012 -1 6 C

SfHPLE ANALYSIS ON PILE GROUP

CENTRIFUGE TEST KP/SMS 8 FRONT P I L E CK m.4.4a SENDING MOMENT, LATERAL PRESSURE 8 DEFLECTION

BOOIKrO. *T

1

WO

DQuLlim m

arm n a r m n

CENTRIFUGE TEST KPISMS 8 REAR P I L E

BENDING MOMENT, LATERAL PRESSURE 8 DEFLECTION TIC m4.4b

Qrmr

l i

Shear

Shearstrain Y

Fig: 5.1 Relationship between shear stress, shear strain and secant modulus

tratum

Stratum

v - ?

Fig: 5 2 Screen 1: Foundation 8s geometry input

Please mtcI typ of loading dismition

Eua LatcralprrssunutopoflayP. pb'?

Lataalprrsntrru~oflayer. ph=?

scREp(2 f i g 3 3

Lateral pressure (x scale factor) kPa 8 1 2 3 4 5 b 7 8 9 10

A CUBIC SPLINE HAS BEEN- TO YOUR DATA Poms

sazEEN2A

Fig: 5.4 '

PLEASE-- PRESSURE SCALING FAclroR = ? PRESSUkATTOP=?

NO OFPTS DEFINING PRESSURE (<18) = ? PRESSURE ATBUITOM = ?

U w * A c LL 0 cn

a

a z U

U3 W

W e

+ 4

d d r(

U Q

0 0 4 n

b E U # 0

r U

c

L Q > 0

- - - .- - .- 3

U a \

e'

* a n

I c B E E

n

W a w

LL 0

W d w

E n

n

8

s E W

LL W P

v)

n u! b6 iz VI

d d d Y / d

a;

3 d d q / h

a; .

A

Ground surface

Unloaded section

0 - 9 - 9 - ---I

I

Fig: 5.7 Lateral pressure on a pile in a deep soft layer at working load (parabolic distribution)

~

PILE - O f W I N G COMPONENTS OF DEFLECTION

- I

Deep soft layer

- -

Fig: 5.8 Relationship between pile loading & deflection components

= 0 LL

4

.- 0 0 bC3a

II II I t -

.

(a) Soil p f i l e data ?- L

0.-

\

1 2-

1 (b) Derails of test pile

(c) Comparison of soil reaction, bending moment and deflection profiles (at 30kN applied lateral load)

Fig: A.l Plancoct pile tcst (after Price, Wade, Frank & Jczquel, 1987)

(Frank, 19881

PLANCOET LATERAL PILE TEST PRESSUREMETER RESULTS

LEGEND

analysis 1981

Fig A.3 Dynamic shear modulus for uncemtnted, ncnmaUy-comdidatcd, predominantly quartz sands - smaU strains (after Robatson & Campanclla, 1983)

r

E

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The Effect of Surcharge Loading Adjacent to Piles, TRL

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