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
~
The effect of surcharge loading adjacent to piles
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
: pile group interaction factor for increase in deflection due to
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
: pile group interaction factor for increase in deflection due to
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
The effect of surcharge loading adjacent to piles page: 3
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)
The effect of surcharge loading adjacent to piles
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.
The effect of surcharge loading adjacent to piles page: 6
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
The effect of surcharge loading adjacent to piles
= (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).
The effect of surcharge loading adjacent to piles page: 10
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
The effect of surcharge loading adjacent to piles
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 effect of surcharge loading adjacent to piles page: 15
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.
The effect of surcharge loading adjacent to piles page: 16
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
The effect of surcharge loading adjacent to piles
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
The eflect of surcharge loading adjacent to piles page: 23
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)
The effect of surcharge loading adjacent to piles page: 25
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
The effect of surcharge loading adjacent to piles page: 26
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 effect of surcharge loading adjacent to piles page: 27
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 efect of surcharge loading adjacent to piles page: 30
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)
The effect of surcharge loading adjacent to piles
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.
The effect of surcharge loading adjacent to piles page: 35
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
The effect of surcharge loading adjacent to piles
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
The effect of surcharge loading adjacent to piles page: 37
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.
The effect of surcharge loading adjacent to piles
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.
The eflect of surcharge loading adjacent to piles page: 40
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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
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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
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Randolph, MF., (1981). The response of flexible piles to lateral loads. Geotechnique 31,
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pp. 1425-1445.
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Lateral loading on piles due to simulated embankment
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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.
The effect of surcharge loading adjacent to piles page: 42
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.
The efect of surcharge loading adjacent to piles page: 43
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).
The effect of surcharge loading adjacent to piles page: 44
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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