The shaft resistance of axially loaded piles in clay

D. M. POTTS* and J. P. MARTINS*

Most design procedures for estimating pile capacities are empirical in nature, and the mechanism of load transfer from a pile to the soil is not well understood. In this Paper the mobilization of shear stress along a rough pile shaft in normally consolidated clay is considered in terms of the effective stresses acting in the clay. Theoretical predictions of the stress changes which occur in the soil adjacent to the pile shaft on loading are presented and shown to be in good agreement with some experimental results. For drained loading conditions reductions in radial effective stress generally occur, and the peak mobilized angle of shaft friction is shown to be independent of initial soil stresses before pile loading. The validity of the theoretical model is shown and the loading behaviour, drained and undrained, of driven piles is examined. Comparison between these predictions and field data suggests that fabric disturbance caused by pile installation may seriously affect pile capacities.

La plupart des méthodes pour évaluer la résistance des pieux sont de caractère empirique et le méchanisme par lequel la charge est transférée du pieu au sol n'est pas bien compris. Dans cet article on admet que la mobilisation de l'effort de cisaillement le long d'un fût de pieu rugeux dans de l'argile normalement consolidée s'effectue en constaintes effectives dans l'argile. Des prédictions théoriques des changements qui ont lieu dans le sol près du fût de pieu lors du chargement sont presentees comme s'accordant bien avec des résultats expérimentaux. Dans des conditions de chargement drainées les contraintes effectives radiales sont généralement réduites, et il est démontré que l'angle maximum du frottement mis en jeu sur le fût est indépendant des contraintes initiales du sol avant le chargement du pieu. L'article démontre aussi la validité du modèle théorique et examine le comportement sous charge des pieux battus dans des conditions drainées et non-drainées. Une comparaison faite entre ces prédictions et les données des recherches in situ donne l'impression que des remaniements de la structure provoque; par ¡'installation des pieux peuvent influencer leur résistance de façon sérieuse.

INTRODUCTION

The shaft resistance of a pile may be estimated by integration of the shear stresses acting on the shaft over its surface area in contact with the soil. If an effective stress approach is adopted the maximum shear stress rmax acting on the pile shaft may be related to the local effective radial stress ct/ by

= ffr'tan()' + ca' (1)

Discussion on this Paper closes on 1 March 1983. For further details see inside back cover.

* Imperial College of Science and Technology.

where u/ is the radial effective stress acting on the pile when the peak shear stress is mobilized, 6' represents the peak mobilized angle of friction acting parallel to the pile shaft, and ca' represents the effective adhesion intercept and is usually neglected on account of the local remoulding assumed to occur during pile installation.

To estimate the maximum shear stress using equation (1), both the radial effective stress and the angle of shaft friction acting at peak conditions must be determined. As both these quantities are likely to be influenced by, among other factors, the soil type and its stress history, the type and length of the pile, the method of installation and the rate of loading, selection of appropriate values of the parameters is not simple.

At Imperial College of Science and Technology a fundamental investigation of the mobilization of shear resistance along a pile shaft is in progress. The philosophy has been to simplify the problem as far as possible, and initially to consider only the effects of pile loading. The intention has been to examine the behaviour of the soil around a short segment of a long pile well away from the influences of either the pile tip or the ground surface. Both experimental and theoretical approaches have been used to consider the effects of loading an element of a pile installed in homogeneous material, with a minimum of disturbance to either the stress field or the soil fabric. The results of some of the experimental work have been reported by Chandler & Martins (1982); the theoretical analysis forms the basis of this Paper.

The behaviour of the soil around a pile is controlled predominantly by displacement and, provided there is no slip between the pile and the soil, kinematic continuity requires that the axial strain in the soil adjacent to the pile is the same as that of the pile (zero if the pile is rigid), and the radial displacement at the interface is zero. On drained shearing most soils tend either to dilate or to contract and so, in order to satisfy the boundary constraints, complex stress changes may be required near the pile. It is therefore likely that the results of any analysis of the problem will be influenced by the kinematic aspects of the chosen constitutive law.

Analysis of the stress conditions adjacent to a pile during loading, assuming the soil to be isotropic elastic, leads to a prediction that the local

NOTATION

b (er2' — o-3')/(o-1' — o"3') cj effective adhesion intercept cu0 undrained shear strength in triaxial compression before pile installation G elastic shear modulus

J {l/6[(<7,'-<T2')2+(<72'-(T3')2

K stress ratio <7r'/<72' KB elastic bulk modulus K0NC in situ stress ratio for one dimensionally normally consolidated soil M slope of critical state line p' mean effective stress Po value of p' at intersection of current swelling line and virgin consolidation line q ffi' — <r}' in triaxial stress space r co-ordinate direction: radius S stress measure u excess pore pressure v specific volume

vt virgin consolidation volume at

unit pressure us specific volume at unit pressure on

. current swelling line z co-ordinate direction

a ratio of peak unit shaft resistance to initial undrained shear strength yrz shear strain

Ô' peak mobilized angle of friction

along the pile shaft 0 lode angle

k slope of swelling line in u—In (p') space

a slope of virgin consolidation line in u-ln (p') space aT', a,', og' effective normal stresses in coordinate directions <7r0', <t,0', ago' effective normal stresses before pile loading

°Y> °Y principal effective stresses

rmax maximum shear stress on pile shaft t,z shear stress mobilized on rz plane t average shear stress on pile shaft </> angle of shearing resistance tp inclination of major principal stress with respect to the vertical direction

Subscripts

r radial direction 0 hoop direction z axial direction 1,2,3 major, intermediate, minor

0 value before pile installation

1 initial

radial and axial stresses remain approximately constant (Lopes, 1980). The changes in radial stress observed by Chandler & Martins (1982) are therefore not predicted. If the soil remains elastic until some form of strength criterion is reached, such as the Mohr-Coulomb condition, then the situation shown in Fig. 1 is obtained. The value of <5' is strongly dependent on the initial stress ratio K (<7ri' = KiT2i') and the c'-<j>' parameters of the soil. The predicted variation of tan ¿'/tan 4>' with K for a material having c' and 4>' values of zero and 23 0 respectively (applicable to the kaolin used in the experimental investigation) is shown in Fig. 2. Comparison with experimental results (Fig. 2) shows the inadequacies of the predictions. Similar conclusions arise, whether the soil is assumed to be linear or non-linear elastic (Lopes, 1980).

To improve the theoretical predictions, analyses assuming the soil to be elasto-plastic, behaving in accordance with a form of Modified Cam Clay (Roscoe & Burland, 1968) were performed. Work at the University of Cambridge has indicated that such a theoretical model provides an adequate description of the behaviour of many normally and lightly overconsolidated soils. Due to the complexity of such an analysis a finite element com-

puter code was used to obtain numerical predictions.

The theoretical procedure and soil model are described; the predictions agree well with the experimental results. The soil model and the theoretical procedures used are similar to those employed by Potts & Martins (1982). Some of the results obtained in this earlier study in which the theoretical procedures were applied to driven piles are considered.

FINITE ELEMENT ANALYSIS

To model the behaviour of the soil around a short segment of a long pile, well away from the influence of the pile tip and ground surface, the geometry in Fig. 3 was used. The dimensions of the mesh were selected for ease of comparison with the experimental conditions but no loss of generality is implied as the predicted results are independent of the assumed scale.

The mesh consists of a horizontal disc of soil 5 mm thick with an external radius of 345 mm. The modelled pile of 7-5 mm radius is co-axial with the disc. This disc was divided into 20 isoparametric elements each with eight nodes. Adjacent to the pile shaft the elements are 0-25 mm wide.

S', mobilized angle of shaft friction Stresses acting on the pile shaft at failure

Direct stress u'

Failure condition Initial conditions

1. Mohr's circle of stress for elastic analysis

Active

Experimental results ---

Elasto-plastlc ^ prediction

Elastic prediction with Mohr-Coulomb criterion

Passive

Fig. 2. Variation of tan (V/tan </>' with initial stress ratio K

To model the loading of the pile, axial displacements were imposed over the boundary AF, To represent the infinite extent of the disc zero displacement boundary conditions were imposed over the boundary region CD. Parametric studies were performed varying the element sizes, the number of elements and the radial distance to the boundary CD in order to verify that the mesh accurately modelled the problem under consideration. Along the boundaries AC and FD the displacements were tied, such that at any radius r the displacements both vertically and radially at corresponding nodes on AC and FD were forced to be identical. This resulted in a vertical line such as EB remaining vertical during loading. The magnitudes of both the vertical and radial displacements of this line are unknown at the outset of the calculation and are determined by the analysis. This tying of displacements was achieved in the finite element analysis by giving the same degree of freedom number to nodes at the same radius along AC and FD. This also resulted in a smaller stiffness matrix and essentially reduced the problem to a one-dimensional situation in which all variables were a function of radius only. Initial stresses specified at the start of the analysis were chosen to represent the stresses believed to exist around the model piles immediately before loading.

Pile displacements were applied incrementally and the finite element equations solved using an accelerated form of the initial stress approach with reduced integration. Typically 50 increments of pile displacement were used with an average of six iterations per increment. A parametric study was performed to ensure that the increment size was sufficiently small to provide accurate predictions.

SOIL MODEL

The soil model adopted for the finite element calculations is a form of the Modified Cam Clay model of Roscoe & Burland (1968). It is assumed that the consolidation characteristics of the soil may be adequately represented in t'-ln (p') space by the virgin consolidation line

v = V, -/.In(p') (2)

and the family of swelling lines

v = vs — icln (p') (3)

where the specific volume v is 1+e, the mean effective stress p' is (a/ + ae' + cr.')/3, /. is the slope of the virgin consolidation line, k is the slope of the swelling lines and u, is the virgin consolidation specific volume at unit pressure. A, k and u, are material properties.

Behaviour under increasing deviator stress is assumed to be elastic until a yield curve of the form

F = S2-(p0'/p'-l) = 0 (4)

is reached, at which point strain hardening/softening plastic behaviour occurs. In equation (4) p0' is the value of p' at the intersection of the current swelling line and the virgin consolidation lines and

S = J/(p'g(0)) (5)

where the second invariant J of the effective stress tensor is defined by

J2 = 0-5 trace s2

= l/6[(<™02+(ff2'~f73')2+((T3'--<>2]

the deviatoric stress tensor s being a —pi. The lode angle 0 is -l/3[sin~' {1.5 v/3.dets/J'5j] where

Co-ordinate system

Pile-r1 face N

'Outer boundary

-46 pile radii

Fig. 3. Schematic diagram of finite element mesh for simulation of ideal case of a short element of a long pile in an infinite soil mass

dets is the determinant of the tensor s. Alternatively 0 = tan~ 1 [_(2b— l)/v'3], where b = (a2 — a3')/(ci' — (see Fig- 4). The function g(0) expresses the manner in which the yield surface varies with the lode angle. In the present studies g(0) is taken as either a Mohr-Coulomb hexagon given by

g(0) = sin 4>'/[cos 0 + l/v/3(sin 0 sin <£')] (6)

where (j)' is the Mohr-Coulomb angle of shearing resistance or as a circle with

g{0) = M/%/3 (7)

where M is the gradient of the critical state line in q -p triaxial space.

Equation (4) plots as an ellipse, in terms of p and J above each swelling line given by equation (3) and the major axis of the ellipse is a function of p0' which varies with v in accordance with equation (2). The intersection of the yield surface with a deviatoric plane produces either a MohrCoulomb hexagon as described by equation (6) or a circle with a radius M/J3.

The plastic strain increment vector is assumed to be perpendicular to a plastic potential surface which is also given by equation (4) but with

g(0) = AV[l + Fsinf3»)]z (8)

where Y and Z are material constants and the parameter X varies such that when the soil is yielding the current plastic potential passes through the current state of stress. The values of the parameters may be determined from experimental data concerning the shape of the plastic potential in the deviatoric plane. However, frequently such data are not available and the parameters may be selected to represent a variety of convex surfaces passing through known end points (as may be determined by triaxial compression and plane strain tests, for example).

The yield function and plastic potential surfaces

therefore differ only in their shapes in the deviatoric plane. In terms of the nomenclature of classical plasticity the yield surface and its plastic potential are non-associated. However, if the constants Y and Z are set to zero and unity respectively the shape of the plastic potential in the deviatoric plane reduces to a circle. If in addition equation (7) is used for defining g(0) appropriate to the yield function then X = M/N/3, and the plastic potential becomes identical to the yield function, producing associated conditions.

Soil behaviour under unloading and reloading of the effective stress p' is assumed to obey equation (3) which gives the elastic bulk modulus KB as

KB = vp'/K (9)

This expression indicates that the elastic bulk modulus depends on the stress level p' and the specific volume v. In the original version of Modified Cam Clay (Roscoe & Burland, 1968) elastic shear strains were neglected; however, if the model is to be incorporated into an elasto-plastic finite element formulation, neglect of elastic shear strains produces problems when purely elastic behaviour is considered. To overcome this difficulty a constant value of the shear modulus G, independent of stress level, has been adopted.

To specify the soil model completely, values of G, M or ()>', /., k, i\, Y and Z are required.

Some of the implications and limitations of the soil model are now examined. If an element of soil originally in a normally or lightly overconsoli-dated state is sheared then peak conditions will occur as the state of stress approaches the critical state (S = 1). The model is unable to predict any shear stress reduction with further shear strain and will not therefore simulate the occurrence of residual conditions. Once peak conditions have been obtained (critical state) the model predicts no further change in volume. This, combined with the fact that in the pile problem under investigation a zero strain constraint is imposed in the axial direction at the soil-pile interface, leads to two observations.

First, at peak conditions the directions of the principal strain increments are inclined at ±45' to the pile axis. As coincidence of stress and strain increment directions have been assumed (in accordance with classical plasticity theory) the principal stress directions are also inclined at + 45 to the pile axis. This leads to the prediction that at the pile-soil interface

<)' = tan-1 (sin </>') (10)

where </>' is the angle of shearing resistance mobilized at the critical state. This result is a direct consequence of the assumption of coincidence of stress and strain increment directions together

with the assumption of no volume change (i.e. critical state conditions) at peak. It is not dependent on the finer details of the model and will result from the adoption of any plastic model which predicts a zero volume strain at peak conditions.

Second, Potts & Gens (1982) showed that in a situation where one of the direct strain increments is zero, in combination with a zero volumetric strain increment, the lode angle 0 at peak conditions is dependent only on the shape of the plastic potential in the deviatoric plane. This implies that by selecting the shape of the plastic potential the lode angle at failure may be preset. For example, if the shape of the plastic potential in the deviatoric plane is specified as circular, then peak conditions will occur at a lode angle of 0 = 0 (or b = 0-5).

These observations lead to the prediction that for a normally or lightly overconsolidated soil the peak mobilized angle of friction along the pile shaft will always be equal to the expression given by equation (10) and is independent of the initial stress conditions. This result is in direct agreement with the experimental observations (Fig. 2).

The adoption of a yield surface that is circular in the deviatoric plane (equation (7)) implies a considerable variation of the angle of peak shearing resistance 4>' with lode angle 0. This is not in accordance with experimental observations as most clays have </>' values which vary little with lode angle, having perhaps only a 1L or 2 variation of 4>' between triaxial compression and plane strain. It is therefore felt that the adoption of the Mohr-Coulomb hexagon given by equation (6), which produces a constant </>' independent of lode angle, is more realistic. However, the interpretation of the resulting predictions is more difficult because of the complex stress paths followed. Finite element calculations using both a surface of revolution and a Mohr -Coulomb hexagon are therefore discussed. The two sets of material parameters selected are

(a) soil model A: M = 0-9, a = 0-25, k = 0-05, r, = 3-65, G = 18 000kN/m2. Y = 0-0, Z = 10

(b) soil model B: <f>' = 23 /. = 0-25, k = 0-05, r, = 3-65, G = 18 000kN/m2, Y = 0-2535, Z = 0-229.

Calculations based on soil model A therefore assume that the shapes of both the yield surface and plastic potential are circular in the deviatoric plane. This will result in peak shaft resistance occurring at a lode angle 0 = 0'. However, calculations based on soil model B assume a Mohr-Coulomb hexagon for the shape of the yield surface and a general shape (equation (8)) for the plastic potential. The values of Y and Z adopted

ensure that the plastic potential is always convex and define the lode angle at peak conditions to be 0 = —9-8' (this is equivalent to b = 0-35).

The values of M, </>', /., k and Vj chosen were obtained from Steenfelt, Randolph & Wroth

(1981), and represent the kaolin used in the experimental investigation (Chandler & Martins, 1982). The value of G = 18 000kN/'m2 was determined from the initial loading stage of a typical pile test.

COMPARISON WITH EXPERIMENTAL RESULTS

The experimental apparatus and testing procedures are described by Chandler & Martins

(1982); only a brief outline is presented here. A cylindrical sample of kaolin, 102 mm in diameter and 150 mm high, was first prepared by one-dimensional consolidation from a slurry. This was then placed in a purpose-built test cell, in which radial and axial stresses could be independently applied to the sample. Anisotropic consolidation with ar' = KaJ was then performed until the required stress level had been reached. A 15 mm dia. pile was then installed by a procedure intended to (and subsequently confirmed to) cause a minimum of disturbance to either the stress field or the soil fabric in the soil surrounding the pile. The apparatus ensured that only shaft resistance and no end-bearing resistance was generated on loading the pile. Loading was performed at a

I D Top platen c

Co-ordinate system

A Bottom platen I -Fi 1 mm-W

-51 mm

Fig. 5. Finite element mesh for simulation of model pile tests

constant rate of axial displacement, sufficiently slow to ensure fully drained conditions in the soil. During the tests the pile load and displacement were monitored and in two tests the radial stress against the pile shaft was measured.

To investigate how well the experimental test apparatus modelled the idealized situation under consideration, analyses using the finite element meshes shown in Figs 3 and 5 were performed. The analysis using the mesh shown in Fig. 5 was performed in order to simulate the experimental conditions. The mesh consisted of 196 isoparametric elements each with eight nodes. Immediately adjacent to the pile shaft the elements were 1 mm wide. The end platens of the experimental apparatus were modelled by imposing zero vertical and radial displacements along the boundary AB and CD. The pile loading was simulated by imposing increments of axial displacement along the boundary region EF, and the radial rigidity of the pile was modelled by preventing radial movement of the boundary. Over the remaining boundaries of the sample the stresses were set to the values applying immediately after pile installation,, and the same stresses were also input as initial stresses in the soil.

The predictions using the two different geometries are compared in Fig. 6 for a test in which K = 0-7. The sample was assumed to be normally consolidated and soil parameters from model A were adopted corresponding to a surface of revolution for the shapes of both the yield surface and plastic potential in the deviatoric plane. In Fig. 6 variations of stresses er/, ae', erz' and xr, are indicated for a pile which is loaded to 90% of peak capacity and is at a displacement of 5-6% of one

pile radius. The close agreement between the two sets of predicted stresses adjacent to the pile is encouraging as this is the region of greatest importance. Further from the pile there is some discrepancy between predictions of irz and az'. This arises as a result of the lack of shear restraint imposed on the circumferential boundary of the sample in the experimental apparatus. In principle this could be rectified by the provision of shear reinforcement on this boundary.

Most tests were performed on samples of kaolin in a normally consolidated state, with different values of initial stress ratio K. The experimental results for a test on initially isotropically consolidated soil (K = 1) are shown in Figs 7-9. Fig. 7 indicates the variation of the pile load with displacement. There is a rapid reduction in pile capacity after peak. The variations of the average shear stress f (i.e. pile load/surface area of the shaft) and the measured radial stress acting on the pile, with pre-peak displacement, are shown in Figs 8 and 9 respectively. Predictions based on soil model B with a Mohr-Coulomb hexagon for the shape of the yield surface in the deviatoric plane are also indicated. There is good agreement between the predictions and the experimental results.

Once peak conditions have been reached the analysis predicts no reduction in shear stress with further pile displacement: a result which is not in agreement with the experimental observations. This lack of agreement after peak is not surprising as the experimental evidence (Chandler & Martins, 1982) suggests that particle orientation effects are becoming important and that residual conditions are being approached. Modified Cam Clay is incapable of predicting such conditions.

Fig. 6. Predicted radial distribution of stresses using the ideal (Fig. 3) and the model test (Fig. 5) meshes

Fig. 7. Experimental load displacement curve (K = 1)

Pile displacement : percentage of pile radius

Fig. 8. Variation of shear stress t with pile displacement — comparison between computer predictions (model B) and experimental results (K = 1)

100 70

/ Computer prediction, model B Model test result

0 5 10 15 20

Pile displacement: percentage of pile radius

Fig. 9. Variation of radial stress ar' with pile displacement—comparison between computer predictions (model B) and experimental results (K, — 1)

Radial distance from pile centre line: pile radii Fig. 10. Variation of shear strain with radial distance from the pile at various stages of loading (drained, K = 1)

Predicted variations of shear strain yrz with radial distance from the pile shaft, for various stages during the pile loading, are shown in Fig. 10 for isotropically consolidated material. As peak conditions are approached extremely high shear strains are predicted in the immediate vicinity of the pile. Curve C in Fig. 10 corresponds to a pile displacement of 0-42 mm; the equivalent shear strain distribution for an isotropic linear elastic soil (G = 6880 kN/m2) at this pile displacement and stress level is also indicated. The difference in shear strain distributions is apparent and the strain magnitudes for the elastic material close to the pile are much smaller. The magnitude and concentrations of strains close to the pile shaft predicted by Modified Cam Clay are in good agreement with the observations made on thin sections taken during the experimental study (Martins, 1982). As such large shear strains are predicted before peak it is not surprising that in practice residual conditions are rapidly approached after peak.

The agreement between prediction and experiment before peak is encouraging and lends credibility to the theoretical analyses. It allows the predicted stress changes within the soil mass to be examined with confidence. Such detailed information about stress would be very difficult, if not impossible, to obtain experimentally. In the experimental study only limited information about the stresses acting around the pile shaft was obtained and so the theoretical predictions may be used to complement the measurements and hence lead to a better understanding of the soil behaviour.

EFFECT OF INITIAL STRESS CONDITIONS Drained loading

To test the theoretical model further, a parametric study was performed so that it was possible to compare the predicted and observed effects of the initial stress ratio on the subsequent pile loading behaviour. It was assumed that the stresses were uniform throughout the soil before pile loading and that the principal stresses were in the ratios ar' = <re' = Ka:'. Values of K of 0-5-2-0 were considered, and in all the analyses the stresses were selected such that the same initial specific volume was used.

The effective stress paths for an element of soil immediately adjacent to the pile shaft are shown in Figs 11 and 12, for fully drained pile loadings. The paths in Fig. 11 are based on the soil parameters of model A (producing a circle for the yield surface in the deviatoric plane). Model B (producing a Mohr-Coulomb hexagon for the yield function in the deviatoric plane) gave the results in Fig. 12. In both plots the values of J and p' have been normalized by the undrained shear strength in triaxial compression before pile installation cu0. As the installation technique caused minimal disturbance, cu0 is also the undrained strength immediately before loading. As the initial specific volumes are equal in all cases, so too are the undrained shear strengths.

Figure 11 indicates that all the initial stress states lie on the curve AB, which represents the intersection of an undrained plane (v constant) with the state boundary surface. In fact the curve AB represents the effective stress path that would be followed during an undrained test performed on

Fig. 11. Stress paths for drained loading (based on soil model A)

a normally consolidated sample at the above specific volume. A measure of the initial undrained shear strength is provided by JA, the value of J at A (the critical state). cu0 and JA are related by

i-u0 = J\ cos

where 0A is the lode angle at A; in this case 0A = 0.

The situation represented in Fig. 12 is more complicated. The curves BC, BD and BE represent the intersection of an undrained plane with the state boundary surface for triaxial compression {0 = — 30 ), triaxial extension (0 = +30) and 0 = — 9-8 respectively. A measure of the undrained shear strength, appropriate to 0 = —9-8°, before pile loading is given by JE. Peak shaft resistance occurs when the stress paths reach the critical state line corresponding to a lode angle of 0 = - 9-8'.

For initial stress ratios less than or equal to unity the stress path travels continuously to the left, reaching the critical state line after considerable reduction in the mean effective stress p'. Where the initial stress ratio exceeds unity the stress path first moves in the direction of increasing p\ but is followed by a considerable reduction as the critical state line is approached. In all cases, with the exception of K = 2-0, there is a net reduction in p'. Had the soil been modelled as an isotropic elastic material then no decrease in p' would have been predicted.

It is predicted that for initial stress ratios below

0-7 and above 2-0 the peak shear stress mobilized by the pile in drained loadings will not be much greater than, and may in fact be less than, the initial undrained shear strength (e.g. K = 0-5).

The variations of several components of stress and strain, with pile displacement, for an element of soil immediately adjacent to the pile shaft, are given in Figs 13 and 14, for the initial stress ratios 0-7 and 1-5 respectively; both analyses were based on soil model B. There is a net reduction in the radial effective stress and in the initial stage of loading S remains approximately constant, with the soil behaving in a predominantly elastic fashion. To sustain the increase in t„ during this stage of loading, considerable rotation of the principal stresses occurs. Predictions for cases starting at different stress ratios followed similar trends.

In Fig. 15 the predicted variation in the radial stress on loading to peak conditions, expressed as a percentage of the initial radial stress, has been plotted as a function of the initial stress ratio. For initial stress ratios of 0-5-0-7 the reduction in radial stress is sensitive to the initial stress ratio, and as the stress ratio approaches active conditions an increase in radial stress is predicted. Fig. 15 also shows the results of the experimental investigation (Chandler & Martins, 1982); again good agreement between the predictions and experimental results is indicated.

The use of the Modified Cam Clay constitutive

Critical state line (9 = 30°)

Undrained stress path 8 = -30° Undrained stress path 9 = -9 8° Undrained stress path 9 = + 30°

Fig. 12. Stress paths for drained loading (based on soil model B)

Fig. 13. Variation with pile displacement of stresses in the soil adjacent to the pile shaft (drained, K = 0-7)

Fig. 14. Variation with pile displacement of stresses in the soil adjacent to the pile shaft (drained, K — 1-5)

Experimental results

# 80- ------

Theoretical prediction, 40 • model B

ol-1-1-1

05 10 1-5 2-0

Initial stress ratio K Fig. 15. Theoretical and experimental variations of the radial stress ar' acting at peak load with initial stress ratio K (drained)

Fig. 16. Stress paths for undrained loading (based on soil model A); stresses normalized by the initial undrained shear strength in triaxial compression

Fig. 17. Stress paths for undrained loading (based on soil model B); stresses normalized by the initial undrained shear strength in triaxial compression

law has led to good agreement between theoretical prediction and experimental results for drained loading. The stress conditions enforced around the model piles were initially uniform. They were chosen for simplicity of interpretation and not intended to represent directly any particular type of field pile or installation procedure. The analysis is now extended to investigate undrained behaviour and the behaviour of driven piles.

Undrained loading

To investigate the soil response to rapid pile loading the parametric study was repeated, enforcing undrained conditions. The total stress paths obtained for the soil adjacent to the pile shaft are shown in Figs 16 and 17. The results in Fig. 16 are based on the assumption that both the yield and plastic potential surfaces are circular in the devia-toric plane (soil model A), whereas the predictions in Fig. 17 are based on the assumption of constant 4>' and with b = 0-35 imposed at peak conditions. In both cases the initial effective stresses before pile loading are consistent with the specific volume used in the investigation of drained loadings. In Fig. 16 the portions of the curve BA to the left of the initial stress state for each value of K represent the effective stress paths followed. Pore pressures generated during pile loading are represented by the horizontal distances between the effective and total stress paths. The adoption of a MohrCoulomb hexagon for the shape of the yield surface in the deviatoric plane has the effect of making interpretation less straightforward as the effective stress paths depend on the initial stress ratio (Fig. 17).

When the initial stress ratio K exceeds unity the mean total stress increases initially and is accom-

panied by a large localized excess pore pressure. For the case in which K is unity the total stress path remains almost vertical, and when K is less than unity the total stress path travels continuously to the left. When the initial stress ratio is 0-7, negative pore pressures are generated initially, but net.positive pressures are predicted at peak load. In the case of K = 0-5 large negative pore pressures remain at peak. The prediction of negative pore pressures during the shearing of a normally consolidated clay may, at first, seem surprising. However, it is a direct consequence of the kinematic boundary conditions of the problem, together with a realistic constitutive soil model, which causes a reduction in the total mean stress that outweighs any pore pressures generated due to shear alone.

DRIVEN PILES

In the field, driven piles may usefully be classified as either full or partial displacement piles, depending on the type of pile and the method of installation. Thus solid piles, closed-end pipe piles and pipe piles which plug during driving are all examples of full displacement piles, whereas pipe piles which do not plug during installation are partial displacement piles.

Installation of low displacement piles will probably have a smaller and more localized effect on stresses in the surrounding soil than will the installation of full displacement piles. A safe assumption about the stresses around a low displacement pile might therefore be that the stresses are unaffected by the installation and may be represented by <rr' = Og = K0 a J. These stress conditions are the same as those used in the model tests and considered analytically. If this is the case,

P'/cui

Fig. 18. Stress path for a soil element immediately adjacent to a pile installed in normally consolidated Boston blue clay

the results presented here may have relevance to the loading of low displacement piles installed in normally consolidated or lightly overconsolidated clays.

The installation of full displacement piles is expected to have a more pronounced effect on the local soil stresses. However, in view of the dearth of reliable field measurements of the radial stresses around displacement piles, the assumption of no change may again be a safe one to make in design, for the present. Research into the prediction of likely stress changes in the soil due to pile driving and subsequent consolidation has been done at the University of Cambridge (e.g. Randolph, Carter & Wroth, 1979); the predictions of the radial effective stresses acting around a pile after consolidation have yet to be verified by field measurements.

This work is based on the cavity expansion theory incorporating the Modified Cam Clay model and the finite element method was used to obtain numerical predictions. An important prediction arising from this research is that, after driving and subsequent consolidation, the soil adjacent to the pile is in a normally consolidated state, irrespective of its overconsolidation ratio before pile installation. Zero vertical strain is assumed throughout the cavity expansion analysis. As this is equivalent to assuming that no heave occurs, the predicted stress changes are likely to form an upper bound to those actually occurring.

In an attempt to examine the stress changes that

may arise on subsequent pile loading the results of two of the analyses presented by Randolph et al. (1979) and Wroth, Carter & Randolph (1980) were used by Potts & Martins (1982) to obtain initial stress conditions for numerical calculations employing the finite element mesh shown in Fig. 3 The cases selected were that of a pile installed in an initially normally consolidated Boston blue clay and that of a pile installed in London clay with an initial overconsolidation ratio of eight. As a form of the Modified Cam Clay model which had rotational symmetry in the deviatoric plane was adopted in the cavity expansion analysis, soil model A was used in order to be consistent. The results arising from these analyses are now summarized.

Pile installed in normally consolidated Boston blue clay

To represent Boston blue clay, the soil parameters for the Modified Cam Clay model were taken as M = 1-2, A = 0-15, k = 0-03, C = 12 000 k N nr.

r, = 2-83, Y = 00 and Z = 1-0.

Pile loading was simulated by applying increments of shaft displacement and the analysis performed first under fully drained conditions. The resulting stress path for a soil element adjacent to the pile shaft predicted by the analysis is shown in Fig. 18 line BC). Fig. 18 indicates that the effective

Pile displacement: percentage of pile radius Fig. 19. Variation of stresses adjacent to a pile installed in normally consolidated Boston blue clay on drained loading

0 5 10

Piledisplacement. percentageof pile radius

Fig. 20. Variation of stresses adjacent to a pile installed in normally consolidated Boston blue clay on undrained loading

-Pore pressures generated on driving

Pore pressures generated on loading

1 3 5 10 2<

Radial distance from pile centre line: pile radii Fig. 21. Pore pressure variation with radius

stress path followed during the loading travels to the left with a consequent reduction in the mean effective stress p'. The variations with pile displacement Of ffr', <7e', <TZ\ T„, J, Vrz and "A for a soil element adjacent to the pile shaft are shown in Fig. 19.

In Figs 18 and 19 the stresses have been normalized by cui, the undrained shear strength appropriate to a lode angle of 0 = 0°, after pile installation and consolidation. There is a reduction in ffr' of about 40% during pile loading.

The analysis was repeated under undrained conditions and the total stress path for a soil element adjacent to the pile shaft is shown in Fig.

18. The variations with pile displacement of cr/, erz', os', Trz, yrz, J, u and t¡/ in this soil element are shown in Fig. 20, where u is the excess pore pressure generated during pile loading. The predicted pore pressure distribution with radius at peak conditions is shown in Fig. 21; the pore pressures have been normalized with respect to the undrained shear strength cu0 before pile installation and the radial distance has been normalized with respect to the pile radius r0 and represented on a logarithmic scale. Also shown are the predicted pore pressures generated during pile driving (Randolph el ai, 1979). During pile loading the pore pressures are much smaller and more localized than those

Fig. 22. Stress path for a soil element adjacent to a pile installed in overconsolidated London clay

0 5 10

Pile displacement: percentage of pile radius Fig. 23. Variation of stresses adjacent to a pile installed in overconsolidated London clay on drained loading

generated on driving. The times for complete dissipation of pore pressures generated on loading are likely to be short compared with the time required for full consolidation following driving, and the question arises as to whether pile loading is a drained or an undrained phenomenon.

Pile installed in overconsolidated London clay

The values of the soil parameters for the Modified Cam Clay model were taken as

M = 0-984, /. = 0161, k = 0-062, G = 6750 kN/rn2, t;, = 2-759, Y = 0-0 and Z = 10.

Pile loading was again simulated by applying increments of shaft displacement and the analysis performed under fully drained conditions. The predicted stress path for a soil element adjacent to the pile shaft is shown in Fig. 22 (line BC). The variations, with pile displacement, of ar', a J, a„', zr,, yr:, iji and J for a soil element adjacent to the pile shaft are shown in Fig. 23. In Fig. 24 the

Pile displacement (S/r) x 1 (r

0 2 3 4

Radial distance from pile centre line: pile radii Fig. 24. Variation of shear strain with radius

Experimental results, peak values

/Predicted results, f model B

1-0 1-5

Initial stress ratio K

Fig. 25. Variation of « with stress ratio K

predicted variations of shear strain yrz with radial distance from the pile shaft are shown for various stages of loading. As peak conditions are approached, high shear strains are predicted in the immediate vicinity of the pile. If the soil model were to incorporate even gradual strain softening then the behaviour after peak would be brittle and progressive failure would be predicted for compressible piles.

APPLICATION TO PILE DESIGN

Common practice in the design of piles is to relate the unit shaft resistance to the undrained shear strength of the soil before pile installation using the empirical relation (Skempton, 1959)

Tshaft = ^''uO (11)

Results from the numerical analysis have been used to determine equivalent values of a corresponding to the model test conditions; these are presented in Fig. 25. The Mohr-Coulomb hexagon was used for the yield surface, and the values of y. were determined using the initial value of undrained shear strength in triaxial compression. The experimentally observed values are shown for comparison. No attempt has been made to model the behaviour after peak, and hence no direct comparison with the residual a values is possible.

The effective stress approach to pile design suggested by Chandler (1968) and Burland (1973)

e- 100

-S 0 75 E

Burland (1973)/Chandler (1968) prediction

Computer prediction model B

10 1-5

Initial stress ratio K Fig. 26. Variation of (r,„,v <rr0' tan </>') with stress ratio K

uses equation (1). The value of ca' was taken to be zero; as a first approximation the radial effective stress at peak load was assumed to be equal to the initial value before pile installation ar0', and S' was taken to be <f>'pcak. The predicted variation of the ratio (Tm^/ar0' tan 4>') with initial stress ratio K is shown in Fig. 26, together with results derived from the experimental work. If 5' is selected as tan " 1 (sin <p') rather than 4>\ better agreement with the experimental data is obtained.

Partial displacement piles in normally consolidated clay

In practice, the observed values of a generally lie in the range 0-5-1-2 for driven low displacement piles in normally and overconsolidated clays (Kraft, Focht & Amerasinghe, 1981), and are hence lower than those observed in the model tests or predicted by the theoretical analysis presented (see Fig. 25). Although there are probably many contributory factors which reduce the field strengths, an important effect is that of the soil fabric disturbance which occurs in the soil adjacent to the pile shaft during pile installation. (This type of disturbance was deliberately minimized in the model tests.) The large relative displacement between soil and pile is thought to result in the formation of a shear zone within the soil immediately adjacent to the pile (Tomlinson, 1970; Martins, 1982) which will have an available strength between the residual strength and the intact strength. The actual strength will depend on the effective stresses in the soil, the method of pile installation and the nature of the soil. On loading the pile, slip will occur on the shear surface when its strength is exceeded and further displacement will cause the strength to decay to the full residual value. This implies that long piles will suffer from the effects of progressive failue, and the y. values measured will tend towards those associated with residual conditions.

In order to obtain a qualitative understanding of the effect of such a shear zone on the measured a values, the drained analyses of the model tests are re-examined from the point of view of reduced angles of shearing resistance acting on a vertical surface adjacent to the pile. Slip is assumed to occur when the limiting angle of shearing resistance is mobilized on this discontinuity. In practice the strength available on such a surface will depend on several factors and so the analysis of the case with K = 1-0 is reviewed to examine the effects of introducing a range of possible strengths on the discontinuity—from the intact value to the true residual value, as measured in a ring shear apparatus. In Fig. 27 the results of the analysis arc plotted in the form of the variation of the ratios nr'/cu0, Tr:/cu0 and Tr:/<jr' with pile displacement.

The analysis used a Mohr-Coulomb hexagon for the shape of the yield surface in the deviatoric plane. If a failure value for the ratio i^/c/ on the discontinuity is selected then the available shear strength may be determined from Fig. 27. For example, if a shear surface with strength Tr./(Tr' = 0-2 is assumed to exist, then the maximum value of xrz/cu0 is 0-75. It is assumed that the presence of the discontinuity does not affect the continuum analysis until the theoretical strength is exceeded.

In Fig. 28 values of a evaluated using this procedure are shown as a function of the threshold values of (xrJar')max on the shear surface. The measured residual strength of the soil modelled corresponds to xrzj<jr' = 0-2, and the assumption of threshold values between the known intact and residual values leads to sensible agreement with field data (Kraft et al., 1981).

Full displacement piles

Randolph et al. (1979) and Wroth et al. (1980) predicted that after installation and consolidation the undrained shear strength of the soil adjacent to a full displacement pile will be approximately 1-6 times the initial in situ value. The drained analyses (assuming the soil around the pile to be intact) showed that the peak shear stress acting on the shaft will be about 20% greater than the undrained shear strength of the soil before loading. Together these predictions imply x values well in excess of unity, and this is contrary to the available field data.

The analysis of the pile installed in normally consolidated Boston blue clay was therefore reexamined to investigate the possible effects of a shear zone formed adjacent to the pile during installation. In Fig. 29 the effect on the overall x value* of various discontinuity strengths is shown. To predict an y. value of unity, a threefold reduction in strength from peak to residual must be postulated on the shear surface. This raises doubts about the applicability of cavity expansion theory (using Modified Cam Clay as the constitutive law) to the prediction of stress changes caused by pile installation. This question can be satisfactorily resolved only by direct measurement of the radial effective stresses around piles as they are installed and subsequently loaded.

CONCLUSIONS

The behaviour of soil around loaded piles has been modelled by finite element methods, using an

* The values of y. have been adjusted in accordance with the factor of 0-85 suggested by Wroth et al. (1980) to account for the variation of </>' in the deviatoric plane implied by the adoption of a surface of revolution for the yield function.

r/ff/ = 0-3 r/o/ = 0-25 r/<7 ' = 0-2

5 10 15 ~

Pile displacement: percentage of pile radius

Fig. 27. Effect of shear surfaces on the available shaft friction

10 1-5

Initial stress ratio K

Fig. 28. Variation of x with stress ratio K, for various possible discontinuity strengths (x,,lar')max

0 0-2 0-4 0-6

Fig. 29. Effect on x of a shear zone parallel to the pile shaft

elasto-plastic constitutive law to represent the soil.

The theoretical model was used to analyse experimental pile tests described by Chandler & Martins (1982) and has shown encouraging agreement with the results. This has led to a better understanding of the load transfer mechanism in a problem dominated by kinematic restraints. The theoretical model was then used to predict the behaviour of driven piles.

A direct consequence of the soil model selected is that the peak angle of friction that can be mobilized along a pile shaft is independent of the initial stress conditions and is given by <5' = tan ~ 1 (sin <p'). This prediction agrees with experimental observations.

Analyses of piles loaded under drained conditions in normally consolidated clay indicate that large reductions in the mean effective stress in the soil adjacent to the piles will occur, and are generally accompanied by a corresponding reduction in the radial effective stress. In the analysis of a full displacement pile a 40% reduction in radial stress was predicted.

All analyses predicted large shear strain concentrations adjacent to loaded piles. This is supported by observations of microfabric changes in the model pile tests, and by the experimental observation that residual conditions are rapidly approached after peak. This is important because of the implication of progressive failure that may occur when long, and thus compressible, piles are used.

Consideration of undrained pile loading indicates that the generation of excess pore pressure is localized and that rapid dissipation will occur. This raises the question of whether pile loadings are drained or undrained in practice. Where pile installation causes the formation of a shear zone along the pile, slip may occur during loading before the largest theoretical pore pressures have been generated. It is believed that these two factors explain why significant pore pressures are seldom measured in practice.

The study has shown the importance of obtaining reliable field measurements of radial effective stresses acting on a pile after installation and during pile loading, and the need to understand better the effects of fabric disturbance caused by pile installation.

ACKNOWLEDGEMENTS

The Authors are indebted to their colleagues, particularly Mr A. Gens and Dr R. J. Chandler, for stimulating discussions and assistance. Special

thanks are due to Professor J. B. Burland for his help and continuing encouragement.

The work described was performed under the auspices of the London Centre for Marine Technology. Mr Martins was supported by an award from the Science and Engineering Research Council, Marine Technology Directorate.

REFERENCES

Burland, J. B. (1973). Shaft friction of piles in clay— a simple fundamental approach. Ground Engng 6, No. 3, 30-42.

Chandler, R. J. (1968). The shaft friction of piles in cohesive soils in terms of effective stresses. Civ. Engng Publ. Wks Rev. 63, 48-51. Chandler, R. J. & Martins, J. P. (1982). An experimental study of skin friction around piles. Geotechnique 32, No. 2, 119-132. Eide, O., Hutchinson, J. N. & Landva, A. (1961). Short and long term test loading of a friction pile in clay. Proc. 5th Int. Conf. Soil Mech., Paris, 45-54. Kraft, L. M„ Focht, J. A. & Amerasinghe, S. F. (1981). Friction capacity of piles driven into clay. J. Geotech. Engng Div. Am. Soc. Civ. Engrs 107, GT11, 1521-1541.

Lopes, F. de R. (1980). Discussion. In Recent developments in the design and construction of piles, pp 387-389. London: Institution of Civil Engineers. Martins, J. P. (1982). Shaft resistance of axially loaded piles in clay. PhD thesis, University of London. In preparation.

Potts, D. M. & Gens, A. (1982). The effect of the plastic-potential in plane strain boundary value problems. In preparation.

Potts, D. M. & Martins, J. P. (1982). Shaft friction of driven piles. Proc. 2nd Int. Conf. Numerical Meth. Offshore Piling, Austin. Randolph, M. f!, Carter, J. P. & Wroth, C. P. (1979). Driven piles in clay—the effects of installation and subsequent consolidation. Geotechnique 29, No. 4, 361-393.

Roscoe, K. H. & Burland, J. B. (1968). On the generalised stress strain behaviour of 'wet' clays. In Engineering plasticity (eds J. Heyman and F. Leckie), pp 535609. Cambridge: University Press. Skempton, A. W. (1959). Cast in-situ bored piles in

London Clay. Geotechnique 9, No. 4, 153-173. Steenfelt, J. S„ Randolph, M. F. & Wroth, C. P. (1981). Instrumental model piles jacked into clay. Proc. 10th Int. Conf. Soil Mech., Stockholm, 2, 857-869. Tomlinson, M. J. (1970). Adhesion of piles in stiff clays. Report 26. London: Construction Industry Research and Information Association. Wroth, C. P., Carter, J. P. & Randolph, M. F. (1980). Stress changes around a pile driven into cohesive soil. In Recent developments in the design and construction of piles, pp. 345-354. London: Institution of Civil Engineers.