Soil deformation pattern around laterally loaded pile

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Soil deformation pattern aroundlaterally loaded piles

Masoud Hajialilue-Bonab PhDAssociate Professor, Department of Civil Engineering, University of Tabriz, Iran

Habin Azarnya-Shahgoli MScGraduate Student, Department of Civil Engineering, University of Tabriz,Iran

Yones Sojoudi MScAno Consulting Co. Tabriz, Iran

1 2 3

In the analysis of soil–pile interaction under lateral load, the behaviour of soil around a pile is an important parameter

which has a great influence on the results. In this paper the three-dimensional deformation pattern of soil around

laterally loaded piles was studied on small-scale physical models in the laboratory using the particle image velocimetry

method. In each step of loading two digital cameras were used to capture the deformed piles and soil, one above and

the other on the side. One of the cameras was placed vertically in front of the test box and the other horizontally on top

of it. Image processing was undertaken to evaluate the three-dimensional behaviour of deformed soil. Particle image

velocimetry analysis was undertaken to obtain the displacement. The deformation pattern and shear strains of soil

around laterally loaded single pile and pile groups were studied. The effects of pile length, stiffness and diameter on the

soil deformation pattern were investigated. The group effect and interaction between piles in pile groups were also

studied. Experimental results showed that a conical passive zone is established in front of laterally loaded piles.

1. Introduction

If the soil bearing capacity is too low to use shallow foundations,

piles will be used to build deep foundations. Applied loads on

piles can be axial (tensile or compressive), lateral and moment.

Nearly all piles are subjected to lateral loads. In some structures

horizontal loads are negligible relative to vertical loads, but in

some cases piles are subjected to considerable lateral loads. For

example, in jetties and harbour structures, retaining structures

supported by piles, pile foundations located in seismic zones and

piers supported by piles, piles are subjected to lateral loads.

Considering the aforementioned topics, it is necessary to study

piles under lateral loads.

Most of the research about piles under lateral loads has to date

been performed by installing strain gauges on piles to investigate

the load-bearing capacity of the piles, pile deflection, pile rotation

and internal forces created in the pile. Remaud (1999) has

performed a set of tests on an instrumented pile and pile group

under lateral static load in centrifuge. Hajialilue-Bonab (2003)

has performed a comprehensive set of tests in centrifuge on single

piles which were instrumented with strain gauges, linear variable

differential transformer (LVDT), acceleration and force sensors

under lateral static and dynamic loads. He obtained static and

dynamic P–y curves. Only a few physical models have been

created to investigate the behaviour of the soil around the pile and

its deformation pattern. Therefore it is necessary to investigate the

soil deformation pattern around laterally loaded piles and pile–

soil interaction in order to improve the level of knowledge on this

subject. Tominaga et al. (1983) studied horizontal displacement of

soil in front of laterally loaded piles. They concluded that the

horizontal displacements are generally larger than the vertical

ones and these two values decrease very rapidly as the distance

from the pile surface increases. Ashour et al. (1998) investigated

strain created in front of a laterally loaded pile using a strain

wedge (SW) model. They concluded that the SW model approach

provides an effective method for solving the problem of a laterally

loaded pile. Patra and Pise (2001) have done some experimental

tests with a pile model (L/B 5 12) and concluded that there is no

group effect for spacing more than 6B. Rollins et al. (2006) have

also shown that the group effect increases when the pile space

decreases by 5?65 pile diameters. Otani et al. (2006) investigated

three-dimensional (3D) failure patterns in sand owing to a

International Journal of Physical Modellingin GeotechnicsVolume 11 Issue 3

Soil deformation pattern around laterallyloaded pilesHajialilue-Bonab, Azarnya-Shahgoli and Sojoudi

International Journal of Physical Modelling in Geotechnics,

2011, 11(3), 116–125

http://dx.doi.org/10.1680/ijpmg.2011.11.3.116

Paper 1000015

Received 19/09/2010 Accepted 19/05/2011

Keywords: deformation/model tests/piles & piling

ICE Publishing: All rights reserved

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laterally loaded pile using X-ray computed tomography (CT).

They concluded that the failure zone is extended and that the

volume and angle of the failure zone increases with the increase in

the pile loading level, but an ultimate value exists at some loading

stages. Also the size of the failure zone decreases with an increase

in the ground depth along the pile and the shape of this failure

zone is almost conical in three dimensions.

It is evident from the above research that the industrial X-ray CT

scanner promises to be a powerful tool even in the geotechnical

engineering field. Unfortunately the use of CT scanners greatly

impacts the costs associated with such research. Hence, White

et al. (2003) developed the deformation measurement system

based on particle image velocimetry (PIV) and close-range

photogrammetry. The PIV method, in addition to being

economical, accurately corresponds with geotechnical tests.

Small-scale laboratory modelling provides researches with full

control of all controllable variables of the model except the key

question providing a strong platform for establishing validity of

the models. A thorough understanding of relevant scaling laws

and the dimensional analysis which controls them is essential.

The equation governing the deformation of the pile is as follows

1. EId4y

dz4~{ky

where EI is flexural rigidity of the pile, y is the horizontal deflec-

tion of the pile, z is the distance measured down the pile and k is

the coefficient of the subgrade reaction that is expected to be propor-

tional to the shear modulus of the soil G (k~bG) (although the pile–

soil interaction is not strictly a process of pure shear) (Wood, 2004).

This equation can be normalised by defining a dimensionless

depth and a dimensionless pile deflection

2. j~z

l,l~

y

y0

where l is the length of the pile and y0 is the lateral deflection of

the pile at its top. The equation then becomes

3.EI

l4

d4l

dj4~{kl

Figure 1 illustrates the parameters of the above equations.

Since k~bG, a natural dimensionless group to characterise the

problem is Q1~ Gl4�

EI� �

, which describes relative pile–soil

stiffness. Then it might be supposed that correct physical

yo

y

z

l

P

Figure 1. Pile under lateral loading

Topview

Loose sand

Marker dot

Load cell

Electromotor

Plexiglass

30 cm LVDT B

Trail of pile

Model pile

L=25~55 cm

Front of pile

t

80 cm

Sideview

70 cm

Figure 2. Schematic view of test set-up

International Journal of Physical Modelling in GeotechnicsVolume 11 Issue 3

Soil deformation patternaround laterally loaded pilesHajialilue-Bonab, Azarnya-Shahgoli

and Sojoudi

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modelling will be obtained if the dimensionless ratio w1 is

identical in the model and the prototype (Wood, 2004).

2. Test set-up and procedure

2.1 Test box

A wooden box with internal dimensions of 80 6 70 6 30 cm3

was used as the test box. A transparent sheet was used in place of

a fourth wooden wall. Plexiglass was used to allow observation

of the deformations in the soil sample. The experimental set-up

is shown in Figure 2. Figures 3(a) and 3(b) represent the

embedded single pile views from the side and top respectively.

2.2 Soil

The soil was fine, dry sand from the Sofian region in the

northwest of Iran. The type of soil is classified as SP in unified

soil classification system (USCS). Some characteristics of the

soil are shown in Table 1.

The soil was placed in the box using a sand raining system in

order to obtain a uniform and homogeneous medium. The

average unit weight and relative density of soil in the boxes

were 14?8 kN/m3 and 24% respectively.

2.3 Model piles, loading system and

instrumentation

The majority of piles considered in this research are long

flexible piles. The theoretical definition of a long pile in

cohesionless soil used here is (Prakash and Sharma, 1989)

4.L

T§4, T~

ffiffiffiffiffiffiEI

nh

5

r

Average particle size of

sand (D50): mm cdmax: kN/m3 cdmin: kN/m3 cdave: kN/m3 nh: kN/m3 A Gs W (ultimate)

0?285 17?08 14?2 14?8 2?2 6 103 200 2?637 28˚

Table 1. Characteristics of soil

Tests no. 1 2 3 4 5 6 7 8 9 10 11 12 13

L: mm 300 250 350 450 550 250 350 450 550 350 350 350 200

B: mm 60 60 60 60 60 60 60 60 60 31 40 60 60

t: mm 2 1?25 1?25 1?25 1?25 2?5 2?5 2?5 2?5 3?1 2 3?1 5

EI: N m2 2?8 0?68 0?68 0?68 0?68 5?46 5?46 5?46 5?46 5?46 5?46 10?4 43?8

L/B 5 4?17 5?83 7?5 9?17 4?17 5?83 7?5 9?17 11?29 8?75 5?83 3?33

L/T 4?53 5?01 7?02 9?02 11?02 3?3 4?63 5?95 7?27 4?63 4?63 4?07 1?74

Material Al Al Al Al Al Al Al Al Al Al St Al Al

Al 5 aluminium; St 5 steel

Table 2. Model single pile properties

(a) (b)

Figure 3. Embedded pile in soil: (a) side view; (b) top view



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where L is the embedded pile length, T is the length factor, EI is

the flexural rigidity of the pile and nh is the subgrade horizontal

reaction constant module k~nhzð Þ. nh was calculated from Equa-

tion 5 (Terzaghi, 1955)

5. nh~Ac

1:35

These parameters are given in Table 1.

Rectangular piles that were slightly thicker than they were wide

were selected in order to apply the similitude law. The smallest

dimensions of piles were in contact with the Plexiglass. The

properties of the model piles are given in Table 2.

In order to investigate the soil deformation pattern around

laterally loaded piles several tests were performed on single

piles with different dimensions and pile groups with different

spacing. In all tests the piles were fixed in the wooden box and

then sand was poured surrounding the piles using a sand

raining system. Lateral load tests on pile groups were carried

out on 2 6 1 pile group models. An aluminous cap was used to

connect two pile heads. Each pile was joined by a hinge (free

rotation) to the cap. An electromotor with uniform velocity

was used to apply lateral load to the pile head. A LVDT

displacement sensor was installed in order to record the pile

head displacement. A sensitive load cell was also applied to

measure the lateral force during the tests. Two Canon Power

shot G6 with resolution 7?1 megapixel (3072 6 2304 pixels)

digital cameras were used for the purpose of facilitating

visualisation of the soil movements during testing and image

processing. In order to eliminate parasitic lights, several

projectors were also used. Pile heads were free to rotate.

Lateral load was applied statically to the pile heads from right

to left with a precise electromotor gearbox.

2.4 Image analysis by the PIV method

Digital photographs were taken of deformed piles and the soil

around them. Two cameras were used simultaneously during

testing, one from above and the other on the side. All controls

such as focus, gain and shutter speed were adopted auto-

matically. The images were processed using the GeoPIV8

software, developed at Cambridge University (White and

Take, 2002). The PIV analysis was undertaken using patches

of 32 6 32 pixels, spaced at 32 pixel centres and a search area

of 64 6 64. This provided sufficient textural detail to give good

tracking of the patches.

3. Test results and discussion

In order to study the (3D) behaviour of soil around a laterally

loaded single pile, 13 tests were performed that were

0

z/B

x/Bx/B

y/B

Single pile

Single pile

Plexiglass0

(a) (b)

00

Soil surfaceLateral load

Lateral load

Soil surface

Figure 4. Single pile: (a) side view; (b) top view

2–2 –1 10

x/B

x/B

z/B

y/B

210–2 –10

1·0

0·5

1·5

2·0

2

1

0

5

4

3

(a) (b)

Figure 5. Soil displacement vectors around pile (test 1,

magnification factor 5 3): (a) side view; (b) top view



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interpreted as follows. Note that in the following figures, x/B 5

0 shows the position of a single pile. The origin of the vertical

axis (z/B 5 0) and horizontal axis (y/B 5 0) is taken as the soil

surface and interior vicinity of Plexiglass respectively.

Schematic views of a single pile in soil from side and overhead

views are shown in Figures 4(a) and 4(b) respectively.

3.1 Soil displacement vectors around a laterally

loaded pile

The displacement vectors around a pile are shown in Figures 5(a)

and 5(b) for pile head deflection 9 mm (0.15B) (test 1). These

vectors have been plotted with a magnification factor of 3. It can

be observed that soil particles located farther from the pile do not

move. The displacement vectors become larger as they approach

the pile. Another observation is that the soil grains located in the

trail of the pile move downwards, while soil grains located in front

of the pile move upwards with small angles. A radical change of

vector angles at pile position can be seen.

Considering Figure 5(a) the maximum horizontal displacement

occurs in the pile head and decreases gradually with depth. At

greater depths the displacements of soil around the pile are

negligible. Since soil grains in front of laterally loaded piles

have observed angles of displacement vectors with respect to

the horizontal axis that are smaller than 45 , it is concluded

that the horizontal displacements of soil in front of laterally

loaded piles are larger than the vertical ones.

In front of a laterally loaded pile both horizontal and vertical

displacements coexist. Vertical displacements occur near the

ground surface in front of the pile, and this has a significant effect

on pile deflection. For this reason the study of vertical displacement

in front of the pile is important. Figure 6 shows typical vertical

displacements around a laterally loaded flexible pile at the ultimate

state for a pile head deflection of 9 mm in test 1, which was

extracted from PIV analysis. These vectors have been plotted with

a magnification factor of 3. This figure shows that the vertical

displacements in front of a pile become zero at a depth of about 1B

(B is pile diameter) and after this depth the soil displacements are

horizontal. It can be observed that in the trail of the pile the vertical

displacements are larger than those in the front of the pile.

In order to investigate the depth at which the vertical

displacements are negligible the results of different tests are

plotted in Figure 7(a). In this figure the vertical axis indicates

the depth of zero vertical displacement (Ldv) divided by pile

width (B). The horizontal axis is normalised length. It can be

observed that for the pile with L/T of about 11, the zero

vertical displacement is 0?7B but for L/T 5 4?6 this depth

varies from 1?1 to 2?25, depending on pile width. It can be

concluded that this depth is not directly dependent on width.

In Figure 7(b) the vertical axis is the depth of zero vertical

displacement (Ldv) divided by pile length (L) and the

horizontal axis is the normalised length. These results can be

fitted to a power-type regression curve and a reasonable

correlation can be observed.

3.2 Shear strains around a laterally loaded pile

Figures 8(a) and 8(b) show maximum shear strain created in

soil around a single pile. It can be observed that the maximum

2–2 –1 10

0

0·5

1·5

2·0

1·0

x/B

z/B

Figure 6. Vertical displacement of soil around pile (test 1,

magnification factor 5 3): side view

0·5

0·4

0·3

0·2

0·1

00 2 4 6 8 10 12

(a) (b)

0

Test dataFitted curve

Test dataFitted curve

1

2

3

0 2 4 6 8 10 12L/T

L/T

Ldv/L

Ldv/B

Figure 7. Vertical displacement depth of soil in front of pile



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shear strain occurred in pile-adjacent soils near the surface. A

triangular strain wedge to the side of the displaced pile is

created. Figure 8(b) shows that in front of a laterally loaded

pile a passive zone is established. This passive zone is similar to

a circle. In the prototype pile, the symmetry of the shear strain

zone is established on the other side of the Plexiglass too. In

composing Figures 8(a) and 8(b) it is concluded that in front of

a laterally loaded pile, the passive zone that is established is

almost conical in shape in three dimensions. This proposed

passive zone is shown in Figure 9.

Considering the applied load direction which is from right to

left, the shear strain zone does not have a symmetric shape

towards the pile place and is inclined to the left. However, the

shear strain created in the soil surface behind the pile is more

than the shear strain in front of the pile. This is because there

are more angles of displacement vectors behind the pile than in

front of the pile (this result has been obtained from Section

3.1).

3.3 Displacement and strain field around a laterally

loaded rigid pile

In order to investigate the soil deformation pattern around a

laterally loaded rigid pile a test was performed on a model rigid

pile (test 13). Figures 10(a) and 10(b) show the displacement

vectors with a magnification factor of 3 and the shear strain of

a rigid pile which had a rotation at a depth of about 2?65B. It

can be observed that, unlike the flexible pile, significant

displacement occurs at increased depths.

3.4 Effects of pile length on soil deformation

patterns around a pile

To study the effect of pile length on soil deformation patterns

under lateral load the results of lateral force plotted against

pile head deflection for piles with different lengths are shown in

Figure 11. These tests were undertaken with piles of two

different stiffness (EI 5 0?68 N m2, EI 5 5?46 N m2) and four

different lengths (250, 350, 450, 550 mm). It can be observed

that for the piles with similar stiffness and width, when the

ratio L/B is bigger than 6, the increase of length has no effect

on the lateral capacity of the piles.

3.5 Effects of pile stiffness on soil deformation


In flexible piles, the pile stiffness is an effective parameter in

lateral load capacity. This parameter significantly influences the

deformation of the surrounding soil. In order to study the effect

of pile stiffness on the soil deformation pattern, three model

piles with various stiffnesses of the same length and width were

tested. Figure 12 illustrates strain wedge formation around these

piles for the same pile head deflection. It can be seen that the

–1

–1–2

1·5

2·0

1·0

1·0

0·8

0·6

0·4

0·2

0

1·0

0·8

0·6

0·4

0·2

0

21

0·5

0 0

(a)x/B

x/B

z/B

y/B

(b)

–2 21

2

3

4

5

1

0

0

Figure 8. Soil shear strain around pile: (a) side view; (b) top view

Passiveconical zone

Zero-displacementpoint

Lateral load

Model pile

Figure 9. Proposed 3-D model of passive zone of soil



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mobilised depth of the strain wedge was increased and the

mobilised angle was decreased with increasing pile stiffness.

For a laterally loaded flexible pile Meyerhof et al. (1988)

suggested that in the absence of pile failure the ultimate load

for soil failure can be estimated using an effective embedment

depth instead of rigid pile depth.

Meyerhof et al. (1988) used the result of theoretical analyses

(Banerjee and Davis, 1978; Poulos and Davis, 1980) and

proposed the average relationship between the effective depth

ratio Le/L of free head pile and the pile stiffness Krs as below

6.Le

L~2:6K0:2

rs ƒ1

7. Krs~EI

EhL4

where Eh is the horizontal soil modulus at the pile tip. Figure 13

shows the comparison of experimental results obtained from this

study with theoretical formulation given by Equations 6 and 7.

As shown in Figure 13 the effective depth obtained in this re-

search is in agreement with the theoretical relationship.

3.6 Effects of pile diameter on soil deformation


To investigate the effect of pile width on soil deformation,

three models of pile with the same length and stiffness but with

various widths were tested. To study the pile diameter effect on

soil deformation patterns, the mobilised strain wedge around

the piles was extracted using PIV analysis. The 1% strain

x/B

(a)

z/B

03.5

1.51.0_1.0_2.0

3.0

2.0

1.0

0

x/B

(b)

z/B

03.5

1.51.0_1.0_2.0

3.0

2.0

1.0

0

0

0.2

0.4

0.8

0.6

1.0

Figure 10. Soil deformation pattern around rigid pile:

(a) displacement vectors (magnification factor 5 3); (b) shear strain

25

EI=0.68 (N m2)

EI=5.46 (N m2)

2015Deflection: mm

105

50 L/B=5.83L/B=7.5L/B=9.17

L/B=4.17

40

30

Load

: N

20

10

00 30

60

Figure 11. Typical load–displacement curve for various embedded

length ratios of piles

1x/B

z/L

0_1_2

Displacement = 20 mm

EI = 0.68 (N m2)EI = 5.46 (N m2)EI = 10.4 (N m2)

_3

0.2

2

0.4

0.6

0.8

0

Figure 12. Mobilised strain wedge around pile



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wedges are illustrated for the same applied load in

Figure 14(a). With increasing pile diameter, the mobilised

strain wedge depth is reduced. To study the slope of the strain

wedge the curves in Figure 14(b) were normalised with respect

to z by strain wedge depth (Le). It can be observed that

although the depth of the strain wedge is decreased by

increasing pile diameter, the effective radius is increased.

3.7 Behaviour of soil around a laterally loaded pile

group

The effective radius has an important effect on lateral load

capacity of pile groups in front of laterally loaded piles in the

load direction and can affect the pile group performance. In

order to investigate the soil deformation pattern around

laterally loaded pile groups and pile–soil–pile interaction, six

tests were performed on a 2 6 1 pile group model by varying

the pile centre-to-centre spacing from 0?5 to 3 times the pile

widths (B) in the direction of the load. The properties of piles

were similar to test 1. The pile cap deflection for these tests was

9 mm (0?15B). In all of the following figures, point x/B 5 0

shows the place of the trail pile in the group. Also, points

x/B 5 20?5, 23 show the place of the lead pile in the pile

groups spaced at 0?5B, 3B respectively. Also, the origin of the

vertical axis (z/B 5 0) is taken as the soil surface. A schematic view

of the 3B pile group in soil from a side view is shown in Figure 15.

Note that the lead pile is at the front of the group in terms of

the direction of motion while the trail pile is at the back. The

displacement vectors around 0?5B and 3B pile groups are

shown in Figures 16(a) and 16(b). These vectors have been

plotted with a magnification factor of 3. These results are

accrued values over the whole test and illustrate the deforma-

tion pattern around the pile group.

It can be observed that radical changes of angle are always

large around the trail pile. For the pile group test with the pile

space equal to 0?5B, the change of angle around the lead pile is

small. If the pile space increases to 3B, the angle change around

the lead pile becomes similar to the trail pile. This demon-

strates that the group effect is negligible in the last case (pile

space is 3B).

In the case of 0?5B space between piles it can be observed that

the displacement vectors between two piles are almost

horizontal (Figure 16(a)). Therefore the soil between the two

piles has a very low resistance against horizontal displacement

of the trail pile. In this case the soil resistance for the piles in

the trailing row is greatly reduced owing to the influence of the

leading row piles on the soil. A slight reduction in soil

resistance for the piles in the leading row in comparison with

the single pile was observed.

In the case of 3B space between piles, the displacements of soil

around each pile have no overlaps. It can be concluded that the

interaction between piles decreases with increasing pile space.

Relative stiffness, Krs

0.8

0.6

0.4E

L e/L

0.2

01×10–31×10–41×10–51×10–6

Test data

Equation 6

1×10–2

1.0

Figure 13. Effective depth obtained from test and theoretical

relationship

B=40 mmB=31 mm

B=60 mmB=31 mm

B=40 mm B=60 mm

_0.5

0

0.5

1.0

1.50 0.5_1

x/B

(a) (b)

x/Le

z/L e

0

0.2

0.4

0.6

0.8

z/L

_3 0 3_6L/T=4.63L/T=4.63

Figure 14. Effect of pile width on mobilised strain wedge depth

and wedge angle



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Figures 17(a) and 17(b) show maximum shear strain created in

soil around 0?5B and 3B pile groups. These results are accrued

values over the whole test.

In the case of 0?5B space between piles (Figure 17(a)) strain

wedges are overlapped, which shows the interaction of two

piles. In this case because the variation of the angles of

displacement vectors around the trail pile is more significant

than around the lead piles, the shear strain created in the soil

around the trail pile is more than around the lead pile. In the

3B pile group (Figure 17(b)) there is no interference and each

pile acts as a single pile. In this case the shear strain created in

the soil around the lead pile is similar to around the trail pile.

In the case of the 0?5B space, the created strain wedge is very

similar to a single pile with larger width. This means that when

two piles are very close to each other, the behaviour of the pile

group would be similar to a single pile. In this case the soil

between the two piles has a very small effect on the lateral

capacity of the pile group. The suggestion would be to put a

minimum space between the piles in the group in order to

mobilise the maximum capacity of the soil for lateral force and

displacements.

4. Conclusions

An extensive series of lateral loading tests has been conducted

on flexible model piles in loose sand. The piles were made of

different embedded length and stiffness to investigate soil

deformation patterns around piles and the influence of pile

length, stiffness and diameter on it. The group effect and

interaction between piles in a pile group were also studied. The

conclusions drawn from this study are summarised below.

(a) A cone-shaped passive zone is established in front of a

laterally loaded pile. This passive conical zone has the

largest section in the ground surface, and the size of this

section decreases with the increase in the ground depth

along the pile.

(b) Soil grains behind the pile moved down, while soil grains

in front of the pile moved up with small angles. In the trail

pile, the shear strain created in the surface soil is more

than that in the front of the pile.

(c) The embedment lengths of piles have less effect than pile

stiffness on lateral load capacity, although with increasing

pile stiffness the effect of embedded length on lateral

capacity increases.

(d) Increasing centre-to-centre pile spacing in a group in the

direction of lateral load will decrease the pile–soil–pile

interaction effects. Consequently both the behaviour of

piles and the soil deformation pattern around them are

similar to single pile ones. For pile cap deflection equal to

0?15B in 3B pile spacing the group effect disappears and

piles in a group behave like a single pile.

–5 –4 –3 –2 –1 10

0

1

3

4

5

2

x/B

(a)

z/B

–5 –4 –3 –2 –1 10

0

1

3

4

5

2

x/B

(b)

z/B

Figure 16. Soil displacement vectors around pile group

(magnification factor 5 3): (a) 0?5B pile group; (b) 3B pile group

_3 0

Trailpile

Leadpile

0 Soil surfaceLateral load

x/B

z/B

Figure 15. 3B pile group (side view)



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(e) When two piles are very close to each other, the

behaviour of the pile group would be similar to a single

pile. In this case the soil between two piles has a very

small effect on the lateral capacity of the pile group.

REFERENCES

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_5

1

2

3

4

5 _4 _3 _2x/B(a)

z/B

_1 0 1 _5 _4 _3 _2x/B(b)

_1 0 1

0

1

2

3

4

5

z/B

0

0.8

0.6

0.4

0.2

0

1.0

0.8

0.6

0.4

0.2

0

1.0

Figure 17. Soil shear strain around pile group: (a) 0?5B pile group;

(b) 3B pile group



and Sojoudi

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Soil deformation pattern around laterally loaded pile

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