evaluation of negative skin friction effects in pile foundations using 3d nonlinear analysis

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Computers and Geotechnics 32 (2005) 210–221

Evaluation of negative skin friction effects in pile foundationsusing 3D nonlinear analysis

Emilios M. Comodromos *, Spyridoula V. Bareka

Department of Civil Engineering, University of Thessaly, Pedion Areos, 383 34 Volos, Greece

Received 20 February 2004; received in revised form 5 January 2005; accepted 25 January 2005

Available online 29 March 2005

Abstract

The aim of this paper is to evaluate the influence of negative skin friction in pile foundations. Three dimensional nonlinear anal-

yses for a single pile and pile groups were carried out for a specific case and some case studies as well. Contrary to simplified con-

ventional analysis in which the predictions are usually overestimated and could be considered as an upper limit, it was found that the

dragload of a pile in a group depends on the surface load, the pile configuration, the pile position in a group, the ultimate skin fric-

tion and the interface stiffness. It has been demonstrated that for fixed-head friction pile groups the dragload group effect is signif-

icantly greater than in the case of free-head end-bearing pile groups. Moreover, predictions for internal piles have shown

considerably smaller dragloads for fixed-head piles, which is in accordance with experimental findings. It has also been demonstrated

that when the construction of an embankment precedes the application of the foundation working load, the effect of negative skin

friction is considerably smaller than in the reverse case.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Negative skin friction; 3D numerical analysis; Soil–structure interaction; Pile group response

1. Introduction

As a result of fill placement or even lowering of phre-

atic surface, the soil surrounding the piles of pile foun-

dations in soft ground settles more than the piles. In

that case, negative skin friction occurs, producing pile

settlement (downdrag) and additional compressive force

(dragload) due to the hanging effect around the pile. Theuse of closed-form equations resulting from conven-

tional analysis [1–4] for estimating dragload assumes

that the negative skin friction is fully mobilised above

the neutral plane (point at which the relative movement

between the pile and the surrounding soil is zero). The

application of this approach leads to exaggerated drag-

loads since large settlements may be needed to fully

mobilise the negative skin friction on a pile. On the

0266-352X/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compgeo.2005.01.006

* Corresponding author. Tel.: +30 421 74143; fax: +30 421 74169.

E-mail address: [email protected] (E.M. Comodromos).

other hand, large settlements are not necessarily needed

to initiate slippage at the interface between soil and pile.

For an accurate evaluation of both downdrag and drag-

load the pile–soil interaction should be taken into ac-

count in the analysis. Therefore, the ultimate skin

friction, the interface stiffness, the soil strength and stiff-

ness as well as the pile group configuration must be ta-

ken into consideration. In the case of a pile group theeffect of soil–pile interaction is more complicated due

to the presence of adjacent piles which tends to reduce

the soil settlement within the group [5]. Thus, the inter-

nal piles of a fixed-head pile group undertake smaller

dragload, while in the case of a free-head pile group they

experience smaller downdrag. These tendencies have

been revealed by the experimental work of Shibata

et al. [6] who demonstrated that dragload on individualpiles in a group is smaller than that on an isolated pile

and that the internal piles are subjected to smaller loads

than the external piles.

mailto:[email protected]

E.M. Comodromos, S.V. Bareka / Computers and Geotechnics 32 (2005) 210–221 211

To analyse the effect of negative skin friction in end-

bearing pile groups Poulos and Davis [7] proposed a

simplified method based on the solution of a point load

in an elastic half-space. At a later stage Kuwabara and

Poulos [5] developed a simplified boundary element

method in which the soil is assumed to be an elastic con-tinuum and slip is allowed at the pile–soil interface. Sim-

ilar approach has been applied by Teh and Wong [8] to

estimate dragload in end-bearing pile groups. A simpli-

fied approach providing a methodology for estimating

the negative friction effect in both end-bearing and fric-

tion piles was also proposed by Poorooshasb et al. [9].

The above methods require idealisations of soil profile

but, in most cases, are able to estimate the effect of neg-ative skin friction at an acceptable level. However, for

important projects where strict criteria of serviceability

are imposed or when the super-structure is sensitive to

differential settlements, a more accurate approach is

necessitated. This approach should provide the ability

of taking into account the ultimate skin friction, the

interface stiffness, the soil strength and stiffness as well

as the particular geometry of the foundation. In such acase, a three dimensional (3D) nonlinear analysis is re-

quired for the prediction of dragload, downdrag and

stiffness reduction factor. According to Lee et al. [10],

although the behaviour of piles in a group is obviously

a 3D problem, until 2002 there was only one reported

3D finite element analysis of the behaviour of a pile

group in the literature [11] which neglected however,

the soil slip at the pile–soil interface and therefore re-ported very large group effects. Lee et al. [10] performed

a 3D finite element analysis for single pile and pile

groups in a simplified soil profile consisting of soft clay

overlying a dense sandy layer. They also carried out

numerical analyses on some case studies of pile groups

taking the effect of soil slip at the pile–soil interface into

account. When comparing the results with those of pre-

vious research works significantly smaller group effectswere found.

In this paper, a 3D numerical analysis is initially used

to estimate the effects of negative friction for a single pile

in a multilayered soil profile. The analysis is then ex-

tended to pile groups and the behaviour of piles consti-

tuting a group is contrasted to that of a single isolated

pile. The effect of the construction sequence (application

Table 1

Material properties used in the analysis by Lee et al. (2002)

Material Model E (kPa) c (kPa)

Concrete pile Isotropic elastic 2,000,000

Soft clay Mohr–Coulomb 5000 3

Bearing sand 50,000 0.1

Notes: Groundwater table is located on the top of the soft clay layer.

Hydrostatic water pressure distribution is assumed.

of the foundation working load prior to or after the con-

struction of the embankment) to the foundation stiffness

and the undertaken load is also investigated and

quantified.

2. Single pile analysis

2.1. Simplified case study

A simplified soil profile was used by Lee et al. [10] in

order to investigate the effect of negative skin friction to

the anticipated dragload and downdrag. The pile was ta-

ken to be 0.5 m in diameter and 20 m long. The upper

soil layer consists of soft clay down to the pile tip, while

the underlying bearing layer is composed of sandy soil.

The material properties used in that analysis are summa-

rised in Table 1. In order to investigate the distributionof shear stress and dragload in the case of a friction pile

in their analysis, Lee et al. [10] took the bearing layer

stiffness to be equal to that of the soft clay, while in

the case of an end-bearing pile, the bearing layer stiffness

was taken 1000 times the soft clay stiffness. In their anal-

ysis the pile was considered as linear elastic material

while for soil layers the Mohr–Coulomb nonassociated

flow rule was adopted. The Coulomb frictional lawwas also used for the interface modelling. The results,

provided using the 3D finite element code ABAQUS,

are shown in Fig. 1, together with the results of the pres-

ent analysis, which are presented below.

Three dimensional nonlinear long-term analysis was

carried out using the finite difference code FLAC3D

[12] to solve the same problem. Fig. 2 illustrates a

cross-section at y = 0.0 m of the finite difference meshutilised in the present analysis, consisting of 2648 finite

difference elements and 3116 nodes. Along the pile

1732 interface elements were used to simulate the pile–

soil interaction. The dimension of the grid is 26 m in

the x and y directions and 25 m deep. At the bottom

plane of the grid all movements are restrained. The lat-

eral sides of the mesh were taken far enough from the

piles to avoid any boundary effect. The planes atx = �13.0 m and x = +13.0 m are free to move in the

y and z directions but not in the x direction. Similarly,

the planes y = �13.0 m and y = +13.0 m are free to

m u (�) w (�) Ko c (kN/m3)

0.3 1.0 25

0.3 20 0.1 0.65 18

0.3 45 10 0.5 20

S = slider

T = tensile strength

D = dilation

k = shear stiffness

k = normal stiffnessP

k

D

T

S ks

n

n

s

target face

3D

0

5

10

15

20

0 100 200 300 400 500 600 700

Dragload (kN)

Dep

th (

m)

-30 -20 -10 0 10 20 30 40

Shear stress (kPa)(a) (b)

End-bearing pile, FLAC 3D

Friction pile, FLAC 3D

End-bearing, Lee et al.(2002), ABAQUS

Friction pile, Lee et al.(2002), ABAQUS

Fig. 1. (a) Dragload and (b) shear stress distributions for the simplified single case analysis.

X

Y

Z

20 m

5 m

26 mSand

Soft Clay

Fig. 2. Finite difference mesh of single pile in simplified soil profile

(FLAC3D).

212 E.M. Comodromos, S.V. Bareka / Computers and Geotechnics 32 (2005) 210–221

move in the x and z directions but not in the y direction.

In order to accelerate calculations the benefit of symme-

try on the vertical plane y = 0.0 m has been adopted and

thus the half grid defined by y P 0 was finally used. The

other half was removed using the �model null� statement

and the boundary conditions were modified accordingly.

Similar boundary conditions are applied for single pileand pile group analyses presented hereafter.

The constitutive model of the interface elements in

FLAC3D is defined by the following linear Coulomb

shear-strength criterion, which limits the shear force act-

ing at an interface node:

F smax ¼ caAþ tanuðF n � uAÞ; ð1Þ

where Fsmax is the limiting shear force at pile–soil inter-

face; ca, adhesion between pile and soil; u, angle of fric-tion between pile and soil; Fn, normal force at pile–soil

interface; u, pore pressure; A, contact area associated

with an interface node.

Fig. 3 illustrates the components of the constitutive

model acting at an interface node. The interface ele-ments are allowed to separate if tension develops across

the interface and exceeds the limit tension of the inter-

face. Once gapping is formed between the pile–soil inter-

face, the shear and normal forces are set to zero.

The shear force Fsi that describe the elastic interface

response at an interface node is determined at calcula-

tion time (t + Dt) using the following equation:

F ðtþDtÞsi ¼ F ðtÞ

si þ ksDuðtþ0:5DtÞsi A; ð2Þ

where Fsi is the shear force; ks, shear stiffness; A, contact

area associated with an interface node; Dusi, incremental

relative shear displacement vector.

When |Fsi| = Fsmax sliding is assumed to occur.

According to the guidelines of FLAC3D user manual

Fig. 3. Components of the interface constitutive model in FLAC .


the appropriate minimum value of shear stiffness ksshould be ten times the equivalent stiffness of the stiffest

neighbouring zone when the limiting displacement

needed to fully mobilise the interface shear strength is

very small. Application of the above guidelines lead to

a value of 107 kPa/m for ks. Higher values could be alsoused with no effect to numerical results, but slowing

down the solution convergence. The strength parameters

of the interface elements were taken as ca = 0 and

u = 16.7�, equal to those used in the analysis with ABA-

QUS. Predicted shear stress and dragload versus depth

are plotted in Fig. 1, demonstrating similar values and

distribution along the pile for both analyses. It may be

noted however that according to Lee et al. [10], theapplication of no-slip linear elastic finite element analy-

sis or simplified linear elastic analysis [13,14] overesti-

mates the dragload. This is mainly due to the fact that

the FLAC3D analysis is able to take into account any

partial mobilisation of skin friction above and below

the neutral plane, contrary to simplified methods in

which the shear strength is assumed to be reached along

the entire length of the pile or the entire length above theneutral point.

Fig. 4. Soil profile and design parameters for the single pile analysis in

multilayered soil.

2.2. Single pile in multilayered soil

The soil profile used in this case corresponds to that

of the area of the new wharf at the harbour of Thessa-

loniki. At this location the subsoil is very compressible

and has very low shear strength. The upper layer, as-

signed as layer A, consists of soft clayey soil with thin

layers of sand, underlying highly plastic soft clay, layer

B. Under layer B, at the level of �18.0 m a layer of med-

ium stiff clay, layer C, of medium plasticity was located,extending down to �42.0 m. From that level to the end

of the borehole, very dense sandy gravel with clay was

detected. The main soil properties of each soil layer de-

rived by the geotechnical investigation are presented in

Fig. 4. Due to the poor soil properties the access road

to the wharf comprises a bridge based on a pile

foundation.

Given the magnitude and the importance of the pro-ject a pile load test was decided to be carried out includ-

ing both vertical and horizontal loading. The influence

of the interaction between the test pile and the reaction

piles has been evaluated using 3D nonlinear back-anal-

ysis and the single pile response has been assessed by

Comodromos et al. [15]. Furthermore, the effect of the

interaction between the piles in a free-head group was

quantified and the bearing capacity and stiffness effi-ciency factors were estimated for various pile configura-

tions. Similar analysis has been carried out by

Comodromos [16] in the case of fixed-head pile groups,

in which the influence of the number of piles, the spacing

and the deformation level to the group response is dis-

cussed. In addition, the contribution of the piles consti-

tuting the group to the total group resistance was

examined, its variability with the settlement level was

established and a relationship allowing a reasonable re-

sponse prediction of a fixed-head pile groups wasproposed.

Following the above referenced process the pile

group response to externally applied axial load can be

numerically assessed with the required level of accuracy.

For the outer abutment, however, where bridge ap-

proach embankments were foreseen, the crucial effect

of negative skin friction should also be taken into ac-

count. At this location downdrag and dragload may cre-ate serviceability problems and they should be taken

into account when evaluating the bearing capacity and

the stiffness of the pile foundation. To estimate this ef-

fect a 3D analysis was carried out initially for a single

isolated pile. The problem has been solved for various

surface loads corresponding to different heights of

embankment. Figs. 5 and 6 illustrate the distribution

of the interface shear stress and the dragload along thepile predicted by the FLAC3D nonlinear analysis. Even

0

10

20

30

40

50

-30 -20 -10 0 10 20 30 < positive friction Shear stress (kPa) negative friction >

Dep

th (

m)

S.L.= 5 kPa S.L.=10 kPa

S.L.=25 kPa S.L.=50 kPa

S.L.=75 kPa S.L.=100 kPa

S.L.=50 kPa, P.A.L.=4500 kN P.A.L.=4500 kN

P.A.L.=4500 kN, S.L.=50 kPa Shear strength

Fig. 5. Interface shear stress distribution along the single pile for various surface loads (SL) and pile axial load (PAL).

0

10

20

30

40

0 1 2 3 4

Dragload (MN)

Dep

th (

m)

S. L.=5 kPa

S. L.=10 kPa

S. L.=25 kPa

S. L.=50 kPa

S. L.=75 kPa

S. L.=100 kPa

Fig. 6. Dragload distribution along the single pile for various surface loads (SL).


for the relatively small surcharge load of 10 kPa the

dragload attained the value of 1.56 MN. It takes its

maximum value of 3.7 MN when a surcharge load of

100 kPa is applied. In that case the appearance of the

distribution along the pile approaches the appearance

of an end-bearing pile. From Fig. 7(a) it can be seen that

the neutral plane is located approximately at the depth

of 30 m even for the relatively small surcharge load of5 kPa. This can be attributed to the fact that the pile

is founded on a very stiff material while the surrounding

soil is of high to medium compressibility. The depth of

the neutral point is gradually increased with surface

load, approaching the end-bearing pile appearance (neu-

tral point at the depth of 40 m) for a surface load of 100

kPa (Fig. 7(b)).

While the estimation of the dragload and the down-

drag for various surcharge loading may be helpful for

understanding the skin friction mechanism and at thesame time to quantify the bounds of the effect, a more

detailed research was deemed indispensable for the

Surface Load= 100kPa

0 50 100 150 200 250 300

Settlement (mm)

neutral point

Surface Load= 5 kPa

-45

-40

-35

-30

-25

-20

-15

-10

-5

00 2 4 6 8 10

Settlement (mm)

Dep

th (

m)

pile settlement

soil settlement

neutral point

(a) (b)

Fig. 7. Pile and surrounding soil settlements for a surface load of: (a) 5 and (b)100 kPa.


combination of the working load (pile axial load,

PAL = 4.5 MN) and the specific surcharge load of 50

kPa, corresponding to the surcharge load of the bridge

approach embankment. Often for practical reasons, it

is not possible to construct the embankment prior to

the installation of the piles. In that case, the construc-tion of the bridge and the approach embankment fol-

low that of the piles. The sequence of these two

construction stages is important for the development

of negative skin friction. It is widely accepted that

the effect of negative skin friction decreases when

embankment construction precedes the construction

of the bridge, i.e. the working load is applied when

the subsoil has already undergone settlement due tothe construction of the bridge approach embankment.

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Pile axial force (MN)

Dep

th (

m)

P.A.L.= 4.5 MN

Superposition of S.L. =50kPa and P.A.L= 4.5 MNS.L=50 kPa + P.A.L.= 4.5 MN

P.A.L.= 4.5 MN + S.L.=50kPa

Fig. 8. Dragload distribution along the single pile for combinations of

pile working load and surface load.

Fig. 8 illustrates the dragload distribution along the

pile for the following characteristic case loading; (a)

application of the working load (PAL = 4.5 MN) with-

out any surcharge load, (b) application of the working

load and then application of the surcharge load, (c)

application of the surcharge load and then applicationof the working load, (d) superposition of the results of

load case (a) with those of the surcharge load (50 kPa).

In case (c) the construction of the embankment pre-

cedes that of the bridge, while case (d) corresponds

to the reverse case. In cases (b) and (c) the simulation

is carried out in two sequential stages within the same

numerical process. On the contrary, case (d), presented

for comparative reasons, arises from the superpositionof the two aforementioned solutions. As anticipated,

the combination of the working load with the surface

load leads to an increase of the axial force of the pile.

More specifically load case (b) provides a considerably

greater axial force than case (c); 6.7 MN for the former

and 4.94 MN for the latter. In case (b) the additional

axial force is 2.2 MN (almost 50% of the working

load), while in case (c) is limited to 0.44 MN (10% ofthe working load).

The pile settlement due to the application of the

working load without any surcharge load is 6.5 mm,

while in case (c) is 28.6 mm and in case (d) is 37.8

mm. Consequently, for the same working load the se-

cant pile stiffness becomes 0.69, 0.12 and 0.16 GN/m

for cases (a), (b) and (c), respectively. The stiffness

reduction factor resulting from the effect of the negativefriction is 82% and 76% for case (b) and (c), respectively.

Given the influence of the secant stiffness on the design

of the superstructure it can be seen that the appropriate

value must be adopted according to the construction

sequence.

Fig. 10. Dragload distribution along the single pile and the charac-

teristic piles of Combarieu�s case study.


3. Pile group analysis

3.1. Combarieu�s case study

Prior to a 3D analysis of the specific bridge founda-

tion a well known case study was considered, in orderto compare the response of predicted dragloads and

group effects. The example analysed by Combarieu [3]

was chosen mainly for its simplicity and the fact that

it was the subject of many previous research works.

The pile group configuration is shown together with

the soil profile properties in Fig. 9.

In their analysis for the above case study, Lee et al.

[10], took the Young�s modulus E of the clay equal to10 MPa, the interface friction coefficient l = 0.4 (inter-

face angle of friction d = 21.8�), while the Poisson�s ra-tio, m, was taken to be 0.35. For comparative reasons

the same values for the above case study are adopted

in the present analysis with FLAC3D. Three dimen-

sional analysis has been carried out for the group and

the single pile as well, in conjunction with a surface

load (SL) of 200 kPa. Fig. 10 shows the predicted drag-loads for the single pile and the three characteristic

piles (interior, corner and perimeter) in the group. It

can be seen that the interior and the perimeter pile car-

ry almost the same dragload while the curve of the cor-

ner pile approaches that of the single pile. This is

mainly due to the very large surface loading. It can

be attributed to a similar conclusion regarding the

group effect for pile groups under vertical loading byComodromos et al. [15], stating that the maximum

group effect is observed for small loads when no plastic

yielding occurs. Reduction of dragload group effect

starts when the yielding of the soil surrounding the piles

begins to take place. Using 3D analysis and taking the

effect of soil slip into account, Lee et al. [10] predicted a

Fig. 9. Soil profile and pile group configuration by Combarieu [3].

dragload of 1.558 MN, which, as they mentioned, is

considerably smaller than the value of 2.640 MN, pre-

dicted from conventional approaches or 3D analysiswith no slip model. The prediction of the present study

for the single pile dragload is 1.588 MN, i.e. very close

to that of Lee et al. [10]. However, an important differ-

ence can be observed when comparing the response of

the characteristic piles of the group. As shown in Table

2 the dragload group effect, defined as the reduction in

maximum dragload compared with an isolated pile car-

rying the same load, is 9%, 20% and 24% for the cor-ner, the perimeter and the interior pile while the

corresponding values predicted by Lee et al. [10] is

5%, 6% and 7%, respectively. When applying a consid-

erably smaller surface load (20 kPa) the dragload pre-

diction for the isolated pile is 0.760 MN. Fig. 11(a)

illustrates the dragload distribution curve for the differ-

ent piles in the group. The dragload group effect for the

same piles is now 43%, 58% and 73%, considerablygreater than in the case of 200 kPa surface load. When

applying a surface load of 50 kPa the dragload for the

isolated pile increases to 1.078 MN. Fig. 11(b) illus-

trates the dragload distribution curve for the character-

istic piles in the group. The dragload group effect for

these piles is now 26%, 38% and 56%. It can be seen

that as the value of surface load increases the dragload

group effect decreases.Based on the fact of similar single pile dragload pre-

diction of the present study and that of Lee et al. [10]

and despite the fact of slightly different dragload group

effect, the same conclusion can be drawn for free head

end-bearing piles:

(a) Conventional design methods usually overestimate

dragload providing values which may be consid-ered as the upper-bound estimate.

Table 2

Predicted dragload and group effect for piles in a free-head pile group

Case Group dragload (MN) Dragload (MN) and group effect (%) Single pile (MN)

Corner Perimeter Interior

Combarieu (1985) (surface load 200 kPa) 10.448 1.265 0.758 0.420 2.640

52% 71% 84%

Lee et al. (2002) (surface load 200 kPa) 17.618 1.486 1.465 1.442 1.558

5% 6% 7%

Present study (surface load 200 kPa) 15.784 1.446 1.264 1.205 1.588

9% 20% 24%


43% 58% 73%


26% 38% 56%

Fig. 11. Dragload distribution along the single pile and the characteristic piles of Combarieu�s case study for a surface load of 20 and 50 kPa.


(b) For elastic-perfectly plastic soil the group effect

depends on the level of surface loading and the

yielding of the soil surrounding the piles. Conven-

tional design methods are usually unable to takethese factors into account and therefore they over-

estimate the group effect.

(c) Three dimensional nonlinear analysis, when taking

the pile–soil interaction into account, provides rel-

atively small group effect for considerable surface

loads, which is consistent with experimental

research work [6].

3.2. Response of fixed-head friction pile group

In order to investigate the effect of negative friction to

the foundation of the outer abutment of the bridge,

where an approach embankment is to be constructed,

a 3D numerical analysis was carried out. The piles of

the groups examined were identical to those of the single

pile, having a diameter D = 1.50 m and a length of 45 m.

The soil profile is presented in Section 2.2. Two cases of

a 3 * 3 configuration were considered; in the first case

the pile spacing was taken as 3.0D, while in the secondthe spacing was increased to 6.0D. In both cases, the

piles were considered as fixed in the pile head. The finite

difference mesh was extended far enough from the piles

in order to avoid any boundary effects. The bottom ele-

vation of the mesh was taken at z = �80.0 m, consider-

ably deeper than the level of the tip of the piles

(z = �45.0 m). At that plane all movements are re-

strained. The lateral sides of the mesh were also taken23.5 m from the central pile. The planes x = �23.5 m

and x = +23.5 m are free to move in the y and z direc-

tions but not in the x direction. Similarly, the planes

y = �23.5 m and y = +23.5 m are free to move in the

x and z directions but not in the y direction. Fig. 12 illus-

trates the finite difference mesh utilised in the analysis,

consisting of 8712 brick elements, 9961 nodes and

X

Y

Z47 m

47 m

80 m

Fig. 12. Finite difference mesh used in the analysis of pile group in

multilayered soil.


7766 interface elements. As a consequence to the fact

that the piles were considered fixed in a rigid pile head,

they have been forced to undertake the same settlement

at that point, while any movement in the horizontal

direction was not allowed for the pile head. To simulatethe fact that the piles were fixed in a rigid pile head, the

degrees of freedom of the nodes at the pile head corre-

sponding to the directions x–x and y–y were eliminated,

while in the z–z direction were considered slave to the

node on which the total load was applied. Analyses

Fig. 13. Dragload distribution for 3 * 3 pile groups with 3

using finer mesh around the piles illustrated negligible

variation of the results. This can be attributed to the

existence of the interface elements which effectively sim-

ulates the soil–pile interaction.

At a first stage a surface loading of 50 kPa was ap-

plied to both group configurations. Fig. 13 illustratesthe dragload predicted for the interior, the perimeter

and the corner piles. It can be seen that for the 6.0D

spacing the dragload distribution curves of these piles

approach that of the single isolated pile. The dragload

maximum values are given in Table 3. In the case of

fixed-head friction pile groups the dragload group effect

is significantly greater than in the case of free-head end-

bearing pile groups for the practically adopted 3.0Dspacing. More specifically the group effect was found

to be equal to 41%, 27% and 16% for the interior, the

perimeter and the corner pile, respectively. When spac-

ing increases to 6.0D the effect is almost negligible and

the corresponding dragload group effect is 9%, 5% and

3%, respectively.

Bearing in mind that downdrag and dragload may

create serviceability problems further analysis was car-ried out. In this final stage the pile group with 3.0D spac-

ing, which is significantly affected by the negative skin

friction is examined under the combination of the mean

working load of 4.5 MN and the surface loading of 50

kPa. As was demonstrated by the single pile analysis,

smaller pile axial loads were observed when constructing

the embankment prior to the application of the working

load. Consequently at the first step of the analysis thesurface load is applied and when equilibrium is reached,

a total force of 40.5 MN (4.5 MN per pile) is applied on

the master node of the pile head at which the nodes at

the top of the nine piles are slaved to. Fig. 14(a) shows

.0D and 6.0D spacing and a surface load of 50 kPa.

Table 3

Predicted dragload and group effect for piles in a fixed-head pile group

Case Applied load

per pile (MN)

Pile head

settlement

(mm)

Group max.

load (MN)

Dragload (MN) and group

effect (%)

Single pile (MN)

Corner Perimeter Interior

Surface load 50 kPa, 3 * 3 group with s = 3D 0 27.0 3.29 2.88 2.32 3.92

16% 27% 41%

Surface load 50 kPa, 3 * 3 group with s = 6D 0 33.7 3.82 3.71 3.58

3% 5% 9%

Max. axial load (MN) and

overall group effect (%)

Surface load 50 kPa, 3 * 3 group with s = 3D 4.5a 45.3 53.7 6.15 5.92 5.44 5.48

133%

Surface load 50 kPa, 3 * 3 group with s = 3D 4.5b 45.9 57.9 6.80 6.30 5.55

143%

Group 3 * 3 group with s = 3D, no surface load

(Comodromos, 2003)

4.5 33 40.5 5.22 4.19 2.79 4.5

116%c 93%c 62%c

a Applied after the construction of the embankment.b Applied prior to the construction of the embankment.c Group effect to the specific pile.

Fig. 14. Axial force distribution for the combination of surface load and working load: (a) application of the surface load (SL) and then the pile axial

working load (PAL); (b) inverse sequence.


the axial force distribution of the characteristic piles for

the aforementioned analysis.

It can be seen that the maximum axial force value of

the interior pile is very close to that of the single pile,

while the perimeter and the corner piles undertake greater

forces. More specifically the interior, the perimeter and

the corner piles undertake 5.44, 5.92 and 6.15 MN,

respectively, while the maximum axial force of the singlepile is equal to 5.48 MN. The summation of the maxi-

mum undertaken load by the nine piles leads to a total

load of 53.7 MN, which is 33% higher than the total

applied load of 40.5 MN. This increment is due to neg-

ative skin friction and should be taken into consider-

ation in order to respect the requirements for the

desired factor of safety. The effect to the secant stiffness

of the foundation which is to be used for the design of

the superstructure is also very important. When the ef-

fect of negative friction (which is the case of the interme-

diate abutments) is not taken into account, the 3Danalysis for the same group configuration and the same

total load led to a settlement of 33 mm. Therefore the

secant stiffness of the pile foundation, defined as the ra-


tio of the applied load divided by the corresponding set-

tlement, is equal to 1.23 GN/m. When negative friction

takes place due to the presence of the embankment sur-

face load of 50 kPa, the estimated pile head settlement is

45 mm and the corresponding overall secant stiffness of

the foundation is 0.9 GN/m. Therefore the stiffness to beused for the foundation of the outer abutments is 27%

smaller than that of the intermediate abutments for

the same value of working load. It may be noted that

the effect of negative friction to the stiffness of the pile

group is considerably smaller (reduction factor 27%)

than in the case of the single pile where the reduction

factor attains the value of 76%.

The situation is aggravated for both the pile groupand the single pile when the working load is applied

prior to the construction of the embankment. In that

case the interior, the perimeter and the corner piles

undertake 5.55, 6.30 and 6.80 MN, respectively, as

shown in Fig. 14(b). The undertaken total load increases

to 57.95 MN, which is 43% higher than the total applied

load of 40.5 MN. However, the settlement of the pile

group remains unchanged (45.3 and 45.9 mm; see Table3). This can be attributed to the fact that the difference

between axial loads at the pile tips is less than 5% no

matter the sequence of loading. More specifically for

internal piles the base load is 4.35 MN (embankment

prior to load) and 4.36 (load prior to embankment).

For perimeter piles the corresponding values are 4.67

and 4.78, while for corner piles the values are 4.86 and

5.07, respectively.It must be also mentioned that in the case of piles

with no negative friction effects the maximum axial

load is acting at the pile head and a gradual decrease

is observed with depth. On the contrary, the pile axial

load increases with depth until the neutral point is

encountered, when negative skin friction occurs. More-

over, it can be also observed that when the working

load is applied after the construction of the embank-ment (Fig. 14(b)) the maximum difference in the axial

load between the piles of the group is encountered at

the point of the neutral point. In the reverse sequence

of loading (Fig. 14(a)) the maximum difference in the

axial load between the piles of the group is observed

at the pile head.

Based on the results and the comparisons from the

analysis for a fixed-head friction pile group the follow-ing conclusions can be drawn:

(a) For spacings greater than 6.0D, the dragload

group effect is negligible (3–9% at 6.0D) and the

dragload value can be considered as equal to the

single isolated pile case.

(b) For spacings of 3.0D, the dragload group effect is

significantly greater than in the case of free head

piles, varying from 41% (interior pile) to 16% (cor-ner pile).

(c) As a result of the negative friction the total under-

taken load was increased by 33%, while an overall

secant stiffness reduction factor of 27% is pre-

dicted. This is valid in the case where the construc-

tion of the embankment precedes the application

of the working load. When the reverse sequenceis followed the effect increases and the axial load

increases by a factor of 43%.

4. Conclusions

In this paper, the effects of negative skin friction in

pile foundations were examined. The case of a single iso-

lated pile in a simplified soil profile was initially exam-

ined and compared with previous research. Good

agreement was observed between the results of the cur-

rent study and those of a similar three dimensional anal-ysis. Further analysis of the effect of the combination of

negative skin friction with the application of the work-

ing load demonstrated that when the construction of

the embankment precedes the application of the work-

ing load, the effect of negative skin friction is consider-

ably smaller than in the reverse case.

Three dimensional nonlinear analysis of pile groups

verified the conclusion drawn from the single pile anal-ysis for overestimation of dragloads when using simpli-

fied elastic approaches. It was also found that the

dragload group effect is significantly higher for fixed

head than free head piles for the practically adopted

spacing of 3.0D. The maximum group effect was ob-

served to be 41% on central pile, whereas the minimum

group effect obtains on the corner piles was 16%. When

spacing increased to 6.0D the effect was almost negligi-ble, varying from 3% to 9%.

The evaluation of the results of the analysis examin-

ing the effect of the construction sequence to the overall

response of pile foundations demonstrated that the neg-

ative friction effect increases when the construction of

the embankment follows the application of the working

load. From the single pile analysis, the additional axial

force due to the negative friction effect was almost50% of the working load. On the contrary, when the

construction of the embankment precedes the applica-

tion of the working load, the additional load is limited

to 10% of the working load. The effect of negative skin

friction to the secant stiffness of the single pile is consid-

erably greater. A stiffness reduction factor of the order

of 80% is observed for the above case.

Similar conclusions can be drawn for the specificfixed-head pile group. More specifically when the con-

struction of the embankment precedes the application

of the working load the effect of the negative skin

friction is minimised. The total undertaken load is

increased by 33%. Further enlargement of this per-


centage to 43% is observed when the construction of

the embankment follows the application of the work-

ing load. Moreover, due to negative skin friction, the

overall secant stiffness of the foundation is reduced by

27% for both cases.

Finally, it should be emphasised that the effect of neg-ative skin friction was quantified from the analysis of the

particular soil profile and that the use of these quantita-

tive data would be unwise in soil profiles and pile group

configurations different to those they were derived from.

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evaluation of negative skin friction effects in pile foundations using 3d nonlinear analysis

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