9.Coupled Effects in Stability Analysis of Pile-slope Systems (1)

7/23/2019 9.Coupled Effects in Stability Analysis of Pile-slope Systems (1)

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Coupled effects in stability analysis of pileslope systems

Jinoh Won a, Kwangho You b, Sangseom Jeong a,*, Sooil Kim a

a Department of Civil Engineering, Yonsei University, Seoul 120-749, Republic of Koreab Department of Civil Engineering, The University of Suwon, Hwasung-Si 445-743, Republic of Korea

Received 12 January 2004; received in revised form 11 February 2005; accepted 18 February 2005

Available online 10 May 2005

Abstract

A numerical comparison of predictions by limit equilibrium analysis and 3D numerical analysis is presented for a slopepile sys-

tem. Special attention is given to the coupled analysis based on the explicit-finite-difference code, FLAC 3D. To this end, an internal

routine (FISH) was developed to calculate a factor of safety for a pile-reinforced slope according to a shear strength reduction tech-

nique. Coupled analyses were performed for stabilizing piles in a slope, in which the pile response and slope stability are considered

simultaneously and subsequently the factors of safety are compared to a solution for a homogeneous slope using an uncoupled anal-

ysis (limit equilibrium analysis). Based on a limited parametric study, it is shown that the factor of safety for the slope is less con-

servative for a coupled analysis than for an uncoupled analysis and thus represents a definitely larger safety factor when the piles are

installed in the middle of the slopes and the pile heads are restrained.

2005 Elsevier Ltd. All rights reserved.

Keywords: Pileslope system; Limit equilibrium analysis; 3D numerical analysis; Shear strength reduction technique; Coupled/uncoupled analysis;

Homogeneous slope; Factor of safety

1. Introduction

The stabilization of slopes by placing passive piles is

one of the innovative slope reinforcement techniques

in recent years. There are numerous empirical and

numerical methods for designing stabilizing piles. They

can generally be classified into two different types: (1)

pressure/displacement-based methods [110]; (2) finite

element/finite difference methods[1115].

The first type of method is based on the analysis ofpassive piles subjected to lateral soil pressure or lateral

soil movements. Generally, the lateral soil pressure on

piles in a row is estimated based on a method proposed

by Ito and Matsui [3]. This model is developed for rigid

piles with infinite length and is assumed that the soil is

rigid and perfectly plastic. Thus, this model may not

represent the behavior of actual piles in the field: this

model does not take into account the actual behavior

of finite flexible piles, soil arching and soft soil, etc.

[8,23]On the other hand, the corresponding lateral soil

movements are estimated using either measured incli-

nometer data or from an analytical result using the finite

element approach, empirical correlations or based on

similar case histories [9,14]. However, a major problem

with the displacement-based methods is the estimation

of free soil displacements, because lateral soil displace-ments are notoriously difficult to estimate accurately.

Moreover, the first method for pile-reinforced slopes

often uses limit equilibrium, where soilpile interaction

is not clearly considered and thereby has some degree

of weakness in representing the real pileslope system.

The second type of method has been used to investigate

the pileslope system, which is analyzed as a continuous

elastic or elasto-plastic medium using either finite-

element or finite-difference formulations. This method

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

doi:10.1016/j.compgeo.2005.02.006

* Corresponding author. Tel.: +82 2 2123 2800; fax: +82 2 364 5300.

E-mail address: [email protected](S. Jeong).

www.elsevier.com/locate/compgeo

Computers and Geotechnics 32 (2005) 304315
mailto:[email protected]:[email protected]


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provides coupled solutions in which the pile response and

slope stability are considered simultaneously and thus,

the critical surface invariably changes due to the additionof piles, even though it is computationally expensive

and requires extensive training because of the three-

dimensional and nonlinear nature of the problem.

For slopes, the factor of safety F is traditionally

defined as the ratio of the actual soil shear strength to

the minimum shear strength required to prevent failure

[16]. As Duncan[17]points out, Fis the factor by which

the soil shear strength must be divided to bring the slope

to the verge of failure. Since it is defined as a shear

strength reduction factor, an obvious way of computing

F with a finite element or finite difference program is

simply to reduce the soil shear strength until collapse oc-curs. The resulting factor of safety is the ratio of the

soils actual shear strength to the reduced shear strength

at failure. This shear strength reduction techniquewas

used as early as 1975 by Zienkiewicz et al. [18], and has

been applied by Naylor [19], Donald and Giam [20],

Matsui and San [21], Ugai and Leshchinsky [22], Cai

and Ugai[23]and You et al. [24], etc.

The shear strength reduction technique is used in this

study. It has a number of advantages over the method of

slices for slope stability analysis. Most importantly, the

critical failure surface is found automatically. Applica-

tion of the technique has been limited in the past due

to a long computational run-time. But with the increas-

ing speed of the desktop computer, the technique is

becoming a reasonable alternative to the method of

slices, and is being used increasingly in engineering

practice.

In this study, factors of safety obtained with the shear

strength reduction technique were investigated for the

one-row pile groups on the stability of the homogeneous

slope. The case of an uncoupled analysis using limit

equilibrium analysis and subsequently the response of

coupled analysis based on the shear strength reduction

method were performed to illustrate the changes of crit-

ical surface invariably due to addition of piles on the

pileslope stability problem. The coupled effects were

tested against other case studies on the pileslope stabil-ity problem (seeFigs. 1 and 2).

2. Uncoupled analysis by limit equilibrium method

A comprehensive study of uncoupled analyses has

been reported by Jeong et al. [10]. They report an uncou-

pled analysis in which the pile response and slope stabil-

ity are considered separately. Here, the slopepile

stabilization scheme analyzed is shown in Fig. 3. The

conventional Bishop simplified method is employed to

determine the critical circular sliding surface, resisting

momentMRand overturning momentMD. The resisting

moment generated by the pile is then obtained from the

pile shear force and bending moment developed in the

pile at the depth of the sliding surface analyzed. It is as-

sumed that the lateral soil pressure exerted by the sliding

slope on the pile results in the mobilization of shear

Fig. 1. One-row piles undergoing lateral soil movements.

Ds

s

Lx

(a) Pileslope system.

lateral soil movement

unstable layer

passiveportion

stable layeractiveportion

(b) Pile response.

P

Pu

y

z

Soil pressure

passive portion

pile

interface

active portion

y

Fig. 2. A pile subjected to lateral soil pressure.

J. Won et al. / Computers and Geotechnics 32 (2005) 304315 305


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forces and bending moment. The plastic state theory

developed by Ito and Matsui [3] is used to estimate the

pressure acting on the pile, q, as follows (Fig. 4):

qAc" 1

N/ tan/ exp D1D2

D2 N/ tan/ tan

p

8 /

4

2N1=2/ tan/ 1

2tan/ 2N1=2/ N

1=2/

N1=2/ tan/N/ 1

#

c D12tan/ 2N

1=2/ N

1=2/

N1=2/ tan/N/ 1

2D2N1=2/

!

cz

N/A exp

D1D2D2

N/ tan/ tan p

8

/

4

D2

;

1

where c is the cohesion intercept; D1 is center-to-center

distance between piles; D2 is opening between piles; /is angle of internal friction of soil; cis unit weight of soil;

zis depth from ground surface; N/= tan2 [(p/4) + (//2)]

and A D1D1=D2N

1=2

/ tan/N/1.

Based on this, the safety factor of the reinforced slope

with respect to circular sliding is calculated as:

FFi DF

MR

MD

Vcr R cos hMcrVhead YheadMD

; 2

where Fiis the safety factor of unstabilized slope; DFisincreased safety factor of slope reinforced with pile; Mcris bending moment developed at critical surface; Vcr is

shear force developed at critical surface; Vhead is shear

force at pile head; R is radius of the sliding surface;

and h is the angle between a line perpendicular to the

pile and the failure surface. A computer program has

been developed using an uncoupled formulation to ana-

lyze the pileslope stability problem as described above

(Fig. 5).

3. Coupled analysis by strength reduction method

3.1. Shear strength reduction technique

To calculate the factor of safety of a slope defined in

the shear strength reduction technique, a series of stabil-

ity analyses are performed with the reduced shear

strength parameters c0trial and /0trial defined as follows

(Fig. 6):

c0trial 1

Ftrialc0; 3

/0trial arctan 1Ftrial

tan /0

; 4

wherec 0, / 0 are real shear strength parameters and Ftrial

is a trial factor of safety. Usually, initial Ftrial is set to be

sufficiently small so as to guarantee that the system is

stable. Then the value ofFtrial is increased byFinc values

until the slope fails. After the slope fails, the Fstart is

replaced by the previous Flow andFinc is reduced by 1/5.

Then the same procedure is repeated until the Finc is less

than user-specified tolerance (e). Fig. 7shows the flow-

chart of the routine to calculate a factor of safety. This

iterative procedure is based on the incremental search

method. This final value ofFlow

, by definition, is identi-cal to the one in limit equilibrium analysis. It should be

noted, however, that in the finite element and finite dif-

ference methods, local equilibrium is satisfied every-

where, whereas in the limit equilibrium analysis, only

global equilibrium for the sliding mass is considered in

the analysis.

3.2. Explicit finite difference scheme

The response of a slopepile system is analyzed by

using a three-dimensional explicit-finite differenceFig. 4. Plastically deforming ground around stabilizing piles[3] .

Fig. 3. Forces on stabilizing piles and slope.

306 J. Won et al. / Computers and Geotechnics 32 (2005) 304315


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approach. The mesh consists of three-dimensional eight-

noded solid elements and is assumed to be resting on a

rigid layer, and the vertical boundaries at the left- and

right-hand sides are assumed to be on rollers to allow

movement of soil layers.

The pile element is assumed to remain elastic at all

times, while the surrounding soil is idealized as a

MohrCoulomb elasto-plastic material. This model

was selected from among the soil models in the library

of FLAC 3D [25], the commercial explicit finite-differ-

ence package used for this work. Factors of safety are

computed using FLAC 3D. In order to consider the

effect of an interface between a pile and soil, shell

elements, which satisfy the shear-yield constitutive

model, are used. The shear stiffness of the shell element

is assumed to be isotropic and is inferred by the follow-

ing equation:

Assume safety factor of slope and critical surfaceby using simplified Bishop methods

Input flexible rigidity (EI), diameter, length andboundary condition of stabilizing pile

Input shape of slope, soil property and pore waterpressure

Input position of stabilizing pile in slopeand center-to-center spacing

Calculate ultimate pressure (Pu)

Input soil pressure(Ito & Matsuis pressure)

Analysis the behavior of stabilizing pilebased on pressure-based method

Calculate displacement, bending moment, shearforce and soil reaction force

Calculate bending moment and shear force oncritical surface

Compare with allowabledisplacement and allowable

bending moment

Calculate safety factor of stabilized slope

Compare with safety factorof un-stabilized slope

Determine optimized flexible rigidity (EI), diameter,position and spacing of stabilized pile

Yes

Modify flexiblerigidity (EI) and

diameter

No

Yes

No

Modifyposition and

spacing

end

start

Fig. 5. Flow chart of computer program.

Fig. 6. A relationship between the actual strength and a strength

reduced by a trial factor of safety.



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Ks aG=l; 5

where lis the minimum length of the shell elements and

Gis the shear modulus of the soil adjacent to the shell

element. It is assumed that a= 20 is large enough to

make the initial slope of the load displacement relation-

ship closely resemble the elastic analytical solution [23].

The normal stiffness for the interface is taken as a very

high value under the reality that a pile and the surround-

ing soil do not overlap at the interface.

For a given element shape function, the set of alge-

braic equations solved by FLAC is identical to that

solved with finite element methods. In FLAC, however,

this set of equations is solved using dynamic relaxation

[26], an explicit, time-marching procedure in which the

full dynamic equations of motion are integrated step

by step. Static solutions are obtained by including

damping terms that gradually remove kinetic energy

from the system.

The convergence criterion for FLAC is the ratio

defined to be the maximum unbalanced force magnitude

for all the gridpoints in the model divided by the average

applied force magnitude for all the gridpoints. If a model

is in equilibrium, this ratio should be close to zero. For

this study, a simulation is considered to converge to

equilibrium when the ratio becomes less than 105.

4. Validation and application of the coupled model

The present coupled method is based on a shear

strength reduction technique using the explicit finite dif-

ference code, FLAC. The validation of the present cou-

pled model was done by the comparison with others

coupled analysis results.Cai et al. [23] performed a numerical analysis to

investigate the effect of stabilizing piles on the stability

of a slope. They performed a coupled analysis based

on a three-dimensional finite element method with an

elasto-plastic constitutive model and the shear strength

reduction technique. The numerical results by their cou-

pled analysis were compared with those obtained by the

present method. However, it should be noted that the

final calculated factor of safety by finite difference meth-

ods depends highly on the size of element unlike finite

element methods in which a shape function can be used

within the elements. In general, the finer the size of ele-

ments is, the more precise the result is.

An idealized slope with a height of 10 m and a gradi-

ent of 1V:1.5H and a ground thickness of 10 m is ana-

lyzed with a three-dimensional finite element mesh, as

shown inFig. 8. A steel tube pile with an outer diameter

(D) of 0.8 m was used. The piles are treated as a linear

elastic solid material and are installed in the middle of

the slope withLx= 7.5 m, and the center-to-center spac-

ing s= 3D. The piles are embedded and fixed into the

bedrock or a stable layer. The material properties for

prediction purposes were selected based on Cai et al.s

assumptions, as shown inTable 1. The safety factor of

a slope stabilized with piles was compared for two differ-ent pile head conditions (free and fixed) and two differ-

ent pile Youngs modulus values (60 and 200 GPa).

When the slope is not reinforced with piles, the Cai

et al.s shear strength finite element method, the finite

Fig. 7. Flowchart of the calculation routine for factor of safety.

Fig. 8. Model slope and finite element mesh[23].



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difference code, FLAC and Bishops simplified method

gave safety factors of 1.14, 1.15 and 1.13, respectively.

Based on this, it is obvious that the failure mechanism,

indicated by the nodal velocities in the shear strength

reduction techniques, agree well with the critical slip

circle given by Bishops simplified method.

On the other hand, the safety factor of a slope stabi-

lized with piles for two different pile head conditions and

two youngs modulus values, were summarized inTable2.Here, the critical depth was taken as the level of the

slip surface associated with the lowest factor of safety

although the FLAC could not predict a clear slip surface

like the limit equilibrium method. By comparing the

magnitude and distribution of the nodal velocities inside

the slope (Fig. 9(a)), especially at the pile position, the

finite difference code, FLAC shows slightly higher values

in terms of predicted safety factors, compared with the

results by the shear strength reduction finite element

method. This is because there is a difference in mesh

refinement in the region surrounding the piles between

the two methods, even though in this study, a relatively

fine mesh was used near the pilesoil interface and be-

came coarser further from the pile. It can be said that

these compare fairly well with each other with respect

to the calculated safety factors. However, the depth of

the slip surfaces predicted by the FLAC 3D analysis

are deeper than those located by Bishops simplified

method, where the reaction force of the piles is deter-

mined by ItoMatsuis equation (Fig. 9(b)). In addition,

the slip surface by the FLAC is divided into two differ-

ent segments around the pile element, compared with

the unique single line by Bishops simplified method.

Thus, the depth and distribution of the slip surface im-

plies that Bishops simplified method cannot indicate

the true failure mechanism for the slope reinforced with

piles.

Bishops simplified method can not incorporate the

pile head conditions well on the calculation of the safety

factor due to the limitation of ItoMatsuis equation,

which is derived for rigid piles. In this respect, Table 2

shows that Bishops simplified method can obtain a

smaller value of the safety factor, compared with the

fixed head pile of FLAC 3D. The reason for this is that

because of the larger soil pressure, followed in order of

fixed and ItoMatsuis pressure, the safety factor pre-

dicted by the FLAC 3D is definitely larger than that ob-

tained by Bishops simplified method, as shown in Fig.

10and inTable 2.

5. Comparison with other coupled analysis

5.1. Model slope

Hassiotis et al. [8] proposed a methodology for the

design of slopes reinforced with a single row of piles.

To estimate the pressure acting on the piles, they usedthe theory developed by Ito and Matsui [3] and pro-

posed a stability number by the friction circle method

to take into account the critical slip surface changes

due to the addition of piles. This is a pressure-based cou-

pled analysis. The slope in Fig. 11 has a height of

13.7 m, a slope angle of 30, and is made of a homoge-

neous material with cohesion 23.94 kN/m2, friction an-

gle 10 and unit weight 19.63 kN/m3. The water table

was not considered here. It was found that the safety

factor of the slope (without the pile reinforcement)

was about 1.08.

The slope is simulated by the FLAC 3D. Two sym-

metrical boundaries are used, so that the problem ana-

lyzed really consists of a row of piles with planes of

symmetry through the pile centerline and through the

soil midway between the piles. The actual size of the

mesh is related to the pile length; the lower rigid bound-

ary has been placed at a depth equal to pile lengths and

the side boundary has been extended laterally to

rm= 2.5L(1 t)[27].It is found that this size was suffi-cient for the analysis of one-row pile groups. The mate-

rial properties used for prediction purposes were

described inTable 3. A numerical comparison of predic-

tions by the two analyses is presented below.

Table 1

Material properties and geometries[23]

Soil

Unit weight (kN/m3) 20.0

Plastic (MohrCoulomb)

Cohesion (kPa) 10.0

Friction angle () 20

Dilation angle () 0

Elastic

Elastic modulus (kPa) 2.0 105

Poissons ratio 0.25

Steel pile


Elastic modulus (kPa) 2.0 108, 6.0 107

Poissons ratio 0.2

Diameter (m) 0.8

Interface


Poissons ratio 0.25

Cohesion (kPa) 10.0


Dilation angle () 0

Table 2

Comparison of numerical methods on safety factor

Youngs modulus

of piles (GPa)

FLAC 3D Cai and Ugai[23] Bishop

Free Fixed Free Fixed Free

60 1.46 1.56 1.36 1.55 1.49

200 1.55 1.56 1.55 1.56 1.49



7/12

5.2. Effect of pile bending stiffness

The effect of the bending stiffness is investigated by

changing only the equivalent Youngs modulus, Ep, of

the piles. The piles are installed with Lx= 12.2 m, and

the center-to-center spacings of 2.5D, 3.0D, 3.5D, and

4.0D. As shown inFig. 12(a), the safety factor of a slope

stabilized with piles for different bending stiffness values

shows that the pile head conditions have more influence

on the safety factor of the slope when the piles are more

flexible (Ep= 1.43 GPa). However, for piles with larger

Youngs modulus (Ep = 25 GPa), the safety factor is

almost the same, regardless of the pile head conditions.

This is because the pressure on the free headed pile with

smaller Youngs modulus (Ep= 1.43 GPa) are consider-

ably smaller than that of fixed head piles, whereas the

piles with larger Youngs modulus (Ep= 25 GPa) have

almost identical pressure distributions, regardless of

the pile head conditions, as shown in Fig. 12(b) and

(c). In addition, the pressure on the piles is almost the

same for the two bending stiffness values when the pile

head is fixed.

In this study, the value of EpIp was taken as con-

stant by assuming the pile elastic. However, the crack-

ing of the pile itself may occur in the loading with a

significant reduction in EpIp. To understand the true

behavior, yielding of the pile is considered by taking

into account the compressive strength of the concrete.

Fig. 13 shows the typical reduction distribution of the

EpIp as the bending moment is increased; therefore, a

Fig. 9. Comparative results between shear strength reduction and Bishops simplified method.

(a) Nodal velocity vectors by FLAC 3D and critical slip circle by Bishops simplified method.

(b) Comparison of the depth and shape of critical slip surface.



8/12

Fig. 10. Pile behavior characteristics by FLAC 3D.

15

12

9

6

3

0

Depth(m)

Flac 3D (free)

Flac 3D (fixed)

Bishop (Ito-Matsui [3])

0 3 6 9 12

Displacement (cm)

15

0 40 80 120 160 200

Soil pressure (kPa)

15

12

9

6

3

0

Depth(m)

Flac 3D (free)

Flac 3D (fixed)


(a) Pile modulus, Ep= 60 GPa.

15

12

9

6

3

0

Depth(m)

Flac 3D (free)

Flac 3D (fixed)


0 2 4 6 8

Displacement (cm)

10

0 40 80 120 160 200

Soil pressure (kPa)

15

12

9

6

3

0

Depth(m)

Flac 3D (free)

Flac 3D (fixed)

Bishop (Ito-Matsui[3])

(b) Pile modulus, Ep= 200 GPa.

Lx

s

sD

16.7

m

3.0

m

1:1.7

10.0m L=23.7m s/220.0m

53.7m

Fig. 11. Model slope and element mesh[8] .

Table 3

Material properties and geometries[8]

Soil


Plastic (MohrCoulomb)

Cohesion (kPa) 23.94


Dilation angle () 0

Elastic


Poissons ratio 0.35

Concrete pile


Poissons ratio 0.2

Diameter (m) 0.62

Elastic modulus (kPa) 2.5 107 1.43 106

Compressive strength of the concrete (kPa) 2.74 104 89.63

Yield strength of the re-bar (kPa) 4.14 105



9/12

modification in EpIp may be needed for accurate com-

putations, especially if deflection will control the

loading.

It is important to mention that in the numerical

results obtained by the FLAC analysis, the safety factor

of slopes reinforced with fixed head piles is larger than

that with free head piles when the piles are more flexible

(Ep= 1.43 GPa). Therefore, a restrained pile head

(fixed) is recommended to stabilize the slope. For a fixed

pile head condition, the safety factor predicted by

uncoupled analysis (e.g., Bishops simplified method) is

excessively conservative.

5.3. Effect of pile spacing (s/D)

When piles with an equivalent Youngs modulus,

Ep = 25 GPa are installed with the horizontal distance

between the slope toe and the pile position, Lx of 7.6,

12.2, and 17 m, the effect of pile spacing on the safety

factor is shown inFig. 14for two different pile head con-

ditions; free and fixed. As expected, the safety factor in-

creases significantly as the pile spacing decreases. Here,

spacing equal to or larger than 2.5 diameters were

selected because the ratios less than 2.5 are not practical.

When a center to center spacing-to-diameter ratio is 2.5,

the safety factor of the slope approaches its maximum

value. This is explained by the fact that the lateral soil

movement between the piles is resisted more and more

by the piles as the spacing becomes closer and closer.

Fig. 14also shows coupled effects in the safety factor

on pile spacings. The present method (FLAC analysis)

shows that the pile head conditions have more influence

on the safety factor of the slope. The safety factor of a

slope reinforced with fixed head piles, obtained by the

present method is a quite similar rate change but is

significantly higher than that obtained the pressure-

based coupled analysis proposed by Hassiotis et al. and

Bishops simplified method. The difference in the safety

2 3 42.5 3.5 4.5

s/D

1

1.2

1.4

1.6

1.8

2

safetyfactor

Ep=25Gpa

Flac 3D (free)

Flac 3D (fixed)

Hassiotis et al. [8]

Bishop

Ep=1.43Gpa

Flac 3D (free)

Flac 3D (fixed)

0 100 200 300

Soil Pressure (kPa)

10

8

6

4

2

0

Depth(m)

free head

2.5D

3.0D

3.5D

4.0D

fixed head

2.5D

3.0D

3.5D

4.0D

80 120 160 200 240 280

Soil Pressure (kPa)

10

8

6

4

2

0

Depth(m)

free head

2.5D

3.0D

3.5D

4.0D

fixed Head2.5D

3.0D

3.5D

4.0D

(a)

(b)

(c)

Ep =1.43 GPa

Ep =25 GPa

Fig. 12. Effect of pile bending stiffness and soil pressure. (b) Ep=

1.43 GPa; (c) Ep= 25 GPa.

Fig. 13. Bending stiffness,EpIpas a function of bending moment for a

pile.



10/12

factor between the coupled and uncoupled analyses can

be explained by the pressure acting on the piles pre-

sented earlier: the larger the pressure on the piles, the

larger the reaction force to the sliding body supplied

by the piles, and the higher the safety factor of the slope

reinforced with piles.

5.4. Effect of pile positions

Fig. 15(a) shows the safety factor as a function of

the relative position of the pile row with s/D of 2.5

on the slope. Here, the pile positions in the slope are

shown with a dimensionless ratio of the horizontal dis-

tance between the slope toe and the pile position, Lx,

to the horizontal distance between the slope toe and

slope shoulder, L. The coupled FLAC results, obtained

with the shear strength reduction technique, show that

the improvement of the safety factor of slopes rein-

forced with piles is the largest when the piles are in-

stalled in the middle of the slopes, irrespective of pile

head conditions. However, Hassiotiss coupled solution

shows that the piles should be placed slightly closer to

the top of the slope for the largest safety factor. This is

the same as the results of the Bishops method. The

reason for this is that when the piles are placed in

the middle portions of the slopes, the shear strength

of the soilpile interface is sufficiently mobilized by

the fact that the pressure acting on the piles is larger

than that on the piles in the upper portions of the

slopes (Fig. 15(b)).

Fig. 16 shows coupling effects in the safety factor

both on pile positions and on pile spacings. The safety

factors of slopes analyzed by coupled analyses are larger

than those by uncoupled analysis, as pile spacing de-

creases. This clearly demonstrates that the coupled effect

exists between piles and soil so that the critical slip sur-

face can change due to the addition of piles. It is noted,

therefore, that the uncoupled analysis, which can only

Fig. 14. Effect of pile spacings on safety factor (Ep= 25 GPa).

2 3 42.5 3.5 4.5

s/D

1

1.2

1.4

1.6

1.8

2

safetyfactor

Flac 3D (free)

Flac 3D (fixed)

Bishop

(c) Lx= 17 m (Lx/L= 0.72).

2 3 42.5 3.5 4.5

s/D

1

1.2

1.4

1.6

1.8

2

safetyfactor

Flac 3D (free)

Flac 3D (fixed)


Bishop

(a) Lx= 7.6 m (Lx/L= 0.32).

2.5 3.5 4.5

s/D

1

1.2

1.4

1.6

1.8

2

safetyfactor

Flac 3D (free)

Flac 3D (fixed)


Bishop

(b) Lx= 12.2 m (Lx/L= 0.51).



11/12

consider a fixed failure surface, should be limited in its

application.

6. Conclusions

In this study, a coupled analysis of slopes stabilized

with a row of piles has been presented and discussed

based on an analytical study and a numerical study.

The numerical results are compared with those obtained

by the limit equilibrium method for slope stability anal-

ysis. A limited study of numerical analysis was carried

out to examine the pileslope coupling effect on relative

pile position and different pile spacings. The numerical

results have clearly demonstrated the important cou-

pling effect of stabilizing piles in a slope with different

head conditions and pile bending stiffness. From the

findings of this study, the following conclusions are

drawn:

(1) A coupled effect has been identified between piles

and soil, so that the critical slip surface invariably

changes due to the addition of piles. It is noted,

therefore, that the uncoupled analysis, which can

only consider a fixed failure surface, should be lim-

ited in its application. Hassiotis et al.s coupled

analysis based on the modified friction circle

method is a relatively effective for a pileslope sys-

tem. However, their approach is intermediate in

theoretical accuracy between coupled FLAC anal-

ysis and uncoupled analysis (Bishops simplified

method).

(2) Through comparative studies, it has been found

that the pile head conditions and the bending

stiffness influence the safety factor of the slopes.

If the piles are more flexible, the safety factor of

the slope is significantly smaller than that of a

slope reinforced with fixed head piles. However,

for piles with larger Youngs modulus

(Ep= 25 GPa), the safety factor is almost the

same, regardless of the pile head conditions. As

a result, for fixed pile head condition, the predic-

tion in the factor of safety in slope is much more

conservative for an uncoupled analysis than for a

coupled analysis.

(3) The numerical results show that the pressure act-

ing on the piles is the largest when the piles are

placed in the middle portion of the slope. There-

fore, the piles should be installed in the middle

of slopes and restrained in the pile head, when

the stability of a slope is required to be improved

optimally. A restrained head condition can be

obtained by connecting the pile heads with a bur-

ied beam which is fixed by the tie-rods or tension

anchors.

0 0.2 0.4 0.6 0.8 1

Lx/L

1

1.2

1.4

1.6

1.8

2

2.2

2.4

Safetyfactor

Flac 3D (free)

Flac 3D (fixed)

Bishop


0.720.51

0 50 100 150 200 250 300

Soil Pressure (kPa)

10

8

6

4

2

0

Depth(m)

Lx/L=0.51

Flac 3D (free)

Flac 3D (fixed)


Lx/L=0.72Flac 3D (free)

Flac 3D (fixed)


(a)

(b)

Fig. 15. Effect of pile positions on safety factor (s/D= 2.5) and soil

pressure (Ep= 25 GPa).

0.2 0.4 0.6 0.80.3 0.5 0.7

Lx/L

1

1.2

1.4

1.6

1.8

2

2.2

Safetyfact

or

2.5D (Flac 3D)

3.0D

3.5D

4.0D

2.5D (Bishop)

3.0D

3.5D

4.0D

Fig. 16. Effects of pile positions and pile spacings on safety factor.



12/12

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9.Coupled Effects in Stability Analysis of Pile-slope Systems (1)

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