Simplified pile-slope stability analysis

Computers Printed

and Geotechnics 17 (1995) 1-16 0 1995 Elsevier Science Limited in Great Britain. All rights reserved 0266-352X195/$9.50

ELSEVIER

SIMPLIFIED

PILE-SLOPE

STABILITY

ANALYSIS

C.Y. Lee, T.S. Hull and H.G. Poulos School of Civil and Mining Engineering The University of Sydney NSW 2006, Australia

ABSTRACT This paper presents a simplified approach to the study of a row of piles used for slope stabilization. The approach is based on an uncoupled formulation in which the pile response and slope stability are considered separately. The pile response when subjected to external lateral soil movements from slope instability is analysed by a modified boundary element method. A conventional simplified Bishop slip circle approach is employed to analyse the slope stability. Applications of the approach are presented and discussed with emphasis on identifying and optimizing some of the important factors that control the performance of piles used for slope stabilization. Several conclusions are drawn regarding the pile-slope stability problem, that of prime importance being the location of the piles for most effective slope stabilization.

INTRODUCTION The use of piles to stabilize active landslides, slopes, has become

one of the important

innovative

recent years. Some of the successful applications

and as a preventive

slope reinforcement

horizontal

movements

of the surrounding

piles. Driven timber piles

techniques

in

of such techniques have been reported by

De Beer et al. 1970, Ito and Matsui 1975, Sommer 1977, Fukuoka 1979. The piles used in slope stabilization

measure in stable

are usually

subjected

1977 and Wang et al. to lateral

soil and hence they are considered

force

by

as passive

have been used to reinforce the slope stability of very soft clays

in Sweden, while cast-in-place

reinforced

been used in Europe and the United

concrete piles as large as 1Sm diameter

States to stabilize

active landslides

have

in stiff clays

2 (Bulley

1965 and Offenberger

been used to stabilize that a sliding (Viggiani

active

slope

landslide

using piles.

Rowe

have been

for assessing and Poulos

diameter

1967). Past experiences factor

dimensional

elastic

finite

for the analysis finite

element

approaches

not suitable

mechanisms

associated

have

suggested

by a few percent

provide

Matsui

(1975)

lateral

pressures

length.

have finite

(1981)

These

length

versatile

et al. (1991)

slope

a plastic

piles

when the piles are closely

useful,

may not represent

and also are unlikely spaced.

piles

acting

purposes.

expensive

of the basic been

et al. (1991). interaction

These

and failure

Ito and

to compute

solutions

the

for slope

for rigid piles with

in the field

to be rigid. Also it may provide

failure

suggested

problem.

model

is derived

piles

and Chameau

are relatively

in limit equilibrium

the actual

approach

Although

have

deformation

from

piles.

Some

slopes

the model

arises

rows of piles. A three

by Oakland

they

stability

extrusion

which

with drilled

and Lee

into the pile-slope

appears

through

solutions,

design

pressures

finite element

has been developed

on a row of passive

this approach

stability

a two-dimensional

of soil flowing

practical

Hull

insight

incorporated

acting

Although

in slope

of surcharged

provide

for routine

better

have

approach

lateral

Reese et al. (1992) have presented

with the use of piles to stabilize

by Viggiani

mechanisms

effect

of stabilization

and usually

discussed

element

to evaluate

in slopes.

(1979) developed

for the three dimensional

infinite

of 300mm

its safety

developed

the improvement

that allowed

stability.

by increasing

are used as reinforcement

a “p - y” approach

such

areas (Taniguchi

may be stabilized

of techniques

piles which

(1984)

steel tube piles

1981).

A number against

1981). In Japan

since

doubtful

the latter solutions

3 An alternative method piles

(Poulos

approach

in limit equilibrium

may be modelled

as an elastic

of

strength

and

interface

element

reaching

an

slip

developed

based

approach

with

state.

circle

The

slope

analyses.

Theoretical

in order to study the most effective

METHOD

and slope stability

is formulated are considered

analysis

means

The pile-soil

response

with nonuniform

variation

a nonlinear

pile-soil

or softening

response

is performed

using

program

solutions

element

of a row of passive

incorporates

A microcomputer-based

on the above

The analysis

stability.

a hardening

stability

boundary

the response

of slope

solution

to represent

The

a modified

or as a set of springs,

depth.

approach.

to study

solutions

continuum,

with the ability

ultimate

simplified

here in which

1973; Hull 1987) is employed

incorporated

stiffness

is presented

prior

Bishop’s

(SLOPIL)

has

have been obtained

of using piles for stabilizing

to

been

by this slopes.

OF ANALYSIS

using an uncoupled

approach

in which

the pile response

separately.

Pile Response The sliding the discretely to the more slope

is

sliding boundary (1991).

placed stable

subjected

movements

soil mass

element

the failure

piles to fomi a barrier underlaying to large

are ignored

surface

above

layers. lateral

surface

that resists

The portion soil

by the external method

lateral

as described

(see

and transfers

embedded

Figure

and bending

soil movements

to be strengthened

soil movements

of the piles

movements

here. The pile shear forces

is assumed

are evaluated

by Hull et al. (1991),

loads

in the sliding

1). The

moments

by

vertical

developed using

and employed

soil at the

a modified by Lee et al.

4

(a) Piled-Slope Stability Problem

FIG.1

SIMPLIFIED

An incremental out with defined complete

and moments

assumed moment

that

the

of the piles.

The

incorporated

in the analysis

the specified

pile-soil

within modelled. correlated Typical

a group

may

interface

also

to the values

undrained

strengths

pressure.

may remain

developed

moments

is assumed

be included.

Different

modulus strength

of K, and K,, are 250-1000

interfaces

The interaction pile

effects head

E, and pile-soil c,

A restriction

to

the piles

are

equal

it is

to the

yield

effects

to yield

they reach

when

of identical base

limiting

and 3-12, respectively

yield,

but nonlineu

and

by multipliers

that

linear in order to balance

When

to be elastic

the pile-soil

can be carried

is the basic requirement

bending

pressures.

shear

pile-soil

loads).

by allowing

In a clay soil, the Young’s

the analysis

by the distributed

soil mass

limiting

element

(i.e., some elements

pile

ANALYSIS

in which

up to the limiting

produced

maximum

STABILITY

has been developed

of pile-soil

must be maintained

the forces

PILED-SOIL

soil deformation

mobilisation

equilibrium

approach

(h) Pile Rc~pon~e

K,

and (Hull

loaded

fixities

pressure K,,

are

piles

may

be

py may be respectively.

et al. 1991,

Lee et

5 al. 1991). The pile-soil increasing

lateral

interaction

problem

soil movements

is solved

up to and beyond

by an incremental

analysis

for

the state at which full pile-soil

interface strength has been mobilised.

Slope Stability The conventional employed moment

to determine

Bishop simplified

the critical sliding surface, resisting

M,. The resisting

moment M,

pile shear force and bending surface analysed,

method of slip circle analysis (Bishop 1955) is

moment

as described

safety of the piled-slope

moment

I$, and overturning

generated by the pile is then obtained developed

in the previous

Frs may be determined

from the

in the pile at the depth of the sliding section. Thus the final overall factor of

as follows:

M +Mv_M FP=L---L MO MO

A microcomputer the uncoupled

formulation

based computer program,

reinforced

solutions

soil slope problem

for a row of hypothetical

into both a unifonn analysed

of 30 kN/m’

soil slope.

is shown in Figure 2. The slope is 10m high

20 degrees to the ground surface. The soil is assumed to be uniform shear strength

cast-in-place

soil and a two-layered

with the rigid base at 1Om below the ground surface. The slope is inclined

undrained

using

SOLUTIONS

have been obtained

concrete piles installed

The uniform

“SLOPIL” has been developed

to analyse the pile-slope stability problem as described above.

PARAMETRIC Theoretical

(1)

and undrained

Poisson’s

at an angle of

soft clay with an

ratio of 0.5. The soil

6 density

is assumed

to be 18.5 kN/m3. The soil Young’s

pressure

are taken

to be 500 and 9 times

diameter

of the concrete

modulus

the undrained

shear

piles is lm and these are discretely

and pile-soil strength,

placed

limiting

respectively.

The

at 3m centre-to-centre

intervals.

Standard Paratneters

xP

,

c, = 30 kN/m2 Soil density = 18.5 kN/m” KEs = 500 KPY = 9 = 26 x lo6 kN/& EP

/ LX

I

I

FIG.2 ILLUSTRATIVE EXAMPLE OF HOMOGENEOUS The piles

are assumed

tips are resting

to be positioned

on the rigid base but derive

tips are free to displace elements pile

and rotate

and the slope is divided

section

strength

reaches

its yield

not mobilised.

N,, which

between

is defined

unless

moment,

the toe and crest

no support otherwise

into 100 slices

across

The piles

the modelled

is terminated

are presented

of the slope.

The pile

from the base. The pile heads

stated.

the analysis

All the solutions

SLOPE

in terms

are divided geometry.

regardless

and

into 20 When

the

of any soil

of an improvement

ratio

as follows:

(2)

where

F,= minimum

factor

of safety

safety

of the slope

stability

problem

of piled-slope

problem

without

The value

piles.

and F,= minimum of the parameters

factor

of

in the

7 problem have been chosen so that F, for the uniform soil slope is approximately (a) Homogeneous

1.00,

Soil Slope

Figure 3 shows the effect of the pile position along the slope on the improvement ratio NrS. The most effective pile positions piled-slope

improvement

are near the toe and crest of the slope with a

ratio of about 1.08. When the piles are positioned

middle of the slope the piled-slope

improvement

ratio becomes

close to the

1.0, indicating

that the

presence of the piles has no effect on stability. This is because the critical sliding surface was found on the stability with the pile heads fixed

is near the pile tips. Little influence

against rotation since the sliding surfaces are not in close proximity to the pile heads.

1.20

I

I

I

I

Free Head Pilc + Fixed Hcnd Pi

0

1.16

1.12

G D.? II z”

1.08

1.04

1.00 _ II

0.6

0.4

0.2

0.8

1.o

xp/Lr FIG.3 EFFECT OF PILE POSITION ON HOMOGENEOUS

The following

parametric

solutions

are obtained

SLOPE

for piles located at the toe (toe

piles) and crest (crest piles), positions at which the piles appear to be most effective.

The piled-slope

improvement

ratio increases

with increasing

pile diameter

as

8

illustrated larger

in Figure

pile resisting

failure.

For pile

effective

4 (where moments

diameter

d,=standard

pile

diameter).

and shears,

hence

increase

ratio,

d/d,,

greater

than the crest piles since the critical

toe piles where

larger pile resisting

than

diameter

the resistance

1.0, the toe piles

sliding

surface

moments

are generated.

I

I

1.20 .

Larger

is closer

piles

induce

of the slope

appear

to

to be more

to the pile top at the

1.16 -

o Tot Pile Crest Pile

l

1.5

1.0

2.0

d/d s FIG.4 EFFECT OF PILE DIAMETER ON HOMOGENEOUS

The effect improvement from

ratio reduces

the piles

through

become

is shown

with increasing

smaller

pronounced

stability.

more like a continuous and

decreases

in Figure pile spacing.

with larger

the larger clear space between

the piles become more

of pile spacing

the

pile spacing

the piles. barrier soil

5 and as expected, The resisting which

In contrast,

allows

and

the piled-slope

moments

contributed

more

soil to move

as the pile spacing

and the influence

movements

SLOPE

of soil arching

hence

increases

decreases becomes the

slope

1.20

+L._ o Toe Pile l Crest Pile

1.16 -

g

1.12 -

B II z”

1.08 -

1.04 -

1.00

’

1

1

I

I

2

3

4

5

s/d s F1G.S EFFECT OF PILE SPACING ON HOMOGENEOUS

I

1.20

I

I

I

SLOPE

I

0 Toe Pile l

Crest Pile

1.16 -

0.2

0.4

0.8

0.6 KPY

1.0

1.2

1.4

JKPYS

FIG.6 EFFECT OF PILE-SOIL LIMITING PRESSURE MULTIPILJER ON HOMOGENEOUS SLOPE

10

Figure

6 shows that the piled-slope

improvement

-standard K,, (where KPYS-

ratio increases

pile-soil limiting

almost linearly

pressure multiplier).

with increasing

multiplier

Larger pile-soil

limiting pressure allows the piles to develop larger pile resisting moments

and increases the stability, since the piles are relatively rigid.

It is found that the soil modulus

and pile stiffness have little or no effect on the

pile failure response and in turn on the piled-slope the ultimate condition.

(b) Two-Layer Figure

However they may influence the pile response prior to failure.

Soil Slope 7 shows

hypothetical

piles embedded

Case A, the upper soft layer is underlain limiting

pile-soil

homogeneous

stability, since the pile failure occurs at

pressure

multipliers

in the two-layer

soil slope. For

by a stiff layer. The soil Young’s modulus and

are assumed to be the same as those used in the

soil slope. For Case B, the lower soft layer is overlain by a stiff layer. The

value of F, for Case A and Case B is about 1.03 and 1.18, respectively.

Case A

w

FIG.7

Case B

Shear Stren,gh (kPd

Density (kN/d)

I

25

16.7

II

SO

18.6

ILLUSTRATIVE

EXAMPLES

OF TWO-LAYER

SLOPE

11

The effect of pile positions assumed

on the piled-slope

improvement

to be free and fixed against rotation is illustrated

most effective pile positions

ratio for pile heads

in Figure 8. For Case A, the

are between the middle and crest of the slope. However for

Case B, the most effective positions

are at the toe and crest of the slope. If the piles are

located at the middle of the slope for Case B, the sliding surface intersects tip resulting

near the pile

in little or no advantage being gained from the piles. In general, the pile head

fixities have very little effect on the stability of the piled-slope

for both cases.

15 q

+

1.4

o Free-Head Pile x Fixed-Head Pile

1.3 II

2

1.2

1.1

1.0

0

0.2

0.4

0.6

0.8

FIG.8 EFFECT OF PILE POSITION ON TWO-LAYER

1.0

SLOPE

12

Figure 9 shows the effect of pile diameter on the two-layer slope stability when the piles are located at the crest. The piled-slope

improvement

ratio increases almost linearly

with pile diameter for Case A because most of the critical sliding surfaces intersect along the upper half of the piles where higher pile bending moments and shear

1.1

1.0 L 0.5

I 1.0

, 1.5

I 2.0

d/ds FIG.9 EFFECT OF PILE DIAMETER ON TWO-LAYER (FREE-HEAD CREST PILE)

forces are developed.

The influence

since most of the critical

sliding

SLOPE

of pile diameter for Case B is much less pronounced surfaces intersect

close to the pile tips, where lower

bending moments and shear forces are developed.

Similarly

the pile spacing has more effect for Case A than Case B, as illustrated in

Figure 10. At a pile spacing, s/d,, of 1.5, the piled-slope

improvement

ratio for Case A is

about 25% higher than Case B. However, the ratio decreases faster with increasing spacing for Case A, implying

that Case B is less dependent on pile spacing.

pile

13

13

I

I

I

2.0

2.s

3.0

I

I

I

3.5

4.0

4.5

1.4

g

1.3

rs” II zg

1.2

1.1

1.0. . 1

.s

S.0

s/d, FIG. IO EFFECT OF PILE SPACING ON TWO-LAYER (FREE-HEAD CREST PILE)

Figure pile-soil

11 shows

limiting

pressure

that the piled-slope for both

improvement with

cases,

ratio

the value

SLOPE

increases

of the ratio

with increasing being

Case A than for Case B.

1.5

I

I

I

I

I

1.4 -

K PY1K PYS FIG.1 1 EFFECT OF PILE-SOJL LIMITING PRESSLJRE MULTIPLIER ON TWO-LAYER SLOPE (FREE-HEAD CREST PILE)

higher

for

14

In general, the piles

the results

embedded

confirm

through

the obvious

the soft (weak)

expectation

layers

that it is desirable

well into the firm

(stable)

to have

underlying

layers.

It should

be emphasized

circular

failure

surfaces

critical

than a circular

failure

surfuces

that the slope

only. In many practical surface.

Extension

stability cases,

analysis

in this paper

a non-circular

of the approach

presented

surfnce herein

considers

may be more to non-circular

is straightforward.

CONCLUSIONS A simplified the pile response Based

pile-slope to lateral

on the analysis,

used in stabilizing investigated. located

slopes

affecting

soil slope,

be expected,

embedded effectiveness limiting verification

the

of the

pressure

to have little effect for a layered

through

soft

piles

by laboratory

on

soil slope,

layers

is also

in a layered

affecting

soil

experiments

and affected slope.

measure

piles.

the overall the piles

extended by the

into

in stable

pile

Theoretical

(e.g. in a centrifuge)

piled-slope are most firm

diameter, solutions

of piles

slopes,

have been

indicate

that piles

slope

are some

However

the

analysis.

the performance

solutions

pressure

in which

stability

the most effective

limiting

of the stabilizing

and discussed

in a slope

the theoretical

may provide

and pile-soil

the performance

appear

factors

and as a preventive

For a homogeneous

pile spacing,

has been presented

is incorporated

of the important

at the toe or crest of the slope

pile stiffness would

analysis

soil movements

some

unstable

The pile diameter, factors

stability

stabilization.

of the important

the soil modulus stability effective or

response. when

stable

spacing presented

they

layers. and

and As are The

pile-soil

here

and by field measurements.

require

15

ACKNOWLEDGEMENTS

The work described

in this paper foms

the effect of seafloor instability Australian

on foundations,

part of a program of research project on which was supported by a grant from the

Research Council.

REFERENCES

Bishop, A.W. (19.55). “The use of slip circle in the stability slopes.” Geotechnique, Vol. 5, No. 1, pp. 7-17.

analysis

of earth

Bulley, W.A. (1965). “Cylinder pile retaining wall constructionRoads and Streets Conference, Seattle, Washington.

Seattle Freeway.”

De Beer, E.E. and Wallays, M. (1972). “Forces induced in piles by unsymmetrical surcharges on the soil around the pile.” Proc. 5th European Conf. on Soil Mechanics and Foundation Engineering, Vol. 1, The Spanish Society for Soil Mechanics and Foundation. Madrid. 4.

Fukuoka, M. (1977). “The effects of horizontal loads on piles due to landslides.” Proc. 10th Spec. Session, 9th Int. Conf. Soil Mechs. and Fndn. Eng., Tokyo, pp. 27-42.

5.

Hull, T.S. (1987). The static behaviour University of Sydney, Australia.

6.

Hull, T.S., Lee, C.Y. and Poulos, H.G. (1991). “Mechanics of pile reinforcement for unstable slopes.” Research Report No. 636, School of Civil and Mining Engineering, University of Sydney, Australia.

7.

Ito, T. and Matsui, T. (1975). “Methods to estimate lateral force stabilizing piles.” Soils and Foundations, Vol. 15, No. 4, pp. 43-60.

8.

Ito, T., Matsui, T. and Hong, W.P. (1979). “Design method for the stabilizing analysis of the slope with landing pier.” Soils and Foundations, Vol. 19, No. 4, pp. 43-57.

9.

Lee, C.Y., Poulos, H.G. and Hull, T.S. (1991). “Effect of seafloor instability offshore pile foundations.” Canadian Geotechnical Journal, 28, pp. 729-737.

10.

Oakland, M.W. and Chameau, J.-L. A. (1984). “Finite-element analysis of drilled piers used for slope stabilization.” Laterally Loaded Deep Foundations: Analysis and Performance, ASTM STP 835, J.A. Langer, E.T. Mosley and C.D. Thompson, Eds., American Society for Testing and Materials, pp. 182-193.

of laterally

loaded piles.

PhD Thesis,

acting

on

on

16

11.

Offenberger, J.H. (1981). “Hillside stabilized with concrete wall.” Public Works, Vol. 112, No. 9, pp. 82-86.

12.

Poulos, JSMFD,

13.

Reese, L. C., Wang, S-T. and Fouse J. L. (1992). “Use of drilled shafts in stabilizing a slope.“ASCE, Geot. Spec. Pub. No. 31, Stability and performance of slopes and embankments - II, Vol. 2, pp. 1318-1332. Rowe, R.K. and Poulos, H.G. (1979). “A method for predicting the effect of piles on slope behaviour.” Proc. 3rd ICONMIG, Achen, Vol. 3, pp. 1073-1085.

14.

H.G. (1973). “Analysis of piles in soil ASCE, Vol. 99, SM5, pp. 391-406.

undergoing

cylinder

pile retaining

lateral

movement.”

15.

Somner, H. (1977). “Creeping slope in a stiff clay.” Proc. 10th Spec. Iut. Conf. Soil Mechs. and Fndn. Eug., Tokyo, pp. 113-118.

16.

Proc. 3rd. Asian Taniguchi, T. (1967). “Landslides in reservoirs.” Soil Mechs. and Fndns. Eng., Bangkok, Vol. 1, pp. 258-261.

17.

Viggiani, C. (1981). “Ultimate lateral load on piles used to stabilize landslides.” Proc. 10th. Int. Conf. Soil Mechanics and Foundation Engineering, Stockholm, Vol. 3, pp. 555560.

18.

Wang, M.C., Wu, A.H. and Scheessele, D.J. (1979). “Stress and deformation in single piles due to lateral movement of surrounding soils.” Behavior of Deep Foundations, ASTM 670, Raymond Lunggren, Ed., American Society for Testing and Materials, pp. 578-591.

Received 11 January 28 August 1993

1993; revised

version

recewed

20 August

1993; accepted

Session,

Regional

9th

Conf.