FINITE ELEMENT ANALYSIS OF
SLOPE STABILIZATION USING PILES
by
Stephen Laudeman
B.S., Colorado School of Mines, 1989
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2002
This thesis for the Master of Science
degree by
Stephen Laudeman
has been approved
by
John Mays
r^o-d
Date
Laudeman, Stephen (M.S. in Civil Engineering)
Finite Element Analysis of Slope Stabilization Using Piles
Thesis directed by Professor Nien-Yin Chang
ABSTRACT
Slope stabilization using vertical piles has been used many
times over the last thirty years to correct slope stability
problems. To predict the performance of slopes reinforced
with piles, and to determine the stresses acting within the
stabilizing piles, many diverse methods of analysis have been
proposed in the relavent civil engineering literature. The
finite element method appears to be the most effective means
to analyze this difficult problem. Several different pile
configurations are assumed for a typical soil slope, which are
analyzed using the NIKE3D finite element program. Results of
the finite element analysis are summarized to determine
stresses and displacementsw within the piles and the adjacent
soil, bending moment within the piles, and optimum pile
configuration.
This abstract accurately represents the content of the
candidate's thesis. I recommend its publication.
111
DEDICATION
I dedicate this thesis to my loving wife and children, for
their support and forebearence during the past six years.
ACKNOWLEDGEMENT
I wish to thank my adviser, Dr. N. Y. Chang, for his energetic
and enthusiastic support. I would also like to thank Dr.
Fatih Oncul for his invaluable assistance and his patient
tolerance of my numerous questions.
CONTENTS
Figures..............................................viii
Tables...............................................xii
Chapter
1. Introduction ...................................... 1
1.1 Problem Statement ................................. 1
1.2 Objectives..........................................2
1.3 Scope of Study......................................3
2. Literature Review...................................4
2.1 Poulos, 1973........................................7
2.2 Ito and Matsui, 1975, 1981, 1982 ................. 14
2.3 Nethero, 1982..................................... 29
2.4 Rowe and Poulos, 1979............................. 34
2.5 Oakland and Chameau, 1984......................... 43
2.6 Hassiotis, Chameau, and Gunaratne, 1997.......... 51
2.7 Hull and Poulos, 1999............................. 60
2.8 Day, 1997......................................... 62
2.9 Discussion.........................................67
2.10 Literature Review Summary and Conclusions. ... 83
3. Limit Equilibrium Analysis.........................85
4. Finite Element Analysis .......................... 90
4.1 Computer Software and Hardware .................. 90
4.2 Input Formulation..................................93
4.3 Pile/Slope Configurations.........................95
5. Finite Element Data Analysis.......................98
6. Discussion of Results.............................130
7. Recommendations for Further Study.................139
8. Conclusions.......................................142
vi
Appendix
A. STABR Input Files ............................. 145
B. STABR Output Files ............................. 151
C. TrueGrid File for Unreinforced Slope............176
D. TrueGrid File for Single Pile Slope.186
E. TrueGrid File for Double Pile Slope.200
F. NIKE3D Input for Single Pile Slope.............224
G. NIKE3D Output for Single Pile Slope.............230
References..........................................282
vii
FIGURES
Figure 1. Uniform Soil Displacement......................10
Figure 2. Distribution of Bending Moment
Developed in Pile..............................12
Figure 3. Effect of End Fixity Condition ............... 13
Figure 4. Assumed Failure Mechanism
for Soil Moving Between Pile...................17
Figure 5. Viscous Flow Model for Soil
Flow Between Piles.............................19
Figure 6. Pile Performance in Data
from Instrumented Installations................22
Figure 7. Schematic of Soil Arching......................30
Figure 8. Forces Acting on Reinforcing Pile..............33
Figure 9. Pile/slope Configurations Analyzed
Using 2-D Finite Element Analysis..............38
Figure 10. Relationshipe Between Pile
Stiffness and Bending Moment..................42
Figure 11. Effect of Pile Stiffness and
Fixity Conditions ........................... 44
Figure 12. Eight-node Element Used to Model Soil .... 47
Figure 13. Eight-node Element Used to Model Pile .... 47
Figure 14. Undeformed and Deformed Meshes.................49
Figure 15. Effect of Pile Location,
Spacing, and Stiffness........................50
Figure 16. Assumed Failure Surface Configuration .... 55
Figure 17. Effect of Varying Pile Location .............. 56
Figure 18. Pile Displacement and Bending Moment...........59
Figure 19. Assumed Distribution of Forces
for Slope/Pile Design ....................... 66
viii
Figure 20. Schematic of Pile/slope Configuration .... 86
Figure 21. Location of Critical Slip Circles
for the Bishops Method of Slices.............88
Figure 22. Undeformed Meshes for
Single Pile Configurations.....................97
Figure 23. Surface Displacement of Unreinforced Slope. 99
Figure 24. Surface Displacement of Slope
with Pile 1 m Behind Crest...................100
Figure 25. Surface Displacement of Slope
with Pile 3 m Beyond Crest...................101
Figure 26. Surface Displacement of Slope
with Pile 7 m Beyond Crest...................102
Figure 27. Surface Displacement of Slope
with Pile 10 m Beyond Crest...................103
Figure 28. Surface Displacement of Slope
with Pile 3 m Beyond Crest,
1.5 m Lateral Spacing.........................104
Figure 29. Surface Displacementof Slope
with Pile 3 m Beyond Crest,
1.0 m Lateral Spacing.........................105
Figure 30. Surface Displacement of Slope
with Piles 1 m Behind and 3m
Beyond Crest ................................ 106
Figure 31. Surface Displacement of Slope
with Piles 3 m and 7 m
Beyond Crest ................................ 107
Figure 32. Surface Displacement of Slope
with Piles 6 m and 10 m
Beyond Crest ................................ 108
Figure 33. Graphical Comparison of
Reduction in Displacement.....................Ill
IX
112
Figure 34. Comparison of Pile Displacements
for Single Pile Configurations .
Figure 35. Pile Behavior at Location
1 m Behind Crest.............................114
Figure 36. Pile Behavior at Location
3 m Beyond Crest.............................115
Figure 37. Pile Behavior at Location
7 m Beyond Crest.............................116
Figure 38. Pile Behavior at Location
10 m Beyond Crest.............................117
Figure 39. Pile Behavior at Location
3 m Beyond Crest,
1.5 m Lateral Spacing........................118
Figure 40. Pile Behavior at Location
3 m Beyond Crest
1.0 m Lateral Spacing........................119
Figure 41. Upper Pile Behavior at Location
1 m Behind Crest..............................120
Figure 42. Lower Pile Behavior at Location
3 m Beyond Crest..............................121
Figure 43. Upper Pile Behavior at Location
3 m Beyond Crest..............................122
Figure 44. Lower Pile Behavior at Location
7 m Beyond Crest..............................123
Figure 45. Upper Pile Behavior at Location
6 m Beyond Crest..............................124
Figure 46. Lower Pile Behavior at Location
10 m Beyond Crest.............................125
Figure 47. Horizontal Stresses on Soil
for Pile 1 m Behind Crest.....................126
x
Figure 48. Horizontal Stresses on Soil
for Pile 3 m Beyond Crest...................127
Figure 49. Horizontal Stresses on Soil
for Pile 7 m Beyond Crest...................128
Figure 50. Horizontal Stresses on Soil
for Pile 10 m Beyond Crest .................129
Figure 51. Pile and Reinforcing Dimensions
for 276 kN-m Bending Moment
Resistance..................................136
xi
TABLES
Table 1. Summary of Results From Finite
Element Analyses ............................. 40
Table 2. Summary of Installation and Design Methods. 68
Table 3. Parameter Values for Soil
in NIKE3D Analyses.............................94
Table 4. Comparison of Reductions in
Surface Displacement ........................ 110
Table 5. Comparison of Maximum Passive Load on Soil
and Corresponding Passive Soil Resistance. 138
xix
1. Introduction
The stabilization of soil slopes has been a common and complex
part of civil engineering practice. Several traditional means
exist to improve the stability of a slope. These include
decreasing the load at the top of the slope, increasing the
load at the base of the slope, and/or improving surface and
subsurface drainage in the vicinity of the slope. Retaining
structures are sometimes built near the lower part of a slope.
Another less common method of slope stabilization is the use
of vertical piles installed through a slope. Piles used in
slope stabilization are similar to traditional retaining walls
and sheet piles, but this stabilization method differs in that
a gap is generally left between the piles, whereas traditional
retaining structures are laterally continuous. This
difference between retaining structures and stabilization
piles produces some difficulties in analyzing piles used in
slope stabilization. In a retaining wall design, the
assumption of plain strain conditions for analysis purposes is
appropriate and produces realistic and useful results. This
is unfortunately not the case for stabilization piles, since
the conditions at the pile are quite different than the
conditions to either side, i.e., where there is a gap between
adjacent piles.
1.1 Problem Statement
Since stabilization piles cannot be analyzed by traditional
means, some other rational method is needed to produce a
1
realistic design. As will be discussed in the Literature
Review section of this thesis, several researchers over the
past thirty years have presented a number of different methods
to approach this problem. Unfortunately, most of these
methods have shortcomings that limit their applicability to
real problems.
1.2 Objectives
The primary objective of this thesis is to analyze vertical
piles used in slope stabilization using the finite element
method. This analysis will show improvements in slope
deformation for a number of different pile configurations,
stresses acting on the piles, and determination of shear and
bending moments in the stabilization piles. Based on these
results, another primary objective will be to determine the
most effective pile configuration for the assumed slope.
There are several secondary objectives, as well. The
Literature Review section of this thesis is intended to be a
comprehensive summary and discussion of the several diverse
methods proposed to address the problem of slope stabilization
using piles. It is hoped that this summary will be useful to
future researchers and practicing engineers. The analyses
discussed herein represent only a fraction of what is needed
to develop a complete design guidance for slope stabilization
using piles. However, this work should for the basis for
additional work toward that end goal. Lastly, this thesis is
intended to demonstrate the usefulness of the finite element
method for analysis of complex geotechnical problems,
2
especially in situations where traditional methods have
produced unacceptable results.
1.3 Scope of Study
The. scope of study for this thesis consists of a total of five
limit equilibrium slope stability analyses and nine finite
element analyses using a consistent slope geometry.
The limit equilibrium analyses are used to get a preliminary
indication of slope improvement using piles for stablization.
The limit equilibrium analyses performed consist of:
one analysis of the unreinforced slope, and
four analyses with single piles at different
locations
The finite element analyses consist of:
one analysis of the unreinforced slope,
four analyses with single piles at different
locations within the slope,
two additional single pile scenarios with
differentspacing between piles (laterally), and
three analyses with two piles grouped at different
locations within the slope.
Each of these analyses will be discussed in more detail in
Chapters 3 and 4.
3
2. Literature Review
The basic mechanism for slope stabilization with piles is
explained in several professional papers in the relavant
engineering literature. Nethero (1982), for example, explains
that vertical piles or piers are placed in the ground, passing
through the failure mass of the slope, and "enabling support
of the landslide forces through the passive restraint provided
by the underlying competent strata." (p. 61). The technical
literature regarding this subject contains numerous
descriptions of applications of piles and piles used for slope
stabilization. Winter, et al. (1983) and Nethero (1982) are
two examples. Other references which focus on actual field
applications include D'Appolonia (1967), DeBeer and Wallays
(1970), Day (1996), Cohen (1999). Along with researchers who
have discussed applications of this stabilization method,
there have been an equal number who have attempted to
establish an appropriate design method for slopes stabilized
with piles. These include Ito and Matsui (1975), Ito, et al.,
(1981 and 1982), Rowe and Poulos (1979), Winter, et al.
(1983), Oakland and Chameau (1984), Lee, et al. (1995), and
Hassiotis, et al. (1997).
There are several methods of analysis for the problem of
slope/pile interaction presented in the engineering
literature. The most critical issue in all design methods
appears to be the determination of the resistance to soil
movement provided by the piles. The process used to determine
this force is the primary difference between the various
methods. In most methods, the resistance provided by the
4
piles is added to the stability determination for the slope as
an additional resisting force or moment. Determination of the
resistance provided by the piles also provides the lateral
load transmitted from the soil to the piles. This allows for
the design of the internal reinforcement for the piles, so
that they will resist the shear stress and bending moments
developed as a result of soil loads. This is required to
ensure that, once the stability of the slope has been
achieved, the stability of the piles can be provided for as
well.
The most basic of the methods for determining lateral
resistance from the piles is a slight modification of the
Rankine active earth pressure method used in the design of
retaining walls. Nethero (1982) and Day (1997) both present
slightly different variations of this method. Another general
approach is to use assumptions about soil stress state or
movement to determine the load acting on the piles. This type
of approach is used by Ito and Matsui (1975), Ito, et al.
(1981 and 1982), Hassiotis, et al. (1997), Lee, et al. (1995),
and Winter, et al. (1983). In each of these methods, the
approach used to determine the load on the piles is somewhat
different. For instance, Ito and Matsui assume that the soil
is in a state of plastic deformation in the zone adjacent to
the piles, where Winter, et al. relate the force on the piles
to the viscosity and flow velocity of the failing block. Yet
another approach is to determine the force on the piles by
coupling the displacement and/or stress distribution in the
soil to the reaction of the piles. This requires the use of
numeric methods, such as the finite difference method, used by
Poulos (1973), or the finite element method, used by Rowe and
Poulos (1979) and Oakland and Chameau (1984). While they do
5
not address slope stabilization, Griffiths and Lane (1999)
describe in some detail the advantages of the finite element
over more traditional deterministic methods of slope stability
analysis.
The work by earlier reseachers varies not only in the approach
for determining the reaction from the piles, but also in how -
and if this reaction is incorporated into the determination
of overall slope stability. Poulos (1973), for instance, uses
variations in the soil displacement to determine shear stress
and bending moment developed in a single pile. While this is
relevant to determining the behavior of the pile, it does not
address the influence of the pile on the stability of the
slope into which it may be installed. Rowe and Poulos (1979),
Oakland and Chameau (1984), and Ito, et al. (1982) consider
not only the load on the piles but also the influence of the
reaction from this load on the overall stability of the slope.
This approach is more useful in practice, as the effect of the
piles on the improvement of the slope can be demonstrated.
These methods assume that the piles are firmly socketted in a
competent bedrock layer below the soil surface. The passive
reaction from the soil below the failure surface is considered
in the design method in Nethero (1982). Where other methods
consider the forces acting on the pile below the failure
surface, it is generally assumed that the underlying material
is capable of resisting these loads. The loads on the piles
below the failure surface are determined to aid in design of
the internal reinforcement for the piles.
This section contains detailed reviews of a number of
professional papers which address design methods for slopes
stabilized with vertical piles. Some of these have already
6
been cited above. The summaries are presented in
chronological order, in an attempt to show the refinement of
the analysis of this interesting problem over the past thirty
years. The references presented here are by no means a
complete list of the relevant engineering literature, but are
meant to be a representative sample of the various approaches.
2.1 Poulos, 1973
Poulos focuses on the deflection and bending moments developed
within a pile subjected to lateral soil movements around and
against the pile. He does not yet consider the improvement of
the soil stability due to the presence of the pile. Poulos
recognizes that the deflection of the pile and bending moments
developed are dependent on the displacement of the adjacent
soil. Therefore, the behavior of the pile and the soil are
coupled in a finite difference analysis. In this analysis,
the matrix equations describing pile displacement and soil
displacement are as follows:
in which {p} is the displacement vector, {p} is the horizontal
pressure vector, [Â£>] is the matrix of finite difference
coefficients, d is the pile width, L is the pile length, Esr is
a reference value of soil modulus, Es is the soil modulus at a
node point, [I] is the matrix of soil displacement factors,
(2-1)
(2-2)
7
and {pe} is the vector of external soil displacements. To
ensure displacement compatibility between the soil and the
pile, these equations are set equal to each other, and the
resulting system of equations is solved for displacement.
Displacement values are in turn entered into the equation for
pile force as a function of displacement, which allows for
determination of load on the pile, shear stress, and bending
moment.
Pile deflections are a function of the applied soil forces.
Soil displacements are a function of the reaction forces from
the pile as well as "external" influences. In most of the
examples cited by Poulos, these external influences are caused
by the construction of an embankment immediately adjacent to
the pile location. Other examples include construction of an
excavation next to the pile, or instability of a slope through
which the pile is placed.
Because he is most interested in the behavior of the pile as
opposed to the soil Poulos uses an assumed soil displacement
pattern for most of his analyses, shown here as Figure 1, but
also considers some predetermined variations in this pattern.
Soil behavior is modeled using Young's Modulus Es and Poisson's
ratio vs. The.influence of the value of Es is investigated by
performing some analyses with a constant value, and others
with Es increasing linearly with depth. The value of vs is
held constant for all analyses at a value of 0.5. The other
soil parameter used is the yield pressure py. This parameter
is the limiting value of soil pressure against the pile. The
yield pressure represents the pressure at which the soil
becomes plastic and continues to yield at a constant stress.
8
The pile is modeled as a thin plastic strip of width d and
length L, and constant flexibility KR = EPIP, where Ep is the
Young's Modulus of the pile and Jp is the moment of intertia of
the pile. For the finite difference analysis, the pile is
divided into a number of elements. For all analyses, the
maximum depth of soil movement adjacent to the pile z is set
equal to the length of the pile L, i.e. z/L = 1.0. Conditions
at the head and tip of the pile are critical to the
performance of the pile. Poulos selects a number of fixity
conditions, consisting of fixed, pinned, or free for the head
of the pile and fixed or pinned for the tip.
After establishing the basic model used for the pile/soil
system, Poulos performs several analyses intended to
demonstrate the relative importance of different parameters.
Results of these analyses are presented graphically. Some of
the parameters varied in these analyses include pile
stiffness, pile end fixity condition, and magnitude and
distribution of soil movement. The basic conclusions of these
analyses are as follows:
(1) The pile property that has the greatest effect on pile
movement is pile stiffness. The displacement of a
relatively flexible pile mimics the displacement pattern
of the soil. A stiff pile experiences greater
displacement at the soil surface than the soil itself.
(2) The pile property that has the least effect on pile
displacement is the pile width.
(3) The distribution of soil properties Es and py with depth
has a significant effect on pile displacement and
bending moments.
9
P/d
Figure 1 Uniform soil displacement pattern used by
Poulos, 1973
10
(4) The distribution and magnitude of soil movement have
significant effect on pile displacement and bending
moments.
The effect of the distribution and magnitude of soil movement
on the performance of the pile is shown in Figures 2 and 3.
For the case of constant soil displacement with depth, pile
displacement is equal to soil displacement until about mid-
depth, at which point pile displacement gradually decreases to
zero at the tip. As the magnitude of the maximum soil
displacement increases, so also does the the maximum pile
displacement. The ratio between pp,max and pSimax varies somewhat
as soil displacement increases, but is relatively consistent
at about 0.77. For a pile of moderate stiffness, the maximum
pile deflection occurs at the same depth as the maximum
external soil displacement.
As shown in Figure 2, the distribution of bending moment
developed in the pile is also affected by the variation in
soil displacement. The greatest bending moment is developed
for the case of uniform soil movement with depth. The effect
of end fixity condition is shown in Figure 3. It can be seen
here that the greatest bending moment is developed for the
case of fully restrained pile tip and free head. The effect
of end fixity on the magnitude of bending moment is much
greater than that of soil displacement distribution.
Poulos goes on to provide some comments on determination of
values for design parameters for soil/pile systems. He notes
the greatest uncertainty is in determination of external soil
displacement. The other unknowns are Es and py. The author
11
^ = 29 vi=0-5 Eipy =10 KR= 0-001
SocKeted Pile, Free Head, Pinned Tip. Constant E, and p
Soil Movements: Cose 1
Case 3
Figure 2 Distribution of bending moment developed in
pile. After Fig, 6 from Poulos, 1973.
12
---------Including yield effects
Elastic solutions
Figure 3 Effect of end fixity condition. After
Fig. 7 from Poulos, 1973.
13
provides some guidance and cites work by others to aid in
determining appropriate design values for these parameters.
The recommended methods of determining py are either
empirically based relationships between Py and soil cohesion,
or are based on earth pressure theory. It is noted that
determination of Young's Modulus with an acceptable accuracy
is generally difficult for soils. Empirical correlations are
presented which relate Es to undrained shear strength or
modulus of subgrade reactional. Large scale field tests are
also recommended.
Lastly, the paper considers three cases of instrumented pile
installations that were subjected to lateral soil movements.
Poulos method to determine pile displacement shows good
general agreement with measured values, but tends to over- or
underestimate some pile behavior.
2.2 Ito and Matsui, 1975, 1981, 1982
This series of papers presents a method of calculating the
lateral force on piles used for slope stabilization and
presents design procedures for slope stabilization using
piles. The first paper (1975) derives the basic equations
for determimation of lateral force acting on the piles. The
second paper (1981) presents a design method for slope
stabilization with a single row of piles. The third paper
(1982) presents a design method for using multiple rows of
piles. The second and third papers rely heavily on the
equations for lateral force derived in the first paper.
14
In the 1975 paper, the authors derive basic equations for
determining lateral force acting on piles subjected to lateral
soil movement. The authors provide references to several
projects in which a row of piles was used to control lateral
movement of soil. Of the cases cited, the authors state that
a common characteristic of each is that the soil is undergoing
plastic deformation around the piles. The shortcoming of the
previous work is that lateral force acting on the piles was
known or assumed in the design. The authors propose in the
current paper that they will derive an expression for lateral
pressure acting on the piles when the soil reaches a state of
plastic failure. It is recognized, however, that the
development of lateral pressure for the case of no soil
movement up to plastic failure of the soil is a separate
phenomenon from determining magnitude of the ultimate load at
plastic failure. The authors state that, at the time of the
paper, the state of the science did not allow for
determination of the growth mechanism of the lateral force.
In the analysis by Ito and Matsui, the authors investigate two
situations: plastic failure of the soil at the Mohr-Coulomb
failure criterion, and plastic flow of the soil considering
the soil as a visco-plastic solid. These are refered to as
plastic deformation and plastic flow, respectively.
To facilitate analysis of the situation of plastic
deformation, several assumptions are made regarding the
soil/pile system. Among the most relevant assumptions are the
following: (1) two sliding surfaces are developed between the
soil and the adjacent piles (see Figure 4), on which the full
Mohr-Coulomb strength is mobilized, (2) the active earth
pressure is acting in the downslope direction on the plane of
15
soil between the piles and (3) the piles are rigid. Following
establishment of these assumptions, a series of expressions is
developed assuming equilibrium forces are developed in the
soil around and in between the piles. This series of
expressions results in another series of differential
equations, which when integrated with consideration of
boundary conditions, yields the following expression for the
lateral pressure acting on each pile as a function of depth:
p = p A>Icr 1
t' t'BB 2 X ) x 0
N^ tan (|>
1
N, tan * tan + *
* Y V8 4))
% y
2N1/2 tan (j) l}
2 tan 4 + 2N1/2 + N~1/2
N\/2 tan $ + - 1
\ (N^ 1/2 tan ((i+w^-l
(2-3)
in which
(2-4)
and other terms are defined in Figure 4.
16
Figure 4 Assumed failure mechanism for soil moving
between pile, after Fig. 2 from Ito and Matsui, 1975.
17
In the analysis of lateral force developed due to plastic flow
of the soil, a separate set of assumptions are made, although
it is again assumed that the piles are rigid. The interval
between the piles is considered to be similar to a pipe or
channel in which a viscous fluid is flowing (see Figure 5).
In the analysis, there are three components of stress acting
on the piles: viscous shear and active earth pressure on EB
amd E'B', and viscous shear acting on AE and A'E'. The
expressions for the x-component of each of these three ,
stresses are summed to yield the following expression for
lateral force on the piles due to plastic flow:
P = Pi + P2 + P3
=
A
1 + Jl +
m
1 +
m
2t 2D2
- Jl +
m
2V?
+ log
2T2D1
A
1 + Jl +
m
2t,A
2U2 J
+
(dx D2)
(J2 i)tc:
m
8A
+
(1~2 l),
7t m
\2
.SD2J
+
n m.
4 d;
m
+
DxD2
+
V2t 2c + yz.
(2-5)
m = 16ri o1A1 / 712
(2-6)
Following derivation of these expressions, a sensitivity
analysis is carried out in which some characteristics of the
18
I
Figure 5 Viscous flow model for soil flow between
piles, after Fig. 5 from Ito and Matsui, 1975.
19
soil/pile system are fixed at typical values and some
parameters are varied over appropriate ranges. This analysis
yields a number of conclusions, some of which are intuitive
and some of which are not. First, it is noted from inspection
of the above expressions that lateral load on the piles
increases linearly with soil density y and depth below the soil
surface z. From the sensivity analysis performed, it is shown
that the lateral force increases as the interval between the
piles D2 decreases. It is also shown that the force on the
piles increases as the either c or (j) increases. This is one
finding that is counter-intuitive. It would seem that, as the
strength of the soil increases, the stability of the system
would increase and the role of the piles would be less, i.e.,
the lateral load on the pile would decrease. This points out
one possible shortcoming of the overall analysis, namely that
the forces acting in the soil/pile system are determined for
plastic failure of the soil, even in the case of a stronger
soil which, due to the overall nature of the problem, may
never reach plastic failure. In other words, the stability of
the soil or soil slope through which the piles are installed
is not considered in this analysis. This apparent discrepancy
is discussed more later in this thesis.
In the next section of the paper, the authors compare the
lateral force developed in five instrumented piles with that
calculated by the methods developed. Each of the five piles
was installed as part of a pile row or rows intended to
stabilize a landslide. For each of the cases presented, site
specific soil and pile parameters are used as input for the
equations derived earlier in the paper. Graphs are presented
(Figure 6) which show the measured lateral force on the each
pile compared to the lateral force predicted. Based on this
20
analysis, it is shown that the predicted lateral force based
on plastic deformation matches the observed lateral force in
magnitude, though not in distribution.
The predicted force increases linearly with depth, while the
observed lateral force shows a triangular or rectangular
distribution with depth. In addition, it is interesting to
note that the lateral force on the downslope side of the pile
below the sliding surface is much greater than t.hat on the
upslope side of the pile above the sliding surface. The
prediction method derived and employed by the authors does not
address lateral loads developed below the sliding surface.
Of the piles considered in this analysis, the magnitude and
distribution of lateral loads determined using the plastic
deformation approach closely matched the measured values in
two of the five cases. In these two cases, the pile heads
were restrained from moving, i.e., the piles had a tieback
anchor installed and anchored upslope of the pile. This head
restraint allowed relatively less pile deflection than in the
other three cases. The plastic deformation theory was
premised on no pile deflection (i.e., the assumption of a
rigid pile) and the case of restrained pile head matches this
assumption more closely than the other unrestrained piles.
This observation leads the authors to conclude that the theory
of plastic deformation gives a good prediction of lateral
force on piles only when the assumptions in the theory are met
in the design. As for other pile head fixity conditions,
i.e., unrestrained or hinged, the plastic deformation approach
yields a predicted lateral load that matches the observed load
in order of magnitude only. Due to difficulty in determining
21
depth (m) . dePth (m)
Theo. Plastic Deform.
'///A. Theo. Plastic Flow
Hennes-
P.M.R.Lr
(a) Katamacbi B pile
force acting on pile (m)
---7/7/?/'
Â¥
2-
4-
>. S.P.T.a 58
8 {
10
S.P/T.-10-20
S. P.T.S 40
-8 -6 -4 -2 0 2 4 6 8 10.x 20 40 60 80 100 120
J_J___1 t 1 I ii|. i-.i i ___t i i t t i I___
sliding surface
-----iir-r
observed value
-u-
tl5!r-iHiiiiiii rn
Theo. Plastic Deform.
Theo. Plastic Flow
Hennes
P.W.R.I.
(b) Kamiyama No. 1 pile
Figure 6 Pile performance in data from instrumented
installations, after Fig. 13 from Ito and Matsui, 1975.
22
force acting on pile (t/m)
2 -
E
** a*
Â£ 6 ' c o
CL
at a - s. a>
8 - ig +* X
. u _
OJ
c
10 2
o
E
3SI
/x^yy----rr-
S.P.T.= 5 8
S.P.T.= 10-20
S.P.T.S: 40
-8 -6 -4 -2 0 2 '4 6 8 20 40 60 80 100 120
l i 1 i l t 1 t | i I l 1 l_ *'
sliding surface
observed value
X *
ti i ii i i i im
Theo. Plastic Deform.
77777. Theo. Plastic Flow
- Hennes
P.M.R.I.
(c) Kamiyama No. 2 pile
force acting on pile (t/m)
7/W7
2 -
10
^ s
= Â§3
- Â¥
5l
0 10 20 30 40
S.T.P.
4 8 12 20 40 60 80 100 ,120
sliding surface
observed value
Theo. Plastic Deform.
Theo. Plastic Flow
Hennes
P.M.R.I.
(d) Higashitono No. 2 pile
Figure 6 (cont.) Pile performance in data from
instrumented installations, after Fig. 13 from Ito and
Matsui, 1975.
23
auojspnni J puojs
force acting on pile (t/m)
-4 -2 0 2 4 6 8 10 20 40 60 80 100 120
i i______ i t____l______' 1 ' '__i__i__l_i__i__i__l__i i
observed
value
/
/
/
r
Theo. Plastic Deform,
'////, Theo. Plastic Flow
Hennes
P.W.R.I.
(e) Higashitono No. 3 pile
Figure 6 (cont.) Pile performance in data from
instrumented installations, after Fig. 13 from Ito and
Matsui, 1975.
24
plastic flow soil parameters, for all cases the plastic flow
theory yields only a range of predicted lateral loads. The
authors conclude that, unless more accurate means of
estimating plastic flow parameters are developed, further
refinement of the plastic flow approach would not appear
fruitful.
In the 1981 paper, Ito and Matsui apply the prediction of
lateral forces developed against piles under plastic
deformation of the surrounding soil to the larger problem of
slope stability. Several points are emphasized in this paper.
First, it is noted that the overall stability of the soil/pile
system is assured only if an acceptable factor of safety is
obtained for the piles (i.e., against bending or shear
failure), and for the slope (i.e., against overall shear
failure). A key component of both approaches is of course the
lateral force acting on the piles, which is in turn equal and
opposite to the resisting force which the piles lend to the
slope. The lateral force on the piles is estimated using
equation 13 from the previous paper, for lateral pressure as a
function of depth assuming plastic deformation of the soil
around the piles. The lateral force acting on the pile is
used to calculate FS for the pile against bending and shear
failure. Regarding pile stability, the authors present means
to determine the bending and shear stresses developed in
piles for a number of head fixity conditions, i.e., free head,
unrotated head, hinged (pinned) head, and fixed (restrained)
head. They conclude that the greatest benefit of piles for
slope stabilization is gained under the the condition of a
hinged or fully restrained pile head. This condition
approximates one of the key assumptions of the design method
derived in the previous paper, that the pile is rigid. It
25
should be noted that the shear stresses and bending moments
calculated for the various head fixity conditions are
determined based on a distributed load which was in turn
calculated based on the method presented in the earlier paper,
i.e., based on the assumption of a rigid pile (fixed head).
As noted in Poulos (1973), the shear and bending stresses
developed in a pile undergoing lateral soil movement are
largey dependent of the fixity condition of the head. To
determine stresses for one fixity condition using an applied
load which was determined based on a different fixity
condition may be cause for concern.
To determine the stability of the reinforced slope, the
calculated lateral force acting on the pile is converted to an
equivalent concentrated load acting in an upslope direction
Frpr which is added to the equation for the stability of the
slope, as in Equation 4:
(F) = Er_ = (Frs + Frp) (2-7)
' s'slope jp TP
rd rd
At this point, the paper moves on to a practical design
example, and presents methods to determine optimal design
parameters such as pile diameter and stiffness, and pile
spacing, which will assure stability of both the piles and the
slope.
The paper is concluded with a summary of the design method
presented. It is determined that the most critical parameters
of the soil/pile system are (1) the interval between the
piles, (2) the fixity condition of the pile head, (3) the pile
26
length above the sliding surface, (4) the pile diameter, and
(5) the pile stiffness. It is also noted that the design
method is premised on the designer knowing beforehand the
depth and location of the the sliding surface.
In the last paper in this series (1982), the authors present a
modification of the earlier design method to allow design of
slope reinforcement using multiple parallel rows of piles.
The authors first present some insight into factors effecting
the performance of the pile/soil system. It is noted (again)
that the stability of the reinforced slope cannot be insured
unless the stability of both the slope and the piles is
verified. Stabilitity of the. slope will be assured when the
forces resisting movement exceed the forces causing movement
with a reasonable factor of safety. Similarly, the stability
of the piles will be assured when the forces tending to cause
shear or bending failure of the piles are resisted by the
piles, again with a reasonable factor of safety. This paper
also contains a discussion of estimation of a distributed load
on a pile by a concentrated load. Based on their analysis,
the authors suggest that approximation using a concentrated
load be used only in the case of an unrestrained pile head.
It is also noted that the lateral force associated with full
plastic deformation of the soil around the piles may not be
mobilized in the stabilized slope. This possibility is
accounted for by the introduction of a mobilization factor a,
which has a value between 0 and 1 and is applied to the
maximum lateral force due to plastic deformation as discussed
in the earlier papers. The value of a will be 0 for no slope
movement, and 1 (the maximum value) for full plastic
deformation of the soil around the piles. The use of the
27
mobilization factor allows for a design of the piles and the
slope based on a lateral force lower than the full lateral
force used in earlier designs. Just as in previous work, this
partial lateral force is then used to design the piles and
determine the stability of the reinforced slope. It is
assumed in this analysis, that the pile rows are located a
sufficient distance apart that the stress distribution in the
soil from adjacent rows does not overlap. The validity of
this assumption is not discussed.
For the purposes of design, the value of a is considered to be
between two values: the lower value is used to determine the
stability of the slope, and the upper value is used to
determine the stability of the piles. The upper value of a
yields the maximum lateral force associated with plastic
deformation, i.e., a mobilization factor equal to one. The
authors describe the lower value of a as corresponding to "the
minimum lateral force reaction needed to prevent a landslide".
This discussion creates an apparent discrepancy between the
definition of the mobilization factor and the use of the
mobilization factor in design. This is discussed in the
Section 2.9 of this thesis.
In explaining the effect of the mobilization factor, it is
shown that the factor of safety of the piles is inversely
proportional to the value of a, i.e., the FS of the piles
decreases as the value of a increases. A converse
relationship for overall slope stability is also shown, with
the FS of the slope increasing as the value of a increases.
The result of such an analysis provides the minimum and
maximum allowable values of the mobilization factor that will
28
allow stability of the slope and the piles, respectively. In
the design example presented, the authors present this
analysis as the key component of the design. This relates the
total pile resistance needed to attain stability of the slope,
and the required mobilization factor needed to attain this
level of resistance. From this point, the stresses acting on
the piles are used to determine required pile stiffness for
various combinations of pile diameter and spacing.
The paper concludes by summarizing the design process
presented. It is noted by the authors that further study is
needed regarding the interaction of reinforcing piles when
they are placed in close proximity.
2.3 Nethero, 1982
In this paper, the author describes several applications of
cantilevered drilled pile retaining structures in the Ohio
Valley. Most of the applications discussed are associated
with road fills built on hillsides which experienced slope
stability problems due to natural river erosion at the base of
the hill or manmade excavations. The typical design consists
of piles of diameter ranging from 18" to 30" (457 mm to 762
mm) spaced 5 to 78 feet (1.5 to 2.1 m) on center. The
principle of soil arching is used to explain how soil between
the piles is restrained (Figure 7). No discussion of the
phenomenon of soil arching is provided, nor are any references
cited.
29
Longitudinal Pier Spacing
2 to 3 D
direction of movement
Soil Arching
between Piers
Figure 7 Schematic of soil arching, after Fig. 2 from
Nethero, 1982.
30
After a brief introduction, the paper describes a number of
case histories in which vertical piles are installed in a
single row to stabilize slopes which have experienced some
movement. Most cases involve installation of piles
immediately adjacent to a roadway which has cracked or
suffered similar damage due to movement of the slope below the
road.
For the design procedure described, there are several
assumptions made that simplify the process. First, the piles
are treated as rigid cantilevered poles, socketed into
competent bedrock at the tip. Deflection of the piles are not
considered in the design. Also, the piles are assumed to be
installed in a single row, oriented perpendicular to the
direction of soil movement. Typical dimensions for piles
designed with this procedure include a depth to the failure
surface usually less than 20 feet and a ratio of embedment
depth below the failure surface L to diameter D of less than
10. It is also noted that the ultimate capacity of the
supporting material (i.e., the competent material below the
sliding surface) is the controlling factor in most designs.
The key design parameters appear to be sufficiently large
embedment length below the sliding surface and sufficiently
small spacing between the piles. The design of piles for
stabilization involves balancing the earth pressures due to
sliding and the resisting earth pressures below the failure
surface. The author states, without citing references, that
the ultimate lateral resistance provided by a group of piles
is considerably less than the sum of the ultimate resistance
of each pile, especially for spacing less than about 4
diameters.
31
The design method presented is very similar to the design of a
retaining wall using Rankine active earth pressure on the
uphill side of the piles, and passive earth pressure on the
downhill side, but only below the failure surface. The design
procedure first calculates the active earth pressure acting on
the piles from the upslope direction, above the failure plane.
Summing forces allows the determination of required passive
resistance below the failure plane, assuming a pivot point
near the base of the pile, L/3 up from the tip (see Figure 8).
The design is adequate if the passive resistance required
below the failure plane is less than one-half the available
resistance, i.e., design FS = 2.0. This method is iterated
using various guesses at the embedment length L until the
required FS is achieved at all locations. After determining
the design distribution of loads on the pile, the points of
maximum shear and bending moment are determined, which are
used to design the internal reinforcing for the the piles.
The author notes some limitations on this method of slope
stabilization. It is recognized from field installations that
the lower portion of the slope may separate from the pile row
and continue to move down slope, resulting in movement of
material downslope of the piles and possibly affecting the
performance of the piles. It is also noted that, after
installation of a pile row, continued slope movement may cause
local failure beyond either end of the row, where movement had
not occurred before. For this reason, it is suggested that
slope reinforcement designed using this method be extended
some distance across the slope beyond the apparent limits of
the failure. For slopes with failure surfaces at a great
depth, it may be necessary to
32
24" dia. Piers (610 mm)
*= D
5* centers (1.52 m) 4
Lateral lagging
/ Sloping grade can be
^7 accounted for (Ref. 12)
Sandy clay with limestone frags.
- 120 pcf (18.85 kN/m3)
avg.
= 130 pcf
(20.4 kN/m3)
Â£> 20 Ksf
. (957.6 kN/m3)
Figure 8 Forces acting on reinforcing pile,
after Fig. 11 from Nethero, 1982.
33
consider piles with tie backs at the top to help keep the pile
design within economic limits.
2.4 Rowe and Poulos, 1979
This paper presents a two-dimensional finite element method
analysis of the performance of vertical piles as reinforcement
for an unstable slope. The authors note in the introduction
that the use of piles to correct slope instability is a common
practice, but that "present design methods appear to be based
upon limited empirical experience and relatively simple
analytical techniques."
In formulating their approach to this problem, the authors
note that the prediction of the stability of an unreinforced
slope using the finite element method is already well
established, but that modifying the analysis to include to the
three dimensional effects of a pile group is somewhat
complicated. So complicated, in fact, as to be impracticle
given the computing resources available at the time. To allow
for a more manageble two dimensional (plane strain) analysis,
some important aspects of the pile/soil system need to be
considered:
1. The need to develop some correlation between the
behavior of an idealized plane strain pile group
and an actual pile group.
2. Determination of the limiting pressure at which
the soil will begin to "flow" between the piles,
34
and a means in the two-dimensional analysis to
represent this.
3. A means to account for the "shielding effect",
caused by the overlapping of the influence of
adjacent pile rows when multiple rows of piles are
placed in a slope.
The soil slope system, including the reinforcing piles, is
represented by a finite element mesh. The soil and pile
displacements at the soil/pile interface nodes are set equal
to each other, until the limiting pressure is attained.
Consideration 2 above is dealt with by allowing the soil to
"flow through" those soil/pile interface nodes when the
pressure at these nodes meets or exceeds the limiting
pressure.
In the numerical formulation of the solution to this problem,
it is first assumed that the soil/pile system can be
represented as a composite body with two separate components,
namely the soil and the pile. The forces acting on these two
components consist of two types: the known tractive forces
(i.e., gravity) which act on both the pile and the soil, and
the unknown forces acting between the soil and the pile. For
the analysis of the soil, the nodal displacements are
represented using matrix notation as the Siam of the
displacements due to tractive forces and the displacements due
to reaction forces from the pile to the soil.
An analogous expression for the nodal displacements of the
pile is also derived, and the two expressions are combined to
yield and expression of the unknown soil and pile nodal
displacements as a function of the applied loads and the known
35
displacements due to tractive forces. The constraints of
static equilibrium are then added to the system of equations,
allowing for a complete matrix expression of the displacements
and forces acting at each node in the system.
Consideration 3 above is dealt with by correlating the lateral
response of an actual three dimensional pile group with that
of the idealized plane strain pile group for a range of
stiffness. This correlation allows an "equivalent stiffness"
of the idealized plane strain pile to be used which causes the
head deflection of the plane strain pile to equal that actual
pile group under similar loading. The relationship thus
generated is not completely representative, unfortunately.
Only the head deflection is equated in this procedure. Other
critical components of pile response, such as head rotation
and lateral load developed with depth are not considered.
The next step in setting up this analysis is to determine the
limiting lateral pressure between the pile and the soil. This
question had been the topic of research for some time, due
primarily to the difficulties in designing piles for lateral
loads applied at the head. The authors state that a limiting
pressure of q/c = 9 (where q is the limiting lateral load and
c is the soil cohesion) is generally accepted, and this
relationship is therefore selected for use. When this
limiting lateral pressure is attained at any node at the
soil/pile interface, the deflection compatibility requirements
at that node are no longer enforced, i.e., the soil can have a
greater displacement in the direction of movement than the
pile. This in effect allows the soil to "flow" past the pile,
thus representing the soil movement between piles in the
actual three dimensional case. With reference to earlier work
36
by others, the authors state that the limiting lateral
pressure for piles in a group requires some modification due
to group effects. The results of an earlier analysis show
that the average qult for piles in a group is reduced somewhat
from the qvlt of an isolated pile.
Once all of these prerequisites of soil and pile behavior have
been addressed, the authors proceed with the actual analysis
of the soil/pile system. The slope configuration used in all
analyses is that of a 1:1 slope, 10 meters high, with a rigid
base at 10 meters below the base of the slope. The ends of
the finite element mesh are placed at 60 m beyond the toe and
60 m behind the crest. A number of analyses are performed in
order to demonstrate the effect of various soil/pile
parameters on the response of the system. A summmary of the
various configuration considered is shown in Figure 9. All
cases consider a slope with three pile rows, one row just
behind the crest of the slope, one at the crest, and one just
downhill of the crest. A number of different conditions are
considered. These include variations of pile stiffness,end
fixity, and pile diameter (0.5 and 1.0 m). In addition, pile
penetration was varied, from half penetration to full
penetration, i.e., pile lengths of 10 and 20 m, respectively.
Lastly, variations in soil properties with depth are accounted
for by analyzing a two layered soil system. In the layered
soil, the slope is comprised of two layers, each 10 m thick.
The undrained shear strength of the lower soil is twice that
of the upper soil. For all analyses, pile spacing was set at
2.0 m, center to center. For simplicity, no negative skin
friction was considered in the analysis, and no pile failure
would occur.
37
f
Layer (a)
f
Layer(b)
(A)
T
10 m
1
~7~~? 7 7 7~7~7
CB)
Figure 9 Pile/slope configurations analyzed using 2-D
finite element analysis. In (B) the pile is free at top
and bottom, in (C) free at top and pinned at botttom, in
(D) fixed at top and pinned at bottom, and in (E) free at
top and fixed at bottom. After Fig. 4 from Rowe and
Poulos, 1979.
38
The results of the analyses of the reinforced slope are
presented in terms of the performance of the homogenous
unreinforced slope relative to the slope with piles in place.
The summary of results is included here as Table 1. Included
for comparison between the unreinforced and reinforced slopes
are displacement reduction ratios at selected points on the
surface of the slope, overall increase in the factor of safety
of the slope, and the maximum bending moment developed in the
pile. As stated above, input parameters varied to produce
these results consist of pile length, pile spacing, pile
stiffness, and layering of the soil.
Several interesting conclusions are drawn based upon the
sensitivity analyses performed. Series 1 included piles which
were pinned at the tip and free at the head, and varied the
stiffness of the piles to determine the effect of pile
stiffness on performance of the reinforced slope. The results
indicate that, while the presence of the piles increases the
stability of the slope and decreases soil displacement, the
pile stiffness has little effect on the performance of the
piles. As stated in the paper, "[t]his situation arises
because the piles (even for large stiffness) tend to move with
the soil, and although they offer some restraint to the deep
seated movement, the rotation of the pile about the base still
allows for quite significant deformation of the slope." As
will be noted later, this analysis also reflects the influence
of tip fixity, and the fact that if the pile is allowed to
rotate about the tip, relatively little benefit will be
derived. Unfortunately, the authors did not include variation
of pile stiffness for a fully restrained pile tip, such as in
configuration E of Figure 9.
39
Soil Slope Arrange- ment (See Fig.lO Spac- ing s/d (EI)p Relative Elastic R^ at X : displacement at y = 16 kH/m3 RH at X RL at Y Rjj at Y Maximum Moment for Y=l6kH/n? (kNm/m) Maximum Moment when 6l at X=250ram (kNm/m)
Homo- 1:1 A - 0 , 1.0 1.0 1.0 1.0 - -
geneous C 1. It 6x10? 0-993 .85 .80 .72 107 132
C It 2.91x10!! 0.972 .67 53 .29 lt95 700
C It 5.83x10"3 0.905 .58 .38 .13 979 1280
Homo- 1:1 A 0 , 1.0 1.0 1.0 1.0 -
geneous B It 2.33x10 0.986 97 99 99 l8.lt l8.lt
C It I.lt6xl0-5 0-993 .85 .80 72 107 132
D ' It 1. It 6x10 5 0.733 51* 58 .36 111 176
E It 1.1(6x10-5 0.968 7lt .6lt .1(7 339 lt8l
Homo- 1:1 A - 0 , 1.0 1.0 1.0 1.0 - -
geneous C 2 2.91X10-J1 0.972 .67 53 29 It 99 735
D 2 2-91x10- 0.505 .29 .33 .10 622 21(20
E 2 2.91x10^ 0.770 .1:7 . 31* .09 1610 3090
2 1:1 A - 0 1.0 1.0 1.0 1.0 - -
layers C It 1. It 6x10-5 JL9I5. 0.92 1.0 .99 36.9 187
R^ = Ratio of lateral displacement at the specified point for the slope with piles to that
same point when there are no piles; RH = corresponding ratio for vertical heave.
Table 1 Summary of results from finite element
analyses, after Table 3 from Rowe and Poulos, 1979.
Another effect of increasing pile stiffness is that the
maximum bending moment developed in the piles increases
dramatically, as shown in Figure 10. For pile configuration
C, as pile stiffness is increased 400 times, the maximum
40
bending moment developed increases nearly 10 times. In
addition, for a fully restrained pile tip (pile configuration
E), the maximum bending moment developed is 3 times that of
the other pile configurations. Configuration E also shows the
greatest improvement in slope performance for all end fixity
conditions, with the exception of fully restrained pile head
(configuration D). It is noted, however, that the large
bending moment developed in the piles under configuration E
may not be achieved in actual practice. For the homogeneous
soil slope, the analyses presented does not consider any
effects below the failure surface. Some brief consideration
of this phenomenon is given in the analysis of the layered
soil slope, in which pile configuration C is shown to increase
slope stability by 23% over the layered slope with no piles.
The results discussed above indicate that the effectiveness of
pile reinforcement depends largely on the pile stiffness and
the fixity conditions of the pile ends. This is illustrated
in Figure 11, where slope deformation is shown relative to
pile stiffness and fixity condition. This figure shows upon
examination that slope deformation decreases as pile stiffness
increases and as the fixity condition goes from free to pinned
to fully restrained.
The authors conclude from the analyses performed that the
fixity condition of the piles ends has a greater effect on
slope performance than the stiffness of the piles, that the
effectiveness of the piles is enhanced in cases where the soil
stiffness and strength increase with depth (i.e., the
41
Scries (i)
Series (ii)
0 (A)
Bending moment (kN-m/m)
Arrangement*
r------ (B)
-------21x10
-------4-2x105 > (C)
(C)
(E)
EI = 2 1 x104
kN- m2/m
8-4 x106
(D)
Figure 10 Relationship between pile stiffness and
bending moment, after Fig. 8 from Rowe and Poulos, 1979.
42
Layered soil analysis), and that the distribution of bending
moment within the piles is a function of slope geometry and
the soil profile. It is further concluded that the
effectiveness of piles is dependent on the complex interaction
of many factors in the soil/pile system. With regard to other
approaches to analyze the soil/pile problem, the paper
concludes with the following statement: "...it would appear
that empirical generalizations and extrapolations should ...
be viewed with considerable caution."
2.5 Oakland and Chameau, 1984
This paper presents findings of a three dimensional finite
element analysis of a slope reinforced with vertical piles. In
the introduction, the authors note that, over the preceeding
twenty years, slope reinforcement with piles has been shown to
be an effective means of increasing stability and decreasing
movement. It is noted that there are two major problems with
the analysis of the soil/pile system: (1) determination of
the load distribution along the length of the pile and (2)
evaluation of the stability of the reinforced slope. Prior
methods of analysis have relied on a number of simplifying
assumptions to get around these two difficulties. Some of
these include assumptions regarding the plane strain behavior
of the soil/pile system with respect to lateral distance along
the slope, the stress/strain behavior of the soil, the
rigidity of the piles, and the movment of soil around the
piles.
43
Scries (i)
300 100 0
6l (mm)
Stillness Arrangement
(EI)kN-m^m
0 2.1x10" 1 (A)
4-2 x105 | (C)
8-4x10* J
Series(ii)
--------- (B)
-----------(C)
---------(D)
---------(E)
El = 2-1x10'
KN-nAm
Series (iii)
i_______i__
300 100 0
6l
Arrangement*
--------- (B)
-----------(C)
---------- (D)
EI=4-2x1C?
kN-m^m
Figure 11 Effect of pile stiffness and fixity
conditions, after Fig. 8 from Rowe and Poulos,
1979.
44
The authors propose that the three dimensional FE analysis
presented offers several advantages over previous design
methods. Of primary importance is that the movment of soil
around the piles can be modeled, allowing the effect of pile
diameter and spacing to be more accurately represented. The
authors give a brief review of prior work by others, including
the plastic deformation approach proposed by Ito and Matsui,
and the finite difference and finite element analyses used by
Poulos (1973) and Rowe and Poulos (1979), respectively.
The three dimensional FE model used by the authors allows for
analysis of soil/pile interaction, soil movement and/or soil
arching between the piles. The three dimensional nature of
the problem is simplified somewhat by considering only the
interval between two adjacent piles, the implication being
that the behavior of all such intervals will be similar. The
lateral boundaries of the problem are parellel to the
direction of slope movement and pass through the centerlines
of the two adjacent piles. The FE mesh is constructed using 8
node parellel-pipeds to model the soil, with each node having
three degrees of freedom, i.e., movement of each node is
allowed in three dimensions (see Figure 12). The piles are
modeled as eight node rectangular prism elements, with four
degrees of freedom, i.e., lateral movement at the top and
bottom, and rotation at the top and bottom (see Figure 13).
The base of the FE mesh corresponds to a firm rock layer.
This is represented in the model by fully restraining the
bottoms of the piles, allowing for no rotation and no lateral
displacement. The instability of the slope is generated by
applying a distributed surcharge to the top of the slope. The
basic algorithm of the FE analysis includes eight steps:
45
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
calculate principal stresses at each node
calculate soil parameters (for soil model)
apply load increment with piles held rigid
generate soil stiffness matrix and solve for
soil displacements
determine soil loads on rigid pile
generate pile stiffness matrix and solve for
pile displacements
iterate between pile displacements and soil
nodal loads until convergence is reached, and
repeat with the next load increment
This model is then used to analyze the performance of a
reinforced slope with the following characteristics: 1 1/2 to
1 slope angle, 6 m high and 9 m in length, with piles placed
at 3 m uphill from the toe, pile dimensions are 0.90 m by 1.80
m, placed at a center to center spacing of 6.0 m. The tips of
the piles are fully restrained, i.e., no rotation and no
lateral displacement allowed. The heads of the piles are
unrestrained.
Slope instability is created by the incremental introduction
of a distributed vertical load directly behind the crest of
the slope.
The results for the initial reinforced slope are presented in
Figure 14. This figure shows the undeformed mesh, the
deformed mesh with no piles, and the deformed mesh with piles.
The discussion in the text regarding the performance of this
slope does not exactly match the displacement indicated on the
figure. The text states that the presence of the piles caused
reduction in lateral displacements
46
dgr*a ol fr**dom
Figure 12 Eight-node element used to model soil, after
Fig. 6 from Oakland and Chameau, 1984
Figure 13 Eight node element used to model pile, after
Fig. 7 from Oakland and Chameau, 1984.
47
ranging from 40% to 100% of the corresponding unreinforced
displacements. The reduction is shear stress within the soil
was also noted, with an 80% reduction in shear stress
indicated for soil nodes downhill of the pile location and a
30% reduction at locations uphill of the piles. The greatest
reduction in displacement was observed at nodes downhill of
the pile location. The effect of pile location on deformation
of the slope is presented in Figure 15. This figure shows a
signficant reduction in displacment as the location of the
piles moves from near the toe of the slope to near the crest.
In each case, the maximum displacment occurs at the node
immediately behind the crest of the slope. The effect of
spacing between the piles is also shown in Figure 15, where
the spacing has been decreased from 6.0 m to 3.9 m. These
results suggest that decreasing the spacing between piles
reduces the deflection below the piles, but has relatively
little effect on displacements above the piles. The effect of
pile stiffness is also presented in Figure 15. Comparison of
displacement considering the two cases of flexible piles and
rigid piles indicates that pile stiffness is not a critical
parameter. The authors note, however, that further parametric
studies are needed to determine the effect of pile stiffness.
While the results presented demonstrate the effect of piles on
the performance of the reinforced slope, the authors note that
the current approach has some shortcomings. One of these,
while not mentioned explicitly, is the lack of computer memory
and computational ability available at the time. Other
concerns include the assumptions regarding boundary
conditions, the geometry of the piles, the behavior
48
Figure 14 Undeformed and deformed meshes, after
Fig. 8 from Oakland and Chameau, 1984.
49
FIG. 9Effect of pier position.
FIG. 10Effect of pier spacing.
FIG. 11Effect of pier stiffness.
Figure 15 Effect of pile location, spacing, and stiffness
after Figs. 9, 10, 11 from Oakland and Chameau, 1984.
50
of the soil/pile interface, and the stress-strain model
selected for the soil. The rectangular elements used to model
the piles do not allow direct correlation to more commonly
used circular piles. The frictional relationship between the
soil and the pile is not considered in detail. Full
accounting of soil/pile friction would require inclusion of
slip elements at this interface, and direct shear testing of
the soil/pile interface. In conclusion, the authors recognize
the efficacy of the finite element method in analyzing this
complex problem, while at the same time suggesting further
enhancements of the approach to fully describe the soil/pile
behavior. Lastly, the authors state that future analyses will
be modified to incorporate creep behavior of the soil.
2.6 Hassiotis, Chameau, and Gunaratne, 1997
This paper presents a design method for the design of slopes
reinforced with piles. In the introduction, the authors note
the complexity of the slope/pile interaction, specifically
that the effect of the piles is difficult to determine due to
the interrelationship of many parameters. Several methods
developed by earlier researchers are discussed briefly. The
method of Ito and Matsui (1975) is selected as the basis for
the method of analysis presented by the authors. This method
has some advantages over others. The lateral force acting on
the piles can be expressed as a function of critical design
parameters, such as soil strength, pile diameter, and pile
spacing. The lateral force acting on the piles can then be
used as a resisting force to slope movement, and thus used to
determine the factor of safety for the stabilized slope. The
authors reiterate some of the statements made by Ito and
51
Matsui, the primary one being that this method allows the
forces acting on the piles to be determined regardless of the
overall stability of the slope. For determination of the
lateral force acting on the piles, the authors present
Equation 2-8, which is a slightly modified version of Equation
2-3 from Ito and Matsui (1975):
q = Ac
tan
I exp
D, D, (71 <(>
---------Nh tan **
EL Y V8 4**
2 tan <|> + 2Nf + N~y2'
- 2Nf tan **
* v 3 Nf tan 4 + - 1**
- c
f 2 tan <(> + 2Nf + N7y2
Dl
V
y~z
Nf tan
2 D2N~y2
+ - i A exp
AT '
^2
22,
N. tan (j) tan
n (f)
V 8 + 4
- 22,
(2-8)
in which most terms are defined in Figure 4 (see above), and
= tan2[(m/4) + (/2)]
A
V2
tan $ + -1
(2-10)
It is noted that the method used by Ito and Matsui for
determination of overall slope stability is somewhat limited
as it assumes that the failure surface of the reinforced slope
52
is the same as that of the unreinforced slope. The method
developed by the authors attempts to overcome this limitation.
For the determination of the factor of safety of the
unreinforced as well as the reinforced slopes, the authors
selected the friction circle method, attributed to Taylor
(1937). This method has an advantage over the method of
slices in that it allows the resistance of the piles to be
added to the equations used to determine the factor of safety.
The equations derived by Wood for determination of the
stability number are modified by the authors to include the
effect of the piles, as in the following equations:
12F
E ~ ---f
Ca = Y#
FnyH 2
6 esc x esc
cos (CEO) H
-----------esc x esc y sin **
sin v 2**
y sin
cos x
sm v
+ csc(u v) cos(x v)
(2-11)
(f + 6r|2 6r| sin (j> esc x esc y)
12 Fp
y H3
A
FCJH
6 esc2 x esc y sin (j>
cos x
sm v
+ csc{u v) cos(x v)
(2-12)
in which most terms are defined in Figure 16, and
E = 1 2(cot2 i + 3 cot i cot x 3 cot i cot y + 3 cot x cot y)
(2-13)
53
This is accomplished by assuming that the distributed lateral
forced acting on the piles can be equated to a concentrated
force acting on the failure block in an uphill direction. It
is assumed that this force is located above the critical
surface one third of the distance from the ground surface to
the critical surface, and acts in a direction parallel to the
critical surface at the location of the piles.
Use of the derived expressions to determine the factor of
safety of the reinforced slope demonstrates that the location
of the critical failure surface changes due to the effect of
the piles. This intuitively obvious effect is shown in Figure
16, in which the critical failure surface for the slope with
piles is shallower than the critical surface for the
unreinforced slope. It is noted that the assumption that the
critical surface does not change after insertion of the piles
would lead to non-conservative results. This is shown is
Figure 17, in which the effect of pile location is also
demonstrated. In this figure, the factor of safety for the
reinforced slope is shown, considering two failure surfaces:
the original critical surface for the unreinforced slope and
the critical surface for the reinforced slope. When the
influence of the piles is included, the calculated factor of
safety for the original surface is higher than that of the
actual critical surface of the reinforced slope. Had only the
original critical surface been considered, only the upper
trace on Figure 17 would have been produced, leading to a non-
conservative result i.e., a design Factor of Safety higher
than the actual Factor of Safety. This situation occurs
because "the reaction force Fp is smaller [for the shallower
critical surface in the reinforced slope] and hence, the
54
actual factor of safety is less than the one computed for the
original surface."
It is shown that the piles provide a much greater increase in
slope stability if they are placed near the middle of the
Figure 16 Assumed failure surface configuration,
after Figs. 3 and 4 from Hassiotis, et al., 1997.
55
Figure 17 Effect of varying pile location. This
Figure also shows the non-conservative results obtained
if the original failure surface is assumed for the
reinforced slope. After Fig. 5 from Hassiotis, et al.,
1997.
56
upper half of the slope. The authors do not provide an
explanation of this relationship between pile location and
increase in factor of safety.
On of the most critical parameters for the determination of
the stability of the reinforced slope is the degree of
mobilization of the lateral resistance provided by the piles.
As noted by Ito and Matsui (1982), the expression for lateral
resistance they derived produces an ultimate or maximum value.
In practice, the actual resistance provided by the piles will
be somewhere between zero and this ultimate value. The
authors of the current paper recommend using the overall
factor of safety of the slope as the estimate of the degree of
mobilization of the lateral resistance from the piles. In the
analysis of the slope using the friction circle method, the
actual factor of safety of the sloped is that at which:
FS(j> = FScohesion = FSsi0pe (2 14)
Use of FSslope as the reduction factor for the lateral
resistance from the piles creates the following relationship:
FS$ FScohesion FSpiie = FSsi0pe (2 15)
This implies that an equal proportion of the three forces
acting to resist slope movement cohesion, friction, and pile
resistance will be used to stabilize the reinforced slope.
After determination of the stability of the reinforced slope,
it is critical to consider the stability of the piles. Design
of the piles requires determination of shearing stress and
bending moment profiles along the length of the pile. These
57
are determined from the applied lateral loads and the
deflection of the piles. The authors treat the segment of the
pile above the failure surface is treated as a cantilevered
beam. Displacements and shear forces for this segment are
calculated using a closed form solution of the beam equation.
The segment of the pile below the failure surface is analyzed
as a beam on an elastic foundation. Displacements and shear
for this segment are determined using a finite difference
method. The results of these analyses are shown in Figure 18.
An example of the design process described by the authors is
presented next. Given the configuration of a slope with an
unacceptably low factor of safety, the first step in the
design process is to select the location of the pile row from
the toe of the slope. An expression for the factor of safety
of the reinforced slope as a function of pile diameter,
spacing, and location is then derived from the expressions for
factor of safety presented earlier. This relationship can be
used to determine a number of allowable combinations of pile
configuration needed to attain the minimum required factor of
safety. For the selected pile configuration, diagrams of
displacement, shear, and bending moment are developed which
allow for the structural design of the piles. It is noted in
the design method that the displacement, shear, and bending
moment for the piles will vary for different head fixity
conditions. The authors assume that the pile head is fully
restrained from lateral movement or rotation, partly because
this is the fixity condition assumed by Ito and Matsui, and
partly because this fixity condition produces the lowest
bending moment in the piles. The length of the piles is
determined by first assuming a pile of infinite depth, and
then determining the point at which the
58
Figure 18 Pile displacement and bending moment determination
after Figs. 10 and 11 from Hassiotis, et al., 1997.
59
bending moment goes to zero. This point defines the required
length of the piles. Any additional pile length would not
contribute to the performance of the piles.
2.7 Hull and Poulos, 1999
In their discussion of Hassiotis, et al. 1997, Hull and
Poulos raise a number of issues regarding the presented
analysis method. Some of the most critical concerns are the
location of the piles, the force distribution on the piles,
and possible failure modes for the reinforced slope.
Regarding the location of the piles, Hull and Poulos note that
the original authors conclude that the greatest improvement in
stability is realized when the piles are placed near the crest
of the slope. Hull and Poulos point out that placement of
pile near the upper part of the slope may result in tension
cracks forming just downslope of the piles, resulting in the
lower part of the slope continuing to move, with the soil
upslope of the piles remaining in place. Obviously, if this
situation were to occur, the piles would have little or no
effect on the stability of the soil downslope of the pile
location. Piles near the top of the slope will also be
subjected to significant negative skin friction, as the
primary component of soil movement in this zone is downward.
This may create problems for the end-bearing resistance of the
piles. The negative skin friction will also tend to resist
failure of the slope, and should be considered in the overall
analysis.
60
Hull and Poulos also have some concern about the applicability
of the method for determining the lateral load acting on the
piles. Hassiotis, et al., use the method derived by Ito and
Matsui in 1975. Hull and Poulos point out that the method
selected by the authors is one of many possible force
distributions, and it may not be the most appropriate in any
given situation.
Regarding the response of the piles in the reinforced slope,
the discussers note that the authors consider only one
possibility, namely that the piles are anchored in a stable
sub-stratum and that they resist the movement of the soil
block through resistance to the bending induced in the piles.
The discussers point out a number of different possible
failure modes, such as the piles tips being dragged through
the sub-stratum, the piles being carried with the failure
block, i.e., the failure surface passes below the tip of the
piles, or the piles may rotate excessively around the tips.
To address some of the concerns they raise, the discussers
present an analysis of the same slope using the method of Lee,
et al., 1995. This analysis results in a FS of 1.45, as
compared to the original authors' result of 1.82. The
discussers feel that this difference is enough to raise
questions about the authors' method of analysis. Furthermore,
the discussers find with their method that the maximum moment
developed in the piles is approximately 2.0 MN-m, which far
exceeds the bending resistance of typical piles.
61
2.8 Day, 1997
In this paper, the author presents a method for design of
slope stabilization with drilled piles. The paper begins with
a brief introduction, with some references to earlier work
regarding this issue. It is noted in the introduction that,
in order for the piles to be effective in stabilizing the
slope, the piles must pass through the failure surface and
transmit lateral loads from above the failure surface to more
competent material below, which provides passive resistance.
Because the unstable soil arches between the piles after
installation, the author suggests that piles can typically be
spaced two to three diameters apart. The large loads
generally developed against stabilizing piles sometimes
require tieback anchors be installed through the piles and
anchored behind the failure surface.
Three case studies are presented: the Portugese Bend
Landslide, the Desert View Drive Embankment failure, and a
fill slope failure. In each case, drilled piles were used to
stabilize an actively moving slope. All three of the case
studies are located in the coastal areas of Southern
California.
In the case of the Portugese Bend Landslide, large scale
movement of the slope began in 1957 after the construction of
a road embankment across the top of the slide area. In 1957,
a cantilevered pile wall was built at the toe of the slide.
The wall consisted of 23 reinforced concrete piles, 1.2 m in
diameter, and embedded 3 m into the underlying material.
62
While initial indications were that the piles slowed movement
of the slide, the piles eventually failed, some being plucked
out of the underlying material, some being toppled by soil
movement, and others being sheared off at depth.
The Desert View Drive embankment was built in the early 1960s,
and was stable until 1990, when an excavation for an adjacent
residential lot started a progressive failure of the
embankment which eventually developed into a large scale wedge
failure. The slip surface was located about 7 to 8 m below
the ground surface, near the contact between the base of the
fill and the underlying shale bedrock. To stop the movement,
40 steel reinforced concrete piles were installed, extending
from the ground surface into the underlying bedrock. Most of
the piles had a diameter of 1.4 m and were set on an average
spacing of 2.4 m. The length of most of the piles was 23 m,
placing the tip of the piles around 15 to 16 m below the
failure surface. As of 1997, the piles appeared to have
stabilized the slide.
The last case study is of a residential lot at which water
from a leaking utility line apparently caused some instability
in a 18 m high, 1.5H:1V fill slope at the rear of the
property. Correction of the instability was achieved by
installation of a row of nineteen 0.9 m diameter piles, spaced
at 2.4 to 2.7 m, anchored into the underlying bedrock.
Tiebacks were used to reduce the bending moments in the ten
most heavily loaded piles.
The author presents two design methods for slopes stabilized
with piles. The first method uses a typical equation for the
factor of safety of the reinforced slope, as in:
63
uL) tan (j)' + Pi
(2-16)
F. S. =
c'L + {w cos a -
W sin a
in which L is the length of the slip surface, W is the total
weight of the failure wedge, u is the average pore pressure
along the slip surface, a is the slope of the failure plane,
and Pi is the required pile resistance. In this equation, the
sum of the forces resisting movement is divided by the sum of
the forces which tend to cause movement. Included in the sum
of forces resisting movement is the lateral reaction from the
reinforcing piles exerted on the failure block. The design
factor of safety is selected, and Equation 2-16 is simply
solved for the single unknown, the resistance from the piles.
The lateral design force acting on each pile is determined as
a function of the distance between the piles. In the second
method, the reaction from the piles is determined using earth
pressure theory. The earth pressure acting on the uphill side
of the pile is assumed to be the Rankine active earth
pressure, and the total reaction per pile is determined as:
PL = 0.5kaytZ2TS
(2-17)
in which ka is the Rankine active earth pressure coefficient,
yt is the total soil unit weight, and S is the pile spacing
(see Figure 19). The second method does not appear to allow
for determination of the factor of safety of the slope,
64
although it is recommended that a factor of safety be added to
Equation 2-17 to allow for a conservative estimate of the
force acting on the piles. It is recommended that the second
method be used to design piles for clay slopes which are
undergoing creep movement. In the second method, it is noted
that the development of passive resistance on the portion of
the pile below the failure surface will require 0.5 to 1.0 %
deflection of the pile (see Figure 19). For both methods, the
calculated force acting on the piles is assumed to act one
third of the way up the pile from the failure surface. After
the location and magnitude of the forces acting on the pile
are known, the structural design of the piles is then
possible.
The length of the piles in the case of cantilevered piles is
determined by the depth at which the sum of the moments about
the tip of the piles is zero. For the case of the tieback
piles, the length is determined by determining at what pile
length the sum of the moments around the top of the piles is
zero.
It is noted that the mechanism that transfers loads from the
soil to the piles is soil arching. Soil arching generally
allows piles to be placed at two to three diameters spacing.
However, in some highly plastic soils, this spacing may be too
great, as the soil will simply flow between the piles.
Recommendations for pile spacing are provided based on the
performance of existing pile walls.
65
APPLY ACTIVE PRESSURE IN TRIBUTARY FASHION AS IF A WALL EXISTS.
APPLY PASSIVE RESISTANCE OVER 2 PIER DIAMETERS
FOR TYPICAL CANTILEVER DESIGN, STRUCTURAL ENGINEER SHOULD ASSUME
ABOUT 0.5 TO 1% ROTATION OF WALL IS REQUIRED TO MOBILIZE MAXIMUM
PASSIVE RESISTANCE. TOTAL DEFLECTION SHOULD BE CALCULATED BY ADDING
THIS ROTATION TO THE STRUCTURAL DEFLECTION FROM BENDING STRESS.
Figure 19 Assumed distribution of forces for slope/
pile design, after Fig. 7 from Day, 1997.
66
2.9 Discussion
It is evident from the foregoing literature summaries that
there are several different approaches to the analysis of
soil/pile interaction in a slope stabilization application.
This section will attempt to address some of the issues
regarding the analytical methods presented in the referenced
professional papers. A summary table containing basic
information about the installation and design methods included
in the referenced papers, plus some others which were reviewed
but not discussed, is provided as Table 2.
To start, it may be best to look at the simplest design
methods, those based on common geotechnical design methods and
empirical observations. Of the referenced papers, Nethero
(1982) and Day (1997) fall into this category.
The design approach offered by Nethero (1982) appears to be
closely related to the accepted design method for sheet pile
retaining walls, as presented in several geotechnical
references and textbooks (i.e., Das (1993)). The stress
distribution on the stabilizing piles as presented by Nethero
is very similar to that for the design of sheet pile retaining
structures. In doing this, the author recognizes the
importance of the resistance provided by soil under the
failure surface. There are some aspects of the soil/pile
problem that make use of this method somewhat questionable,
however. For instance, the assumption of Rankine active earth
pressure may not be admissible due to the fact that Rankine's
assumed conditions are dramatically different than those in a
pile reinforced slope. In addition, Nethero's
67
Table 2 Summary of installation and design methods for slope stabilization with
piles.
Pile Diam. Pile Length Length Above Failure Surface Cross- Slope Spacing Material Actual Install-
(m) (m) (m) (m) ation? Comment
1.07 9.9 3.0 Concrete w/ steel beam reinforcement Yes DeBeer and Wallays, 1970. Two rows, one near toe, one -1/3 up slope
1.28 9.9 3.0 II If II
1.50 20.0 2.0 n It II
0.3 >8 6.3 4.0 Concrete pipe, t=60 mm Yes Ito and Matsui, 1975. Katamachi Slide. Pile top 2.17 m below ground surface
0.318 >11 5.0 5.5 4.0 Steel Pipe, t=6.9mm Yes Ito and Matsui, 1975. Kamiyana and Higashitono Slides. Pile top 1.0m below ground surface
0.5 10 or 20 No Rowe and Poulos, 1979. FEM analysis
1.0 10 or 20 No II
1.016 3.0 No Ito, et al., 1981. Design example
0.8128 3.0 No II
0.762 1.5 C.I.P. Concrete Yes Nethero, 1982
0.457 2.1 Concrete Yes II
Table 2 (cont.) Summary of installation and design methods for slope
stabilization with piles.
o>
KO
Pile Diam.
(m)
Pile Length
(m)
Length
Above Failure
Surface
(m)
Cross-
Slope
Spacing
(m)
Material
Actual
Install-
ation?
Comment
0.61 2.1 II Yes Nethero, 1982
0.61 1.5 II Yes II
0.61 2.1 II Yes If
0.61 1.5 II Yes II
0.762 1.5 II Yes II
0.1 -5 1.75 Steel pipe filled with concrete Yes Winter, et al., 1983. Seven rows of piles. Field obs. indicate piles failed.
0.42 -3.5 4 II Yes Winter, et al., 1983. Same slope, two rows midslope, pile length = 25 m
3 ~20 -15 9 II Yes Winter, et al., 1983. One row near toe of slope.
0.9x1.8 (rectangular) -9 (varies) 3.9 or 6.0 No Oakland and Chameau, 1984. 3D FEM analysis. Three rows at crest.
Table 2 (cont.) Summary of installation and design methods for slope
stabilization with piles.
-j
o
Pile Diam.
(m)
Pile Length
(m)
Length
Above Failure
Surface
(m)
Cross-
Slope
Spacing
(m)
Actual
Material Install-
ation? Comment
0.5 to 2.0 10 to 20 (varies) 3 No Lee, et al., 1995. For homogeneou s slope, piles most effective at toe or crest.
1.2 Steel reinforced concrete Yes Day, 1997. Ave. depth to F.S. 30 to 40 m, 23 piles embedded 3 m below F.S., all piles failed.
1.4 (most) 23 2.4 (most) Concrete reinforced with 20 #18 bars Yes Day, 1997. Depth to F.S. 7 to 8 m, 40 piles
0.9 2.4 to 2.7 Yes Day, 1997. 19 piles.
0.91 5 2.3 No Hassiotis, et al., 1997. Piles most effective within upper ~l/3 of slope.
approach is perhaps overly conservative as it ignores the
overall stability of the slope, i.e., no credit is given for
the resistance to movement provided by the failure plane. On
the other hand, the use of Rankine active earth pressure may
be greatly non-conservative, as Rankine assumes a failure
block of limited size, while the failure block being
stabilized in this application could be relatively large. In
addition, no consideration is given to development of new,
deeper failure surfaces under the reinforced slope.
Regarding the paper by Day (1997) the primary value of this
paper is that it presents the results of actual installations
of reinforcing piles. Though these case studies are brief,
they provide some insight into the performance of pile
reinforced slopes. The paper also includes some practical,
empirically based design and construction recommendations. It
should also be noted that this paper is the only one in which
it is recognized that some strain (i.e., deflection of the
piles) will be required to develop the passive resistance
below the failure surface, similar to the passive resistance
provided at the toe of a cantilevered retaining wall.
Unfortunately, Day's approach has some of the same limitations
present in Nethero's method. The primary issue has to do with
the determination of the lateral load acting on the piles.
Other researchers have recognized that the complex
interactions of the failure block and the piles make it
difficult to determine the actual loads acting on the piles.
Day, however, makes some broad assumptions that may lead to
unrealistic results. In the first method for slope design,
the resistance from the piles is determined simply by solving
71
the factor of safety expression. The author states that this
produces the lateral resistance from the piles. What is
actually determined is the required resistance, while the
actual resistance developed is still unknown. In the second
method, the assumption of Rankine active earth pressure may
not be admissible, as with Nethero's approach. Also, in both
methods, it is not determined whether or not the pile acting
with the soil below the failure surface can provide the
required resistance.
As with other researchers, Day suggests use of tiebacks near
the heads of the piles to reduce bending moments in the piles.
The author states that the tiebacks must be anchored behind
the failure surface. The effect of the tiebacks on the
overall stability of the slope is not addressed, however.
This effect, while it may be small, should be included for a
complete analysis of the soil/pile system. In addition, the
performance of any tiebacks would be effected by shear and
bending in the tiebacks where they cross any failure surface.
Day's observations of the movement of plastic soil around the
piles lends some veracity to the mechanism on which Ito and
Matsui base their design method. This soil movement was
observed only in the clayey soil, however, and not it the
other cases. In cases of low-plasticity soils, the
observations of the author imply that soil arching occurs
between the piles. This may suggest that the Ito and Matsui
method has limited applicability in soils that are not prone
to plastic deformation. What soil properties control the
mechanism of pile loading, i.e., arching or plastic
deformation, is not clear at this point.
72
While the design methods presented by Nethero and Day have
some value, it is apparent that such approaches may not fully
capture the effect of the piles on slope performance, and may
therefore lead to an inappropriate or worse, inadequate -
design. The second broad classification of design methods
include those which require fewer simplifying assumptions, and
therefore present what would hopefully be more realistic
results. The papers that fall into this category include
those by Ito and Matsui (1975), Ito, et al. (1981 and 1982),
and Hassiotis, et al. (1997). As can be seen in the summaries
of these papers presented above, the methodologies used to
address the soil/pile problem vary significantly. Some of the
advantages and disadvantages of each of these are discussed in
the following paragraphs.
The series of papers by Ito and various co-authors (1975,
1981, and 1982) present a very thorough analysis of soil/pile
interaction in a slope stabilization application. It is
interesting to note that the basic formulation for the lateral
force acting on the piles in this method is derived from the
manufacturing process of rolling sheets of steel. It follows
from this that the authors would determine the force acting on
the piles considering plastic deformation of the surrounding
soil, just as steel would be undergoing plastic deformation
during shaping between rollers. In any event, the method
presented in this series of papers appears to be the first in
which the actual stress state in the soil is considered. When
compared to results from actual instrumented piles, the method
presented appears to show good order of magnitude correlation.
The summary of this series of papers presented above includes
some brief observations regarding apparent inconsistencies in
73
the approach presented. Among these is the fact that the
method yields a greater force acting on the piles as the
strength of the soil increases. This is contradictory to the
more likely scenario in which the overall stability of the
slope increases for greater soil strength and any force acting
on the piles would therefore be lower. Of greater concern is
the use in the third paper of a "mobilization factor". It is
to the authors' credit that they condsider, as have other
researchers, that the actual developed resistance of the piles
may be much less that the theoretical ultimate resistance.
However, there appears to be some inconsistency in the
definition and use of the mobilization factor. In the initial
discussion of this factor, it is stated that the mobilization
factor is a function of the amount of movement of the sliding
soil, a statement that appears to be intuitively correct and
is verified by other researchers. However, in explaining the
design procedure, the authors appear to select a mobilization
factor based on the lateral resistance needed from the piles
to attain stability of the slope. The analysis describes
determination of the "minimum allowable value of the
mobilization factor" for various combinations of pile
dimensions. In this way, the mobilization factor therefore
becomes a measure of the required lateral reaction from the
piles needed to attain slope stability. The earlier statement
that the mobilization factor is a function of the magnitude of
movement of the slope is not considered in the design process.
The question of whether or not sufficient movement will occur
to develop the lateral forces of the magnitude required is not
addressed.
74
Of the design methods which fall into the currently considered
group, the most recently published is that by Hassiotis, et
al. (1997). The related discussion by Hull and Poulos (1999)
was also reviewed. The method presented by Hassiotis, et al.
varies somewhat from those presented by most earlier
researchers in that the performance of the piles as well as
the factor of safety of the slope are both considered
together. More importantly, the authors realize that the
critical failure surface through a slope will change due to
installation of the piles, where work by others assumed the
critical surface would stay the same. As demonstrated by the
authors, use of the unreinforced critical surface for analysis
of the reinforced slope leads to non-conservative results.
This issue is further addressed by Hull and Poulos in their
discussion. They point out that not only will the failure
surface change, but that the mode of failure of the piles
should be considered as well.
One item of concern regarding the proposed design method has
to do with the applicability of the Ito and Matsui method. It
is stated by the original authors and the current authors that
this method is applicable regardless of the state of
equilibrium of the slope. This method, however, is premised
on the soil being in a state of plastic deformation around the
piles, i.e., the soil is "flowing" between the piles. This
condition would seem to imply that failure of the slope has
already occurred, thus the statement that the lateral force is
independent of the stability of the slope would not be
correct. This problem is addressed by Ito and Matsui (1982)
by the introduction of a mobilization factor, and by
Hassiotis, et al. by dividing the ultimate lateral pile
resistance by the factor of safety of the slope. In both
75
cases, the selection of a mobilization factor seems to be
somewhat arbitrary. Dividing the ultimate pile resistance by
the factor of safety of the slope implies that the pile
resistance develops linearly from zero to the maximum value as
FSsiope goes from infinity to 1.0. The development of pile
resistance could just as easily be non-linear as FSsiope
decreases. Also, in the case where the factor of safety of
the slope is less than 1.0, the proposed relationship would
yield a mobilized pile resistance greater than the ultimate
value, which of course would not be physically possible. The
point of this discussion is that determining actual pile
resistance as a fraction the ultimate value may not be
representative of what actually occurs in the reinforced
slope.
The assumptions made regarding the pile resistance reaction
force are also cause for concern. Ito and Matsui (1981)
advise against using a concentrated load as the resultant of
the distributed load on the piles. Yet Hassiotis, et al. use
a point load acting one third of the way up the portion of the
pile above the failure surface. Their selection of the
location of the reaction force implies a triangular
distribution of the distributed load. Ito and Matsui show the
predicted distributed load to be closer to a trapezoid, and
the actual measured distributed load to vary in its
distribution.
One advantage of the approach described by Hassiotis is that
the critical surface for the reinforced slope is allowed to
change from that of the unreinforced slope. This is a clear
advantage over earlier methods in which the failure surface is
assumed to remain the same. An additional analysis that would
76
be necessary in some cases, however, is determination of the
stability of the slope for a failure surface passing just
under the tips of the reinforcing piles.
The authors state that the optimum fixity condition for the
pile heads is fully restrained, with no rotation and no
lateral displacement allowed. This condition minimizes the
bending moment developed in the pile and more closely
replicates the conditions assumed by Ito and Matsui in their
earlier work. The authors suggest that this head restraint
condition could be attained by connecting the piles with a
below grade beam and installing tiebacks through the piles.
It is unclear, however, what effect the below grade beam and
the tie backs would have on overall slope performance. The
beam itself could have significant effect on soil movement
between the piles. In the design example presented by the
authors, the distance from the ground surface to the failure
surface is 5.0 m at the location of the piles. If a beam 1.0
m high is place between the piles, 20% of the window between
the piles would be blocked by the beam. It would seem that
this would have some effect on performance of the slope. A
similar concern can be raised with regard to the tiebacks.
For the tiebacks to perform, they would have to be anchored in
the competent soil below (behind) the failure surface, and
they would therefore have some effect on the overall stability
of the slope, not unlike soil nails or rock bolts. The
influence of the tiebacks, such as the effect of the increased
normal force at the location of the tiebacks or the pullout
resistance of the tiebacks, should be considered in the
overall stability of the slope.
77
Regarding the method of analysis selected by the authors, it
is noted that the friction circle method allows analysis of
homogeneous slopes only. This would be a distinct
disadvantage in cases where a layered slope is in need of
reinforcement. Also, the forces acting on the portion of the
pile below the failure surface are determined using a method
more suited to analysis of strip foundations. As pointed out
by Nethero (1982), the resistance to pile movement developed
in the soil below the sliding surface is provided by soil in a
passive state. It is well documented that development of full
passive resistance is dependent on significant strains
occurring in the direction of soil movement. It does not
appear that the method used by the authors takes this into
consideration.
Lastly, it is somewhat troubling that Hull and Poulos find a
significantly lower factor of safety using their method when
analyzing the same reinforced slope as the original authors.
This leads to the question of which method is more
appropriate. It also points out that the problem of analysis
of pile reinforced slopes needs further analysis. As stated
by Hull and Poulos in the introduction of their discussion,
"[a]nalysis of the influence of piles on the stability of
slopes ... has attracted the interest of engineers for many
years, but it still remains a problem with no definitive
approach that has found universal approval."
The veracity of the statement by Hull and Poulos is
demonstrated by the wide range of design and analysis methods
developed by various engineers over the last thirty years. Of
all the methods presented, those based exclusively on
numerical methods appear to have the most promise. Three of
78
the papers reviewed fall into this category. They are Poulos
(1973), Rowe and Poulos (1979), and Oakland and Chameau
(1984).
The earliest use of numeric methods to analyze the soil/pile
interaction problem was by Poulos in 1973. The finite
difference method presented in this paper shows several clear
advantages over other deterministic methods of analysis which
appear in the engineering literature at around the same time
(i.e., DeBeer and Wallays (1970) and Ito and Matsui (1975)).
For example, fewer assumptions are required regarding the
stress state of the soil or the pile and the displacement
pattern of the soil is considered in the analysis. Most
importantly, the resistance to soil movement provided by the
pile is allowed to develop as a function of movement of the
surrounding soil, as it would in an actual application. Other
methods available at the time give little consideration to the
development of the pile resistance or the magnitude or
distribution of soil movement. DeBeer and Wallays recognize
this as a shortcoming of their method (see quote above). Ito
makes similar statements in his papers.
The method presented by Poulos has some deficiencies, though.
One of the most significant is the lack of any assessment of
the stresses or displacement of soil or pile below the base of
lateral soil movement. This would be analogous to the zone
below the slip surface in a slope stabilization application.
As noted elsewhere, this is an issue for several of the papers
reviewed. Results from instrumented piles contained in Ito
and Matsui (1975) show that the greatest lateral load on a
stabilizing pile develops in the zone immediately below the
failure surface. It should also be noted that Poulos uses an
79
assumed soil displacement pattern in his analyses. This is
probably due to the limited computing resources available at
the time. A more complete numeric analysis would determine
soil displacement based on slope configuration and other
problem parameters. Indeed, Poulos notes that the
distribution and magnitude of soil displacement are critical
factors in the behavior of the piles. The last significant
concern has to do with the method by which soil movement past
the pile is modeled. In this case, this condition is
accounted for by uncoupling the soil and pile displacements at
soil stresses greater than the yield pressure. This in effect
allows the soil to move "through" the pile, but does not fully
capture the three dimensional nature of the problem.
Poulos apparently had some continuing interest in the
application of numeric methods to the question of slope
stabilization with piles, as evidenced by his coauthoring of
Rowe and Poulos (1979). This paper represents a significant
move forward in analysis of this problem. The two dimensional
finite element analysis allows for a number of different
scenarios to be modelled.
Of all the references reviewed for my research, this paper is
without a doubt the most comprehensive treatment of the
soil/pile system using numerical methods. The analyses
presented point out some of the clear advantages of numerical
analysis over other approaches, namely that no assumptions
need to be made about the state of the soil or the failure
mechanism of the slope. It is also possible to realistically
model the bending moments developed in the piles, an important
criteria for pile design that other methods do not capture
well.
80
On the other hand, the analyses presented are somewhat
limited. As with much of the early work involving numeric
methods, this is likely due to the limited computing resources
available at the time. A more complete analysis would have
included consideration of more varied slope configurations and
pile locations, perhaps considering the effect of pile rows
nearer the toe of the slope as well as at the crest. Similar
to many other papers, the method presented by Rowe and Poulos
does not consider the passive resistance developed below the
failure surface. Also, a full three dimensional analysis
would allow for the movement of soil past the piles to modeled
more realistically, instead of relying on a two-dimensional
approximation. Lastly, some comparison to actual field
applications would be of great value. A very brief general
discussion of the distribution of bending moments in the piles
is presented (p. 1084), comparing modeled distributions to
those reported by earlier researchers. However, most other
papers reviewed relied largely on actual field applications to
verify their design methods.
Some of the concerns surrounding early two dimensional FE
analysis are addressed by Oakland and Chameau (1984). As
noted earlier, this paper presents the results of a three
dimensional FE analysis, of the soil/pile system. This paper
describes what appears to be a sound finite element approach
to analyzing this complex problem. As the authors indicate,
the primary advantage of the FE approach is that no
assumptions need to be made regarding the distribution of load
on the pile or the effect of the piles on the stability of the
slope. This is a significant improvement over other
81
approaches in which assumptions regarding certain critical
aspects of the problem are required to allow analysis.
The authors' recommendations for further improvements to this
approach are noted. However, some other aspects of the
problem may also need to be considered. For one, the authors
make brief note of the role of the soil underlying the failure
surface in taking the load transferred from the sliding soil
via the piles, yet they do not consider the ability of this
soil to accept this load. As noted earlier in these
discussions, the performance of the piles will likely depend
in large part on the performance of the soil below the failure
surface.. Also, the authors briefly mention the effect of soil
arching between piles. This phenomenon is also mentioned by
other researchers (i.e., Nethero (1982) and Day (1997)).
Determination of the role of soil arching as a function of
pile spacing and soil properties may lead to a better
understanding of the effect of piles. Also, it is noted that
the authors present all results in terms of displacment of the
slope as a function of pile configuration, but make no mention
of the overall factor of safety against failure. While
displacement is critical, it should be noted that a stable
slope can undergo displacement but not be at risk of failure.
Future analyses should therefore consider the factor of safety
of the slope as well as the displacement. Lastly, it is
somewhat counter-intuitive that the piles would cause a
decrease in shear stress and displacement downslope of the
pile location, while having little effect on these parameters
upslope of the piles. Oakland and Chameau present results
indicating such a relationship. "The displacements below the
pile are reduced...while the reduction above the piles is not
82
significant." It would seem further investigation of this
phenomenon would be warranted.
2.10 Literature Review Summary and Conclusions
It is obvious from the above summaries that there has been and
continues to be a wide range of methods for the design and
analysis of pile reinforced slopes. Furthermore, it is
obvious from the discussion of the advantages and
disadvantages of each method that there are a number of
problems with the available methods. Some of these are
limited to particular approaches, but there are some common
problems as well.
The most critical shortcoming of the available methods is that
the passive resistance provided by soil adjacent to the lower
part of the reinforcing pile is generally not considered
quantitatively. Many researchers note that the resistance
provided by soil below the failure surface is critical to the
performance of the pile reinforced slope. When results from
actual instrumented piles are reported, as in Ito and Matsui
(1975), it can be seen that the largest lateral load on the
piles occurs just below the failure surface.
There are a number of other issues with current and past
design methods. One of these is the consideration of
different failure surfaces for the reinforced and unreinforced
slopes. Only Hassiotis, et al. (1997) consider this
possibility in a quantitative manner. In actual practice, the
development of a failure surface below the tips of reinforcing
piles would limit the effectiveness of any reinforcement.
83
Also, the actual mechanism of pile resistance has not been
completely described. In the case of plastic deformation of
the soil, the method of Ito and Matsui (1975) appears to
adequately describe the ultimate pile resistance developed.
However, as noted by Day (1997), plastic deformation occurs
only in certain soils. Soil arching between piles provides
the resistance to movement in less plastic soils. The
relationship between soil arching, plastic deformation, and
pile resistance is not clear based on current research.
The concerns described here clearly demonstrate that this
commonly used means of slope stabilization requires further
analysis. Uncertainties in design methods can lead to
inadequate designs and failure or overdesign. Either option
presents unacceptable consequences and/or costs for the
designer. If the soil/pile reinforcement problem were more
completely understood, optimization of designs could lead to
reduced frequency of failure as well as cost savings by
avoiding overly conservative designs. The use of numerical
methods appears to be the most promising means to attain this
optimization. As noted in the above discussion, numerical
models allow the development of stresses and deflections in
both soil and piles to be modeled more realistically, and will
thereby lead to greater insight into the complex interactions
in pile reinforced slopes and refinements in design methods.
84
3. Limit: Equilibrium Analysis
While the overall objective of this thesis is finite element
analysis of a slope stabilized with piles, an initial analysis
of the subject slope as performed using limit equilibrium
methods. This initial analysis was intended to show the
degree of improvement in slope performance predicted by
traditional analysis methods, and also to allow direct
comparison between methods for the same slope configuration.
The slope configuration used for both analysis methods is
shown in Figure 20. This slope consists of a 10 m high slope
at an angle of 45 degrees, with a firm foundation layer 2 m
below the toe of the slope. Input and output files from the
STABR runs are included in Appendix A and Appendix B,
respectively.
The limit equilibrium analysis of this slope was carried out
using the STABR program, published in 1985 by Duncan and Wong
(Duncan and Wong, 1985). The STABR algorithm uses the
modified Bishops Method of Slices, and uses a circle center
search to find the most critical (i.e., lowest factor of
safety) circle for a given slope configuration. Slope
geometry is defined by vertical sections and the elevation of
different material boundaries at each section. This input
format lends itself well to the incorporation of vertical
zones of high strength material used to represent concrete
piles through the slope.
STABR allows two options for defining the strength parameters
for soil. In the first option, the user may specify values
85
Figure 20 Schematic of pile/slope configuration
for cohesion and friction angle. In the second, values for
unconfined compressive strength as a function of depth are
specified for each material. The data format using the
cohesion/friction angle option did not allow for the inclusion
of vertical layers of high strength material (i.e., concrete
piles). For this reason, the unconfined compressive strength
option was used to define the strength of the soil. For the
weak slope soil, the unconfined compressive strength varied
from 30 Pa at the surface to 40 Pa at the top of the
foundation layer. The unconfined compressive strength of the
foundation soil was assigned a value of 200 Pa throughout.
To allow comparison of these strength values to the material
properties later used in the finite element analysis, the
relationships between shear modulus (G), bulk modulus (K), and
Young's modulus were used along with an approximate
relationship between unconfined compressive strength and shear
modulus developed by Weiler (1988) and referenced in Kramer
(1996). The values of bulk modulus for weak soil (3.33 x 108
Pa) and foundation soil (3.33 x 109 Pa) used in the finite
element analysis equate to unconfined compressive strength
values of approximately 300 Pa and 3000 Pa, respectively.
However, use of these strength values did not produce useful
results from STABR, and the values were therefore modified to
those used (i.e., 30 40 Pa and 200 Pa, repsectively).
For the reinforced condition, the concrete pile was modeled as
a vertical zone of high strength material at locations 1 m
behind the crest of the slope, and 3m, 7m, and 10 m beyond
the crest. Since the STABR algorithm assumes a unit thickness
(i.e., 1 m) transverse to the slope direction, and since the
pile diameter is 0.5 m, the strength of the pile material was
reduced by a proportionate factor.
87
NO PILE, FS = 1.187
PILE AT +10, FS = 1.257
CO
CO
0.5 M DIAM.
Figure 21 Location of critical slip circles
for the Bishops Method of Slices, unreinforced
and reinforced slope.
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