Finite element slope stability analysis of Souk Tleta dam by shear strength reduction technique
Innov. Infrastruct. Solut.
Finite element slope stability analysis of Souk Tleta dam by shear strength reduction technique
Ryma Afiri 0
Smail Gabi 0
0 Geomaterials, Environment and Development Laboratory, University Mouloud Mammeri of Tizi-Ouzou , Tizi Ouzou , Algeria
Slope stability analysis of earth dam is very important to ascertain the stability of the structure. The stability of earth dam depends on its geometry, components materials, water pressure and the forces to which it is subjected. Souk Tleta earth dam, currently under construction, is located on Bougdoura River, in north Algeria. The main purpose of the dam is to store surface water, for irrigation and domestic supply. In this study, reducing gradually the shear strength parameters technique is used to analyze the static slope stability of Souk Tleta zoned embankment dam based on the numerical simulation using Plaxis 2D finite element software. The deformations within the dam and the foundation at the end of construction and reservoir impoundment loading conditions and the corresponding factor of safety have been simulated. The results show that the displacements occurred in the dam body and foundation are the largest at the end of construction and lower during the reservoir filling. The safety factor in the different conditions decreases with the increase in reservoir water level.
Slope stability; Static analysis; Earth dam; Finite element software; Factor of safety; Shear strength reduction; Displacement
Slope stability is a challenging problem in geotechnical
engineering. Evaluation of embankment dam stability and
deformation is a crucial aspect that each earth dam structure
must be verified.
Slope stability is one of the main and classical problems
of embankment dams that have been studied by numerous
authors in 2D using variety of methods based on traditional
limit equilibrium approach [
Limit equilibrium analysis is widely used in practice to
calculate the safety factor of slopes. Fellenius [
] used the method to analyze the problem of soil
slope stability at failure using the elastic perfectly plastic
Mohr–Coulomb criterion. All thought the principle of the
method has been refined and became simplified methods by
dividing the soil into slices. These methods include:
Bishop’s modified method [
], Janbu’s generalized procedure of
], Morgenstern and Price’s method [
Spencer’s method [
Due to its simplicity, limit equilibrium method has been
for a long time one of the most popular methods in
In the last few decades, with the development of personal
computer, finite element method has been increasingly used
in slope stability analysis. Comparing with the traditional
limit equilibrium approach, the finite element method has
many advantages such as no advance assumption about
location or shape of the failure surface, slice side forces and their
directions, and a good application for complex soil profiles.
With numerical methods using finite element method,
there are two basic approaches for calculating the factor
of safety “shear strength reduction technique” [
“enhanced limit method” introduced by [
The shear strength reduction technique is one of the
important numerical methods for dam slope stability
analysis and successfully used in the study of geotechnical
structures (excavations, embankments, earth dams and landfills).
It can get the safety factor, displacement and deformation of
the dam slope.
Strength reduction means reducing gradually the shear
strength parameters (cohesion C and internal friction angle
φ) of soil slope by applying finite element [
8, 13, 28
finite difference programs [
] until the first indication of
The calculation of factor of safety (FOS) based on finite
element is possible using the strength reduction method and
it is defined as the ratio of soil or rock at failure to the shear
strength on the failure surface.
The concept of shear strength reduction method was first
introduced by Zienkiewiez et al. [
] to evaluate the
performance of slopes. This technique has been subsequently used
as a common approach in several numerical codes for slope
stability analysis, such as [
6, 8, 10, 13, 15, 16, 18, 19, 22,
23, 28, 29
] and many other researchers.
The case study is Souk Tleta zoned embankment dam,
located on Bougdoura River immediately downstream of the
confluence of Tleta and Tala Imedrane Rivers, 20 km West
of Tizi-Ouzou city in north Algeria (Fig. 1). Souk Tleta dam
has a crest length of about 200 m, a maximum height above
the river bed level of about 95 m and an estimated total
storage capacity of about 96 million m3. The stored water
will be used for various purposes, including irrigation and
Earth dams need to be checked for a number of different
load cases of slope failure such as during and at the end of
Fig. 1 Location of Souk Tleta
construction, steady-state seepage conditions, operational
conditions which include rapid drawdown conditions,
construction modification and earthquake loading.
According to the Algerian Earthquake Regulations
RPA99 Version 2003 of Algeria, the site is situated in a
zone known as moderate to weak seismicity. Therefore, this
study discusses the static slope stability analysis.
The aim of the present study is to examine numerically
the slope stability of Souk Tleta earth dam using the finite
element method with strength reduction technique in
twodimensional computer program Plaxis Version 2010.
In this paper, it is proposed to evaluate the displacements
and the corresponding factor of safety of the Souk Tleta
dam for four different essential conditions in the service life
of a dam: the stage at the end of construction where large
deformations are expected in the dam and its foundation, the
minimum water level condition, where the pore pressures
appear in the dam, the normal water level condition, which
corresponds to the most frequent state and the maximum
water level condition caused by an exceptional flood.
This study also allows checking the geometric design
of the dam and making the right choice of the
embankment construction materials through the determination, in
the laboratory and in situ tests, of the various geotechnical
parameters affecting the slope stability.
Geological factor plays a major role in designing and
constructing a dam. The regional geology of Souk Tleta dam
and its reservoir are located on the meridional bank of
sedimentary basin of Lower Miocene (Burdigalian)
of Tizi-Ouzou city. In the area of the dam, Burdigalian
sediments cover the site of under-Miocene with
a transgressive facies which crops out at the upstream of the gorge of
Souk Tleta valley, and covers a large surface right up to the
foot of limestone chain of Djurdjura.
Geological overview of Fig. 2 shows the outcrops
extension of lithofacies in the dam site. The foundation of Souk
Tleta dam is composed of two layers: first, an alluvial
sediments layer at the top, having an average thickness of about
21 m; second: Burdigalian sandstone which forms the two
supports of the dam, it is a transgressive sandstone formation
on phylladic basement. The transgression is characterized by
a series of conglomerate, composed of few meters of
puddingstone locally coarse, and then follows fine sandstone,
siltstone/pelites in alternation. The conglomerate series
thickness ranges between 15 and 20 m. Above
conglomerate, Burdigalian becomes fairly homogenous sandstone and
stratified in layers; the joints of stratification dip toward the
North, toward downstream according to the flow direction
of the river with a dip of 15°–20°.
Geometry and soil properties of the studied earth dam
Every slope soil is subjected to shear stresses on
internal surfaces and its stability is highly correlated with its
geometry. The influence of geometry variation on
stability of earth dam has been the subject of many studies;
Yuzhen and Zhang [
] investigated the 3D slope stability
Fig. 2 Outcrops extension of
lithofacies in the dam site
under effect of geometrical characteristics and topography
of the canyon site of core thickness on stability, Vrubel
and Říha [
] evaluated the safety factor for several small
dams shape and Khanna et al. [
] studied the influence of
geometry of an earth dam on its slope stability.
Figure 3 shows schematic cross section of the Souk
Tleta earth dam and its foundation layers considered in
this paper. Table 1 illustrates the geometrical
characteristics of the dam. The study was conducted at the cross
section of the dam with the largest section, i.e. with the
Souk Tleta dam will be constructed with locally
available materials. Material deposits of five different areas
near the dam site are investigated for construction purpose.
The volume of aggregates required for the construction
of the Souk Tleta dam is approximately 1,173,000 m3.
The construction materials need to have the correct
physical properties to permit the dam safety. Laboratory and
in situ tests were performed to discover the physical and
mechanical properties of 62 selected core samples taken
from boreholes. To achieve this, 38 boreholes, with a total
length of 977 m were drilled on the 5 areas.
To assess the condition of the dam foundations,
Laboratory experiments were carried out on 32 samples to
determine the physical and mechanical properties. In this
work, 19 boreholes with 870 m length were drilled on the
The computational parameters φ and C of
Mohr–Coulomb model and elastic modulus E for all dam materials are
determined through the triaxial compression test. Poisson’s
ratio ν is determined through engineering experience.
The permeability k of dam materials is measured in
laboratory from falling head permeability tests. In dam
foundation, Water Pressure Tests (WPT) are used to determine
the permeability of the rock mass. The laboratory tests are
carried out in the Laboratory of Geomaterials, Environment
and Development (LGED).
Clay core 18
Sandstone fill 1 19.5
Sandstone fill 2 21
Upstream backfill 16
Rip rap 21
The investigations were performed to characterize the
materials and determine the relevant parameters for slope
stability analyses. The necessary input material properties
used for the slope stability evaluation are summarized in
Table 2. Only the soil mechanics parameters and properties
concerning the slope stability analysis of the body of the
Souk Tleta earth embankment dam are given.
Stability analysis and loading conditions
Finite element method has been widely accepted for the
analysis of slope stabilities. To reflect the behavior of Souk
Tleta dam in this study, PLAXIS 2D finite element software
is used with Elastic-perfectly plastic Mohr–Coulomb model
for all layers of dike and foundation materials.
PLAXIS computer program is applicable to many
geotechnical problems, including stability analysis calculations
and was used for the slope stability analysis of earth dams in
numerous publications [
12, 17, 24, 26
] and others.
Stage of construction has a significant effect on stress
distributions and deformations; therefore, analysis is carried
out in different stages to reflect the construction conditions.
In the finite element method, a continuum is divided into
a number of elements; each element consists of a number
of nodes. The slope was modeled in the input module of
PLAXIS, based on 15-nodded elements in a plane strain
model. The finite element mesh generated in the simulation
of slope stability analysis is a very fine mesh to obtain the
least possible factor of safety (FOS), and consists of (12983)
15-nodded triangular elements. The vertical boundaries are
free to move, whereas the horizontal boundary is considered
to be fixed.
The finite element mesh generated in the simulation of
slope stability analysis is a very fine mesh to obtain the
least possible factor of safety (FOS). It consists of (12,983)
15-nodded triangular elements and 1587 elements which
have an average size of 8.915 m. The vertical boundaries
are free to move, whereas the horizontal boundary is
considered to be fixed.
The 2D view for the finite element mesh of the dam and
its surrounded soil mass is illustrated in Fig. 4.
Two conditions of reservoir filling were examined, as
Right after construction condition
The calculation for the analysis of the dam after construction
is divided into alternate construction phases until the end of
construction. The critical condition to be analyzed is at the
completion of embankment dam construction but prior to
filling with water.
Cases of steady‑state seepage conditions
The FE stability analysis with Plaxis 2D and steady state
seepage analysis was conducted for Souk Tleta embankment
dam for low and high water levels in the river. Reservoir
impoundment is carried out gradually over several phases
– The minimum water level, corresponding to the
minimum stored water level (88 m ASL).
– Normal water level (122 m ASL).
– The highest water level (flood level: 125 m ASL).
Slope stability analysis results and discussion
The safety factor was assessed for the dam cross section of
the greater height and computed using the ‘c − φ
reduction’ procedure. For each load case of steady state condition,
appropriate slope stability analysis is computed based on
shear strength reduction method employed with the use of
finite element method.
Two-dimensional program Plaxis 2010 [
] computes the
factor of safety as the ratio of the available shear strength
to the strength at failure by summing up the incremental
multiplier (Msf) as defined by:
shear strength at failure
= value of
Typical minimum acceptable values of factor of safety are
about 1.3 for the end of construction and multistage loading,
and 1.5 for normal long-term loading conditions.
The values of factor of safety listed in Slope Stability
engineer manual from US Army Corp EM 1110-2-1902 [
provide guidance but are not prescribed for slopes other than
the slopes of new embankment dams.
End of construction condition
The end of Construction Condition is a critical stage for
the upstream and downstream slopes. In this first stage, the
stability analyses have been performed for different upstream
and downstream slopes for the purpose of optimizing the
volume of the dam body and materials. The analyses have
been performed for the most critical cross-section taken
along the highest part of the dam.
The result of upstream slope analysis under
end-of-construction condition is similar to that for downstream slope.
Numerical analysis of unsaturated dam in the end of
construction gives a safety factor of 1.62.
The total displacements are very important when studying
slope stability problems. For this study, the total settlement
which is computed for the end of construction stage can be
seen in Fig. 5.
The dam body undergoes a maximum displacement of
24 cm which is due to dead load of the dam and the
settlement of different zones and foundation of the structure. The
calculation of the displacements during this step is
necessary because the imposed loads are very high and can lead
to instability and even to a slope failure.
Fig. 5 Total displacements in
the dam right after construction,
FS = 1.62
As the dam rests on alluvial sediments, the settlements
of the crest increased by the compression of the
foundation materials produced by the weight of the dam. Usually,
only the dead load of the dam acts during the construction
period until the end of its construction. The sequence of
constructing the embankment dam, by placing compacted
layers of material, causes settlements of its crest, slopes
and foundation (Fig. 5).
The minimum water level (88 m ASL)
Before reservoir filling analysis, all displacements
obtained from the construction model were set to zero.
This was done to exclude construction related
deformations and obtain accurate displacement created by the first
Following the construction of Souk Tleta
embankment dam, deformations occur during the first
reservoir impoundment period. The study of minimum water
level condition is justified by the fact that during the first
impounding, the dam experiences small deformations
(1 cm). Deformations occur at the upstream toe of the dam
at the level of 88 m and correspond to an establishment of
a new steady state of the dam led by both water and pore
pressures at the upstream.
When the water in the reservoir is at its lowest level,
total displacements in the dam are illustrated in Fig. 6.
Numerical analysis of dam for the minimum water level
shows a factor of safety equal to 1.62.
Normal water level (122 m ASL)
Throughout the service life of a dam, the Normal water level
is the level that is frequently reached and deformations can
occur in the embankment and its foundation especially when
the level undergoes fluctuations over the seasons alternating
wet and dry periods.
The impoundment modeling is divided into smaller
substages to enable a gradual increase of water level to be
simulated. When the storage reservoir filling reaches the normal
water level of 122 m ASL, the seepage line is at the same
level, and this is considered as a critical condition.
The rise of water level in the reservoir and seepage
through the dam body increase both pore water pressure
and weight of the dam. Displacements increase from the
bottom to the crest, the total displacements obtained for both
upstream and downstream are illustrated in Fig. 7, and the
factor of safety obtained for this condition is 1.54.
The highest water level (125 m ASL)
The highest water level can be caused by heavy rainfalls
and waves action. The Souk Tleta dam must be designed to
withstand exceptional floods that would cause the rising of
water level in the reservoir. This condition is considered as
critical in the service life of a dam, although for Algerian
dams this level is rarely reached.
To evaluate how resistant materials are to water flow, total
displacements obtained in case of steady state condition with
the highest water level are illustrated in Fig. 8.
Fig. 6 Total displacements in
the dam in minimum
steadystate water level of 88 m ASL,
FS = 1.62
When the reservoir filling reaches the highest level, the
lowest factor of safety of 1.52 is observed.
During construction, settlement rapidly increased with a
continuous increase in dam weight load. During reservoir
filling, settlement increased with water pressure, but the
deformation rate was slower than that during dam
construction. The settlement increased slowly and tended to stabilize
after reservoir filling. However, the displacement appeared
by the fill load can be compensated by filling more
materials (Fig. 8).
For the behavior of the dam after impounding,
displacements occurred by water pressure in the dam body and
alluvium foundation are observed. The maximum displacements
are 1, 6 and 2 for minimum, normal and highest water level
Factor of safety for all examined analysis conditions are
summarized in Table 3. The results show that the safety
factor of the dam decreased along with water level increasing
in the reservoir. The Factor of Safety values under static
condition are found to be greater than 1.5, which means the
slope is safe under static condition.
The aim of the present study was to examine numerically the
slope stability of Souk Tleta earth dam via the shear strength
reduction method with the use of PLAXIS two dimensional
software. The stability for each load case combination of the
dam was expressed via a safety factor.
Fig. 8 Total displacements in
the dam in steady-state high
water level of 125 m ASL,
FS = 1.52
Factor of safety
Analyzing the static simulation of Souk Tleta dam using
the strength reduction principle, displacements and
corresponding safety factor are obtained for both end of
construction and reservoir filling conditions.
The study was performed on the highest profile of the
zoned embankment dam. The dam body and its foundation
parameters used for the analysis were determined based on
laboratory and in situ test results. Using these parameters,
slope stability was conducted.
The total displacements are very important when studying
most of geotechnical problems. The analysis results
indicated that the displacements occurred in the dam body and
in the alluvium foundation layer are the largest at the end of
the construction. The displacements are mainly caused by
the fill materials load which can be compensated by filling
The stability of the dam body at the end of construction is
highly related to fill strength parameters obtained from site
geotechnical investigations. It is particularly recommended
that laboratory tests to be performed in accordance with real
The construction materials must be selected very
carefully. This selection of materials allows composing the dam
of homogeneous zones. It is also necessary to mention that
maximum compaction of material layers gives maximum
strength to the dam and minimum permeability to the
On the other hand, the analysis results revealed that after
the dam construction completion, lower displacements
occurred in the dam body and foundation by impounding.
The reservoir filling makes the upstream side of the dam
saturated, and causes its uplift according to Archimedes’
The process of filling induces also settlements, as far as
water causes movements of individual particles and further
compaction of the dam materials.
Finally, it is worth mentioning that the behavior of Souk
Tleta dam in its largest cross section was reasonable in term
of displacements at the different conditions. The slope
stability is controlled by the shear strength of the dam materials
and the foundation.
Factor of safety presents the main key for the slope
stability analysis. The safety factor evaluated using PLAXIS is
found to be greater than 1.5 for all studied conditions which
means that the dam slopes are stable under static conditions.
It can be concluded that the soil properties chosen for the
construction of the dam are adequate and provide relatively
high factor of safety which means less risk of failure.
The stability criteria have been well satisfied with the
designed shape of the dam body during and at the end of
construction and also for different water level conditions.
The numerical results show that the strength reduction
method used in 2D finite element method is very effective in
capturing the progressive failure induced by reservoir dead
load and water level fluctuations.
In view of the obtained results, when studying the
problems related to slope stability in earth dams, it is
recommended that inspections should be carried out on the dam
body during its service life, so that the results serve to assess
the accuracy and reliability of the calculation approaches.
According to the Algerian Earthquake Regulations
RPA99 version 2003 of Algeria, the site of Souk Tleta dam
is situated in a zone known as moderate to weak
seismicity. Based on this information, a static study of the slope
stability of the dam was carried out. This does not prevent
the completion of this work by a dynamic study taking into
consideration the data of the largest earthquake recorded
in north Algeria.
Similarly, to get closer to reality, a numerical analysis
with plaxis 3D can be proposed to understand the effect of
the third dimension and compare its FOS and deformations
results to those obtained from the 2D analyses.
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