finite element analysis of road cut slopes using hoek & brown
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Finite Element Analysis of Road Cut Slopes using Hoek & Brown
Failure Criterion
A. KAINTHOLA, P. K. SINGH, A. B. WASNIK, M. SAZID and T. N. SINGH Department of Earth Sciences, Indian Institute of Technology Bombay, Mumbai, India-400076
Email: [email protected], [email protected], [email protected], [email protected],
Abstract: The failure of cut slopes along highways can be disastrous, especially along the hills. The slope collapses
can lead to huge economic losses as well as puts human life in grave danger. The state highway-72, connecting the
Poladpur town to Mahabaleshwar, is infested with problem of slope instability. The SH-72 remains closed during
the monsoon season. For the first time a study has been carried to assess the health of cut slopes along the highway.
A finite element code has been used for seven chosen road sections. The results throw light on the stability of slopes
during both dry and saturated conditions.
Keywords: Finite element,Hoek and Brown failure criterion, Road cut slopes, Mahableshwar
1. Introduction:
The hill stations are a favored tourist destination around
the world and a major source of revenues for local
development. The approach to these hilly areas is
mainly roads, which isexcavated along the hill slopes.
These cut slopes pose serious problem of collapse due
toheavytraffic and disturbance due to construction of
civil structures viz. road widening. These slopes are
hardly constructed after proper scientific investigation
and reckless excavation resulted vulnerability in slope
instability. Failures of these cut slopes, both man-made
and natural; include rock falls, overall slope instability
and landslides (Sarkar& Singh, 2010). The consequence
of such failures ranges from direct costs of removing the
failed rock material and stabilizing the slope to a wide
variety of indirect costs viz. damage to vehicles and
injury to passengers on highways, traffic delays,
business disruptions, flooding and disruption to water
supplies where rivers are blocked by slides (Hoek&
Bray, 1981). The chances of a slope failure is increased
many folds along the road cut which disturbs the
already fragile dynamic and static stress distribution
along the slope mass. The displacement of material
during excavation affects the geotechnical and geo-
hydrological characteristics of the hill slopes, markedly
reducing the shear strength of the slope forming
material to its residual or 'ultimate ' strength. Hence,
engineering works undertaken on them could disturb the
road cut slopes, which are in a state of near limiting
equilibrium. The day-by-day increase in vehicle traffic
volume also further aids to the instability of the road cut
slopes.
Mahabaleshwar is one of the important tourist
attractions in Maharashtra, India, with its peculiar
climate and aesthetic locales. The approach to the town
is made up of 41.3 Km long road (SH-72) excavated on
the hills composed of basalt flows, red boles and
laterite.The 17 Km stretch from Pratapgarhroad
intersection is particularly vulnerable to road cut
collapses due to presence of weak laterites, red boles
and weathered basalts composing the slopes (Figure 1).
These geo-materials undergo significant reduction in
strength when they encounter water. The area having a
high rainfall of 1121 mm per year, witness a number of
slopes failures along the road cuts during the monsoon
leading to the temporary closure of the highway. This
incessant menace of slopes failures along the road cut
puts the lives and properties of travellers in jeopardy. So
far, no study on slope stability has been done in this area
and hence the present study aims at the finite element
method (FEM) analysis of these cut slopes along the
17.4 Km vulnerable tract. The study has been conducted
for both the dry and saturated conditions to assess its
more critical stability. Seven locationswere chosen for
the FEM safety analysis with their distinct geometry and
material composition based on field observation and
record. The study employs Geological Strength Index
(GSI) and Hoek and Brown failure criterion for the
estimation of few input parameters for the FEM analysis
(Hoek, 2000; Hoek et al., 2002). The analysis divulges
information on the deformational mechanics of the cut
slopes as well as the effect of water ingress on the
material strength and the overall slope stability.
1101 A. KAINTHOLA, P. K. SINGH, A. B. WASNIK, M. SAZID and T. N. SINGH
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 05, No. 05, October 2012, pp. 1100-1109
Figure 1: Google Image of the Study Area with Marked Locations
2. Geology of the Study Area:
The study area falls under the western Deccan plateau
province in India. The Deccan traps in Western India
are the largest accretion of continental lava flows
covering an area of 518,000km2 (Beane, et al.,
1986).Mahabaleshwar area is composed of well exposed
flows of Wai sub-group (Figure 2). The Wai-group
consists of Poladpur formation at the base, Ambenali
formation in the middle and the topmost
Mahabaleshwar formation (Table 1). There is reported
that the area have 41 to 47 flows, with a total thickness
of approximately 1150m (Konda, 1971; Najafi et al,
1981). Najafi et al. (1981) classified Mahabaleshwar
area into three distinct formations on the basis of trace
element geochemistry.
Table 1: Stratigraphic Sequence of Wai Sub-Group
(after K.V. Subbarao, M. S. Bodas, S. F. R. Khadri and
J. L. BEane, 2000,)
Formation Field Characteristics
Mahabaleshwar
Well defined, large and
simple flows, oxidised
flow tops/ lateritic. Well
preserved bole horizon
Ambenali
Well defined, large and
simple with red,
oxidised flows. Presence
of Bole horizons.
Poladpur
Well defined, large and
simple plagioclase
phyric flows with fine
grained matrix.
They have concluded that the Mahabaleshwar and
Poladpur formations show evidences of crustal
contamination, while the Ambenali is relatively
uncontaminated and olivine rich. Nine red bole marker
beds are recognized in Poladpur-Mahabaleshwar
horizon besides one green bole layer. These red bole
horizons are more prominent in the Ambenali and
Mahabaleshwar formations. Mahabaleshwar formation
at upper reaches shows marked
laterization(Babita&Jadhav, 2010). The presence of
these bole horizons is critical for cut slope stability.
3. Field Investigation and Geo-mechanical
Classification:
An extensive field investigation was carried out to
assess the geomechanical properties of the road cut
slopes along 17 km patch of the state highway-72 from
Pratapgarh road intersection till the Mahabaleshwar
town. Seven vulnerable road sections (M1- M7) were
identified for stability analysis (Figure 1). Location M1
and M2 are 8m to 10m high steep slopes, composed of
lateriteandare situated near Mahabaleshwar along Sh-72
(Figure 2). LocationM3 is 15 m high vertical slope
composed of 15 m weathered basalt having a 30cm
thick red bole layer (Figure 3). Location M4 and M5 are
also steep cut composed of fresh severely jointed basalt.
Slope M5 is underlain by 1.8cm thick red bole layer,
which tapers in the direction of Mahabaleshwar. The red
bole has a varying thickness at the location ranging
from 0.5m to 2.5 m (Figure 4). Slopes M6 and M7 are
composed of highly decomposed weathered basalt. The
original discontinuity pattern is preserved along these
slopes though they have undergone extreme level of
weathering.
1102 Finite Element Analysis of Road Cut Slopes using Hoek & Brown Failure Criterion
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 05, No. 05, October 2012, pp. 1100-1109
Figure 2: Geological Map of the Study Area (Modified After Choudhary, B., Jadhav, G., (2010)
3. Field Investigation and Geo-mechanical
Classification:
An extensive field investigation was carried out to
assess the geomechanical properties of the road cut
slopes along 17 km patch of the state highway-72 from
Pratapgarh road intersection till the Mahabaleshwar
town. Seven vulnerable road sections (M1- M7) were
identified for stability analysis (Figure 1). Location M1
and M2 are 8m to 10m high steep slopes, composed of
lateriteandare situated near Mahabaleshwar along Sh-72
(Figure 2). LocationM3 is 15 m high vertical slope
composed of 15 m weathered basalt having a 30cm
thick red bole layer (Figure 3). Location M4 and M5 are
also steep cut composed of fresh severely jointed basalt.
Slope M5 is underlain by 1.8cm thick red bole layer,
which tapers in the direction of Mahabaleshwar.
Figure 3 (a & b): A View of Mahabaleshwar Field along SH-72
Figure 4: Jointed Basalt Overlying Red Bole Layer
along SH-72, Mahabaleshwar
The red bole has a varying thickness at the location
ranging from 0.5m to 2.5 m (Figure 4). Slopes M6 and
M7 are composed of highly decomposed weathered
basalt. The original discontinuity pattern is preserved
along these slopes though they have undergone extreme
level of weathering.
The rock mass strength parameters were obtained using
the Hoek- Brown (HB) failure criterion aided by the
laboratory tests on the samples. The failure criterion
allows for the reliable assessment of rock mass strength
parameters. The HB failure criterion employs intact
uniaxial compressive strength ( , GeologicalStrength
Index (GSI),the joint surface property and the
disturbance factor,D(Marinos et al, 2005 andLiet
1103 A. KAINTHOLA, P. K. SINGH, A. B. WASNIK, M. SAZID and T. N. SINGH
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 05, No. 05, October 2012, pp. 1100-1109
al.,2008).For fewsamples, point load tests were used for
the estimation of their compressive strength, where
required size and sample were not obtained (Singh et
al., 2012). The Hoek& Brown failure criterion can be
expressed as:
Where,
are major and minor effective principal
stresses at failure.
is the uniaxial strength of intact rock.
Figure 5: Relationships between Major and Minor
Principal Stresses for Hoek-Brown and Equivalent
Mohr-Coulomb Criteria (Hoek, Wood and Shah, 1992).
,
α =
The HB parameters were converted to equivalent Mohr
coulomb parameters. This is done by fitting an average
linear relationship to the curve generated by solving
equation for a range of
minor principal stressvalues which are defined by σ1,σ3,
σ3max as shown inFigure 5.The fitting process involves
balancing areas above and below the Mohr-Coulomb
plot which results in the following equations for the
angle of friction (ϕ’) and cohesive strength (c’) (Hoek-
Brown, 2002).
Where, =
The calculations for the conversion of HB rock mass
parameters into equivalent Mohr Coulomb parameters
were derived using the Rocscience's freeware
RocLab(RosScience, 2012). The material properties
obtained for simulation are given in table 2 and 3 for
dry and saturated conditions respectively.
All the tests for geotechnical parameters were
conducted in the laboratory for the dry and saturated
conditions, while their GSI was estimated based in field
observation and information’s. The mi valueswere given
to the rock type based on the recommendations by Hoek
(Hoek-Brown, 2002). These strength parameters were
used as input indexes for the numerical model for the
analyses of cut slopes.
Table 2: The Averaged Strength Parameters (dry condition)
Location
Uniaxial compressive
strength σCi (MPa) GSI
Ei
(GPa)
Cohesion
(MPa)
Phi (φ)
(deg)
Shear stress
σT(MPa)
M1 5 25 5 0.158 23.07 0.002
M2 3.5 25 4.5 0.110 23.07 0.001
M3 8 30 8 0.282 24.60 0.004
M4 54 55 36 3.554 38.01 0.091
M5 53 45 38 3.088 34.99 0.043
M6 5 20 2 0.138 21.49 0.001
M7 4 25 3 0.189 22.4 0.0014
1104 Finite Element Analysis of Road Cut Slopes using Hoek & Brown Failure Criterion
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 05, No. 05, October 2012, pp. 1100-1109
Table 3: Averaged Strength Parameters (Wet Condition)
Location Uniaxial compressive
strength σCi(MPa) GSI
Ei
(GPa)
Cohesion
(MPa)
Angle of
internal friction
(φ)(deg)
Shear stress σT
(MPa)
M1 3 25 4 0.095 23.07 0.001
M2 2.5 25 3.5 0.076 22.25 0.001
M3 6 30 5.5 0.211 24.60 0.003
M4 46 55 24 3.028 38.01 0.077
M5 47 45 28 2.688 34.99 0.037
M6 4.1 20 1.7 0.118 21.1 0.001
M7 3.2 25 2.3 0.169 21.4 0.001
4. Finite Element Analysis:
There are numerous tools to gauge into health of a slope
viz., physical methods, empirical methods,
mathematical methods and numerical methods (Verma
et al., 2011; Sarkar& Singh, 2008). The numerical
methods allow the analysis of slope stability problems
involving complexities related to geometry, material
anisotropy and nonlinear behavior (Li et al, 2009;
Kainthola et al., 2011). They simulate the physical
behaviorof earth material using computational tools
without the need to simplify the problem (Alkasawneh
et al., 2008).Numerical methods such as the Finite
Element Method (FEM) have now been successfully
applied to slope stability analysis over the years. It is
now assumed as one of the best alternative over
traditional limit equilibrium methods, because of less
number of prior assumptions required for the solution
(Hammah et al., 2009; Kainthola et al., 2012). A
primary advantage of FEM is their versatility i.e., they
can model a broad range of continuous and
discontinuous rock mass behaviors whether it is planar,
rotational or wedge type failure. Though most FEM
codes can only model small displacement but it can
include material heterogeneity, non-linear behavior, as
well as complex boundary conditions (Eberhardt, 2003).
The gravity increase method (Swan &Seo, 1999) and
strength reduction method (Matsui & San, 1992)are the
most widely used methods to estimate the factor of
safety (FOS) of a slope. One of the most common
methods applied in calculating factor of safety along cut
slopes is through Shear Strength Reduction (SSR)
approach. The Shear Strength Reduction technique in
the finite element method involves successive reduction
(by some factors, called strength reduction factor, SRF)
in the shear strength of the slope forming material until
it fails, which is indicated by the non-convergence to a
solution of the finite element model (Griffiths and Lane,
1999).
FF
c
F
'' tanφτ+=
Where τ is the shear strength of the material and F is the
strength reduction factor (SRF). The approach can be
used for materials following both the linear Mohr-
Coulomb strength criteria and non-linear generalized
Hoek-Brown criteria (Hammah et al, 2002). The terms
SRF and FOS have been used interchangeably
henceforth in this article.
The present analysis was carried out in a finite element
code for the seven sections along the 17 km patch of
SH-72. The geometry ofFE model created for the seven
slopes is based on the fielded inspection of the cut
slopes (Figure 6). The effective slope length, pertaining
to the collapse hazard has been considered for the
analysis. Theslope models have been uniformly
discretized using a four noded quadrilateral mesh with
1200 elements to fasten up the calculations (Cook et al.
1972). Only gravity induced stresses was applied on the
model. The analysis was carriedout twice to gauge into
the stability and deformational aspects under both dry
and saturated conditions. The data from laboratory as
well as field investigation was used as the input
parameter for the model. Initial HB failure parameters
were calculated which were converted into the
equivalent Mohr-Coulomb parameters to be used in the
model.
1105 A. KAINTHOLA, P. K. SINGH, A. B. WASNIK, M. SAZID and T. N. SINGH
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 05, No. 05, October 2012, pp. 1100-1109
Figure 6: FE Models for the Analyzed Cut Slopes
1106 Finite Element Analysis of Road Cut Slopes using Hoek & Brown Failure Criterion
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 05, No. 05, October 2012, pp. 1100-1109
Figure 7: FE Results for the Analyzed Cut Slopes Depicting Maximum Shear Strain Concentration along the Slope
5. Results and Discussion:
The problem of the landslides is ubiquitous along this
highway, which forces it to be halted during monsoon
season. To tackle this menace of slope failure the
17kmlong vulnerable patch of cutslopeswas analyzed in
a finite element code. The seven locations based on the
lithology and slope geometry were chosen for the
examination. The analysis was carried out for both dry
1107 A. KAINTHOLA, P. K. SINGH, A. B. WASNIK, M. SAZID and T. N. SINGH
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ISSN 0974-5904, Vol. 05, No. 05, October 2012, pp. 1100-1109
as well as saturated conditions for their FOS (Table 4).
The cut slope M1 composed of laterite was found to be
critically stable under the dry condition with an FOS of
1.21, while it showed prominent collapse under the
saturated conditions. Slope M2 was relatively stable
under the dry conditions while it was theoretically stable
under the saturated conditions. Slope M3, composed of
weathered basalt was critically stable under the dry
condition, while the introduction of water led to the
failure of slope in the FEM model. The cut slopes M4
and M3 were composed of hard basalts, which were
relatively stable under both dry and saturated
conditions, but deteriorate with time due to presence of
discontinuities. The cut slope M6, failed due to
reduction in strength in the FEM model, while it was
found to be stable under dry conditions. The cut slope
M7, near the road intersection to Pratapgarh, was be
stable under both dry and saturated conditions.
A study wasalso carried out to judge the deformational
characteristics of the slope. The strain generation along
the slope face was analyzed for both dry and saturated
condition at the critical SRF (C SRF) and an SRF higher
above the C SRF (Figure 8 & 9).
The highest strain was developed at the toe region in
both the cases. The strain generation was higher in dry
condition as compared to the saturated conditions due to
brittleness in the rock mass. The strain generated for
each slope was higher at an SRF above C SRF. This is
due to the drastic increase in stress above the C SRF
(Kainthola et. al., 2011).
Table 4: The FOS Calculated for the Cut Slopes.
Location
Critical
SRF/
FOS
(Dry)
Critical
SRF/
FOS
(Saturated)
M1 1.21 0.8
M2 1.48 1.01
M3 1.16 0.86
M4 2.33 1.6
M5 1.9 1.75
M6 1.09 0.94
M7 2.28 1.15
Figure 8: The Shear Strain Generation for the Dry Condition along the Slope Length for the Analyzed Cutslopes.
Figure 9: The Shear Strain Generation for the Saturated Conditions along the Slope Length for the Analyzed Cut
Slopes.
1108 Finite Element Analysis of Road Cut Slopes using Hoek & Brown Failure Criterion
International Journal of Earth Sciences and Engineering
ISSN 0974-5904, Vol. 05, No. 05, October 2012, pp. 1100-1109
For the saturated conditions,maximum strain was
accumulated for cut slope M6. The strain generation
was also found to depend on the slope geometry. The
FEM study is in agreement with the field conditions as
demonstrated by the recurrent failure of the cut slopes.
The strain generation for slope M6 at a FOS higher
above the critical FOS was highest, its value being,
0.003. This high value signifies the slope collapse at the
region, different for various studied slopes, depending
on the slope geometry.
6. Conclusion:
For the first time stability, study has been conducted for
the cut slopes in this region using the numerical
technique. A 17 km patch along the SH-72 was
analyzed with finite element code which is infested with
cut slope failures problems especially during the rainy
season. Seven locations were chosen for the
examination. Their FOS was calculated for both the dry
and saturated conditions. The cut slopes composed of
laterite and weathered basalt near Mahabaleshwar, were
found to be relatively stable in dry condition while they
demonstrated collapse and critical stability under
saturated conditions. The basalt cut slopes were rather
stable. Further works need to be done in this area for the
stability assessment of the jointed rock mass using
discontinuum codes.
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