Finite Element Analysis of Road Cut Slopes Using Hoek & Brown

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ISSN 0974-5904, Volume 05, No. 05

October 2012, P.P. 1100-1109

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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],

[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


simple with red,

oxidised flows. Presence

of Bole horizons.

Poladpur


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



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




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




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.




Figure 6: FE Models for the Analyzed Cut Slopes




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




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.




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.

References:

[1] Alkasawneh, W., Malkawi,A.I.H., Nusairat,J.H.

and Albataineh,N., (2008). A comparative study of

various commercially available programs in slope

stability analysis, Computers and Geotechnics, v.

35, 428–435

[2] Beane, J.E., Turner, C.A. and Hooper, P.R., (1986).

Stratigraphy, composition and form of the Deccan

Basalts, Western ghats, India, Bulletin of

Volcanology, v. 48, 61-83.

[3] Choudhary, B., Jadhav, G., (2010). Melt Inclusion

Geothermometric Studies of the Deccan Lavas

from Mahabaleshwar Section, Maharashtra, India:

A Reconnaissance, Origin and evolution of

Deep continental crust, Narosa publication, New

Delhi (ISBN:978-81-8487-055-8 ), 187-196.

[4] Cook R.D., Malku, D.S., Plesha, M. E., (1974).

Concepts and Application of finite element

analysis, Edition.3, New York, John Wiley & Sons.

[5] Eberhardt, E., (2003). Rock slope stability analysis-

Utilization of advanced numerical

techniques,Canada: Earth and Ocean Sciences,

University of British Columbia

[6] Griffiths, D. V. and Lane, P.A., (1999). Slope

stability analysis by finite elements, Geotechnique,

v. 49 (3), 387-403.

[7] Hammah, R.E. and Yacoub, T.E., (2009),

Probabilistic slope analysis with the finite element

method,RocscienceInc, 4th

US- Canada Rock

Mechanics symposium., June 2009.

[8] Hoek, E., and J. Bray (1981), Rock Slope

Engineering, Inst. of Min. and Metal., London

[9] Hoek, E., Carranza-Torres, C. and Corkum, B.,

(2002).Hoek-Brown criterion – 2002 edition. Proc.

NARMS-TAC Conference, Toronto, v. 1, 267-273.

[10] Kainthola, A., Verma, D., Singh,T. N.,(2011).

Computational Analysis for the Stability of Black

Cotton Soil Bench in an Open Cast Coal Mine in

Wardha Valley Coal Field, Maharashtra, India,

International Journal of Economic and.

Environmental Geology. v. 2(1), 11-18

[11] Kainthola,A.,Verma,D.,Gupte, S.S. and Singh,T.

N., (2011). A coal mine dump stability analysis-A

case study, International journal of Geomaterial, v.

1, 1-13.

[12] Konda, T., (1971). Deccan Basalts at

Mahabaleshwar, India. Contribution to Mineralogy

and Petrologyv. 32, 69-73.

[13] Li, A.J., Merifield,R.S. andLyamin, V., (2008).

Stability charts for rock slopes based on the Hoek–

Brown failure criterion, International. Journal of

Rock Mechanics.and Mining Science., v. 45, 689-

700.

[14] Li, L.C., Tang,C.A., Zhu,W.C. and

Liang,Z.Z.,(2009). Numerical analysis of slope

stability based on the gravity increase method,

Computers and Geotechnics v. 36, 1246–1258.

[15] Marinos, V., Marinos, P., Hoek,E., (2005). The

geological strength index: application and

limitations, Bulletin of Engineering. Geology and

Environment Journal., v. 64, 55-65

[16] Matsui, T., San, K., (1992). Finite element slope

stability analysis by shear strength reduction

technique, Soils Foundation; v. 32, 59–70.

[17] Najafi, S., Cox, K.G and Sukeshwala, R.N., (1981).

Geology and geochemistry of the basalt flows,

Deccan Traps, of the Mahad-Mahabaleshwar

section, India; In: Volcanism and related

provinces in other parts of the world, Geol.

Soc. of India, v. 3, 300-315.

[18] Rocscience, (2012).RocLabdownload.rocscience.

com/products/RocLab.asp.

[19] Sarkar, K., and Singh,T.N.,(2008). Slope stability

study of Himalayan Rock- A Numerical Approach,

International Journal of Earth Science. and

Engineering. 7-16.

[20] Sarkar, K. and Singh, T.N., (2010). Road cut

stability analysis along NH-22 in Luhri area,

Himanchal Pradesh, Rock Mechanics in Civil and

Environmental Engineering (Zhao,Labiouse,Dudt




and Mathier,Eds), Taylor and Francis

publication,659-662.

[21] Singh, T. N.,Kainthola,A.,Venkatesh, A., (2011).

Correlation between Point Load Index and Uniaxial

Compressive Strength for different rock types,

Rock Mechanics Rock Engineering 45(2):259–264.

[22] Swan, C.C., Seo, Y., (1999). Limit state analysis of

earthen slopes using dual continuum/FEM

approaches. Int. J. of Num. and Analytical Methods

in Geomechanics; v. 23, 1359–71.

[23] Subbarao,K.V. ,Bodas, S.F.,KhadriR. and

BEane,J.L.,2000, Field excursion guide to the

western deccan basalt province, Geological Society

of India, Penrose.

[24] Verma, D., Thareja, R..,Kainthola, A. and Singh, T.

N.,(2011). Evaluation of open pit mine slope

stability analysis, International Journal of Earth

Sciences and Engineering, v.4 (4), 590-600.

Finite Element Analysis of Road Cut Slopes Using Hoek & Brown

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