Stability Assessment of a Heavily Jointed Rock Slope using Limit Equilibrium and Finite Element Methods

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1 Indian Geotechnical Conference 2017 GeoNEst December 2017, IIT Guwahati, India Stability Assessment of a Heavily Jointed Rock Slope using Limit Equilibrium and Finite Element Methods Aswathi CK Amalesh Jana Arindam Dey Sreedeep S Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati aswathi@iitg.ernet.in; janaaamalesh@gmail.com, arindamdeyiitg16@iitg.ernet.in, srees@iitg.ernet.in ABSTRACT Equivalent continuum model considering homogeneous system of reduced rock mass strength parameter derived from Geological strength index, is very useful to predict the stability of heavily jointed rock slope where incorporation of all joints requires high computational efficiency. Selection of an appropriate method of stability analysis is an important task and effort should be given to understand their failure mechanism which resembles the actual field instability. Detailed study of working principles of two most common methods, LEM and FEM with reference to the stability analysis of a rock slope is performed. FEM analysis is performed using shear strength reduction(ssr) technique to find the factor of safety value without assuming any predefined failure surfaces. Since SSR does not need to assume failure shape and location, failure mechanism is well simulated by FEM. Among all the Limit Equilibrium methods Morgenstern Price method satisfies all the equilibrium methods and can be used for any shape of failure surface and failure slip surface from the FEM analysis is in fair agreement with that obtained from this method. The present study reports about the stability analysis of a typical cut slope along a road way in Rudraprayag, Uttarakhand, India. Keywords: Limit equilibrium methods; Finite element method; Factor of safety; Jointed rock slop: Shear strength reduction technique 1. Introduction Failure mechanism of a heavily jointed rock slope is guided by a general failure surface which might be developed through intact rock and joints. In order to perform stability analysis of a heavily jointed rock slope, incorporation of all the joints in numerical model, require immense computational efficiency. Under such cases, equivalent continuum model (Hoek et al. 2002) considering isotropic, homogeneous system of reduced rock mass strength parameter derived from Geological strength index, is useful to predict the stability of rock slope. However, selection of an appropriate method of stability analysis is an important task and effort should be given to understand their failure mechanism which resembles the actual field instability. Stability analysis considering different types of failures can be performed using different techniques. Each of these procedures accounts for different assumptions to achieve the factor of safety values. The aim of the study is to compare the FOS values and the corresponding failure mechanism obtained from LEM and FEM techniques, considering equivalent continuum model. Limit equilibrium method (LEM) and finite element methods (FEM) are the two most common methods used in the geotechnical computations. Detailed study of working principles of LEM and FEM with reference to the stability analysis of a rock slope along NH- 109, Uttarakhand, India, is presented in this paper. Two software packages of Rocscience, Slide and phase 2 are used for the LEM and FEM analysis respectively. 1.1 Study area The study area lies along NH -109 in Uttarakhand, India, which runs from Rudraprayag to Kedarnath, is situated at the confluence of the Mandakini and the Alaknanda rivers. As transportation and communication in this region is entirely dependent on the NH-109 road constructed in the hilly area, Stability analysis is essential to minimize the losses due to slope failure. The highest and lowest elevations in this area are 1650 and 600m respectively. The study area occurs in the Garhwal Group of the Lesser Himalaya, which comprises diverse rock types of Paleoproterozoic to Mesoproterozoic ages. Rudraprayag metavolcanics

2 Paper title type rock is selected for this study. Rudraprayag metavolcanics are massive and jointed in rock mass with quartz, pyroxene, plagioclase, epidote as mineral constituents. Slope geometry of 30 m height and 65degree slope angle is used in this case study. (R K. Umrao et al.2011) (a) (b) Figure 1 (a) Location map of study area (b) A view of exposed hill-cut slopes along NH-109 as well as the slope at the banks of the mandakini river 2. Background of the study Stability of rock slopes is mainly influenced by structural discontinuities present in the rock such as bedding plane, schistosity, foliation, joint, cleavage, fracture, fissure, crack, or fault plane etc. The common types of failures in rock slopes are circular, non- circular, planar and wedge failures. Circular and non-circular failure occurs in heavily jointed or fractured, and highly weathered rock slopes. Wedge, planar and toppling failures are influenced by the orientation and spacing of joints. Selection of an appropriate method of stability analysis is an important task and effort should be given to understand their failure mechanism which resembles the actual field instability The conventional limit equilibrium and Kinematic analysis and numerical methods are the common methods of stability analysis. Numerical modelling techniques have been widely used and is divided into three approaches continuum, discontinuum and hybrid methods. In case of heavily jointed rock slopes a general failure surface is developed through intact rock and joint, incorporation of all the joints is a very difficult task It practically impossible to explore orientation of all joints and to find out all the mechanical and geological characteristics and implementing them in numerical model. In that case Equivalent continuum model considering homogeneous system of reduced rock mass strength parameter derived from Geological strength index, is very useful to predict the stability. Equivalent continuum model considers rock slope as continuum mass without any joints and effect of discontinuity is introducing by reducing strength and properties of intact rock into rock mass. 2.1 Evaluation of the rock mass properties The geo mechanical properties of intact rock obtained from the laboratory test are used to obtain corresponding rock mass properties. Roc Lab software program is used to obtain the rock mass strength parameters which is based on generalized Hoek Brown failure criterion. Hoek Brown criteria calculates rock mass strength properties based on the following equation (Hoek et al. 2002). (1) Where, σ 1 and σ 3 are major and minor principal stresses at failure, σ ci is the uniaxial compressive strength of the intact rock the reduced value of the material constant and is given by, (2) s and a are constants for the rock mass given by (3) / / (4) GSI is the Geological strength index, D is the Disturbance factor which depends upon the degree of disturbance to which the rock mass has been subjected by blast damage and stress relaxation. The value of the D varies from 0 for undisturbed rock mass and 1 for the disturbed rock mass. Since there are some difficulties in applying SSR technique directly in Hoek- Brown criteria in FEM analysis, we use equivalent Mohr-Coulomb envelope to get the rock mass properties Mohr-Coulomb Criterion The equivalent Mohr-Coulomb parameters, cohesion and friction angle are obtained by fitting a line to the curve generated by the equation 1 as shown in the figure 2 ˈ sin 6, 2126,,, ( a1), ci[(1 2 as ) (1 am ) b 3n]( smb 3n) c, ( a1) (1 a)(2 a) (1 (6 amb( smb 3n) ) / (1 a)(2 a) Where,,, / Here the range of minor principal stress is defined by, 2

3 Where, is the upper limit of confining stress over which the relationship between the Hoek Brown and Mohr-Coulomb criteria is considered. Figure 2. Mohr-Coulomb curve fitting 3. Methodology The basic purpose of slope stability analysis is to assess the current state of vulnerability of a slope against a potential failure. Such an evaluation is presented in terms of the Factor of safety, provided in terms of the mobilized shear strength along the most probable failure envelope. In this study, Limit equilibrium analysis of the slope was performed using ordinary, Bishop s simplified, Janbu s simplified, Janbu s corrected, Spencer and GLE/Morgenstern Price methods for both circular and non-circular slip surfaces. FEM analysis is performed using shear strength reduction(ssr) technique to find the factor of safety value without assuming any predefined failure surfaces. 3.1 Limit Equilibrium Method of analysis The limit equilibrium method (LEM) is a traditional method of analyzing slope stability that is used to estimate Factor of safety (FOS) considering static force and moment equilibrium above a predefined failure surface based on the method of slices. The material above the slip surface is divided into different vertical slices. The stability of the material above the slip surface is analyzed by considering the static equilibrium of the individual slices and the entire equilibrium of the failing slope. Several methods are available to perform Limit equilibrium analysis, each of these procedures accounts for different assumptions to achieve the factor of safety values. Fellenius (1936) introduced the first method which satisfies the moment equilibrium for a circular slip surface, but neglects both the interslice normal and shear forces. Bishop s method (1955) satisfies moment and vertical force equilibrium. Janbu s Generalized method (1954) can be used for any slip surfaces which considers interslice normal forces but neglects the shear forces. Lowe Karafiath s method satisfies only force equilibrium. Corps of Engineers method considers both interslice normal and shear forces and satisfies only force equilibrium Morgenstern Price method /GLE procedure and Spencer s method satisfies all the equilibrium conditions and can be used for both circular and non -circular failure surfaces. Slide software of Rocscience is used to perform the Limit equilibrium method of analysis in this case study. Equivalent Mohr coulomb strength parameters obtained from Roc Lab are used for the analysis. 3.2 Finite element analysis The factor of safety computed in LEM is not uniquely determined, because of the different assumptions made for the slip surface and the result may not be reliable for nonhomogeneous and anisotropic conditions. Finite element analysis is a better solution in such cases which considers the interrelationship of forces, stress, strain and displacements. In this case study Phase 2 software of Rocscience is used for numerical modelling which is based on FEM using shear strength reduction(ssr) technique. The shear strength reduction technique is used widely in numerical modelling which gives better results compared to the conventional methods. SSR does not need to assume failure shape and location, failure mechanism. SSR automatically satisfy all the equilibrium conditions and the factor of safety of a slope can be computed by reducing the rock shear strength based on the equation 7 and 8, until the failure occurs. Actual shear strength properties cohesion (c) and internal friction angle ( ) are reduced for each trial using equations 7 and 8. The trial factor of safety is gradually increased until the slope fails and the shear strength reduction factor at failure is taken as the factor of safety value. (7) (8) 3

4 Paper title In this case study numerical modelling is performed in rock slope considered as continuum mass without any joints and effect of discontinuity is introducing by reducing strength and properties of intact rock into rock mass to get equivalent Mohr coulomb strength parameters. The entire slope model is divided in to six nodded finite elemental mesh and deformation at each nod is calculated. Roller type boundary condition is given at the right boundary and base of the model is restrained against vertical and horizontal movement. 3.3 Material properties To perform numerical simulation, intact rock properties reported in Singh R et al. (2014) Table 1. Intact rock properties UCS(MPa) GSI Mi D Ei Unit weight (KN/m 3 ) Table 2. Rock mass properties Cohesion Friction (KPa) angle Tensile Strength (KPa) Here the lower limit ( ) and upper limit(, ) of confining stress over which the relationship between the Hoek Brown and Mohr-Coulomb criteria is considered are MPa and MPa respectively. 4. Important Outcomes The minimum FOS value obtained from the LEM is 2.34, as which is predicted by Morgenstern-Price methods using auto refine search algorithm to generate non-circular slip surface as shown in figure 3. Shear strength reduction technique incorporated in FEM predicts non- circular critical slip surface with a critical SRF of It can be seen from the Fig. 4. that the failure slip surface shape from the FEM analysis is in fair agreement with that obtained from LEM based on Morgenstern Price methods 5. Conclusions Among all the limit equilibrium methods Morgenstern Price methods, predicts minimum FOS and gives better result for non-circular slip surface. FEM, using shear strength reduction technique predicts the critical slip surface without assuming any predefined failure surface. The result shows that the FOS obtained from FEM analysis is less than that obtained from LEM. In case of heavily jointed rock slopes a general failure surface is developed through intact rock and joint. Equivalent continuum model reduces the complexity in implementing all the joint in a heavily jointed rock slope. Since SSR does not need to assume failure shape and location, failure mechanism is well simulated by FEM. This enhances the applicability of FEM equivalent continuum model to predict stability of heavily jointed rock slope. References Hoek, E., Carranza-Torres, C. and Corkum, B. (2002) Hoek-Brown criterion-2002 edi., Proceed. of the NARMS-TAC Conf., 10 July 2002, Toronto, Can. 1, University of Toronto Press. Umrao, R.K., Rajesh S. and Singh T.N. (2014) Stability evaluation of road-cut slopes in the Lesser Himalaya of Uttarakhand, India: conventional and numerical approaches, Bull Eng Geol Environ., 73: Umrao, R.K., Singh, R., Ahmad, M. and Singh, T.N. (2011) Stability Analysis of Cut Slopes Using Continuous Slope Mass Rating and Kinematic Analysis in Rudraprayag District, Uttarakhand, Geomaterials., 1, Pain, A., Kanungo, D.P. and Sarkar, S. (2014) Rock slope stability assessment using finite element based modelling examples from the Indian Himalayas, Geomech. and Geoengg. Int. j., 9(3), Hammah, R.E. and Yacoub, T., A. (2005) comparison of finite element slope stability analysis with conventional limit-equilibrium investigation, Rocscience Inc., Toronto, Canada Fig. 3 Critical failure surfaces for LEM Fig. 4 Critical failure surfaces for FEM 4

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