Variation of Failure Mechanisms of Slopes in Jointed Rock Masses with Changing Scale

This paper demonstrates the ability of Shear Strength Reduction (SSR) analysis based on the Finite Element Method (FEM) to model the scale effects of discontinuity networks on the stability and failure mechanisms of slopes in blocky rock masses. Through three examples, it shows how these mechanisms depend on joint network geometry and change with increasing slope height. Introduction Scale Effects and the Stability of Slopes in Rock Masses It has been long recognized in rock mechanics that discontinuities (geological structures) significantly influence the response of rock masses to loadings and excavation (Goodman et al, 1968, Manfredini et al, 1975, Cundall et al, 1975, Bandis et al, 1983). It has also been long observed from slope and other failures that this influence is not the same at different scales (excavations sizes). Generally, at smaller scales discontinuities exert greater influence on behaviour than do intact rock properties. In small slopes, failure mechanisms such as planar wedges, which are controlled by joints, are common. As the scale increases more complex mechanisms such as step-path failures and rotational shear failure, which combine failure along discontinuities with shearing through intact rock bridges, begin to occur. These complex mechanisms can follow overall curved paths that can be similar to those encountered in soils. Toppling and columnar flexural bending or buckling are other failure mechanisms that can occur with increasing slope scale. At intermediate and large scales, anticipation or prediction of the stability of rock slopes and the manner in which they can fail can be very difficult. This is because at such scales stability is affected by the strength and deformation properties of both intact rock and joints, the geometry and distribution of joints throughout a rock mass, and stress and groundwater conditions. Of the numerical methods used for the stress analysis today, the family of Discrete Element Methods (DEMs) and Discontinuous Deformation Analysis (DDA) have been considered to be the most wellsuited to the problems of blocky rock masses. Recently however, it has been demonstrated that the Finite Element Method (FEM) with explicit representation of discontinuities with joint elements is a credible alternative (Hammah et al, 2009, 2008 and 2007). This paper examines the ability of the FEM to capture the variation of factor of safety and failure mechanism of blocky rock mass slopes with scale. The paper will show that such modelling can help engineers to understand the behaviour of blocky rock slopes at different scales much better, and to more accurately predict failure mechanisms and factors of safety. Application of the Finite Element Method (FEM) to Problems of Blocky Rock Masses Due to the widespread availability of powerful desktop and laptop computers, the FEM with explicit modelling of the behaviour of individual joints can be used for practical engineering in blocky rock masses. This has also been facilitated by the development of techniques for generating networks of discrete fractures, and the development of the Shear Strength Reduction (SSR) method. SSR analysis (Dawson et al, 1999, Griffiths and Lane, 1999, Matsui and San, 1992) allows factors of safety of slopes to be calculated with numerical methods. Studies have confirmed the accuracy of the FEM-SSR technique in general and for the variety of failure mechanisms encountered in rock slope engineering (Dawson et al, 1999, Griffiths and Lane, 1999, Hammah et al, 2005 and 2007). Although FEM-based SSR analysis is an alternative to conventional limit equilibrium methods in many cases, its ability to readily combine slip along joints with failure through intact material offers several advantages in the modelling of blocky rock mass problems. The method can model the broad range of behaviours of slopes at different scales, from wedge sliding to toppling and rotational failures (Hammah et al, 2007). As well it can easily handle cases in which fractures intersect in a manner such that discrete blocks may not necessarily be formed, i.e. cases in which joints may terminate within intact rock and not only at intersections with other joints (Hammah et al, 2008). Perhaps, the greatest benefit of FEM-based SSR analysis is that it can automatically determine the broad variety of failure mechanisms with no prior assumptions regarding the type, shape or location of these mechanisms. These advantages will be demonstrated on simple slope examples to be described next. Three Test Examples The ability of FEM-SSR to capture the effects of scale on stability (factor of safety) and mode of failure of slopes in blocky rock masses was tested on three simple examples. The strength and deformation properties of intact rock and joints are provided in Table 1. Phase, a two-dimensional finite element program for modelling geotechnical excavations, was the numerical analysis tool used. Factors of safety were determined within a tolerance of 0.05. This degree of accuracy facilitated a good balance between reasonably fast computation and accurate factor of safety values. Table 1: Strength and deformation properties of intact rock and joints.