Slope stability analysis using fracture mechanics approach

Abstract The analysis of slope failure is complicated due to its mechanism as well as the geological history of the slope. In classical slope stability analysis, the slope failure is assessed using the basic continuum mechanics or the limit equilibrium approach. This analysis, however, must be slightly modified when tension cracks exist at the upper edge of the slope. From post-mortem analyses of slope failures in the past, it was found that tension cracks had some considerable importance affecting the failure mechanism of the slope. Some attempts had also been directed in the past towards simple vertical cut slopes with tension cracks. Terzaghi [40]. Using an elasto-plastic model and a few analytical assumptions, Terzaghi [40] obtained an expression for a critical height of a vertical cut slope. However, since the stress distribution is changing during crack propagation, the failure mechanism cannot in principle conjecture from a static (undisturbed) stress field alone. In this report, a unified numerical approach combining Finite Element Method (FEM), fracture mechanics and remeshing technique is used to model the failure analysis of vertical cut slopes with tension cracks. Using this approach, the crack can be extended incrementally under a certain energy based failure criterion (Strain Energy Density criterion - SED) while taking into account the existing stress singularity field in the vicinity of the crack-tip. The use of fracture mechanics in soils, however, poses some difficulties in obtaining its relevant parameters due to the granular structure of soil. Because of its granular structure, the shear strength of soil depends on cohesion and the applied confining pressure making the determination of fracture parameters in soil difficult. These relevant parameters are not yet available in literature and hence, certain assumptions and interpolations had to be made in obtaining these parameters. Future research direction in this area is badly needed. Using a certain set of soil properties and crack geometry, a series of curves relating parameters S (Strain Energy Density Factor) and a non-dimensional variable N ( = H/C - slope height vs. crack distance from edge ratio) for vertical cut slopes can be constructed through numerous parametric studies. These curves can serve as a quick guide to obtain the critical height for a given vertical cut slope geometry with tension cracks.