Investigation by limit analysis on the stability of slopes with cracks

A full set of solutions for the stability of homogeneous c, φ slopes with cracks has been obtained by the kinematic method of limit analysis, providing rigorous upper bounds to the true collapse values for any value of engineering interest of φ, the inclination of the slope, and the depth and location of cracks. Previous stability analyses of slopes with cracks are based mainly on limit equilibrium methods, which are not rigorous, and are limited in their capacity for analysis, since they usually require the user to assume a crack depth and location in the slope. Conversely, numerical methods (e.g. finite-element method) struggle to deal with the presence of cracks in the slope, because of the discontinuities introduced in both the static and kinematic fields by the presence of cracks. In this paper, solutions are provided in a general form considering cases of both dry and water-filled cracks. Critical failure mechanisms are determined for cracks of known depth but unspecified location, cracks of known location but unknown depth, and cracks of unspecified location and depth. The upper bounds are achieved by assuming a rigid rotational mechanism (logarithmic spiral failure line). It is also shown that the values obtained provide a significant improvement on the currently available upper bounds based on planar failure mechanisms, providing a reduction in the stability factor of up to 85%. Charts of solutions are presented in dimensionless form for ease of use by practitioners