Growth of slip surfaces in 3D conical slopes

Abstract

Out-of-plane curvature of real submarine slopes imposes limitations on applicability of existing planar criteria for catastrophic growth of slip surfaces. In this paper, the growth of an initially weakened zone in three-dimensional (3D) convex and concave slopes is investigated using the process zone approach. The geometry of the problem is presented in a curvilinear coordinate system for which the governing equations for the three-dimensional slip surface growth are derived. Solution of these equations for an axisymmetric problem is obtained both analytically and numerically (using a finite differences scheme) and benchmarked against Coupled Eulerian-Lagrangian finite element simulations. It is shown that the application of the planar slope solution to conical slopes constitutes an overestimation of the slope's stability. The closed form criteria for an unstable 3D slip surface growth in both convex and concave slopes are proposed and validated by fitting numerical results for various sizes and aspect ratios of the initially pre-softened zone.