A two-dimensional boundary element method for calculating elastic gravitational stresses in slopes

Elastic stresses arising from gravitational loads in a two-dimensional slop e of arbitrary shape are calculated easily using a displacement-discontinui ty boundary element method (BEM). A long stress-free crack simulates the to pographic surface. Gravity-induced stresses (i.e., body forces) in a latera lly confined body are simulated by vertical and horizontal "far-field" stre sses equal to pgy and [V/(1 - nu)]pgy, respectively. Here rho is material d ensity, nu is Poisson's ratio, g is gravitational acceleration, and gamma i s elevation, with gamma = 0 along the surface far from a ridge top or valle y floor. BEM stress solutions compare well with analytical solutions for sy mmetric topography based on conformal mapping. Our analyses indicate that s lope failures are likely to initiate near the bases of bedrock ridges and t o be widespread along the slopes of gentle valleys cut in bedrock. The BEM method can be applied to the slopes of arbitrary shape and steepness, and i t is well suited for evaluating the near-surface propagation of fractures o r fracture-like structures, such as dikes and landslide failure surfaces. O ur analysis also highlights the critical importance of properly accounting for the boundary conditions in a boundary value problem.