Solving Gravitational Problems

Abstract

Many practical rock-engineering problems involve gravitational stresses. Rock slope stability and shallow tunnel stability are two examples where the gravity stresses cannot simply be ignored or simplified as far-field in situ stresses. In such cases, uneven gravitational stresses at different depths of the rock mass must be explicitly considered.

Modelling gravitational stresses with boundary element (BE) methods is not as straightforward as in finite element (FE) method where the mass and weight of the rock are distributed into each element. Because the elements in BE methods are only located at the boundaries, they are not able to directly represent the gravitational force inside the rock body. To effectively represent this gravitational force, we need to: (1) account for the uneven gravitational stresses at the centre of all boundary elements; (2) superposition the gravitational stresses at any point inside the rock. This chapter provides the formulations to consider the effect of gravitational forces.