﻿ Formulation of the element matrices and vectors for elasticity problem > Consistent element nodal loads > Excavation loads

When a portion of material (soil) is excavated, either in the open excavations (cuts) or in enclosed tunnels, forces must be applied along the excavated surface such that the remaining material should experience the correct stress relief effect and the new free surface is stress- free. Let us suppose that the body A is to be removed from body B as shown in Figure (26), and let us denote the stresses in the two part of the body before excavations as and respectively. Any external loads are taken into account in forming these stresses prior to removal of the body A. Since both bodies are in equilibrium forces FAB must be applied to body B due to body A to maintain and, similarly FBA must act on body A. These forces are equal in magnitude but are opposite in sign. The excavation forces acting on a boundary depend on the stress state in the excavated material and on the self-weight of that material. It can be shown that:

 (76)

Where B is the strain-displacement matrix, VA the excavated volume, N the element shape functions and γ the soil unit weight.

 (a)   Initial stress state (b) Forces FAB (c)   Forces FBA acting on the dislocated volume B d   Excavation forces FAB Fig. 26. Excavation loads