The subsidence phenomenon of near surface excavations is numerically treated in this study. The most important mechanical parameters are the induced stresses, displacements and strains around the excavation and also on the ground surface above the excavated area. In this paper the stresses and displacements around the excavations are obtained numerically using an indirect boundary element method. The vertical and horizontal strains and tangential stresses on the ground surface and along the boundary of the excavation can be obtained by implementing a finite difference scheme on the displacement results already obtained by the boundary element analysis. Underground and near surface excavations having rectangular shapes are studied in this context. Several example problems are solved and the results are graphically shown in the related figures.
Underground mining of raw materials is often the cause of ground movements at the surface which can produce considerable damage to the structures located within the area of influence. It is too often considered that damage depends on ground strain which in turn is affected by its geometrical and geomechanical properties. Therefore, structural stresses are evaluated for estimating different mechanical properties of the ground and the structure, as well as for different amplitudes of ground movements. There are several basic methods for predicting subsidence phenomenon which can be grouped as: 1 empirically derived relationships, 2 profile functions, 3 influence functions, 4 analytical and numerical models and 5 physical models . In most of these analyses the ground movements are mainly divided into two parts: ground subsidence and horizontal strains. In this paper, the analytical and numerical modeling procedure is used and the subsidence phenomenon is considered as an elastic problem. The elastic treatment of subsidence for various geometric conditions has recently gained a considerable attraction. In this study, the semianalytical indirect boundary element method known as displacement discontinuity method is used for the elastic analysis of the subsidence . This numerical method has been widely used for the stress and displacement analysis of many engineering problems and its details are explained in the literature [3–9].
A brief explanation of the higher order indirect boundary element method specially modified for the half plane problems with traction free surfaces is given bellow. The quadratic element displacement discontinuity is based on the analytical integration of quadratic collocation shape functions over collinear, straight-line displacement discontinuity elements .
The subsidence problems can be treated as halfplane problems which can also be solved by infinite boundary element methods. However, a more accurate and economic way for solving semi-infinite problems with a traction free surface, using the method of images as explained by Crouch and Starfield (1983) for the constant element displacement discontinuity method . They used the analytical solution to a constant element displacement discontinuity, over the line segment |x|≤ a, y= 0 in the semi-infinite region y≤ 0 as shown in Figure 3.