A displacement discontinuity method has been developed for solving three-dimensional dynamic problems. The technique has been used to investigate the dynamic response of supported and unsupported excavations in tabular orebodies. A case is also presented in which slip on a natural feature produces significant effects in the mined excavation. The new technique provides predictions of velocities and dynamic stress concentrations which are not provided by conventional static methods. It is shown that the dynamic response may be significantly different from that inferred from static analyses, and that this method is a useful tool for the analysis of realistic mining situations in which dynamic events such as rockbursts occur.
Boundary element methods have evolved to the stage that they are now widely accepted as an alternative to methods such as finite elements in many fields of mechanics. This paper describes the development of a boundary element method known as the three-dimensional Explicit Dynamic Displacement Discontinuity Method (EDDDM), and presents several examples of problems which illustrate its use for computing the dynamic displacements and stresses caused by sudden changes in the geometry of an underground excavation, and by mining-induced slip on a joint or fault plane (in three dimensions). The prediction of velocities of closure occurring in mined excavations offers the ability to predict the behavior of support elements. Also, quantitative estimates of dynamic stress concentrations should lead to a better understanding of the mechanisms of transient phenomena such as rockbursts, where the dynamic stresses may differ significantly from the static values. The mining problems addressed by the EDDDM all involve excavations in tabular orebodies, which are thin (a few meters or less) in one dimension and extensive (hundreds or even thousands of meters) in the other two. Static boundary element methods (in particular, displacement discontinuity methods) are a standard design tool for problems of this type (Plewman et al. 1969; Starfield and Crouch 1973; Crouch and Starfield 1983; Ryder 1988) and similar kinds of problems can be solved with the dynamic model. The same numerical model can be used to study the associated problems of sudden slip or separation on a pre-existing geological discontinuity.
This brief description of the three-dimensional dynamic displacement discontinuity method is given only to indicate the principles on which it is based, and to highlight some of the advantages and disadvantages compared to other methods. This approach falls into the class of boundary element methods known as indirect methods but the solution quantities have physical significance in the problems investigated here. Boundary element methods are numerical schemes to solve the same physical problems which are typically posed as differential equations, except that they are cast in integral form. By appropriate manipulation, the integral equations over the entire domain are converted into surface integrals over only the boundary of the domain. The boundary is divided into elements (boundary elements) and the boundary conditions are satisfied approximately on the elements, usually at the center of each element.