OFR-57-75 A Computer-Controlled Electrical Resistance Network Analog For Rational Mine Design ? Summary

An important class of mining problems involves excavations in planar seam or vein-type deposits. In many instances it can be assumed that the seam is at 'infinite' depth in a homogeneous, isotropic or transversely isotropic, linearly elastic rock mss, and that the normal to the plane of the seam is a principal stress direction. Rational planning of excavations in such deposits requires a knowledge; of the stresses and displacements induced by complicated, irregular excavation geometries in the plane of the seam. This problem previously has been solved either numerically or by means of an electrical resistance network analog. Both of these methods effectively simulate the mined portions of the seam as a dislocation in an otherwise continuous mass, and determine the complete solution in terms of the stresses and displacements at the seam. In both cases, the plane of the seam is divided into a number - say, M x N - of squares, and the solution to the problem is determined in terms of the solution to an M x N system of equations. The numerical approach requires that these equations be solved explicitly, while the analog; solves them instantaneously with current analogous to stress and voltage to displacement. A purely numerical solution of practical problems can require a substantial amount of computer time, particularly in situations that demand some sort of sequential analysis, either due to successive mining or to nonlinear behavior of the seam material. This report describes a combined analog-digital computer system for solving problems that are impractical when either device is used separately. The digital computer and the analog are interfaced so that the digital computer can receive information from the analog via a switching matrix and an analog to digital converter, and can activate points of the analog via another switching matrix and a set of digital to analog converters. The resulting hybrid system can be used to simulate arbitrary "stress-strain" characteristics for any portion of the seam by an iterative procedure similar to the initial strain method used in nonlinear finite element analysis. Thus, the hybrid system combines the speed of analog computation with the decision-making capability of the digital computer: the analog instantaneously solves the set of equations, and the digital computer decides how the initial strains must be altered for the solution to be compatible with the prescribed "stress-strain" characteristics for the seam material. The hybrid computer system has many implications for rational planning of underground excavations, since it allows practically any type of inelastic seam behavior or artificial support characteristics to be simulated. Inelastic seam behavior, for example, might be due to either rock failure or to time-dependent deformation.