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This paper describes a digital computer method for calculating the stresses and displacements induced by mining seam- or vein-type deposits. The method, which does not employ conventional finite element techniques, is based on a three-dimensional analysis of a linearly elastic rock mass. It can be used to compute stresses and displacements at locations in the immediate roof or floor of an excavation, or further into the rock mass. The method can be applied to complicated excavation geometries in the plane of the seam, which may be inclined at any angle to the primitive stress directions. Generalizations of the method can take into account the effects of backfill, artificial roof support, and nonlinear or time-dependent seam behavior. Examples are given to demonstrate the practical value of this work as an aid to rational planning of mining layouts.
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Underground mining often takes place in plane, relatively thin seam or vein-type deposits. Rational planning of the extraction of such deposits must take into account such questions as:
What is a suitable pattern of extraction and sequence of mining operations in the seam?
What is the effect of backfill and artificial support, and when and where can they be introduced most effectively?
How do mining operations in the seam alter the stresses in the vicinity of planned or existing haulages or roadways?
These questions become more important as the depth of mining or the amount of material extracted from the seam increases, or as more complicated excavation geometries are produced. Any attempt to answer them involves making some sort of estimate of the stresses and displacements caused by mining.
The distribution of stresses and displacements around an underground excavation depends on the behavior of the surrounding rock mass, which ordinarily consists of blocks of rock divided by joints and intersected by faults. It is not practical to attempt to model the detailed geology of a rock mass, and some simplifying assumptions must be made. For relatively deep workings it can be hypothesized that inelastic behavior is confined to the immediate vicinity of the excavations, while the bulk of the rock mass behaves in a linearly elastic fashion. There is a growing body of evidence in support of this hypothesis. Measurements in South African gold mines (ORTLEPP and COOK, 1964; ORTLEPP and NICOLL, 1964) have shown that it leads to accurate predictions. SALAMON and ORAVECZ (1 970) have found similar validation of elastic theory for coal deposits. More recently, McCLAIN and STARFIELD (1971) established that the rate of creep of salt pillars can be predicted reasonably well by assuming that creep is confined to the pillars and that the surrounding rock salt responds elastically.
Even with the assumption of a linearly elastic rock mass, there still exists the problem of computing stresses and displacements for an extensive and geometrically irregular mining pattern in the seam. Three-dimensional finite element analysis on any practical scale is economically well beyond the limits of current capabilities.
