Model for simulation of residual stress in rock

Abstract

Rocks in mines, quarries, and many outcrops commonly show evidence of being under high stress. Saw cuts and drillholes close in, partly mined coal bursts violently, and pillars crush and rock spalls in mines even at moderate depths. Similarly, strong and massive rocks such as granite and sandstone naturally divide themselves into sheets that lie more or less parallel to their outward topographic form. The sheets may be either convex or concave. Thin plates of bare rock surfaces bow up and buckle. Such effects often cannot be explained by the obvious loads now acting on the rock, that is, by loads resulting from overburden, topographic irregularities, or stress concentration around openings. The stresses exceed those that would result from such loads. Two interpretations of such excess stresses have been made. In one, the stresses are assigned in origin to now active tectonic forces. In the other, they are regarded as leftover and locked in from some previous state at which higher pressures prevailed. These two sources may both operate and they generally cannot be distinguished easily in the field. There are other complicating sources of stress such as temperature gradients and chemical alteration. Nevertheless, some bodies of rock, by exfoliating, show evidence of high internal stress even though they are practically unweathered and so isolated topographically that the presence in them of significant stress due to exterior loads or active tectonic forces seems unlikely. Moreover, completely isolated rocks are known to change density shape, or size; to expand under constant compressive stress; and even to disintegrate without the intervention of weathering processes. The stresses involved here must be truly residual in the sense long used by metallurgists; that is, residual stresses in a body are those that remain, aside from the effect of gravity or temperature gradients, even after the boundaries are freed from loads. Residual stress within rock can exist only in a system of internally balanced forces. The existence of such balanced forces has been recognized for a long time--at least 180 years--to judge from an incomplete survey of the literature. Discussions have been presented more recently by Voight, Friedman, Emery, Price, Denkhaus, Kieslinger, and other engineers and geologists. Briefly, a simple version of the concept is that if a granite crystallizes at depth and is then unloaded by uplift and erosion, the compressed mineral grains cannot completely relax, owing to interlocking boundaries and mutual interference. A sandstone that becomes cemented while constituent grains are under high pressure cannot completely relax when cut free. Thus, a balance is achieved between forces of expansion in the interior of the crystalline grains and those of restraint at grain boundaries or in the cement.