Studying edge effects near rectangular mine workings weakened by a crack

Abstract

Edge effects in a rock mass near a system of periodic mine workings crossed by a crack (fold fault) are considered. The stress state near the mine workings is determined by solving an elastic problem using the piecewise-homogeneous medium model. The original differential problem is reduced to a discrete problem based on the concept of a base scheme. Methods are proposed to solve the discrete problem, and the issue of optimizing the numerical analysis is discussed. The stress distribution around mine workings is analyzed. The stress isolines that represent the boundaries of edge effect zones and indicate their maximum decay length are plotted Keywords: edge effect, periodic system of mine workings, crack (fold fault), discrete problem, numerical methodIntroduction. The determination of the stress-strain state near mine workings is one of the main problems in rock mechanics. Cracks (faults) in a rock mass greatly affect its strength near a mine working. It is of practical interest to analyze and allow for this factor in developing construction-and technology-related measures that ensure trouble-free mining operations. The edge effects near a system of parallel horizontal mine workings of rectangular cross-section were analyzed in [3]. In [4], edge effects are determined using a difference approach that employs the concept of base factors to set up difference equations and formulate a discrete problem. A real rock mass was considered there. The isolines of stress s 22 defining the boundaries of edge effect zones with prescribed accuracy r% were plotted as an example. Such an approach was used in [7-10] to study edge effects in structural members made of layered and fibrous composites.Continuing the study [3], the present paper determines the edge effect in a rock mass containing a periodic system of deep horizontal mine workings. The workings are aligned along the Îx 3 -axis, are parallel to the Ox 1 -axis, and are crossed by a crack symmetric about the Ox 2 -axis (Fig. 1). The analysis of the edge effect is reduced to the determination and analysis of the stress-strain state near a mine working, analysis of the geometry of the edge effect zone, and the determination of its decay length with prescribed accuracy.