Stability of an elliptical working fixed with absolutely rigid lining in a rock mass with moment stresses

Abstract

Conducting an underground structure in a solid rock mass violates its continuity property and can lead to its collapse, which poses a threat to the lives of workers and also causes material and financial damage. To date, many methods have been developed for solving the classical problem of determining the stress-strain state of rocks with underground structures. However, there is no unified theory for describing the stress-strain state of rocks with moment stresses around underground workings, since the task is complicated by the fact that, in addition to such deformations of the rock mass as compression-tension and shear, it becomes necessary to calculate the deformation of bending and rotation. This article proposes a solution to the problem of determining the buckling zones of an elliptical mine in a rock mass with moment stresses under creep conditions, which is fixed with an absolutely rigid lining so that the rock walls and lining are rigidly linked to each other along the entire contour. The stress-strain state of an elastic plane with a hole consists of the sum of the main stresses caused by the stressed state of the plane without a hole, and additional stresses caused by the presence of a hole. At the same time, the solution of the problem of determining the stress-strain state of an elastic-creeping mass with moment stresses around an unsecured non-circular horizontal working is reduced to solving a sequence of similar problems for a circular working by the small parameter method. This method expands the stress functions are expanded into numerical series in powers of a parameter that characterizes the deviation of the excavation shape from a circle. Numerical results were obtained to determine the stress-strain state of the rock under the influence of ordinary and moment stresses on the contour of the excavation, secured by an absolutely rigid support with adhesion under creep conditions. Calculations were carried out to determine the rock pressure on the excavation contour from normal and moment stresses were carried out to analyze the behavior of siltstone over time $t=120$ hours and $t=600$ hours in polar coordinates. The constructed diagrams of the desired total, in the zero and first approximation, momentary rock pressure on an absolutely rigid support at $t=120$ hours and $t= 600$ hours show that it increases over time, therefore, in zones of maximum growth it is required to strengthen it to increase stability.