Limit equilibrium problem of a collapse vault over curvilinear underground structures and its practical application

Abstract

The paper deals with the problem of ultimate equilibrium of a collapse vault formed over underground structures of curvilinear outline. A detailed critical analysis of the normative methodology is given. It is shown that the normative methodology has a number of drawbacks related to the impossibility to determine the strength coefficient other than by the descriptive scale of M. M. Protodyakonov or by formula referring to the same scale. The following is a review of some solutions to the problem of the collapse vaulting in rocky soils, namely: the problem of the vaulting of the limit equilibrium (collapse) over a mine excavation, considered by W. Ritter (1879). Ritter (1879); the problem of J. O. Stakhnev (2023), in which Ritter's solution was developed, first of all, in terms of taking into account not only normal, but also tangential stresses acting along the contour of the collapse vault; the solution of the problem of the limit equilibrium of the collapse vault in rocky soils, obtained according to the Ritter – Stakhnev scheme, but with the use of methods of calculus of variations, obtained earlier by the authors, is also analysed. This solution was obtained in closed form. A distinctive feature of the obtained results is the rejection of the notion of strength coefficient in favor of standard strength characteristics of rocky soils. Further in the theoretical part of the paper the solution of the problem of collapse vaulting over curvilinear underground structures (over calotte) as a problem of variation calculus is given. The paper shows that the presence of the calotte does not affect the outline of the collapse vault, but reduces the load from the rock pressure on the underground structures. The results section of the study describes a practical method for calculating the ground pressure on curvilinear underground structures.