An analytical model for stability analysis of rock layers over a circular opening

The objective of the study presented is to provide an analytical solution f or determining the stability of a flexible rock laver overlying a circular opening, This problem is of general interest to the mining community but is particularly relevant to the oil and gas industry where drilling of deep w ellbores often results in sand production around the well and hence opening of cavities that extend upwards until they encounter a competent caprock. One of the critical design issues in completing the wellbores is the overal l stability of the formation around the well which is largely governed by t he stability of the rock layer spanning over the opening. The proposed meth od is based on the assumption that both the caprock and the overlying soil behave plastically under compression upon reaching the yield criterion with out brittle failure. It is assumed that a compression dome is formed in the caprock that carries the weight of the caprock and the overburden pressure to the surrounding soil. A plastic region in the form of a cylinder is ass umed to develop above the caprock. The overburden pressure is assumed to be the minimum vertical stress between the caprock and the plastic region req uired for the stability of the overlying soil. The validity of the assumpti ons embodied in the proposed analytical model and the methodology used to d evelop the formulations are checked against the results obtained from a gen eral numerical model. Despite the inherent constraints placed on most analy tically-based models with respect to boundary conditions and material behav iour, the results from the proposed model show surprisingly consistent resp onse against the numerical results, The differences between the models are rigorously discussed in this paper. The proposed method is considered to pr ovide the designers a viable tool for solving practical problems in a cost- effective fashion. (C) 2001 Elsevier Science Ltd. All rights reserved.