A simple boundary equation technique for elastic stress analysis of underground cavities

Summary A boundary integral equation approach is illustrated which does not require the solution of singular integrals in order to compute the coefficients of the final system of linear equations. This characteristic allows the carrying out of all the necessary integrations by means of numerical techniques, leading to a rather simple and compact solution algorithm. In addition the approach permits the evaluation of a measure of the error affecting the numerical solution. The stability and the accuracy of the procedure, which is based on the minimization of the difference between known boundary tractions and corresponding numerically derived stresses, are discussed with reference to some rock engineering problems and it is shown that the approach is particularly suitable for stress analyses related to underground openings. To get some insight into the overall performance of the procedure, the results obtained in the analysis of a tunneling problem of practical interest are compared with those deriving from a standard Finite Element calculation.