Stress–strain field around elliptic cavities in elastic continuum

The paper is related to the determination of stress and strain fields around unsupported, stress free surface of an ellipsoidal cavity situated in a stressed elastic continuum. This is a most common requirement for the estimate of structural safety of underground rock excavations. The analytical approach elaborated in the paper avoids the solutions of the same problem that lead to expressions that contain rather complex integrations. The significant simplifications of all expressions from definition of the problem to its resolving have been achieved by application of ellipsoidal coordinates. Thus the presented solutions provide the applicable and explicit expressions for stresses and strains developed in infinite series with easily determinable coefficients by the use of contemporary mathematical packages. The numerical examples are also included to confirm the convergence of the obtained solutions.