An approximate solution for the cylindrical cavity expansion under the non-axisymmetric displacement boundary condition on hypotenuse

Abstract

Based on the virtual image technique, stress function method and Boussinesq’s solutions, an approximate solution of the cylindrical cavity expansion is investigated under the non-axisymmetric displacement boundary condition on hypotenuse. The stress harmonic functions on the ground surface are improved. At first, the elastic solution without any correction is deduced, considering the combined effects of the actual and image sources. Then, stress on the ground surface is revised by the improved stress harmonic function. Stress on the slope surface boundary is corrected by integrating Boussinesq’s solution and then applying the coordinate transformation technique. Moreover, the newly induced stresses on the ground surface boundary (resulting from the correction process of the slope surface boundary) are further revised by the improved stress harmonic function. Finally, the linear elastic superposition principle is adopted to obtain the approximate solution under the non-axisymmetric and free displacement boundary conditions on hypotenuse. In addition, the proposed solution is validated by the numerical results. The numerical analysis results show that it is helpful to control the safety reserve of stress and displacement considering the boundary effects and stress revisions. Larger vertical displacement of the ground surface could result from larger slope inclination, shorter limb distance, smaller cylindrical cavity depth, larger expansion pressure and smaller elastic modulus of soils.