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.

Solution of Strain-Softening Surrounding Rock in Deep Tunnel Incorporating 3D Hoek-Brown Failure Criterion and Flow Rule

“…The radius of each ring is a known quantity and the radial stress of the th ring can be obtained from (17). So the axial normal stress can be given by…”

“…Combining (3), (17), and (22), stress at the outer ring can be obtained and the radial stress at the th ring is calculated by using linear interpolation:…”

“…Zou and Su [14] presented an analytical solution of the surrounding rock based on the generalized Hoek-Brown failure criterion and elastic-brittle-plastic model, and this solution is compared with Wang et al [11] to verify its correctness using the method of parameter transformation. The theoretical solutions for the elastic-brittle-plastic and elastic-plastic rock mass incorporating the out-of-plane stress and seepage force were proposed by Zou et al [14][15][16][17][18].…”

A Numerical Approach for the Quasi-Plane Strain-Softening Problem of Cylindrical Cavity Expansion Based on the Hoek-Brown Failure Criterion

“…Brown failure criterion is adopted and expressed by [22][23][24] . is a factor that depends on the degree of disturbance to which the rock has been subjected in terms of blast damage and stress relaxation.…”