A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plastic and governed by the unified strength theory (UST).Different major principal stresses in different engineering situations and different support yielding conditions are both considered.The unified solution obtained in this work is a series of results,rather than one specific solution,hence it is suitable for a wide range of rock masses.In addition,parametric study is conducted to investigate the effect of intermediate principal stress.The result shows the major principal stress should be rationally chosen according to different engineering conditions.Finally,the applicability of the unified solution is discussed according to the critical pressures.
Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated soil are obtained using integral transform methods.The Cauchy type singularity of the boundary integral equation is discussed.The effectiveness of the properties of soil mass and incident field on the dynamic stress concentration and pore pressure concentration around a cavity is analyzed.Our results are in good agreement with the existing solution.The numerical results of this work show that the dynamic stress concentration and pore pressure concentration are influenced by the degree of fluid–solid coupling as well as the pore compressibility and water permeability of saturated soil.With increased degree of fluid–solid coupling,the dynamic stress concentration improves from 1.87 to 3.42 and the scattering becomes more significant.With decreased index of soil mass compressibility,the dynamic stress concentration increases and its maximum reaches 3.67.The dynamic stress concentration increases from 1.64 to 3.49 and pore pressure concentration improves from 0.18 to 0.46 with decreased water permeability of saturated soil.
