弹性半空间中衬砌洞室对平面P波和SV波的散射(Ⅰ)——方法

Scattering of plane P and SV waves by a lined tunnel in elastic half space(Ⅰ) :method

采用一种高精度的间接边界积分方程法,求解了弹性半空间中任意形状衬砌洞室对入射平面P波和SV波的散射问题。在衬砌内外表面附近引入虚拟波源面,由该面上的柱面膨胀波源和剪切波源构造衬砌内外的散射波场,继而由边界条件建立方程并求解得到虚拟波源密度,总波场可由散射场和自由场的叠加而得。通过精度验证和稳定性检验,表明该方法具有极高的数值精度和数值稳定性。

This paper presents an indirect boundary integration equation method （IBIEM）of high precision for solving the scattering of plane P and SV waves by a two - dimensional lined tunnel of arbitrary shape in elastic half - space. EmploYing the Green＇ s functions of compressional and shear wave source in half - space, the scattered waves in the lining and half space were constructed using the fictitious wave sources close to the lining surfaces, and the magnitude of the fictitious wave sources were determined by boundary conditions, then the total response can be obtained by the superposition of the free field and the scattered field. Through the comparison of numerical results, it is shown that the IBIEM has excellent numerical accuracy and numerical stability.