Abstract A scattering problem of a plane dilatational wave disturbed by a lined tunnel with an imperfect interface embedded in an infinite unsaturated poro-elastic solid is investigated. By means of the Helmholtz theory and the wave function expansion method, the corresponding displacements and stresses are obtained in terms of the wave functions, where the coefficients involved are determined by solving a series of linear equations. Numerical calculations are carried out to illustrate the influence of the saturation, stiffness of the interface and the frequency of the incident wave on the distribution of the radial displacement and the dynamic stress concentration factor (DSCF) in the unsaturated substrate. The present analytical solutions may serve as a starting point for future engineering practices.

中文翻译：

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P波作用下非饱和多孔弹性介质中嵌入不完善界面的圆形衬砌隧道的动力响应

摘要 研究了内嵌在无限不饱和多孔弹性固体中的具有不完美界面的衬砌隧道扰动的平面膨胀波的散射问题。借助亥姆霍兹理论和波函数展开法，根据波函数得到相应的位移和应力，其中所涉及的系数是通过求解一系列线性方程来确定的。数值计算说明了界面的饱和度、刚度和入射波频率对径向位移分布和非饱和基体动态应力集中系数（DSCF）的影响。目前的分析解决方案可以作为未来工程实践的起点。