This paper aims at deriving a closed‐form solution for deep lined tunnels within a saturated anisotropic poro‐elastic medium. The derivation of the solution is carried out with the assumption of plane strain conditions along the tunnel axis, an isotropic elastic liner, a steady‐state flow, and perfect contact between the liner and rock. For this purpose, the complex potential function approach pioneered by Lekhnitskii for the anisotropic elastic body was used to develop the mechanical response of the rock mass. A complex hydraulic potential function is also introduced to solve the steady state fluid flow. Then the well‐known Biot theory is chosen to describe the hydro‐mechanical coupling of the anisotropic saturated rock. The stress and displacement solutions of both the liner and the surrounding rock, considering the tunnel face advance with respect to the considered section, are derived based on the principle of the convergence‐confining method. Comparisons with previous closed‐form solutions for isotropic case and finite element solution for anisotropic case were made to show the accuracy of the current closed form solution. Sensitivity analysis is performed based on this analytical solution to highlight the effect of some rock parameters on the stress and displacement of the liner.

中文翻译：

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考虑掌子面超前的各向异性岩石深衬砌隧道孔隙弹性解析解


本文旨在导出饱和各向异性多孔弹性介质中深衬砌隧道的封闭式解决方案。求解的推导是在沿隧道轴线的平面应变条件、各向同性弹性衬砌、稳态流动以及衬砌与岩石之间完美接触的假设下进行的。为此，采用 Lekhnitskii 针对各向异性弹性体首创的复势函数方法来开发岩体的力学响应。还引入了复杂的水力势函数来求解稳态流体流动。然后选择著名的Biot理论来描述各向异性饱和岩石的水力耦合。考虑到隧道掌子面相对于所考虑断面的超前，基于收敛约束法的原理，得出了衬砌和围岩的应力和位移解。与先前各向同性情况的封闭式解和各向异性情况的有限元解进行比较，以显示当前封闭式解的准确性。基于该解析解进行敏感性分析，突出一些岩石参数对衬管应力和位移的影响。