Analytical solution for a deep tunnel with arbitrary cross section in a transversely isotropic rock mass
Analytical solution for a deep tunnel with arbitrary cross section in a transversely isotropic rock mass
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横观各向同性岩体任意断面深埋隧道解析解
DOI：
10.1016/j.ijrmms.2011.10.001
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发表时间：
2011-12
影响因子：
7.2
通讯作者：
Sun, Yuzhou
中科院分区：
文献类型：
--
作者：
Zhang, Zhizen;Sun, Yuzhou
深埋隧道（如威尔斯和公路隧道）是常见的岩土工程结构，其稳定性和安全性研究的重要内容之一是求解其解析解。但是，由于理论和实践的复杂性，它仍然是一个艰巨的挑战。Poulos和Davis [1]、Pender [2]、Carter和Booker [3]以及Verruijt [4]分别研究了圆形隧道在不同边界条件下的解析解。Exadaktylos给出了无限弹性体中半圆形隧道的解析解[5]。Muskhelishvili和Cai推导了不同边界条件下椭圆形隧道的解析解[6，7]。Lu和Zhang得到了任意断面隧道在不同地应力条件下的解析解[8，9]。在上述所有研究中，围岩被视为各向同性介质。众所周知，岩体往往表现出各向异性。但由于各向异性引起的数学复杂性，各向异性岩体中隧道的解析解并不多见。Lekhnitskii [10]研究了轴对称地应力条件下横观各向同性岩体中的圆形筒仓。但是，如果隧道的横截面是任意形状的，而岩体被视为各向异性介质，问题变得更加复杂。
Deep tunnels such as wells and highway tunnels are common geotechnical structures, and it is of interest to derive analytical solutions in studying the stability and safety of tunnels. But, it remains a hard challenge due to the theoretical and practical complexity. Analytical solution for a circular tunnel under different boundary conditions have been studied, respectively, by Poulos and Davis [1], Pender [2], Carter and Booker [3], and Verruijt [4]. Exadaktylos gave the analytical solution for the case of a semi-circular tunnel in an infinite elastic body [5]. Muskhelishvili and Cai derived the analytical solution for an elliptical tunnel subject to the different boundary conditions [6, 7]. Lu and Zhang obtained the analytical solution for a tunnel with the arbitrary cross section under different ground stress conditions [8, 9].In all above studies, the surrounding rock is regarded as an isotropic medium. It is well known that rock masses often display anisotropy. But analytical solutions for tunnels in anisotropic rock masses are rare, because of the mathematical complexity induced by the anisotropy. A circular silo in transversely isotropic rock mass under axisymmetric ground stress condition has been studied by Lekhnitskii [10]. But, the problem becomes more complex if the cross section of a tunnel is of arbitrary shape while the rock mass is viewed as the anisotropic medium.
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DOI：
10.1007/978-1-4613-4277-9_4
发表时间：
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