This study introduces the fractional order Merchant model to analytically solve the stress and displacement fields of the transversely isotropic viscoelastic surrounding rock along shallow elliptical tunnels. First, the stress and displacement solutions of fractional order viscoelastic and transversely isotropic half planes under arbitrary loads are obtained using the Laplace transform and the elastic‐viscoelastic correspondence principle. Second, based on the above half plane solution and the solution of the deep buried elliptical tunnel problem, the Schwarz alternating method is introduced to obtain the analytical solution of the shallow buried elliptical tunnel. A MATLAB program is developed, and the accuracy of the theory and program in this study is verified by comparing it with the results of ABAQUS. Finally, the effects of transversely isotropic parameters, tunnel burial depth, and viscoelastic parameters on the stress and displacement of tunnel surrounding rock are analyzed.

中文翻译：

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沿浅埋椭圆隧道横向各向同性围岩的分数粘弹性分析


本研究引入了分数阶 Merchant 模型，以解析求解沿浅椭圆隧道的横向各向同性粘弹性围岩的应力场和位移场。首先，利用拉普拉斯变换和弹性-粘弹性对应原理，得到任意载荷下分数阶粘弹性和横向各向同性半平面的应力和位移解。其次，基于上述半平面解和深埋椭圆隧道问题的解，引入 Schwarz 交替方法得到浅埋椭圆隧道的解析解。开发了一个 MATLAB 程序，并通过将其与 ABAQUS 的结果进行比较来验证本研究中理论和程序的准确性。最后，分析了横向各向同性参数、隧道埋深和粘弹性参数对隧道围岩应力和位移的影响。