Fractional Viscoelastic Analysis of Transversely Isotropic Surrounding Rock Along Shallow Buried Elliptical Tunnel

IF 3.4 2区工程技术 Q2 ENGINEERING, GEOLOGICAL International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2024-10-22 DOI:10.1002/nag.3877

Zhi Yong Ai, Yi Xuan Pan, Zi Kun Ye, Da Shan Wang

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Abstract

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.

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浅埋椭圆形隧道沿线横向各向同性围岩的分数粘弹性分析

本研究引入分数阶 Merchant 模型，对浅椭圆隧道沿线横向各向同性粘弹性围岩的应力场和位移场进行分析求解。首先，利用拉普拉斯变换和弹性-各向同性对应原理，得到任意荷载作用下分数阶粘弹性半平面和横向各向同性半平面的应力和位移解。其次，在上述半平面解法和深埋椭圆隧道问题解法的基础上，引入施瓦茨交替法，得到浅埋椭圆隧道的解析解。开发了 MATLAB 程序，并通过与 ABAQUS 的结果对比，验证了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。

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来源期刊

International Journal for Numerical and Analytical Methods in Geomechanics 工程技术-材料科学：综合

CiteScore

6.40

自引率

12.50%

发文量

160

审稿时长

9 months

期刊介绍： The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.