Analytical Solution for Stress and Displacement of the Arbitrary‐Shaped Shallow Tunnel Excavated in Orthotropic Rock

IF 3.6 2区工程技术 Q2 ENGINEERING, GEOLOGICAL

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2025-09-27 DOI:10.1002/nag.70086

Yulin Zhou, Ning Zhang, Aizhong Lu

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引用次数: 0

Abstract

Excavating tunnels in anisotropic rock induces greater stress concentrations at the excavation boundary compared to isotropic rock. However, existing analytical solutions for the shallow tunnel are founded on the simplifying assumption of isotropic rock masses. To clarify the deformation mechanism and mechanical behavior of the shallow tunnel, we proposed an analytical method for solving stress and displacement of the arbitrary‐shaped shallow tunnel excavated in orthotropic rock mass, incorporating the effects of body forces and anisotropy of rock mass. Proposing the specific forms of the analytical functions for the shallow tunnel in anisotropic rock, which can reflect body forces and the anisotropy of the rock mass. A linear equation system, derived from stress boundary conditions at the surface and tunnel excavation, is solved by the boundary collocation method. In the solution process, conformal transformation techniques are employed to construct three polar coordinate systems, which aid in resolving boundary conditions. Subsequently, we analyzed the effects of tunnel depth and anisotropic parameters on the stress and displacement of a horseshoe‐shaped tunnel and verified the correctness of the results through ANSYS software.

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正交各向异性岩石中开挖任意形状浅埋隧道的应力和位移解析解

在各向异性岩石中开挖隧道比在各向同性岩石中开挖隧道在开挖边界处产生更大的应力集中。然而，现有的浅埋隧道解析解是建立在岩体各向同性的简化假设基础上的。为明确浅埋隧道的变形机理和力学行为，提出了一种考虑体力和岩体各向异性影响的正交各向异性开挖任意形状浅埋隧道应力和位移的解析方法。提出了各向异性岩石中浅埋隧道解析函数的具体形式，可以反映岩体的体力和各向异性。采用边界配置法求解了地表应力边界条件和隧道开挖应力边界条件的线性方程组。在求解过程中，采用保角变换技术构造了三个极坐标系统，有助于求解边界条件。随后，我们分析了隧道深度和各向异性参数对马蹄形隧道应力和位移的影响，并通过ANSYS软件验证了结果的正确性。

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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.