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Semi-analytical solution for stress and displacement of lined circular tunnel at shallow depths
Applied Mathematical Modelling ( IF 5 ) Pub Date : 2021-08-18 , DOI: 10.1016/j.apm.2021.08.005
Hui Cai 1 , Ai-zhong Lu 1 , Yao-cai Ma 1 , Chong-lin Yin 1
Affiliation  

In this study, a new approach is presented to determine the stress and displacement field of a shallow buried circular tunnel subject to gravity and arbitrary lateral stress based on the complex variable method. The soil mass and lining are conformally mapped onto two ring regions. A more effective method than the power series method is used to solve the undetermined coefficients of complex potential functions. The interaction mechanism between the lining and the soil mass is fully considered. The boundary conditions along the inner boundary of the lining and the ground surface and the stress and displacement continuity conditions along the excavation line are used in the analytical derivation. In the verification, the stress and displacement distributions obtained in the semi-analytical solution agree with the numerical results and satisfy the boundary and continuity conditions. Using examples, the stress distributions along the inner boundary of the lining and interface are presented to examine the influence of key parameters including the Young's modulus and buried depth. The effect of the lining in reducing stress concentration and restricting tunnel convergence is quantitatively analyzed.



中文翻译:

浅层衬砌圆形隧道应力位移半解析解

在这项研究中,提出了一种基于复变量法确定受重力和任意侧向应力作用的浅埋圆形隧道的应力和位移场的新方法。土壤质量和衬砌被共形映射到两个环形区域。比幂级数法更有效的方法用于求解复势函数的待定系数。充分考虑了衬砌与土体的相互作用机制。沿衬砌内边界和地表的边界条件以及沿开挖线的应力和位移连续性条件用于解析推导。在验证中,半解析解得到的应力和位移分布与数值结果一致,满足边界和连续性条件。通过实例,展示了沿衬砌内边界和界面的应力分布,以检查包括杨氏模量和埋藏深度在内的关键参数的影响。定量分析了衬砌在降低应力集中和限制隧道收敛方面的作用。

更新日期:2021-08-29
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