Abstract This paper investigates the stability of two circular tunnels at different depths in cohesive-frictional soils subjected to surcharge loading using a stable node-based smoothed finite element method (SNS-FEM). In the present method, the numerical integration domains are approximately circular regions of the node-based smoothing domain by the node-based smoothed finite element method (NS-FEM). Four additional integration points are employed for each node to form the stabilization items associated with the variance of the smoothed shape function gradient. The tunnels are modelled under plane strain conditions, and the soil is described as a uniform Mohr-Coulomb material, and it obeys an associated flow rule. The stability numbers of two circular tunnels are obtained directly by solving the optimization problems. In this study, the effects of soil properties (γD/c), the ratio of tunnel diameter to its depth (H/D), the horizontal and vertical spacing ratio (S/D, L/D) and soil internal friction angle (ϕ) on the stability numbers (σs/c) are investigated. Several numerical results of two circular tunnels have been carried out showing that the proposed approach can demonstrate the efficiency and reliability solutions. Based on upper bound limit analysis using SNS-FEM, the results are presented in the form of design tables and charts for engineers to use.

中文翻译：

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基于稳定节点的平滑有限元方法用于粘性摩擦土中不同深度的两个圆形隧道稳定性分析

摘要 本文使用基于稳定节点的平滑有限元方法 (SNS-FEM) 研究了粘性摩擦土中不同深度的两个圆形隧道在承受超载载荷时的稳定性。在本方法中，数值积分域是基于节点的平滑有限元方法(NS-FEM)的基于节点的平滑域的近似圆形区域。每个节点采用四个额外的积分点来形成与平滑形状函数梯度的方差相关的稳定项。隧道在平面应变条件下建模，土壤被描述为均匀的 Mohr-Coulomb 材料，它遵循相关的流动规则。通过求解优化问题直接得到两条圆形隧道的稳定数。在这项研究中，土体性质（γD/c）、隧道径深比（H/D）、水平竖向间距比（S/D、L/D）和土内摩擦角（φ）对隧道的影响研究了稳定性数 (σs/c)。两个圆形隧道的几个数值结果表明，所提出的方法可以证明效率和可靠性解决方案。基于使用 SNS-FEM 的上限分析，结果以设计表和图表的形式呈现给工程师使用。两个圆形隧道的几个数值结果表明，所提出的方法可以证明效率和可靠性解决方案。基于使用 SNS-FEM 的上限分析，结果以设计表和图表的形式呈现给工程师使用。两个圆形隧道的几个数值结果表明，所提出的方法可以证明效率和可靠性解决方案。基于使用 SNS-FEM 的上限分析，结果以设计表和图表的形式呈现给工程师使用。