For stability analysis of shallow shield tunnels in cohesive-frictional (clayey–sandy) soils, an analytical method of continuous upper bound limit analysis is developed to determine the most critical slip line position and the minimum required tunnel support pressure. The ground displacement field due to composite volume loss is calculated using a complex variable solution, and the optimization problem is solved by employing the particle swarm optimization technique. Energy dissipation at the potential slip boundary, which is determined through a system of tracking schemes, and in the corresponding potential plastic zone is taken into account. Example calculations are carried out to verify the proposed method via finite element simulations and comparisons with solutions from existing methods, and to study the effects of soil strength properties and tunnel size and depth. The results show that both the internal friction and the cohesion of the surrounding soil may help reduce the range of the potential collapse zone and the magnitude of the necessary support pressure. This study represents the first attempt to deal with cohesive-frictional soils via an analytical and continuous approach, and the developed method can be extended for various tunnel and other geotechnical stability problems involving cohesive-frictional soils.

中文翻译：

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粘性摩擦土中浅层盾构隧道稳定性的连续上限分析方法

对于粘性摩擦（粘土-砂质）土壤中浅层盾构隧道的稳定性分析，开发了一种连续上限分析的分析方法，以确定最关键的滑移线位置和所需的最小隧道支撑压力。复合体积损失引起的地面位移场采用复变量解法计算，优化问题采用粒子群优化技术求解。通过跟踪方案系统确定的潜在滑动边界处的能量耗散以及相应的潜在塑性区中的能量耗散都被考虑在内。进行示例计算以通过有限元模拟和与现有方法的解决方案进行比较来验证所提出的方法，并研究土壤强度特性和隧道尺寸和深度的影响。结果表明，内摩擦力和周围土壤的内聚力都可能有助于减小潜在坍塌带的范围和必要的支撑压力的大小。这项研究代表了通过分析和连续方法处理粘性摩擦土的首次尝试，所开发的方法可以扩展到涉及粘性摩擦土的各种隧道和其他岩土工程稳定性问题。