This paper presents a three-dimensional trench stability analysis in non-uniform undrained clay adopting the kinematic approach of limit analysis. Rather than assuming a classic curved cylinder (“torus”) shape, the failure surface of the proposed rotational mechanism is formulated by a spatial discretization technique in order to accommodate the non-uniformity profile of soil’s undrained shear strength in a multi-layered ground as well as better adaptation to typical trench geometries in practice. The present study agrees well with the traditional torus rotational mechanism in terms of the normalized trench stability number in uniform clay when trench length to depth ratio is greater than 0.6, while significant improvement to the previous solution is achieved for shorter trench panels. A linear variation pattern between trench stability number and soil shear strength gradient is found for non-uniform soil profiles, in particular for shorter trenches. A simplified method is thereafter introduced for preliminary trench stability evaluation in non-uniform clay profiles. For trenches in two-layered clay, a more notable change in trench safety factor with layer thickness ratio is observed when the top layer is weaker than the bottom layer.

本文采用极限分析的运动学方法，对不均匀不排水黏土进行三维三维稳定性分析。不是采用经典的弯曲圆柱（“ torus”）形状，而是通过空间离散技术制定了所提出的旋转机构的破坏面，以适应多层地面中土壤不排水抗剪强度的非均匀分布。并在实践中更好地适应典型的沟槽几何形状。当沟槽长度与深度之比大于0.6时，就均匀粘土中的归一化沟槽稳定性数而言，本研究与传统的环面旋转机制非常吻合，而对于较短的沟槽板，则可以对先前的解决方案进行重大改进。对于不均匀的土壤剖面，特别是对于较短的沟槽，发现沟槽稳定性数与土壤抗剪强度梯度之间存在线性变化模式。此后，引入了一种简化的方法，用于初步评估非均匀粘土剖面中的沟槽稳定性。对于两层粘土中的沟槽，当顶层比底层弱时，观察到沟槽安全系数随层厚比的变化更为显着。