盾构隧道开挖面被动极限支护压力的三维解析解

摘要

文章基于莫尔-库仑屈服准则，通过优化楔形块体的倾角并考虑土体粘聚力的影响，对现有的楔形块+倒棱台的土体破坏模型进行改进，建立了能够得到盾构隧道开挖面处于被动极限平衡状态下支护压力的三维计算模型；同时推导得出了相应的计算公式，并通过优化计算得到了开挖面处被动支护压力最小时楔形块体的倾角及极限支护压力；结合一算例，将所建模型的预测结果与经典的上限解进行了分析对比，验证了其合理性；最后探讨了土体内摩擦角、土体粘聚力、隧道上覆土厚度与隧道开挖面处被动极限压应力间的相互关系。研究结果表明：土体的粘聚力越大，开挖面处被动极限支护压应力越大，两者呈线性关系；土体的内摩擦角越大，被动极限支护压应力越大，且其变化速率也越快；随着隧道上覆土厚度的增加，被动极限支护压应力逐渐增加，且变化速率越来越快，两者之间近似呈指数函数关系。%Based on the Mohr-Coulomb yield criteria, the failure model of a wedge block + inverted truncated pyramid is improved by considering the influence of soil cohesion and optimizing the inclined angle of the wedge block, and a three-dimensional model is established to calculate limit support pressure when the excavation face is in the passive limit equilibrium state. Meanwhile, a corresponding formula is deduced to calculate the limit support pressure, and its solution is obtained by optimization analysis. Based on a calculation example, a comparison between the predicted results from the proposed model and the classic upper bound solution is made to verify its rationality. Finally, the relationship among the passive limit pressure, cohesion of the soil, friction angle of the soil, and thickness of the overburden is studied. Results show that there is a linear relationship between the cohesion of the soil and the passive limit support pressure, which means that the greater the cohesion of the soil, the greater the passive limit support pressure; the larger the friction angle of the soil, the greater the passive limit support pressure and the faster its rate of change is; and with an increase of the overburden of the tunnel, the passive limit support pressure increases gradually, and the rate of change becomes faster and faster, which presents an approximate exponential function relationship.