Mindlin解在复合地层盾构隧道施工地表沉降计算中的应用

Application of Mindlin Solution in Calculation of Ground Settlement in Composite Stratum Shield Tunnel Construction

在我国华南、东南及华北沿海地区隧道工程中,隧道围岩常为“上软下硬”的复合地层,即洞身上部是软弱的土层、下部为强度很高的硬岩地层,在该类地层中进行盾构施工引起的地面沉降问题目前还鲜见研究报道。针对此现状,延续采用Mindlin解求解地表沉降的思路,为了克服扩展Mindlin解面对非均匀地层时的局限性,引入层面状态向量,利用积分变换和矩阵推导解决了位移与应力在不同层面之间的传递问题,建立了适用于复合地层的扩展Mindlin解。对比了Mindlin解及扩展Mindlin解对复合地层中盾构隧道地表沉降问题的适应性,并与背景工程监测数据对比。推导过程表明,运用Mindlin解或扩展Mindlin解来求解地表沉降都面临困境,需要进行一定的简化。而工程监测数据则表明,采用Mindlin解计算结果偏大,可作为工程设计的参考;扩展Mindlin解计算地表沉降的方法有一定的准确性。

In the coastal areas of South China,Southeast China and North China,it is common that the upper part of the tunnel body is a soft soil layer,and the lower part is a hard rock stratum with high strength.The problem of land subsidence caused by shield tunneling has not been studied at present.To address this situation,the idea of using Mindlin solution to solve for surface subsidence was continued.In order to overcome the limitations of extended Mindlin solution for non-uniform strata,the layer state vector was introduced,and the integral transformation and matrix derivation were used to solve the relationship between displacement and stress at different layers.An extended Mindlin solution for composite formations was established.Finally,the adaptability of the Mindlin solution and the extended Mindlin solution to the surface subsidence of shield tunnels in composite strata were compared and compared with the actual engineering monitoring data.The derivation process shows that using the Mindlin solution or the extended Mindlin solution to solve the surface subsidence faces difficulties and needs to be simplified to a certain extent,while the engineering monitoring data show that the calculation results of the Mindlin solution are large,which can be used as a reference for engineering design.The method of extended Mindlin solution for calculating surface subsidence has certain accuracy.