地表堆载下盾构隧道纵向非线性变形简化解析解

既有盾构隧道在地表堆载下将会导致纵向不均匀沉降,威胁地铁列车的安全。目前地表堆载下盾构隧道的沉降预测方法没考虑到土体变形非线性的特点。基于所提的非线性地基模型,推导得到在地表堆载影响下盾构隧道纵向非线性变形简化解析解。地表堆载引起的隧道附加荷载通过Boussinesq解估算,通过连续梁模拟隧道的变形,推导得到在地表附加荷载下盾构隧道沉降的微分方程,引入有限差分法与Newton迭代法相互结合数值求解方法。通过三维有限元结果验证了其正确性,可以为在地表堆载下盾构隧道的沉降变形预测提供理论支持。

Simplified analytical solution for nonlinear longitudinal deformation of shield tunnels under surface surcharge

Surface surcharge will induced longitudinal deformation of shield tunnels, which threats the safety of running trains. The current prediction methods for the settlement of shield tunnels are not taken the nonlinear deformation of soils into consideration. Based on the proposed nonlinear foundation model, the simplified analytical solution for nonlinear longitudinal deformation of a shield tunnel under surface surcharge is derived. The additional load on the shield tunnel due to surface surcharge is estimated by the Boussinesq solution, and the deformation of the shield tunnel is modeled using continuous long beam. The differential function for the settlement of the shield tunnel is then obtained. The numerical solution of tunnel settlement is solved using the combined method of the finite difference and Newton’s iteration method. The effectiveness of the proposed method is verified using 3D FEM model. The proposed method may provide a theoretical support for evaluating the deformation of shield tunnels under surface surcharge.