基坑开挖诱发下卧盾构隧道纵向非线性变形研究

Nonlinear longitudinal deformation of underlying shield tunnels induced by foundation excavation

目前预测基坑开挖诱发下卧盾构隧道纵向变形的简化计算方法大多采用弹性地基模型考虑隧道–地基的相互作用,无法进一步反映土体非线性变形特征。通过引入非线性Pasternak地基模型考虑隧道–地基的非线性相互作用,推导得到基坑卸载下盾构隧道纵向变形控制微分方程。通过有限差分法将隧道纵向变形控制微分方程转化为矩阵–向量形式,利用牛顿迭代法求解得到基坑卸载下盾构隧道纵向变形的数值解答。通过与三维有限元算例和2个工程案例进行对比分析,验证所提方法的合理性和适用性。研究表明:当基坑开挖引起盾构隧道纵向隆起量较小时,基于Winkler和Pasternak弹性地基模型的简化计算方法与所提方法均能较好地预测隧道纵向隆起位移量;而当基坑开挖引起盾构隧道纵向隆起位移较大时,基于Winkler和Pasternak弹性地基模型的简化计算方法明显低估盾构隧道的隆起量,而采用非线性Pasternak地基模型预测计算方法则提供更加可靠的预测结果。

Current simplified analytical methods for predicting shield tunnel longitudinal deformation due to excavation commonly adopt elastic foundation model to consider the ground-tunnel interaction and hence,fail to reflect the nonlinear deformation characteristics of subsoils. Introducing nonlinear Pasternak foundation model for considering the tunnel-soil nonlinear interaction,in this paper,a differential equation for shield tunnel longitudinal deformation owing to overlying excavation is derived. The differential equation is transferred into matrix-vector form according to the finite difference method,and then the numerical solution for shield tunnel longitudinal deformation induced by excavation is solved using the Newton’s iteration method. The applicability and feasibility of the proposed method is verified by three-dimensional finite element simulations and two field cases. The results show that,when the longitudinal heave of shield tunnels induced by excavation is smaller,both the simplified analytical methods based on the Winkler and Pasternak elastic foundation models and the proposed method provide good predictions for shield tunnel longitudinal heave,while that,for a considerable large longitudinal heave of shield tunnel,the proposed method based on the nonlinear Pasternak foundation model always offers a more reliable prediction of the heave of shield tunnels but the simplified methods give a significant underestimation.