层状地基中隧道开挖对临近既有隧道的影响分析

首次采用弹性层状半空间地基模型,建立了多层地基中隧道开挖对临近既有隧道影响的连续弹性分析方法,改变了过去采用简化分析方法仅能在均质地基中求解此类工程问题的状况。首先,采用Laplace积分变换得到了直角坐标系下单层地基应力和位移的初始函数,在此基础上,运用矩阵递推技术,给出了竖向荷载作用下层状地基中应力和位移的解析表达式并将其作为分析该问题的基本解。然后,采用弹性层状半空间地基模型将既有隧道视为Euler-Bernoulli梁,地基土体连续位移采用弹性层状半空间体系的基本解进行计算,并引入临近隧道开挖引起的土体自由位移场影响建立该问题的连续弹性求解方程,从而可以求得隧道纵向位移和内力。最后,结合离心模型试验和有限元数值模拟算例进行分析,验证了本文方法的有效性。此外,为考察地基土成层性对既有隧道性状的影响,还对几种典型层状地基中的隧道进行了参数分析。成果可为合理制定地下工程施工对临近既有隧道的保护措施提供一定的依据。

Analysis on response of existing tunnels due to adjacent tunneling in multi-layered soils

A continuous elastic method for deformation responses of the existing tunnels in multi-layered soils caused by adjacent tunneling is presented based on the elastic layered half space soil model, whereas solutions only existed in homogeneous soils by the simplified method before. First, the initial functions of stress and displacement for single-layered soils are obtained by using the Laplace integral transformation. Analytical solutions are then obtained for multi-layered soils under vertical loads by means of the transferring matrix method, which is taken as basic solutions for the question. Second, the existing tunnel is regarded as the Euler-Bernoulli beam, and the continuous soil displacement can be calculated using the basic solutions of the elastic layered system. Composing free-soil settlements caused by the adjacent tunneling to the existing tunnel, the displacements and internal forces from the continuous elastic solution equation are obtained. Finally, the accuracy of the proposed method is verified by use of centrifuge model test data and the results from numerical methods, and the influences of the soil stratification on the tunnel response are also investigated. The proposed method provides a theoretical basis for the determination of rational protective measurements of the existing tunnels influenced by adjacent underground construction.