上覆非饱和层地基-隧道动力响应半解析算法

Semi-analytical Method for Dynamic Respones Calculation of Tunnel Buried in Foundation with Unsaturated Super-stratum

摘要:

分别采用非饱和土波动方程与壳的振动方程描述地基土的波动及隧道衬砌的振动特性。基于Helmholtz矢量分解定理与分离变量法，获得包含柱面波与平面波的总场表达式。利用波函数转换性质进行不同界面处平面波与柱面波的转化，结合地表边界、土层交界面以及隧?土交界面等边界假设进行耦合求解，提出了上覆非饱和层的饱和地基?隧道系统动力响应半解析算法。通过既有模型对比，验证了该算法的正确性。最后，基于该方法进行了算例分析，结果表明：上覆非饱和层对隧道底部土体位移响应影响较小，对地表位移响应影响较大；而临界速度受上覆土层饱和度的影响较小，其主要受隧道穿越土层性质的影响。

Abstract:

This paper presents an analytical method to calculate the dynamic response of tunnel embedded in saturated foundation with an unsaturated super-stratum. The vibration characteristics of foundation soil and tunnel lining were simulated by unsaturated wave equation and shell vibration equation respectively. Based on the method of separating variables and Helmholtz vector decomposition theorem， the expression of total wave field can be obtained， which includes cylindrical wave and plane wave. The system dynamic response was solved by the wave function transformation method， based on the boundary assumptions of foundation surface， soil interface and tunnel soil interface. The proposed method was verified by comparing with the existing models. Finally， based on the proposed method， the dynamic response of system was analyzed by a cases study. The results show that the displacement response of the ground is affected by the overlying unsaturated soil layer. The critical velocity is less affected by the saturation of overlying soil and mainly affected by the characteristics of soil that tunnel located.