既有隧道在上覆基坑卸荷下的形变响应简化算法

基坑开挖将打破土体原有应力场,对下卧隧道产生不利影响。鉴于此,提出一计算既有隧道在上覆基坑卸荷影响下的形变响应简化计算法。首先,利用搁置于Pasternak地基上的Euler-Bernoulli梁来模拟既有隧道,分析中,采用可考虑隧道埋深影响的地基反力系数;其次,借助于Mindlin解给出基坑开挖所引起的隧道轴线位置处的土体自由位移;然后,再结合隧道-地基土的位移耦合条件建立起隧道的变形控制方程;最后,通过有限差分法给出基坑开挖引起的下卧既有隧道的纵向响应解答。通过与三维有限元和既有理论解的对比验证了所提方法的准确性和适用性。接着对不同因素对隧道形变响应的影响做了参数分析,包括:隧道埋深、基坑-隧道相对空间位置、基坑开挖深度、基坑几何形状、隧道-地基土的相对刚度等。在此基础之上,进一步提出下卧隧道在上覆基坑开挖卸荷影响下的最大竖向位移简化预测公式。上述研究结论可为类似工程提供一定理论支持。

Simplified method for evaluating deformation responses of existing tunnels due to overlying basement excavation

The excavation of the basement will break the original stress field of ground and hence has an unfavorable effect on the underlying tunnel. In this paper,a new simplified method is developed to evaluate the response of the existing tunnel duo to the unloading of the basement excavation. Firstly,the Euler Bernoulli beam resting on the Pasternak foundation was used to simulate the interaction between the existing tunnel and ground,and the coefficient of subgrade reaction considering the effect of the burial depth of the existing tunnel was adopted. Secondly,the ground displacement at the tunnel center induced by basement excavation was obtained with the application of Mindlin’s solution. Then,a deformation control equation of tunnels was established based on the displacement coupling condition between the existing tunnel and the ground. Finally,the solution of the longitudinal response of the existing tunnel caused by adjacent excavation was obtained using the finite difference method. The accuracy and applicability of the proposed method were verified by comparison with the three-dimensional finite element method analysis and theoretical solutions published in other literature,and the influence of different factors on tunnel response was analyzed including the tunnel buried depth,relative space position between the basement and the existing tunnel,the excavation depth of the basement,the geometry of the basement,the relative rigidity between the existing tunnel and the ground,etc. Finally,a simplified formula for predicting the maximum vertical displacement of the tunnel induced by excavation was presented. The results could provide some theoretical support for similar projects.