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对于均质弹性地基中单隧道和多隧道开挖施工,本文给出了用于计算二维和三维地面沉降的近似的显式解析解。该解析解是对点荷载下Mindlin位移解进行积分并利用泰勒级数展开而得。利用该解析解,可以计算多个任意相对位置的隧道掘进引起的地面沉降。对于隧道开挖面不同支护程度的情况,可以采用一个原位应力释放度(系数)来模拟。通过一个单隧道开挖的弹性有限元计算对比,对简化的解析解进行了检验,两者计算结果的差距在9%以内。简化解析解的有效性,通过两种情况(两条相互平行隧道和两条相互垂直隧道)的计算得到验证。
For single tunnel and multi-tunnel excavation in a homogeneous elastic foundation, an explicit analytical solution for the approximation of two-dimensional and three-dimensional ground subsidence is given. This analytical solution is obtained by integrating the Mindlin displacement solution under point load and expanding it with Taylor series. Using this analytical solution, ground subsidence caused by tunneling at any number of relative locations can be calculated. For different levels of excavation tunnel excavation situation, you can use an in situ stress relaxation (coefficient) to simulate. Through a single-tunnel excavation elastic finite element calculation comparison, simplified analytical solution was tested, the difference between the two calculated results within 9%. Simplifying the validity of the analytical solution is verified by the calculation of two cases (two parallel tunnels and two perpendicular tunnels).