隧道地表沉降预测的黏弹模型

在隧道开挖及运行过程中,不可避免地会对岩土体产生扰动,引起隧道地表产生沉降,对于隧道地表沉降分析,目前尚无成熟的基于力学理论的解析模型。针对该问题,将水平隧道地表沉降问题近似为半无限空间内水平圆柱形孔洞受力收缩导致的边界位移问题,并通过求解弹性无限域内的轴对称平面应变问题,运用叠加原理推导得到含水平圆柱形孔洞的半无限空间地表沉降的弹性积分形式解析解。然后运用对应原理,将体积变形视为弹性,畸变视为Maxwell黏弹性,对地表沉降弹性积分形式解析解进行拉普拉斯变换,得到时空域上的地表沉降的黏弹性积分形式解析解,从而建立隧道地表沉降的黏弹模型。模型揭示隧道地表沉降槽宽度系数为0.6,与多地区沉降监测数据吻合良好,为隧道地表沉降预测提供了一套新的基于力学理论的方法。

Viscoelastic Model of Surface Subsidence above Tunnels

Surface subsidence will be induced by rock-soil mass being disturbed in the process of excavation and long-term operation of tunnels. At present,there is no mature analytical model based on the theory of mechanics. In this research,the surface subsidence above tunnel is approximated to boundary deformation in the elastic semi-infi-nite space containing a horizontally cylindrical cavern with shrinkage force. By solving the symmetrically plan-strain problem in elastic infinite space,the elastic analytical solution of the surface subsidence in integral form is derived with the principle of superposition. Subsequently,the viscoelastic analytical solution in integral form in space-time domain is obtained by Laplace transformation of elastic analytical solution with volume deformation regarded as elas-ticity and distortion as Maxwell viscoelasticity. The proposed model reveals that the width coefficient of settlement troughs above tunnels is 0.6,in good agreement with the monitoring data in many other regions. The method in this article offers a theoretical approach for surface subsidence prediction in the process of excavation and long-term op-eration of tunnels.