矩形隧道下穿对既有隧道受力变形的计算方法

Calculation Method of Stress and Deformation of Existing Tunnel Caused by an Undercrossing Rectangular Tunnel Excavation

摘要:

为研究矩形隧道下穿施工对既有隧道变形的影响规律,提出了关于矩形隧道下穿既有隧道的半解析解。首先,基于矩形隧道开挖后断面收敛变形的特点,基于随机介质理论推导出矩形隧道开挖诱发的地层变形规律,将既有隧道视为搁置在Kerr地基模型上的Euler-Bernoulli梁,最终获得既有隧道的纵向受力平衡微分方程,并采用有限差分获得矩形隧道下穿对既有隧道受力变形的计算方法。通过与室内模型试验值进行对比,验证了本文计算结果的准确性。最后,针对矩形隧道宽度、埋深、土体内摩擦角、既有隧道抗弯刚度和地层损失率等关键参数展开影响分析。结果表明:矩形隧道半宽和地层损失率增大会导致既有隧道的竖向变形线性增加;隧道埋深减小会导致既有隧道竖向峰值显著增大,但会缩小对隧道沉降的影响范围;增大土体内摩擦角会导致既有隧道的竖向变形显著增大,同时使隧道变形槽略微减小;随着既有隧道抗弯刚度的增加,隧道的竖向变形会明显减小。

Abstract:

In order to study the influence of a rectangular tunnel undercrossing construction on the deformation of the existing tunnel, a semi-analytical solution for the rectangular tunnel undercrossing the existing tunnel is proposed. Firstly, based on the characteristics of the convergence deformation of the section after the excavation of the rectangular tunnel, the law of the ground deformation induced is derived by using the random medium theory. The existing tunnel is regarded as an Euler-Bernoulli beam on the Kerr foundation model. Consequently, the differential equation of longitudinal force equilibrium of the existing tunnel is obtained, and the finite difference method is used to obtain the calculation method of the stress and deformation of the existing tunnel caused by the undercrossing rectangular tunnel excavation. By comparing with the experimental values of the indoor model, the accuracy of the calculation results in this paper is verified. Finally, the influence of key parameters such as rectangular tunnel width, tunnel depth, internal friction angle of soil, bending stiffness of the existing tunnel and ground loss rate is analyzed. The results show that the increase of half-width and ground loss rate of the rectangular tunnel leads to the linear increase of vertical deformation of the existing tunnel. The decrease of the tunnel depth leads to a significant increase in the vertical peak deformation of the existing tunnel, but narrows the influence range on the tunnel settlement. The increase of the internal friction angle of soil leads to a significant increase in the vertical deformation of the existing tunnel and a slight decrease in the tunnel deformation trough. With the increase of the bending stiffness of the existing tunnel, the vertical deformation of tunnel is significantly reduced.