地面堆载诱发下既有盾构隧道纵向变形的解析解

Analytical Solution of Longitudinal Deformation of Existing Shield Tunnel Induced by Surface Surcharge

为研究地面堆载作用对既有盾构隧道纵向变形的不利影响,将既有盾构隧道简化为置于Pasternak地基上的Timoshenko梁(定义为T-P模型),通过理论推导得到考虑盾构隧道剪切效应和地基剪切刚度的地面堆载诱发下,既有盾构隧道纵向变形的解析解。研究结果表明:1)与其他模型计算结果相比,在实测数据的最大值附近,T-P理论模型计算结果与实测数据更为吻合,从而验证该模型的可靠性。2)在隧道纵向变形计算上,T-P模型相比常用Euler-Bernoulli梁模型计算结果较大,而稍小于T-W模型计算结果,更接近实际监测数据;在内力计算上,Euler-Bernoulli梁模型计算结果较大,常用的EB-W模型弯矩、剪力最大值均为T-P模型的1.3倍。3)随着隧道与堆载中心水平距离的增大,隧道竖向变形减小;提高土层弹性模量以及隧道等效抗弯刚度可以有效减少隧道竖向变形;当等效剪切刚度超过一定数值后,隧道变形趋于稳定。

The study of adverse effect of surface surcharge on the longitudinal deformation of existing shield tunnel is of great significance.As a result,an analytical solution for the longitudinal deformation of existing shield tunnel induced by surface surcharge considering the shearing effect of shield tunnel and shearing stiffness of the foundation is presented.This solution assumes that the shield tunnel is a Timoshenko beam resting on Pasternak foundation(defined as T-P Model).The results show that:(1)Compared with other model calculation results,the results of theoretical model proposed in this paper are more consistent with the measured data near the maximum value,which verifies the reliability of T-P model.(2)As for the calculation of the longitudinal deformation of tunnel,the results of T-P model proposed in this paper is larger than that of the Euler Bernoulli beam model,but smaller than that of the T-W model,which shows that the T-P model results are closer to the actual monitoring data;as for the calculation of internal force,the calculation results of Euler Bernoulli beam model are larger,and the maximum bending moment and shearing force of EB-W model are 1.3 times that of T-P model proposed in this paper.(3)With the increase of the horizontal distance from the tunnel axis to the load center,the vertical deformation of tunnel decreases gradually;by increasing the elastic modulus of soil layer and the equivalent bending stiffness of tunnel,the vertical deformation of tunnel can be effectively reduced;when the equivalent shearing stiffness exceeds a certain value,the tunnel deformation tends to be stable.