上伏溶洞下深埋隧道塌落破坏的上限分析

为了预测上伏溶洞下深埋岩溶隧道塌落范围及上伏溶洞与隧道的临界高度，构建上伏溶洞下深埋岩溶隧道的横、纵断面上的塌落机制，结合非线性Hoek-Brown强度准则和极限分析上限法，并考虑孔隙水压力的作用下对上伏溶洞下深埋隧道的塌落范围进行研究，将孔隙水压力当作外力进行做功且根据虚功率方程和变分法原理推导出上伏溶洞下深埋隧道的塌落范围理论公式以及上伏溶洞与隧道的临界高度计算公式，利用数值计算软件MATLAB对公式进行求解和绘制隧道的塌落形状。将所提方法和既有研究、有限元数值模拟进行对比，所提方法和既有研究的计算结果误差为-4.32%~7.63%，和有限元数值模拟的计算结果误差为4.31%~6.73%，误差均在一定的精度范围内，充分验证了所提方法的合理性。分析不同参数对上伏溶洞下深埋隧道塌落范围的影响规律。研究结果表明：不同参数对上伏溶洞的深埋岩溶隧道塌落范围影响显著，孔隙水压力系数增大将导致深埋隧道的塌落面增大，上伏溶洞与隧道的高度H越大深埋隧道的塌落越不容易塌穿至溶洞，为深埋隧道提供适当的支护力可有效地抑制塌落风险。因此，上伏溶洞对深埋隧道的稳定性影响显著，该方法可为上伏溶洞下深埋隧道的塌落范围预测及上伏溶洞与隧道的临界高度的确定提供理论依据。

Upper Bound Analysis of Collapse Failure in Deep Buried Tunnel Under Upper Cave

To predict the collapse range of the deep-buried karst tunnel and the critical height of the upper karst cave and tunnel, a collapse mechanism of the horizontal and vertical sections of the deep karst tunnel under the upper karst cave was constructed, in combination with the nonlinear Hoek-Brown strength criterion and the limit analysis upper bound method. Under the action of pore water pressure, the collapse range of the deep tunnel under the upper cave was studied. The pore water pressure was used as an external force for the work according to the virtual power equation and variational method. This principle was applied to deduce the theoretical formula for the collapse range of the deep tunnel under the upper cave and the calculation formula for the critical height of the upper cave and tunnel. The numerical calculation software Matlab was used to solve the formulae and to draw the collapse shape of the tunnel. The method was compared with the existing research and finite element numerical simulation. The error between the method and existing research results is between -4.32% and 7.63%, the error is within a certain accuracy range, and the calculation results obtained by the finite element numerical simulation exhibit good consistency, thereby verifying the rationality of the method. The influence of the variation in the variables on the collapse range of the deep buried tunnel under the upper cave was analyzed. The results demonstrate that different parameters have a significant influence on the collapse range of the deep buried karst tunnel in the upper cave, and the increase in the pore water pressure coefficient will lead to deep burial. Moreover, the collapse surface of the tunnel will increase. A greater height H of the upper karst cave and tunnel means that collapse into the cave is less likely. Appropriate support for deep tunnels can effectively suppress the risk of collapse. Therefore, the effect of the upper karst cave on the stability of the deep tunnel is obvious. This method may provide a theoretical basis for the prediction of the collapse range of the deep tunnel under the upper karst cave and the determination of the critical height of the upper karst cave and tunnel.