矩形断面二维浅埋硐室顶部双层围岩塌落面上限分析

Upper bound analysis of two-layer rock collapseoverlying a two dimensional shallow rectangular chamber

基于极限分析上限定理和Hoek-Brown破坏准则,构建了浅埋矩形硐室双层围岩塌落破坏机制,并根据虚功原理获得了一个围岩塌落形态方程的泛函。利用变分法得到极限状态下围岩塌落破坏曲线函数,并根据边界条件得到待定系数,进而得到围岩塌落破坏曲线的解析式。当双层围岩退化为单层围岩时,与已有研究成果完全一致,可以证明本文分析模型的正确性。在此基础上,分析了各参数对浅埋隧道双层围岩塌落破坏形状的影响规律,可为浅埋硐室顶部双层围岩潜在塌落范围的预测提供理论依据。

Based on the upper bound theorem of limit analysis and the Hoek-Brown failure criterion, the collapse failure mechanism of two layers shallow tunnels was constructed in this paper, and according to the virtual work principle, a functional was deduced. To obtain the analytic expression of the failure curve, the function of the failure curve and the unknown coefficients were obtained firstly under limit state by means of the variational method and the boundary conditions. Then the research result was consistent with that of single-layer surrounding rock when two-layer surrounding rock degenerates into single-layer surrounding rock, which proved the analytical model in this paper is correct. Lastly, the influence law of each parameter on the collapse failure shape of the two-layer shallow buried tunnel was analyzed, which could provide a theoretical basis for the potential collapse area of surrounding rock in the layered shallow rock.