偏心荷载下溶洞顶板冲切破坏上限分析

Upper bound analysis of the punching shear failure of cave roof in karst area

针对冲切破坏模式下溶洞顶板极限承载力问题,进行了不同顶板厚度以及不同荷载偏心距下溶洞顶板极限承载力室内试验研究,依据试验结果将偏心荷载作用下的溶洞冲切破坏假定为轴对称问题,引入Griffith强度准则,基于极限分析上限法,提出了一种适用于轴对称和偏心荷载作用下溶洞顶底板极限承载力的计算方法,并给出了能发生冲切破坏范围的估算方法。试验结果表明:在同一偏心距下,随着顶板厚度的增加,在达到基岩极限承载力之前,顶板极限承载力呈线性增长;当顶板厚度一定时,顶板极限承载力随着偏心距的增加呈非线性增长,偏心距e在能发生冲切破坏的范围之外时趋于平缓,并逐渐达到基岩极限承载力;理论计算结果与试验结果吻合较好。

Under the punching shear failure mode, the experiments were conducted on the karst cave roof to study the bearing capacity under different roof thicknesses and load eccentricities in the laboratory. The failure mode of karst cave under eccentric loading was assumed to be axisymmetric according to the experimental results. Based on the upper bound limit analysis method and Griffith strength criterion, a new method was proposed for calculating the ultimate bearing capacity of karst cave roof both under axial symmetrical and eccentric loading. Besides, a method was given for estimating the range of the punching failure area. The experimental results show that at the same eccentric distance, the ultimate bearing capacity of the roof increases linearly with the increase of the roof thickness before reaching the ultimate bearing capacity of the bedrock. When the roof thickness is constant, the ultimate bearing capacity increases nonlinearly with the increase of eccentricity. In addition, the eccentricity e tends to be gentle and reaches the ultimate bearing capacity of the bedrock at the outside the range of punching shear failure. The theoretical calculation results are in good agreement with the experimental results.