冲切破坏模式下溶洞顶板极限承载力计算  

Calculation of ultimate bearing capacity of cave roof under punching failure mode

作　　者：雷勇[1] 刘一新[1] 邓加政 尹君凡 张宗堂[1] LEI Yong;LIU Yixin;DENG Jiazheng;YIN Junfan;ZHANG Zongtang(Hunan Provincial Key Laboratory of Geotechnical Engineering for Stability Control and Health Monitoring,Hunan University of Science and Technology,Xiangtan,Hunan 411201,China;Chongqing Municipal Research Institute of Design,Chongqing 400020,China)

机构地区：[1]湖南科技大学岩土工程稳定控制与健康监测湖南省重点实验室,湖南湘潭411201 [2]重庆市市政设计研究院,重庆400020

出　　处：《岩石力学与工程学报》2018年第9期2162-2169,共8页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家自然科学基金资助项目(51208195);湖南科技大学岩土工程稳定控制与健康监测湖南省重点实验室开放基金资助(E21618)~~

摘　　要：基于溶洞顶板的冲切破坏模式,采用极限分析上限法建立冲切体的三维功能方程,推导泛函形式的溶洞顶板承载力表达式。运用变分原理得到冲切破坏线方程,进一步利用偏导求得冲切体的底部直径和三维溶洞顶板极限承载力显示计算公式。通过对比试验验证了理论方法的合理性,并重点分析岩体地质力学分类指标GSI对溶洞顶板极限承载力及冲切体底部直径的影响。结果表明:(1)顶板厚度h为1D^4D时,溶洞顶板极限承载力随着h的增加大致呈线性增长,h=5D时,极限承载力与基岩一致;(2)厚径比为定值时,顶板极限承载力随着GSI的增大呈非线性增长,当h=1D,GSI取44时溶洞顶板的承载力系数为0.73,GSI取100时其值为1.42,后者接近前者的2倍;(3)同一溶洞顶板厚度下,冲切体底部直径随着GSI的增大大致呈线性减小。当GSI取44,1D顶板厚度时冲切体底部直径为0.20 m,分别是GSI取65,85,100时的1.25,1.54,1.70倍,对于其他顶板厚度时也存在类似的关系。Based on the punching failure mode of the cavern roof,a functional equation of the failure surface of the punching body was established by using the upper bound method in limit analysis so that the functional expression of the ultimate bearing capacity of the three-dimensional cavern roof was derived.The breaking line equation of the punching body is obtained with variation method.The formula for the bottom diameter of the punching body and the ultimate bearing capacity of the three-dimensional cavern roof were obtained through the partial derivative.The rationality of the theoretical method was verified through comparison with the experimental results.The impact of GSI on the ultimate bearing capacity of cavern roof and the bottom diameter of the punching body were analyzed.The results indicated that when h is 1D to 4D,the ultimate bearing capacity of cavern roof increases approximately linearly with the increasing of h.When h is 5D,the ultimate bearing capacity of cavern roof is the same as the that of bedrock.When the ratio of thickness to diameter is constant,the ultimate bearing capacity of roof increases nonlinearly with the increasing of GSI.When h is 1D and GSI takes 44,the capacity coefficient of cavern roof is 0.73,and when GSI takes 100,the value is 1.42,which is about twice the former.Under the same thickness of cavern roof,the diameter of the bottom of the punching body decreases approximately linearly with the increasing of GSI.When GSI takes 44 and the thickness of the cavern roof is 1 D,the diameter of the bottom of the punching body is 0.20 m,which is 1.25,1.54 and 1.70 times of that when the GSI is taken as 65,85 and 100,respectively.Similar relationships exist for other thickness of cavern roof.

关 键 词：基础工程 溶洞顶板 极限承载力 冲切破坏 试验研究 极限分析上限法 

分 类 号：TU47[建筑科学—结构工程]