冲切破坏模式下溶洞顶板极限承载力计算
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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.
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.
引文
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[12]雷勇,陈秋南,马缤辉.基于极限分析的桩端岩层冲切分析[J].岩石力学与工程学报,2014,33(3):631–638.(LEI Yong,CHEN Qiunan,MA Binhui.Punching analysis of rock at pile tip on limit analysis[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(3):631–638.(in Chinese))
[13]雷勇,尹君凡,陈秋南,等.基于极限分析法的溶洞顶板极限承载力研究[J].岩土力学,2017,38(7):1 926–1 932.(LEI Yong,YIN Junfan,CHEN Qiunan,et al.Study on ultimate load capacity of karst roof based on limit analysis[J].Rock and Soil Mechanics,2017,38(7):1 926–1 932.(in Chinese))
[14]FRALDI M,GUARRACINO F.Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(4):665–673.
[15]CHEN W F.Limit analysis and soil plasticity[M].Amsterdam:Elsevier Science,1975:28–63.
[16]SERRANO A,OLALLA C.Tensile resistance of rock anchors[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(4):449–474.
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[18]柏华军.考虑溶洞顶板自重时桩端持力岩层安全厚度计算方法[J].岩土力学,2016,37(10):2 945–2 952.(BAI Huajun.A method for calculating the safety rock thickness of pile bearing strata with considering deadweight of karst cave roof[J].Rock and Soil Mechanics,2016,37(10):2 945–2 952.(in Chinese))
[19]RATHIE R N,SILVA P D.Applications of lambert wfunction[J].International Journal of Applied Mathematics and Statistics,2011,23(11):1–15.
[20]阳生权,阳军生,岩体力学[M].北京:机械工业出版社,2008:118–119.(YANG Shengquan,YANG Junsheng.Rockmass mechanics[M].Beijing:China Machine Press,2008:118–119.(in Chinese)
[2]张慧乐,张智浩,王述红,等.岩溶区嵌岩桩的试验研究与分析[J].土木工程学报,2013,46(1):92–103.(ZHANG Huile,ZHANG Zhihao,WANG Shuhong,et al.Experimental research and analysis of Rock-Soil-rock-soiling pile in karst area[J].China Civil Engineering Journal,2013,46(1):92–103.(in Chinese))
[3]张慧乐,马凛,张智浩,等.岩溶区嵌岩桩承载特性影响因素试验研究[J].岩土力学,2013,34(1):92–100.(ZHANG Huile,MA Lin,ZHANG Zhihao,et al.Test research and analysis of influencing factor of rock-socked pile bearing capacity in karst area[J].Rock and Soil Mechanics,2013,34(1):92–100.(in Chinese))
[4]黎斌,范秋雁,秦凤荣.岩溶地区溶洞顶板稳定性分析[J].岩石力学与工程学报,2002,21(4):532–536.(LI Bin,FAN Qiuyan,QIN Fengrong.Analysis on roof stability of karst cave in karst areas[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(4):532–536.(in Chinese))
[5]阳军生,张军,张起森,等.溶洞上方圆形基础地基极限承载力有限元分析[J].岩石力学与工程学报,2005,24(2):296–301.(YANG Junsheng,ZHANG jun,ZHNAG Qisen,et al.Finite element analysis of ultimate bearing capacity of the circular footing above karst area[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(2):296–301.(in Chinese))
[6]刘之葵,梁金城,朱寿增,等.岩溶区含溶洞岩石地基稳定性分析[J].岩土工程学报,2003,25(5):629–633.(LIU Zhikui,LIANG Jincheng,ZHU Shouzeng,et al.Stability analysis of rock foundation with cave in karst area[J].Chinese Journal of Geotechnical Engineering,2003,25(5):629–633.(in Chinese))
[7]汪华斌,刘志峰,赵文锋,等.桥梁桩基荷载下溶洞顶板稳定性研究[J].岩石力学与工程学报,2013,32(增2):3 655–3 662.(WANG Huabin,LIU Zhifeng,ZHAO Wenfeng,et al.Study on the stability of karst cave roof under the load of pile foundation[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(Supp.2):3 655–3 662.(in Chinese))
[8]JIANG C,LIU L,WU J.A new method determining safe thickness of karst cave roof under pile tip[J].Journal of Central South University,2014,33(3):1 190–1 196.(in Chinese))
[9]赵明华,曹文贵,何鹏祥,等.岩溶及采空区桥梁桩基桩端岩层安全厚度研究[J].岩土力学,2004,25(1):64–68.(ZHAO Minghua,CAO Wengui,HE Pengxiang,et al.Study on safe thickness of rock mass at end of bridge foundation′s pile in karst and worked-out mine area[J].Rock and Soil Mechanics,2004,25(1):64–68.(in Chinese))
[10]刘辉,杨峰,阳军生.空洞上方浅基础地基破坏模式与极限承载力分析[J].岩土力学,2010,31(11):3 373–3 378.(LIU Hui,YANG Feng,YANG Junsheng.Analysis of the failure mode and ultimate bearing capacity of shallow foundation in hollow top[J].Rock and Soil Mechanics,2010,31(11):3 373–3 378.(in Chinese))
[11]赵明华,雷勇,张锐.岩溶区桩基冲切破坏模式及安全厚度研究[J].岩土力学,2012,33(2):524–530.(ZHAO Minghua,LEI Yong,ZHANG Rui.Study of punching failure mode and safe thickness of pile foundation in karst region[J].Rock and Soil Mechanics,2012,33(2):524–530.(in Chinese))
[12]雷勇,陈秋南,马缤辉.基于极限分析的桩端岩层冲切分析[J].岩石力学与工程学报,2014,33(3):631–638.(LEI Yong,CHEN Qiunan,MA Binhui.Punching analysis of rock at pile tip on limit analysis[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(3):631–638.(in Chinese))
[13]雷勇,尹君凡,陈秋南,等.基于极限分析法的溶洞顶板极限承载力研究[J].岩土力学,2017,38(7):1 926–1 932.(LEI Yong,YIN Junfan,CHEN Qiunan,et al.Study on ultimate load capacity of karst roof based on limit analysis[J].Rock and Soil Mechanics,2017,38(7):1 926–1 932.(in Chinese))
[14]FRALDI M,GUARRACINO F.Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(4):665–673.
[15]CHEN W F.Limit analysis and soil plasticity[M].Amsterdam:Elsevier Science,1975:28–63.
[16]SERRANO A,OLALLA C.Tensile resistance of rock anchors[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(4):449–474.
[17]雷勇,尹君凡,陈秋南.岩溶区桩端基岩极限承载力及破坏模式试验研究[J].应用力学学报,2017,34(4):774–780.(LEI Yong,YIN Junfan,CHEN Qiunan.Experimental study on ultimate bearing capacity and failure mode of pile end bedrock in karst area[J].Chinese Journal of Applied Mechanics,2017,34(4):774–780.(in Chinese))
[18]柏华军.考虑溶洞顶板自重时桩端持力岩层安全厚度计算方法[J].岩土力学,2016,37(10):2 945–2 952.(BAI Huajun.A method for calculating the safety rock thickness of pile bearing strata with considering deadweight of karst cave roof[J].Rock and Soil Mechanics,2016,37(10):2 945–2 952.(in Chinese))
[19]RATHIE R N,SILVA P D.Applications of lambert wfunction[J].International Journal of Applied Mathematics and Statistics,2011,23(11):1–15.
[20]阳生权,阳军生,岩体力学[M].北京:机械工业出版社,2008:118–119.(YANG Shengquan,YANG Junsheng.Rockmass mechanics[M].Beijing:China Machine Press,2008:118–119.(in Chinese)
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