岩溶区条形刚性基础下伏孔洞顶板冲切极限承载力变分分析
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摘要
基于Hoek-Brown破坏准则及相关联流动法则,构建岩溶区条形刚性基础下伏孔洞岩体冲切破坏机制;根据极限分析上限定理,计算冲切破坏极限状态下的内能耗散功率和外力功率;根据虚功率原理得到极限承载力的泛函;利用变分原理结合边界条件,推导出冲切破坏曲面函数表达式,进而得到冲切极限承载力及冲切破坏形状。分析了岩体单一参数变化时,自由冲切和非自由冲切条件下极限承载力的变化情况和破坏模式。结果表明:材料参数B的变化对刚性基础的极限承载力的影响较为显著。随着材料参数B增大,条形刚性基础下伏孔洞顶板冲切极限承载力不断减小,自由冲切条件下孔洞破坏宽度减小,非自由冲切破坏时破坏曲线趋近于直线。
Based on the Hoek-Brown failure criterion and the associated flow rule, the punching failure mechanism of the rock with an underlying rectangular chamber was constructed. The power of internal energy dissipation and the power of the external forces under the punching failure limit state were calculated, according to the upper bound theorem of limit analysis. The functional of the bearing capacity was obtained by means of the virtual work principle. The function expression of blanking failure surface is derived by using variational principle and combining boundary conditions, further, the punching ultimate bearing capacity(UBC) and the failure shape were obtained. In this paper, the changes of failure modes and the ultimate bearing capacity under the conditions of free blanking and non-free cutting are analyzed with the variation of single parameter of rock mass. The results show: the influence of the material parameter B on the ultimate bearing capacity of the rigid foundation is much more significant, the ultimate bearing capacity decreases gradually when B increases, the failure width of the chamber decreases under free punching condition and the failure curve is close to a straight line under non free condition.
Based on the Hoek-Brown failure criterion and the associated flow rule, the punching failure mechanism of the rock with an underlying rectangular chamber was constructed. The power of internal energy dissipation and the power of the external forces under the punching failure limit state were calculated, according to the upper bound theorem of limit analysis. The functional of the bearing capacity was obtained by means of the virtual work principle. The function expression of blanking failure surface is derived by using variational principle and combining boundary conditions, further, the punching ultimate bearing capacity(UBC) and the failure shape were obtained. In this paper, the changes of failure modes and the ultimate bearing capacity under the conditions of free blanking and non-free cutting are analyzed with the variation of single parameter of rock mass. The results show: the influence of the material parameter B on the ultimate bearing capacity of the rigid foundation is much more significant, the ultimate bearing capacity decreases gradually when B increases, the failure width of the chamber decreases under free punching condition and the failure curve is close to a straight line under non free condition.
引文
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[7] 曹文贵, 李媛, 翟友成. 基于Info-Gap理论的基桩下伏岩溶顶板稳定性的主动分析方法[J]. 岩石力学与工程学报, 2013, 32(2): 393-400.CAO Wengui, LI Yuan, ZHAI Youcheng. Active analysis method for stability of karst roof under foundation pile based on info-gap theory[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(2): 393-400. (in Chinese)
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[9] 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(增刊): 3655-3662.WANG Huabin, LIU Zhifeng, ZHAO Wenfeng, et al. Research on stability of cave roof under pile loading in bridge construction engineering[J]. Chinese Journal of Rock Mechanics and Engineering, 2013(S2): 3655-3662. (in Chinese)
[10] 贺建青, 喻畅英, 肖兰, 等. 基于上限定理确定岩溶区桩端极限承载力及其下伏溶洞顶板安全厚度[J]. 自然灾害学报, 2017, 26(2): 47-52.HE Jianqing, YU Changying, L Xiao, et al. Determination of ultimate bearing capacity of pile tip and safety thickness of cave roofs under pile tip in karst area based on upper bound theorem[J]. Journal of Natural Disasters, 2017, 26(2): 47-52. (in Chinese)
[11] GAO Shijuan, WANG Lichang, LONG Wei. Variation of the ultimate bearing capacity of karst cave roof under the loading of pile foundation[J]. Electronic Journal of Geotechnical Engineering, 2014(19): 8467-8483.
[12] 赵明华, 邱志博, 张锐. 岩溶区地基极限承载力上限有限元数值模拟分析[J]. 水文地质工程地质, 2014, 41(6): 57-62.ZHAO Minghua, QIU Zhibo, ZHANG Rui. Numerical simulation analysis of foundation ultimate bearing capacity in Karst area using upper bound finite element method[J]. Hydrogeology & Engineering Geology, 2014, 41(6): 57-62. (in Chinese)
[13] 赵明华, 卢晓明, 张锐. 下伏空洞地基极限承载力与破坏模式上限有限元法[J]. 岩土力学, 2017, 38(1): 229-236.ZHAO Minghua, LU Xingming, ZHANG Rui. Upper bound finite element method for ultimate bearing capacity and failure mechanism of subgrade above void[J]. Rock and Soil Mechanics, 2017, 38(1): 229-236. (in Chinese)
[14] 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): 1926-1932.LEI Yong, YIN Junfan, CHEN Qiunan, et al. Determination of ultimate bearing capacity of cave roof using limit analysis method[J]. Rock and Soil Mechanics, 2017, 38(7): 1926-1932.
[15] 宋建波. 岩体经验强度准则及其在地质工程中的应用[M]. 北京: 地质出版社, 2002.SONG Jianbo. Empirical Strength Criterion and Application of Rock Mass in Greological Engineering[M]. Beijing: Geological Publishing House, 2002. (in Chinese)
[16] Hoek E, Carranza-Torres C, Corkum B. Hoek-Brown criterion-2002 edition[M]. Proceedings of NARMS-TAC Conference, Toronto, Canada, 2002.
[17] Hoek E, Brown E T. Practical estimate the rock mass strength[J]. International Journal of Rock Mechanics and Mining Science, 1997, 34(8): 1165-1186.
[18] 张学言. 岩土塑形力学[M]. 北京: 人民交通出版社, 1993. ZHANG Xueyan. Geotechnical Plastic Mechanics[M]. Beijing: China Communication Press, 1993. (in Chinese)
[19] 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.
[2] 张惠乐, 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 study and analysis on rock-socketed pile in karst area[J]. China Civil Engineering Journal, 2013, 46(1): 92-103. (in Chinese)
[3] 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, 24(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, 24(1): 64-68. (in Chinese)
[4] 赵明华, 张锐, 胡柏学, 等. 岩溶区桩端下伏溶洞顶板稳定性分析研究[J]. 公路交通科技, 2009, 26(9): 13-16.ZHAO Minghua, ZHANG Rui, HU Boxue, et al. Analysis of stability of cave roof under pile tip in karst area[J]. Journal of Highway and Transportation Research and Development, 2009, 26(9): 13-16. (in Chinese)
[5] Walraven J C. Fundamental analysis of aggregate interlock[J]. ASCE, Journal of the Structural Division, 1981, 107(ST11): 2245-2270.
[6] 黄明, 付俊杰, 陈福全, 等. 桩端荷载与地震耦合作用下溶洞顶板的破坏特征及安全厚度计算[J]. 岩土力学, 2017, 38(11): 3154-3162. HUANG Ming, FU Junjie, CHEN Fuquan, et al. Damage characteristics of karst cave roof and its safety thickness calculation under the coupling effect of pile-tip load and seismic wave[J]. Rock and Soil Mechanics, 2017, 38(11): 3154-3162. (in Chinese)
[7] 曹文贵, 李媛, 翟友成. 基于Info-Gap理论的基桩下伏岩溶顶板稳定性的主动分析方法[J]. 岩石力学与工程学报, 2013, 32(2): 393-400.CAO Wengui, LI Yuan, ZHAI Youcheng. Active analysis method for stability of karst roof under foundation pile based on info-gap theory[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(2): 393-400. (in Chinese)
[8] JIANG Chong, LIU Lang, WU Junping. A new method determining safe thickness of karst cave roof under pile tip[J]. Journal of Central South University, 2014, 21(3): 1190-1196.
[9] 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(增刊): 3655-3662.WANG Huabin, LIU Zhifeng, ZHAO Wenfeng, et al. Research on stability of cave roof under pile loading in bridge construction engineering[J]. Chinese Journal of Rock Mechanics and Engineering, 2013(S2): 3655-3662. (in Chinese)
[10] 贺建青, 喻畅英, 肖兰, 等. 基于上限定理确定岩溶区桩端极限承载力及其下伏溶洞顶板安全厚度[J]. 自然灾害学报, 2017, 26(2): 47-52.HE Jianqing, YU Changying, L Xiao, et al. Determination of ultimate bearing capacity of pile tip and safety thickness of cave roofs under pile tip in karst area based on upper bound theorem[J]. Journal of Natural Disasters, 2017, 26(2): 47-52. (in Chinese)
[11] GAO Shijuan, WANG Lichang, LONG Wei. Variation of the ultimate bearing capacity of karst cave roof under the loading of pile foundation[J]. Electronic Journal of Geotechnical Engineering, 2014(19): 8467-8483.
[12] 赵明华, 邱志博, 张锐. 岩溶区地基极限承载力上限有限元数值模拟分析[J]. 水文地质工程地质, 2014, 41(6): 57-62.ZHAO Minghua, QIU Zhibo, ZHANG Rui. Numerical simulation analysis of foundation ultimate bearing capacity in Karst area using upper bound finite element method[J]. Hydrogeology & Engineering Geology, 2014, 41(6): 57-62. (in Chinese)
[13] 赵明华, 卢晓明, 张锐. 下伏空洞地基极限承载力与破坏模式上限有限元法[J]. 岩土力学, 2017, 38(1): 229-236.ZHAO Minghua, LU Xingming, ZHANG Rui. Upper bound finite element method for ultimate bearing capacity and failure mechanism of subgrade above void[J]. Rock and Soil Mechanics, 2017, 38(1): 229-236. (in Chinese)
[14] 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): 1926-1932.LEI Yong, YIN Junfan, CHEN Qiunan, et al. Determination of ultimate bearing capacity of cave roof using limit analysis method[J]. Rock and Soil Mechanics, 2017, 38(7): 1926-1932.
[15] 宋建波. 岩体经验强度准则及其在地质工程中的应用[M]. 北京: 地质出版社, 2002.SONG Jianbo. Empirical Strength Criterion and Application of Rock Mass in Greological Engineering[M]. Beijing: Geological Publishing House, 2002. (in Chinese)
[16] Hoek E, Carranza-Torres C, Corkum B. Hoek-Brown criterion-2002 edition[M]. Proceedings of NARMS-TAC Conference, Toronto, Canada, 2002.
[17] Hoek E, Brown E T. Practical estimate the rock mass strength[J]. International Journal of Rock Mechanics and Mining Science, 1997, 34(8): 1165-1186.
[18] 张学言. 岩土塑形力学[M]. 北京: 人民交通出版社, 1993. ZHANG Xueyan. Geotechnical Plastic Mechanics[M]. Beijing: China Communication Press, 1993. (in Chinese)
[19] 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.
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