基于上限分析法的含夹层边坡地震稳定性分析
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摘要
为了判断含夹层岩质边坡在地震荷载下的稳定性,丰富岩质边坡在地震荷载下的稳定性分析方法,探讨极限分析中的上限分析法如何应用于评价边坡在地震荷载作用下的稳定性,文中介绍了上限分析法在边坡稳定性判断中的应用和极限分析法的基本原理,并详述了如何基于波动理论计算地震波对边坡中滑动体的做功功率,针对能量系数随时间变化的特性,提出了以最小平均能量系数作为边坡稳定性的评价标准。最后结合室内振动台模型试验,通过计算最小平均能量系数判断的稳定性结果与模型的实际破坏结果进行对比,验证极限分析上限法应用于地震稳定性分析的合理性。研究表明:以正弦波代替地震波,基于波动理论可以求得该正弦波对边坡滑体的做功功率,该功率为一个随时间变化的函数,因此提出以最小平均能量系数作为评价标准,当最小平均能量系数Esmin> 1时,消耗的功率大于外力做功功率,边坡处于稳定状态;当最小平均能量系数Esmin<1时,消耗功率小于外力做功功率,边坡发生滑动破坏;当最小平均能量系数Esmin=1时,边坡处于极限稳定状态;应用极限分析上限法计算出的最小平均能量系数判断的模型边坡破坏状态与实际破坏基本一致,上限法求得的最小平均能量系数可作为含夹层边坡的稳定性判断标准。
To judge the stability of slope containing interlayer and enrich the analysis method of rock slope stability under seismic load,and discuss how to apply the upper bound analysis method in limit analysis to evaluate the stability of slope under seismic load,the application of upper bound analysis method in slope stability judgment and the basic principle of limit analysis method are introduced,and the way of calculating the working power of seismic wave to sliding body in slope based on wave theory is described in detail. In view of the characteristics of energy coefficient varying with time,the minimum average energy coefficient is proposed as an evaluation criterion for slope stability. Finally,combining with the indoor shaking table model test,the judged stability result by calculating the minimum average energy coefficient is compared to the actual model failure result,and the rationality of limit analysis upper bound method applied to seismic stability analysis is verified. The result shows that( 1) The sinusoidal wave can be used to replace the seismic wave,and the working power of sinusoidal wave to the slope sliding body can be calculated based on the wave theory the power is a function of time,therefore,the minimum average energy coefficient is proposed as the evaluation criterion. When the minimum average energy coefficient Esmin> 1,the power consumed is greater than the external power,the slope is in a stable state; when the minimum average energycoefficient Esmin< 1,the power consumed is less than the external power,and the slope slips and destroyed;when the minimum average energy coefficient Esmin= 1,the slope is in a limit stable state.( 2) The failure state of the model slope judged by the minimum average energy coefficient which calculated by the upper limit analysis method is basically consistent with the actual failure,the minimum average energy coefficient obtained by the upper limit analysis method can be used as the criterion for judging the stability of slope contains interlayer.
To judge the stability of slope containing interlayer and enrich the analysis method of rock slope stability under seismic load,and discuss how to apply the upper bound analysis method in limit analysis to evaluate the stability of slope under seismic load,the application of upper bound analysis method in slope stability judgment and the basic principle of limit analysis method are introduced,and the way of calculating the working power of seismic wave to sliding body in slope based on wave theory is described in detail. In view of the characteristics of energy coefficient varying with time,the minimum average energy coefficient is proposed as an evaluation criterion for slope stability. Finally,combining with the indoor shaking table model test,the judged stability result by calculating the minimum average energy coefficient is compared to the actual model failure result,and the rationality of limit analysis upper bound method applied to seismic stability analysis is verified. The result shows that( 1) The sinusoidal wave can be used to replace the seismic wave,and the working power of sinusoidal wave to the slope sliding body can be calculated based on the wave theory the power is a function of time,therefore,the minimum average energy coefficient is proposed as the evaluation criterion. When the minimum average energy coefficient Esmin> 1,the power consumed is greater than the external power,the slope is in a stable state; when the minimum average energycoefficient Esmin< 1,the power consumed is less than the external power,and the slope slips and destroyed;when the minimum average energy coefficient Esmin= 1,the slope is in a limit stable state.( 2) The failure state of the model slope judged by the minimum average energy coefficient which calculated by the upper limit analysis method is basically consistent with the actual failure,the minimum average energy coefficient obtained by the upper limit analysis method can be used as the criterion for judging the stability of slope contains interlayer.
引文
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[8]宋玉环.西南地区软硬互层岩质边坡变形破坏模式及稳定性研究[D].成都:成都理工大学,2011.SONG Yu-huan.Failure Mode and Instability of Slopes with Soft and Hard Rock Interbedded Laminated Structure in Southwest China[D].Chengdu:Chengdu University of Technology,2011.
[9]王根龙,伍法权,张茂省.平面滑动型岩质边坡稳定性极限分析上限法[J].工程地质学报,2011,19(2):176-180.WANG Gen-long,WU Fa-quan,ZHANG Mao-sheng.Method of Upper Bound Limit Analysis for Plane Sliding of Rock Slopes[J].Journal of Engineering Geology,2011,19(2):176-180.
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[12]吴兆营,薄景山,刘红帅,等.岩体边坡地震稳定性动安全系数分析方法[J].防灾减灾工程学报,2004,24(3):237-241.WU Zhao-ying,BO Jing-shan,LIU Hong-shuai,et al.AMethod for Evaluating Dynamic Safety Factor Rock Slope Seismic Stability Analysis[J].Journal of Disaster Prevention and Mitigation Engineering,2004,24(3):237-241.
[13]李永靖,乔朋庆,邢洋,等.地震荷载下煤矸石路基变形室内试验与数值模拟分析[J].中国地质灾害与防治学报,2014,25(2):54-59.LI Yong-jing,QIAO Peng-qing,XING Yang,et al.Experimental Study and Numerical Simulation on Deformation Characteristics of Coal Gangue Fill Subgrade under Seismic Loads[J].The Chinese Journal of Geological Hazard and Control,2014,25(2):54-59.
[14]方勇,符亚鹏,周超月,等.公路隧道下穿双层采空区开挖过程模型试验[J].岩石力学与工程学报,2014,33(11):2247-2257.FANG Yong,FU Ya-peng,ZHOU Chao-yue,et al.Model Test of Highway Tunnel Construction under Doubledeck Mined-out Area[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(11):2247-2257.
[15]张延杰,王旭,梁庆国,等.湿陷性黄土模型试验相似材料的研制[J].岩石力学与工程学报,2013,32(2):4019-4024.ZHANG Yan-jie,WANG Xu,LIANG Qing-guo,et al.Development of Model Test Similar Material of Collapsible Loess[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(2):4019-4024.
[16]杨俊杰.相似理论与结构模型试验[M].武汉:武汉理工大学出版社,2005:5-11.YANG Jun-jie.Similarity Theory and Structure Model Test[M].Wuhan:Wuhan University of Technology Press,2005:5-11.
[17]万利军,单伟,袁建新.自锚式悬索桥静力特性模型试验研究[J].公路交通科技,2014,31(6):108-114.WAN Li-jun,SHAN Wei,YUAN Jian-xin.Experimental Study on Static Characteristics Model of Self-anchored Suspension Bridge[J].Journal of Highway and Transportation Research an Development,2014,31(6):108-114.
[18]关振长,龚振峰,陈仁春,等.基于正交设计的岩质相似材料配比试验研究[J].公路交通科技,2016,33(9):92-98,111.GUAN Zhen-chang,GONG Zhen-feng,CHEN Ren-chun,et al.Experimental Study on Mix Proportion of Rock Similar Material Based on Orthogonal Design[J].Journal of Highway and Transportation Research an Development,2016,33(9):92-98,111.
[2]宋玉环.西南地区软硬互层岩质边坡变形破坏模式及稳定性研究[D].成都:成都理工大学,2011.SONG Yu-huan.Failure Models and Instability of Slopes with Soft and Hard Rock Interbedded Laminated Structure in Southwest China[D].Chengdu:Chengdu University of Technology,2011.
[3]徐冠军.滇西南地区高边坡抗震性能振动台模拟试验研究[D].西安:长安大学,2015.XU Guan-jun.Study on Seismic Behavior of High Slope through Shaking Table Test in Southwest Yunnan[D].Xi'an:Chang'an University,2015.
[4]何满朝.软岩工程力学的理论与实践[M].北京:中国矿业大学出版社,1996.HE Man-chao.Theory and Practice of Soft Rock Engineering Mechanics[M].Beijing:China Mining University Press,1996.
[5]时少波.地震荷载作用下风积沙高路堤稳定性模型试验研究[D].西安:长安大学,2015.SHI Shao-bo.Test Research of Aeolian Sand Embankment Stability under Seismic Load[D].Xi'an:Chang'an University,2015.
[6]冯志仁,刘红帅,于龙.地震作用下含软弱夹层顺层岩质边坡表面放大效应研究[J].防灾减灾工程学报,2014,34(1):96-100.FENG Zhi-ren,LIU Hong-shuai,YU Long.Surface Amplification Effect of Bedding Rocky Slope with Weak Interlayer under Earthquake[J].Journal of Disaster Prevention and Mitigation Engineering,2014,34(1):96-100.
[7]陈国庆,黄润秋,石豫川,等.基于动态和整体强度折减法的边坡稳定性分析[J].岩石力学与工程学报,2014,33(2):243-256.CHEN Guo-qing,HUANG Run-qiu,SHI Yu-chuan,et al.Stability Analysis of Slope Based on Dynamic and Whole Strength Reduction Methods[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(2):243-256.
[8]宋玉环.西南地区软硬互层岩质边坡变形破坏模式及稳定性研究[D].成都:成都理工大学,2011.SONG Yu-huan.Failure Mode and Instability of Slopes with Soft and Hard Rock Interbedded Laminated Structure in Southwest China[D].Chengdu:Chengdu University of Technology,2011.
[9]王根龙,伍法权,张茂省.平面滑动型岩质边坡稳定性极限分析上限法[J].工程地质学报,2011,19(2):176-180.WANG Gen-long,WU Fa-quan,ZHANG Mao-sheng.Method of Upper Bound Limit Analysis for Plane Sliding of Rock Slopes[J].Journal of Engineering Geology,2011,19(2):176-180.
[10]陈祖煜.土力学经典问题的极限分析上、下限解[J].岩土工程学报,2002,24(1):1-11.CHEN Zu-yu.Limit Analysis for the Classic Problems of Soil Mechanics[J].Chinese Journal of Geotechnical Engineering,2002,24(1):1-11.
[11]刘汉龙,费康,高玉峰.边坡地震稳定性时程分析方法[J].岩土力学,2003,24(4):553-556,560.LIU Han-long,FEI Kang,GAO Yu-feng.Time History Analysis Method of Slope Seismic Stability[J].Rock and Soil Mechanics,2003,24(4):553-556,560.
[12]吴兆营,薄景山,刘红帅,等.岩体边坡地震稳定性动安全系数分析方法[J].防灾减灾工程学报,2004,24(3):237-241.WU Zhao-ying,BO Jing-shan,LIU Hong-shuai,et al.AMethod for Evaluating Dynamic Safety Factor Rock Slope Seismic Stability Analysis[J].Journal of Disaster Prevention and Mitigation Engineering,2004,24(3):237-241.
[13]李永靖,乔朋庆,邢洋,等.地震荷载下煤矸石路基变形室内试验与数值模拟分析[J].中国地质灾害与防治学报,2014,25(2):54-59.LI Yong-jing,QIAO Peng-qing,XING Yang,et al.Experimental Study and Numerical Simulation on Deformation Characteristics of Coal Gangue Fill Subgrade under Seismic Loads[J].The Chinese Journal of Geological Hazard and Control,2014,25(2):54-59.
[14]方勇,符亚鹏,周超月,等.公路隧道下穿双层采空区开挖过程模型试验[J].岩石力学与工程学报,2014,33(11):2247-2257.FANG Yong,FU Ya-peng,ZHOU Chao-yue,et al.Model Test of Highway Tunnel Construction under Doubledeck Mined-out Area[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(11):2247-2257.
[15]张延杰,王旭,梁庆国,等.湿陷性黄土模型试验相似材料的研制[J].岩石力学与工程学报,2013,32(2):4019-4024.ZHANG Yan-jie,WANG Xu,LIANG Qing-guo,et al.Development of Model Test Similar Material of Collapsible Loess[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(2):4019-4024.
[16]杨俊杰.相似理论与结构模型试验[M].武汉:武汉理工大学出版社,2005:5-11.YANG Jun-jie.Similarity Theory and Structure Model Test[M].Wuhan:Wuhan University of Technology Press,2005:5-11.
[17]万利军,单伟,袁建新.自锚式悬索桥静力特性模型试验研究[J].公路交通科技,2014,31(6):108-114.WAN Li-jun,SHAN Wei,YUAN Jian-xin.Experimental Study on Static Characteristics Model of Self-anchored Suspension Bridge[J].Journal of Highway and Transportation Research an Development,2014,31(6):108-114.
[18]关振长,龚振峰,陈仁春,等.基于正交设计的岩质相似材料配比试验研究[J].公路交通科技,2016,33(9):92-98,111.GUAN Zhen-chang,GONG Zhen-feng,CHEN Ren-chun,et al.Experimental Study on Mix Proportion of Rock Similar Material Based on Orthogonal Design[J].Journal of Highway and Transportation Research an Development,2016,33(9):92-98,111.
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