考虑岩石蠕变与损伤的直立层状边坡倾倒模型
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摘要
倾倒破坏是直立层状岩质边坡失稳破坏的模式之一,目前仅研究了岩石分别为线弹性体、损伤体或蠕变体时在自重作用下边坡倾倒临界高度的计算方法,而实际工程中,岩体则往往同时具有损伤及蠕变特性。为此,针对软岩中同时存在的损伤与蠕变特性,在经典欧拉压杆模型的基础上分别假定岩石为Maxwell蠕变体、基于Weibull分布的统计损伤体及损伤与蠕变共存的复合体等三种模型,获得了相应的边坡倾倒临界高度计算方法,并讨论了相关参数对计算结果的影响。研究结果表明,在直立层状边坡倾倒计算中,应同时考虑细观损伤与蠕变对计算结果的影响,当考虑岩石蠕变性时,边坡倾倒临界高度随时间增加近似呈指数规律下降。
Toppling failure is one of the main instability modes of the vertical slabbed rock slope.However,the current calculation methods of the slope toppling critical height is based on the assumptions that the rock is a linear elastic body,a damage body or a creep body,respectively.However,the rock mass in engineering practices often has the damage and creep properties,and therefore the existing studies cannot meet the practical engineering needs.In this paper,considering the soft rock having both damage and creep properties,the corresponding calculation methods of the slope toppling critical height are obtained based on the classical Euler compression rod model when the rock is assumed as the Maxwell creep body,the Weibull statistical damage body and the combined body with damage and creep properties,respectively.In addition,the effect of the relevant parameters on the calculation results is discussed.The calculation results show that the effect of the mesoscopic damage should be considered in toppling calculation of the vertical slabbed rock slope.When the rock creep property is taken into account,the slope toppling critical height decreases generally following an exponential law with the elapsed time.
Toppling failure is one of the main instability modes of the vertical slabbed rock slope.However,the current calculation methods of the slope toppling critical height is based on the assumptions that the rock is a linear elastic body,a damage body or a creep body,respectively.However,the rock mass in engineering practices often has the damage and creep properties,and therefore the existing studies cannot meet the practical engineering needs.In this paper,considering the soft rock having both damage and creep properties,the corresponding calculation methods of the slope toppling critical height are obtained based on the classical Euler compression rod model when the rock is assumed as the Maxwell creep body,the Weibull statistical damage body and the combined body with damage and creep properties,respectively.In addition,the effect of the relevant parameters on the calculation results is discussed.The calculation results show that the effect of the mesoscopic damage should be considered in toppling calculation of the vertical slabbed rock slope.When the rock creep property is taken into account,the slope toppling critical height decreases generally following an exponential law with the elapsed time.
引文
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[9]张天军.直立顺层边坡的流变特性研究[J].西安科技大学学报,2005,25(1):103-105.Zhang T J.Instability lag of bluff rock[J].Journal of Xi’an University of Science and Technology,2005,25(1):103-105.(in Chinese)
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[12]谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2004.Xie H P,Chen Zh H.Rock mechanics[M].Beijing:Science Publishing House,2004.(in Chinese)
[13]Krajcinovic D,Silva M A G.Statistical aspects of the continuous damage theory[J].International Journal of Solids&Structures,1982,18(7):551-562.
[14]Weibull W.A statistical distribution function of wide applicability[J].Journal of Applied Mechanics,1951,18:293-297.
[15]袁小清,刘红岩,刘京平.基于宏细观损伤耦合的非贯通裂隙岩体本构模型[J].岩土力学,2015,36(10):2 804-2 814.Yuan X Q,Liu H Y,Liu J P.Constitutive model of rock mass with non-persistent joints based on coupling macroscopic and mesoscopic damages[J].Rock and Soil Mechanics,2015,36(10):2 804-2 814.(in Chinese)
[16]凌建明,孙钧.脆性岩石的细观裂纹损伤及其时效特征[J].岩石力学与工程学报,1993,12(4):304-312.Ling J M,Sun J.On mesocrack damage of brittle rocks and its time-dependent characteristics[J].Chinese Journal of Rock mechanics and Engineering,1993,12(4):304-312.(in Chinese)
[2]Cavers D S.Simple methods to analyze bulking of rock slopes[J].Rock Mechanics,1981,14:87-104.
[3]Qin S,Jiao J J,Wang S.A cusp catastrophe model of instability of slip-buckling slope[J].Rock Mechanics and Rock Engineering,2011,34(2):119-134.
[4]Qi S W,Lan H X,Dong J Y.An analytical solution to slip buckling slope failure triggered by earthquake[J].Engineering Geology,2015,194:4-11.
[5]刘红岩,刘冶,邢闯锋,等.直立层状岩质边坡失稳模型及临界高度分析[J].中国地质灾害与防治学报,2012,23(4):27-30.Liu H Y,Liu Y,Xing Ch F,et al.Instability model of vertical layer rock slope and analysis of its critical heigth[J].The Chinese Journal of Geological Hazard and Control,2012,23(4):27-30.(in Chinese)
[6]刘红岩,丹增卓玛,刘冶,等.基于统计损伤模型的直立层状岩质边坡失稳模型[J].地质力学学报,2013,19(2):198-205.Liu H Y,Dan Z Zh M,Liu Y,et al.Instability model of vertical layer rock slope based on the statistical constitutive damage model[J].Journal of Geomechanics,2013,19(2):198-205.(in Chinese)
[7]孙钧.岩石流变力学及其工程应用研究的若干进展[J].岩石力学与工程学报,2007,26(6):1 081-1 106.Sun J.Rock rheological mechanics and its advance in engineering applications[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(6):1 081-1 106.(in Chinese)
[8]张天军,李云鹏.直立顺层边坡的黏弹性稳定性分析[J].力学与实践,2003,25(6):51-54.Zhang T J,Li Y P.Linear viscoelasticity stability analysis of bluff rock slope[J].Mechanics in Engineering,2003,25(6):51-54.(in Chinese)
[9]张天军.直立顺层边坡的流变特性研究[J].西安科技大学学报,2005,25(1):103-105.Zhang T J.Instability lag of bluff rock[J].Journal of Xi’an University of Science and Technology,2005,25(1):103-105.(in Chinese)
[10]Shames I H,Pitarresi J M.Introduction to solid mechanics[M].3rd ed.New Jersey:Prentice-Hall,2004.
[11]张尧,熊良宵.岩石流变力学的研究现状及其发展方向[J].地质力学学报,2008,14(3):274-285.Zhang Y,Xiong L X.Rock rheological mechanics:present state of research and its direction of development[J].Journal of Geomechanics,2008,14(3):274-285.(in Chinese)
[12]谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2004.Xie H P,Chen Zh H.Rock mechanics[M].Beijing:Science Publishing House,2004.(in Chinese)
[13]Krajcinovic D,Silva M A G.Statistical aspects of the continuous damage theory[J].International Journal of Solids&Structures,1982,18(7):551-562.
[14]Weibull W.A statistical distribution function of wide applicability[J].Journal of Applied Mechanics,1951,18:293-297.
[15]袁小清,刘红岩,刘京平.基于宏细观损伤耦合的非贯通裂隙岩体本构模型[J].岩土力学,2015,36(10):2 804-2 814.Yuan X Q,Liu H Y,Liu J P.Constitutive model of rock mass with non-persistent joints based on coupling macroscopic and mesoscopic damages[J].Rock and Soil Mechanics,2015,36(10):2 804-2 814.(in Chinese)
[16]凌建明,孙钧.脆性岩石的细观裂纹损伤及其时效特征[J].岩石力学与工程学报,1993,12(4):304-312.Ling J M,Sun J.On mesocrack damage of brittle rocks and its time-dependent characteristics[J].Chinese Journal of Rock mechanics and Engineering,1993,12(4):304-312.(in Chinese)
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