地震效应下非线性抗剪强度参数对裂缝边坡稳定性影响的上限解析
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摘要
基于非线性Mohr-Coulomb破坏准则,结合极限分析上限法和拟静力分析法,建立功能方程,推导了地震效应下裂缝边坡的安全系数计算方程。采用数学规划方法,计算了不同参数组合条件下的边坡安全系数值,详细分析了非线性条件下一系列参数对边坡稳定性的影响。研究表明,边坡安全系数随非线性参数和地震效应的增大而减小。对比分析可知,在非线性破坏准则下,裂缝深度较大时,裂缝对边坡稳定性影响显著,且边坡越陡影响越大;当裂缝深度超过某个值后,临界破坏面起始端可能不穿过裂缝最底端,而是从裂缝中间某部位穿过。在地震效应作用下,非线性抗剪强度参数对安全系数影响显著。研究成果进一步完善了裂缝边坡稳定性分析内容,所列图表为边坡的设计与施工提供有益参考。
The expression of safety factor for slopes with cracks subjected to seismic forces is deduced through establishing an energy equation using upper bound limit analysis and pseudo-static analysis based on nonlinear Mohr-Coulomb failure criterion. Safety factors are calculated using mathematical programming method with combinations of different parameters. A detailed parametric study is performed to determine the influence of slope angle, upper slope angle, horizontal seismic coefficient, vertical seismic coefficient, crack depth, geotechnical parameters on slope stability based on nonlinear failure criterion. Results show that safety factor decreases as the nonlinear parameter and seismic forces increase. Cracks can significantly influence on slope stability under nonlinear failure criterion when crack depth is large, especially for steep slope. When the value of crack depth exceeds a certain value,the beginning of critical failure surface may not pass through the lowest end of crack, but cross at a middle part the crack. It is also observed that when slopes is subjected to seismic effect, the safety factor depends significantly on the nonlinear shear strength parameters. Research results perfect the contents of stability analysis of slopes with cracks and the charts provide an useful reference for design and the construction of slop parameters on stability of slopes with cracks.
The expression of safety factor for slopes with cracks subjected to seismic forces is deduced through establishing an energy equation using upper bound limit analysis and pseudo-static analysis based on nonlinear Mohr-Coulomb failure criterion. Safety factors are calculated using mathematical programming method with combinations of different parameters. A detailed parametric study is performed to determine the influence of slope angle, upper slope angle, horizontal seismic coefficient, vertical seismic coefficient, crack depth, geotechnical parameters on slope stability based on nonlinear failure criterion. Results show that safety factor decreases as the nonlinear parameter and seismic forces increase. Cracks can significantly influence on slope stability under nonlinear failure criterion when crack depth is large, especially for steep slope. When the value of crack depth exceeds a certain value,the beginning of critical failure surface may not pass through the lowest end of crack, but cross at a middle part the crack. It is also observed that when slopes is subjected to seismic effect, the safety factor depends significantly on the nonlinear shear strength parameters. Research results perfect the contents of stability analysis of slopes with cracks and the charts provide an useful reference for design and the construction of slop parameters on stability of slopes with cracks.
引文
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[23]胡卫东,张国祥.非线性破坏准则下的边坡稳定塑性极限分析[J].岩土力学,2007,28(9):1909-1913.HU Wei-dong,ZHANG Guo-xiang.Plastic limit analysis of slope stability with nonlinear failure criterion[J].Rock and Soil Mechanics,2007,28(9):1909-1913.
[24]TERZAGHI K.Mechanisms of landslides(engineering geology(Berdey)colume)[M].[S.l.]:Geological Society of America,1950.
[25]唐高朋,赵炼恒,李亮,等.基于MATLAB的边坡稳定性极限上限分析程序开发[J].岩土力学,2013,34(7):2091-2098.TANG Gao-peng,ZHAO Lian-heng,LI Liang,et al.Program development for slope stability using MATLAB software and upper bound limit analysis[J].Rock and Soil Mechanics,2013,34(7):2091-2098.
[26]JIANG J C,BAKER R,YAMAGAMI T.The effect of strength envelope nonlinearity on slope stability computations[J].Canadian Geotechnical Journal,2003,40(2):308-325.
[27]CHARLES J A,SOARES M M.The stability of slopes in soils with nonlinear failure envelopes[J].Canadian Geotechnical Journal,1984,21(3):397-406.
[28]LI D,CHENG Y.Lower bound limit analysis using nonlinear failure criteria[J].Procedia Earth and Planetary Science,2012,5:170-174.
[29]BAKER R.Tensile strength,tension cracks,and stability of slopes[J].Japanese Society of Soil Mechanics and Foundation Engineering,1981,21(2):1-17
[30]SHUKLA S K,KHANDELWAL S,VERMA V N,et al.Effect of surcharge on the stability of anchored rock slope with water filled tension crack under seismic loading condition[J].Geotechnical and Geological Engineering,2009,27(4):529-538.
[31]EID H T.Stability charts for uniform slopes in soils with nonlinear failure envelopes[J].Engineering Geology,2014,168:38-45.
[2]UTILI S.Investigation by limit analysis on the stability of slopes with cracks[J].Geotechnique,2013,63(2):1-15.
[3]MICHALOWSKI R L.Stability assessment of slopes with cracks using limit analysis[J].Canadian Geotechnical Journal,2013,50(10):1011-1021.
[4]MICHALOWSKI R L.Cracks in slopes:Limit analysis approach to stability assessment[C]//Proceedings of Geocongress.Oakland:[s.n.],2012:442-450.
[5]MICHALOWSKI R L.Stability charts for uniform slopes[J].Journal of Geotechnical and Geoenvironmental Engineering,2002,128(4):351-355.
[6]ZHANG K,CAO P.Slope seismic stability analysis on kinematical element method and its application[J].Soil Dynamics and Earthquake Engineering,2013,50:62-71.
[7]郑颖人,叶海林,黄润秋.地震边坡破坏机制及其破裂面的分析探讨[J].岩石力学与工程学报,2009,28(8):1714-1723.ZHENG Ying-Ren,YE Hai-Lin,HUANG Run-Qiu.Analysis and discussion of failure mechanism and fracture surface of slope under earthquake[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(8):1714-1723.
[8]BAKER R,SHUKHA R,OPERSTEIN V,et al.Stability charts for pseudo-static slope stability analysis[J].Soil Dynamics and Earthquake Engineering,2006,26(9):813-823.
[9]ZHANG Y B,CHEN G Q,ZEN K,et al.Limit analysis of seismic slope stability based on tension-shear failure mechanism[C]//Slope Stability:International Symposium on Rock Slope Stability in Open Pit Mining and Civil Engineering.Vancouver:[s.n.],2011:18-21.
[10]LADE P V.Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces[J].International Journal of Solids and Structures,1977,13(11):1019-1035.
[11]AGAR J G,MORGENSTERN N R,SCOTT J D.Shear strength and stress-strain behaviour of Athabasca Oil Sand at elevated temperatures and pressures[J].Canadian Geotechnical Journal,1987,24(1):1-10.
[12]SANTARELLI F J.Theoretical and experimental investigation of the stability of the axisymmetric wellbore[D].London:Imperial College London,University of London,1987.
[13]刘宝琛,崔志莲,涂继飞.幂函数型岩石强度准则研究[J].岩石力学与工程学报,1997,16(5):437-444.LIU Bao-chen,CUI Zhi-lian,TU Ji-fei.A study of strength criterion in power function for rock material[J].Chinese Journal of Rock Mechanics and Engineering,1997,16(5):437-444.
[14]HOEK E,BROWN E T.Empirical strength criterion for rock masses[J].Journal of Geotechnical and Geoenvironmental Engineering,1980,106(GT9):1013-1035.
[15]HOEK E,BROWN E T.Practical estimates of rock mass strength[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(8):1165-1186.
[16]ZHANG X J,CHEN W F.Stability analysis of slopes with general nonlinear failure criterion[J].International Journal for Numerical and Analytical Methods in Geomechanics,1987,11(1):33-50.
[17]赵炼恒,李亮,但汉成,等.极限上限分析中“切线法”引入非线性破坏准则的探讨[J].长江科学院院报,2010,27(8):34-39.ZHAO Lian-heng,LI Liang,DAN Han-cheng,et al.Discussion on generalized tangential method led in nonlinear failure criterion in upper boundary limit analysis[J].Journal of Yangtze River Scientific Research Institute,2010,27(8):34-39.
[18]ZHAO L H,LI L,YANG F,et al.Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique[J].Journal of Central South University of Technology,2010,17:836-844.
[19]ZHAO L H,YANG F,ZHANG Y B,et al.Effects of shear strength reduction strategies on safety factor of homogeneous slope based on a general nonlinear failure criterion[J].Computers and Geotechnics,2015,63:215-228.
[20]张迎宾,李亮,赵炼恒,等.基于非线性破坏准则的边坡稳定性极限分析[J].岩土力学,2011,32(11):3313-3318.ZHANG Ying-bin,LI Liang,ZHAO Lian-heng,et al.Limit analysis of slope stability based on nonlinear failure criterion[J].Rock and Soil Mechanics,2011,32(11):3313-3318.
[21]YANG X,CHI S.Upper bound finite element analysis of slope stability using a nonlinear failure criterion[J].Computers and Geotechnics,2013,54:185-191.
[22]YANG X L,YIN J H.Slope stability analysis with nonlinear failure criterion[J].Journal of Engineering Mechanics,2004,130(3):267-273.
[23]胡卫东,张国祥.非线性破坏准则下的边坡稳定塑性极限分析[J].岩土力学,2007,28(9):1909-1913.HU Wei-dong,ZHANG Guo-xiang.Plastic limit analysis of slope stability with nonlinear failure criterion[J].Rock and Soil Mechanics,2007,28(9):1909-1913.
[24]TERZAGHI K.Mechanisms of landslides(engineering geology(Berdey)colume)[M].[S.l.]:Geological Society of America,1950.
[25]唐高朋,赵炼恒,李亮,等.基于MATLAB的边坡稳定性极限上限分析程序开发[J].岩土力学,2013,34(7):2091-2098.TANG Gao-peng,ZHAO Lian-heng,LI Liang,et al.Program development for slope stability using MATLAB software and upper bound limit analysis[J].Rock and Soil Mechanics,2013,34(7):2091-2098.
[26]JIANG J C,BAKER R,YAMAGAMI T.The effect of strength envelope nonlinearity on slope stability computations[J].Canadian Geotechnical Journal,2003,40(2):308-325.
[27]CHARLES J A,SOARES M M.The stability of slopes in soils with nonlinear failure envelopes[J].Canadian Geotechnical Journal,1984,21(3):397-406.
[28]LI D,CHENG Y.Lower bound limit analysis using nonlinear failure criteria[J].Procedia Earth and Planetary Science,2012,5:170-174.
[29]BAKER R.Tensile strength,tension cracks,and stability of slopes[J].Japanese Society of Soil Mechanics and Foundation Engineering,1981,21(2):1-17
[30]SHUKLA S K,KHANDELWAL S,VERMA V N,et al.Effect of surcharge on the stability of anchored rock slope with water filled tension crack under seismic loading condition[J].Geotechnical and Geological Engineering,2009,27(4):529-538.
[31]EID H T.Stability charts for uniform slopes in soils with nonlinear failure envelopes[J].Engineering Geology,2014,168:38-45.
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