基于统一强度理论的岩质边坡稳定动安全系数计算
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摘要
岩质边坡稳定性分析中常用的Mohr-Coulomb、Drucker-Prager屈服准则,其未考虑中间主应力效应或拉压不等效应,较难反映三维复杂边坡空间应力状态。统一强度理论包含了一系列破坏准则,通过调整参数b可反映中间主应力或中间主切应力的影响程度。利用ABAQUS开发了基于统一强度理论材料子程序(UMAT),首先以三维含结构面岩质边坡为例,采用强度折减法,分别计算b为0、0.25、0.5、0.75与1共5种考虑中间主应力不同程度情况下三维含结构面岩质边坡动安全系数曲线。计算结果表明:不同b值情况下所得动安全系数数值不同,但曲线变化形状一样,最小安全系数均发生在相同时刻;另外,为更清晰地了解三维真实应力状态对安全系数的影响,从三维岩质边坡中抽取二维剖面进行了同样的计算。结果表明,在相同b值情况下,三维模型计算所得安全系数较二维模型大;随着b的增大,安全系数增大,说明不考虑中间主应力的二维计算结果低估了安全系数的大小,即三维真实应力状态下的边坡应具有更高的稳定性。
The Mohr-Coulomb and Drucker-Prager,yield criteria commonly used in slope stability analysis,which have not considered the intermediate principal stress effect or the differential effect of tension and compression,are difficultly to reflect the three dimensional stress state of rock slope.Unified strength theory contains a series of failure criteria;and the parameter b of this theory reflects the intermediate principal stress or the intermediate principal shear stress effect.This paper developed a user material subroutine(UMAT) based on unified strength theory using ABAQUS;taking a three-dimensional slope including discontinuities as a numerical example,and using strength reduction approach to calculate the dynamic safety factor curves for three-dimensional rock slope under five conditions(b = 0、0.25,0.5,0.75 and 1)with different intermediate principal stress extents.The results show that the safety factor varies with the b;but the curve shapes are similar;the smallest value occurs at same time.To understand the influence of intermediate principal stress on the safety factor clearly,a two-dimensional cross-section is extracted from the three-dimensional slope to carry out the calculation under same conditions.The results show that safety factor of three-dimensional model is larger than two-dimension's under the same parameter b.The safety factor is increasing with b increases.The two-dimensional results underestimate the safety factor magnitude;and the reality stress state of three-dimensional rock slope should be of higher stability.
The Mohr-Coulomb and Drucker-Prager,yield criteria commonly used in slope stability analysis,which have not considered the intermediate principal stress effect or the differential effect of tension and compression,are difficultly to reflect the three dimensional stress state of rock slope.Unified strength theory contains a series of failure criteria;and the parameter b of this theory reflects the intermediate principal stress or the intermediate principal shear stress effect.This paper developed a user material subroutine(UMAT) based on unified strength theory using ABAQUS;taking a three-dimensional slope including discontinuities as a numerical example,and using strength reduction approach to calculate the dynamic safety factor curves for three-dimensional rock slope under five conditions(b = 0、0.25,0.5,0.75 and 1)with different intermediate principal stress extents.The results show that the safety factor varies with the b;but the curve shapes are similar;the smallest value occurs at same time.To understand the influence of intermediate principal stress on the safety factor clearly,a two-dimensional cross-section is extracted from the three-dimensional slope to carry out the calculation under same conditions.The results show that safety factor of three-dimensional model is larger than two-dimension's under the same parameter b.The safety factor is increasing with b increases.The two-dimensional results underestimate the safety factor magnitude;and the reality stress state of three-dimensional rock slope should be of higher stability.
引文
[1]陈祖煜.土质边坡稳定性分析-原理.方法.程序[M].北京:中国水利水电出版社,2003.
[2]刘华丽,朱大勇,刘德富.边坡安全系数的多解性讨论[J].岩土力学,2007,28(8):1661-1664.LIU Hua-li,ZHU Da-yong,LIU De-fu.Discussion onmultiple solution of safety factor of a slope[J].Rock andSoil Mechanics,2007,28(2):1661-1664.
[3]李海波,肖克强,刘亚群.地震载荷作用下顺层岩质边坡安全系数分析[J].岩石力学与工程学报,2007,26(12):2385-2394.LI Hai-bo,XIAO Ke-qiang,LIU Ya-qun.Factor of safetyanalysis of bedding rock slope under seismic load[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(12):2385-2394.
[4]马芳芳.基于地震动力时程反应的有限元边坡稳定性分析[D].大连:大连理工大学,2005.
[5]俞茂宏.岩土类材料的统一强度理论及其应用.岩土工程学报,1994,16(2):1-9.YU Mao-hong.Unified strength theory for geomaterialsand its applications[J].Chinese Journal of GeotechnicalEngineering,1994,16(2):1-9.
[6]俞茂宏,杨松岩,范寿昌,等.双剪统一弹塑性本构模型及其工程应用[J].岩土工程学报,1997,19(6):2-10.YU Mao-hong,YANG Song-yan,FAN Shou-chang,et a1.Twin shear unified elastoplastic constitutive model and itsapplications[J].Chinese Journal of GeotechnicalEngineering,1997,19(6):2-10.
[7]俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998.
[8]赵尚毅,郑颖人,时卫民,等.用有限元强度折减法求边坡稳定安全系数[J].岩土工程学报,2002,24(3):343-346.ZHAO Shang-yi,ZHENG Ying-ren,SHI Wei-min,et al.Analysis of safety factor of slope by strength reductionFEM[J].Chinese Journal of Geotechnical Engineering,2002,24(3):343-346.
[9]栾茂田,武亚军,年廷凯.强度折减有限元法中边坡失稳的塑性区判据及其应用[J].防灾减灾工程学报,2008,23(3):1-8.LUAN Mao-tian,WU Ya-jun,NIAN Ting-kai.Acriterion for evaluating slope stability based ondevelopment of plastic zone by strength reduction FEM[J].Journal of Disaster Prevention and MitigationEngineering,2003,23(3):1-8.
[10]张鲁渝,郑颖人,赵尚毅.有限元强度折减系数法计算土坡稳定安全系数的精度研究[J].水利学报,2003,(1):21-27.ZHANG Lu-yu,ZHENG Ying-ren,ZHAO Shang-yi,et al.The feasibility study of strength-reduction method withFEM for calculating safety factors of soil slope stability[J].Journal of Hydraulic Engineering,2003,20(1):21-27.
[11]杨曼娟.ABAQUS用户材料子程序开发及应用[D].武汉:华中科技大学,2005.
[2]刘华丽,朱大勇,刘德富.边坡安全系数的多解性讨论[J].岩土力学,2007,28(8):1661-1664.LIU Hua-li,ZHU Da-yong,LIU De-fu.Discussion onmultiple solution of safety factor of a slope[J].Rock andSoil Mechanics,2007,28(2):1661-1664.
[3]李海波,肖克强,刘亚群.地震载荷作用下顺层岩质边坡安全系数分析[J].岩石力学与工程学报,2007,26(12):2385-2394.LI Hai-bo,XIAO Ke-qiang,LIU Ya-qun.Factor of safetyanalysis of bedding rock slope under seismic load[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(12):2385-2394.
[4]马芳芳.基于地震动力时程反应的有限元边坡稳定性分析[D].大连:大连理工大学,2005.
[5]俞茂宏.岩土类材料的统一强度理论及其应用.岩土工程学报,1994,16(2):1-9.YU Mao-hong.Unified strength theory for geomaterialsand its applications[J].Chinese Journal of GeotechnicalEngineering,1994,16(2):1-9.
[6]俞茂宏,杨松岩,范寿昌,等.双剪统一弹塑性本构模型及其工程应用[J].岩土工程学报,1997,19(6):2-10.YU Mao-hong,YANG Song-yan,FAN Shou-chang,et a1.Twin shear unified elastoplastic constitutive model and itsapplications[J].Chinese Journal of GeotechnicalEngineering,1997,19(6):2-10.
[7]俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998.
[8]赵尚毅,郑颖人,时卫民,等.用有限元强度折减法求边坡稳定安全系数[J].岩土工程学报,2002,24(3):343-346.ZHAO Shang-yi,ZHENG Ying-ren,SHI Wei-min,et al.Analysis of safety factor of slope by strength reductionFEM[J].Chinese Journal of Geotechnical Engineering,2002,24(3):343-346.
[9]栾茂田,武亚军,年廷凯.强度折减有限元法中边坡失稳的塑性区判据及其应用[J].防灾减灾工程学报,2008,23(3):1-8.LUAN Mao-tian,WU Ya-jun,NIAN Ting-kai.Acriterion for evaluating slope stability based ondevelopment of plastic zone by strength reduction FEM[J].Journal of Disaster Prevention and MitigationEngineering,2003,23(3):1-8.
[10]张鲁渝,郑颖人,赵尚毅.有限元强度折减系数法计算土坡稳定安全系数的精度研究[J].水利学报,2003,(1):21-27.ZHANG Lu-yu,ZHENG Ying-ren,ZHAO Shang-yi,et al.The feasibility study of strength-reduction method withFEM for calculating safety factors of soil slope stability[J].Journal of Hydraulic Engineering,2003,20(1):21-27.
[11]杨曼娟.ABAQUS用户材料子程序开发及应用[D].武汉:华中科技大学,2005.
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