基于扩展有限元法对土体滑坡破坏过程的模拟
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摘要
边坡失稳一般经历滑裂面萌生、扩展和贯通的过程。近年发展起来的扩展有限元法(XFEM)可以合理地模拟这一过程,但在实际应用中仍未克服需要预先设定滑裂面的起始位置,以及滑裂面前端扩展方向的判断精度较低等缺陷。首先介绍滑裂面萌生和扩展的判断和程序实现机制。然后提出了确定滑裂面起始位置的方法,重点描述了其中的自动判断裂缝萌生位置的方法,即根据单元内的应力状态求得拉应力水平和剪应力水平,根据其相对关系并结合应力历史进行判断。接着介绍了联合运用扇形控制域和圆形控制域确定滑裂面前端扩展方向的新方法。该方法可提高XFEM对滑坡破坏过程的模拟精度。最后通过两个边坡失稳算例的计算分析验证所提方法的可靠性。
A soil slope failure usually experiences the initiation, development, and run-through of the slip plane. The extended finite element method(XFEM) has been applied to simulate the process of slope failure in recent years. However, there are still some shortcomings to be overcome in practical applications of XFEM to landslides. For example, the initial position of the slip plane needs to be prescribed, and the extending direction of the slip front-end cannot be tracked accurately. In this paper, the mechanism of slip-plane initiation and development is introduced, and the process of automatically determining the initial position of the slip plane based on the stress history and the relative relationship between the tensile stress level and the shear stress level in the soil element is proposed and described in detail. Then, a new method for determining the front-end propagation direction of the slip plane by using the sector control domain and the circular control domain is introduced, which effectively improves the simulation precision of the XFEM for the landslide failure process. Finally, two typical slope cases with different failure types are analyzed to verify the reliability and rationality of the proposed method further.
A soil slope failure usually experiences the initiation, development, and run-through of the slip plane. The extended finite element method(XFEM) has been applied to simulate the process of slope failure in recent years. However, there are still some shortcomings to be overcome in practical applications of XFEM to landslides. For example, the initial position of the slip plane needs to be prescribed, and the extending direction of the slip front-end cannot be tracked accurately. In this paper, the mechanism of slip-plane initiation and development is introduced, and the process of automatically determining the initial position of the slip plane based on the stress history and the relative relationship between the tensile stress level and the shear stress level in the soil element is proposed and described in detail. Then, a new method for determining the front-end propagation direction of the slip plane by using the sector control domain and the circular control domain is introduced, which effectively improves the simulation precision of the XFEM for the landslide failure process. Finally, two typical slope cases with different failure types are analyzed to verify the reliability and rationality of the proposed method further.
引文
[1]时卫民,郑颖人,唐伯明.滑坡稳定性评价方法的探讨[J].岩土力学,2003,24(4):545-548.SHI Wei-min,ZHENG Ying-ren,TANG Bo-ming.Discussion on stability analysis method for landslides[J].Rock and Soil Mechanics,2003,24(4):545-548.
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[3]SKEMPTON A W.Long-term stability of clay slopes[J].Géotechnique,1964,14(2):77-102.
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[13]SONG J H,AREIAS P M A,BELYTSCHKO T.Amethod for dynamic crack and shear band propagation with phantom nodes[J].International Journal for Numerical Methods in Engineering,2006,67(6):868-893.
[14]喻葭临,张其光,于玉贞,等.扩展有限元中非连续区域的一种积分方案[J].清华大学学报(自然科学版),2009,49(3):351-354.YU Jia-lin,ZHANG Qi-guang,YU Yu-zhen,et al.An integration scheme for discontinuities in the extended finite element method[J].Journal of Tsinghua University(Science and Technology),2009,49(3):351-354.
[15]李明.开挖条件下土坡的破坏机理与变形规律研究[D].北京:清华大学,2012.LI Ming.Research on failure mechanism and deformation rules of cohesive slopes under excavation conditions[D].Beijing:Tsinghua University,2012.
[16]喻葭临,于玉贞,张丙印,等.基于扩展有限元方法的Carsington坝失稳过程分析[J].工程力学,2012,29(8):180-183.YU Jia-lin,YU Yu-zhen,ZHANG Bing-yin,et al.Failure process analysis of Carsington dam using extended finite element method[J].Engineering mechanics,2012,29(8):180-183.
[17]SKEMPTON A W,VAUGHAN P R.Discussion:the failure of Carsington dam[J].Géotechnique,1995,45(4):719-739.
[18]POTTS D M,DOUNIAS G T,VAUGHAN P R.Finite element analysis of progressive failure of Carsington embankment[J].Géotechnique,1990,40(1):79-101.
[2]DAI F C,LEE C F,NGAI Y Y.Landslide risk assessment and management:an overview[J].Engineering Geology,2002,64(1):65-87.
[3]SKEMPTON A W.Long-term stability of clay slopes[J].Géotechnique,1964,14(2):77-102.
[4]BJERRUM C.Progressive failure in slopes of overconsolidated plastic clay and clay shales[J].Journal of the Soil Mechanics and Foundations Division,1967,93(5):3-49.
[5]连镇营,韩国城,孔宪京.强度折减有限元法研究开挖边坡的稳定性[J].岩土工程学报,2001,23(4):407-411.LIAN Zhen-ying,HAN Guo-cheng,KONG Xian-jing.Stability analysis of excavation by strength reduction FEM[J].Chinese Jounal of Geotechnical Engineering,2001,23(4):407-411.
[6]UGAI K.A method of calculation of total safety factor of slope by elasto-plastic FEM[J].Soils and Foundations,1989,29(2):190-195.
[7]万少石,年廷凯,蒋景彩,等.边坡稳定强度折减有限元分析中的若干问题讨论[J].岩土力学,2010,31(7):2283-2288.WAN Shao-shi,NIAN Ting-kai,JIANG Jing-cai,et al.Discussion on several issues in slope stability analysis based on shear strength reduction finite element methods(SSR-FEM)[J].Rock and Soil Mechanics,2010,31(7):2283-2288.
[8]BELYTSCHKO T,BLACK T.Elastic crack growth in finite elements with minimal remeshing[J].International Journal for Numerical Methods in Engineering,1999,45(5):601-620.
[9]石路杨,余天堂.多裂纹扩展的扩展有限元法分析[J].岩土力学,2014,35(1):263-272.SHI Lu-yang,YU Tian-tang.Analysis of multiple crack growth using extended finite element method[J].Rock and Soil Mechanics,2014,35(1):263-272.
[10]罗先启,郑安兴.岩体裂隙模拟的扩展有限元法应用研究[J].岩土力学,2018,39(2):728-734.LUO Xian-qi,ZHENG An-xing.Application of extended finite element method in modelling fracture of rock mass[J].Rock and Soil Mechanics,2018,39(2):728-734.
[11]喻葭临,于玉贞,张丙印,等.土坡中剪切带形成过程的数值模拟[J].工程力学,2012,29(2):165-171.YU Jia-lin,YU Yu-zhen,ZHANG Bing-yin,et al.Numerical simulation of the evolution of shear band in soil slope[J].Engineering Mechanics,2012,29(2):165-171.
[12]SANBORN S E,PRéVOST J H.Frictional slip plane growth by localization detection and the extended finite element method(XFEM)[J].International Journal for Numerical&Analytical Methods in Geomechanics,2011,35(11):1278-1298.
[13]SONG J H,AREIAS P M A,BELYTSCHKO T.Amethod for dynamic crack and shear band propagation with phantom nodes[J].International Journal for Numerical Methods in Engineering,2006,67(6):868-893.
[14]喻葭临,张其光,于玉贞,等.扩展有限元中非连续区域的一种积分方案[J].清华大学学报(自然科学版),2009,49(3):351-354.YU Jia-lin,ZHANG Qi-guang,YU Yu-zhen,et al.An integration scheme for discontinuities in the extended finite element method[J].Journal of Tsinghua University(Science and Technology),2009,49(3):351-354.
[15]李明.开挖条件下土坡的破坏机理与变形规律研究[D].北京:清华大学,2012.LI Ming.Research on failure mechanism and deformation rules of cohesive slopes under excavation conditions[D].Beijing:Tsinghua University,2012.
[16]喻葭临,于玉贞,张丙印,等.基于扩展有限元方法的Carsington坝失稳过程分析[J].工程力学,2012,29(8):180-183.YU Jia-lin,YU Yu-zhen,ZHANG Bing-yin,et al.Failure process analysis of Carsington dam using extended finite element method[J].Engineering mechanics,2012,29(8):180-183.
[17]SKEMPTON A W,VAUGHAN P R.Discussion:the failure of Carsington dam[J].Géotechnique,1995,45(4):719-739.
[18]POTTS D M,DOUNIAS G T,VAUGHAN P R.Finite element analysis of progressive failure of Carsington embankment[J].Géotechnique,1990,40(1):79-101.
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