断层面的有限单元模拟方法综述
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摘要
有限单元法是研究地球科学问题的重要工具之一。本文概述了国内外学者利用以连续介质理论为基础的有限单元法研究地学,特别是地震学、地壳形变学科时,对具有非连续性特点的断层所采用的几大主流处理方法,并阐述了各断层模型基础上(弱化带模型、劈节点模型、接触模型以及块体模型)所展开的地学研究。
In the field of earth science research,finite element method has long been deemed as one of the most important analysis tools.In this paper several main-stream fault-simulation approaches are summarized when international scholars conduct scientific researches in geosciences,especially in seismology and crustal geomorphology using continuum-based numerical method and finite element method,their relevant progress in geosciences are expounded.Generally speaking,the simulation models of geological faults can be categorized into four types: weak zone model,split node model,contact model,and block model.
In the field of earth science research,finite element method has long been deemed as one of the most important analysis tools.In this paper several main-stream fault-simulation approaches are summarized when international scholars conduct scientific researches in geosciences,especially in seismology and crustal geomorphology using continuum-based numerical method and finite element method,their relevant progress in geosciences are expounded.Generally speaking,the simulation models of geological faults can be categorized into four types: weak zone model,split node model,contact model,and block model.
引文
[1]邓起东.活动断裂研究的进展与方向[M].北京:地震出版社,1991.
[2]闻学泽.活动断裂地震潜势的定量评价[M].北京:地震出版社,1996.
[3]薄万举.地壳形变与地震预测[M].北京:地震出版社,2001.
[4]李兴才.断层的震前滑动对唐山地震发生的影响[J].地震学报,1992,14(3):304-308.
[5]周硕愚.断层形变测量与地震预报[J].地壳形变与地震,1994,14(4):90-97.
[6]Sibson R H.Fault rocks and fault mechanisms[J].J.Geol.,1977,133:191-213.
[7]Strehlau J.A discussion of the depth extent of rupture in largecontinental earthquakes[J].Geophys.Monogr.,1986,37:131-145.
[8]Dieterich J H.Earthquake on faults with rate and state-de-pendent friction[J].Tectonophysics,1992,11:115-134.
[9]Gomberg J.Beeler N M.Earthquake triggering by transientand static deformation[J].J.Geophys.Res.,1998,103(B10):24411-24426.
[10]刘桂萍,傅征祥.摩擦状态-速率依从的区域地震触发模型研究[J].地震,2004,24(1):176-183.
[11]王仁.有限单元等数值方法在我国地球科学中的应用和发展[J].地球物理学报,1994,37(增刊):128-138.
[12]王妙月,底青云,张美根.地震孕育、发生、发展动态过程的三维有限元数值模拟[J].地球物理学报,1999,42(2):218-227.
[13]王爱国,袁道阳,梁明剑.兰州盆地最大潜在地震变形数值模拟[J].西北地震学报,2008,30(3):232-238.
[14]章纯.中国东部地区地震活动与构造应力场关系的有限元数值模拟[J].西北地震学报,2007,29(3):230-234.
[15]张彬,杨选辉,陆远忠.地震动态应力触发研究进展[J].西北地震学报,2008,30(3):298-303.
[16]马胜利.模拟断层带摩擦滑动性状与变形特征[J].中国地震,1986,2(2):72-78.
[17]王仁,何国琦,殷有泉.华北地区地震迁移规律的数学模拟[J].地震学报,1980,2(1):32-42.
[18]王仁,孙苟英,蔡永恩.华北地区近700年地震序列的数学模拟[J].中国科学(B辑),1982,8:745-753.
[19]殷有泉,张宏.模拟地震的应变软化的数学模型地球物理学报[J].1982,25(5):414-423.
[20]王继存,续春荣.唐山地震断层破坏及其力学过程的数值模拟地震地质[J].1989,11(4):71-76.
[21]Liu M,Yang Y.Extensional collapse of the Tibetan Plateau:Results of three-dimensional finite element modeling[J].J.Geophys.Res.,2003,108(8):2361.doi:10.1029/2002JB002248.
[22]陆远忠,叶金铎,蒋淳.中国强震前兆地震活动图像机理的三维数值模拟研究[J].地球物理学报,2007,50(2):499-508.
[23]陈连旺,陆远忠,张杰,等.华北地区三维构造应力场[J].地震学报,1999,21(2):140-149.
[24]陈连旺,陆远忠,郭若眉,等.华北地区断层运动与三维构造应力场的演化[J].地震学报,2001,23(4):249-361.
[25]陈连旺,陆远忠,刘杰,等.1966年邢台地震引起的华北地区应力场动态演化过程的三维粘弹性模拟[J].地震学报,2001,23(5):480-491.
[26]陈化然,陈连旺,马宏生,等.川滇地区应力场演化与强震间相互作用的三维有限元模拟[J].地震学报,2004,26(6):567-575.
[27]李平,卢良玉,卢造勋,等.辽宁及邻区地壳构造应力场及其与地震活动关系的三维有限元数值模拟研究[J],地震学报,2001,23(1):24-35.
[28]Melosh H J,Raefsky A.A simple and efficient method for in-troducing faults into finite element computations[J].Bull.Seism.Soc.Am.,1981,71(5):1391-1400.
[29]Melosh H J,Williams C.A Mechanics of graben formation incrustal rocks:A finite element analysis[J].J.Geophys.Res.,1989,94(B10):13961-13973.
[30]Jungels P H.Models of tectonic processes associated withearthquakes[D].Pasadena:California Institute Technology,California,1973.
[31]Jungels P H,Frazier G A.Finite element analysis of the re-sidual displacements for an earthquake rupture:source param-eters for the San Fernando earthquake[J].J.Geophys.Res.1973,78:5062-5083.
[32]Yoshioka S,Tokunaga Y O.Numerical Simulation of Dis-placement and Stress Fields Associated with the 1993Kushi-ro-oki,Japan,Earthquake[J].Pure appl.geophys.,1998,152:443-464.
[33]Hearn E H.What can GPS data tell us about the dynamics ofpost-seismic deformation[J].Geophys.J.Int.,2003,155:753-777.
[34]Sheu S Y,Shieh C F.Viscoelastic-afterslip concurrence:apossible mechanism in the early post-seismic deformation ofthe Mw7.6,1999Chi-Chi(Taiwan)earthquake[J].Geo-phys.J.Int.,2004,159(3):1112-1124.
[35]Buiter J H,Govers Rob,Wortel M J.A modeling study ofvertical displacements at convergent plate margins[J].Geo-phys.J.Int.2001(147):415-427.
[36]Hu Y,et al.Three-dimensionalviscoelastic finite elementmodel for postseismic deformation of the great 1960Chileanearthquake[J].J.Geophys.Res.,2004,109.doi:10.1029/2004JB003163.
[37]Hyodo M K,Hirahara.A viscoelastic model of interseismicstrain concentration in Niigata-Kobe Tectonic Zone of cen-tral Japan[J].Earth Planets Space,2003,55:667-675.
[38]Zhao S,et al.3-D finite element modelling of deformation andstress associated with faulting:effect of inhomogeneous crus-tal structures[J].Geophys.J.Int.,2004,157:629-644.
[39]Dixon T J,Decaix F,Farina K.Seismic cycle and rheologicaleffects on estimation of present-day slip rates for the AguaBlanca and San Miguel-Vallecitos faults,northern Baja Cali-fornia,Mexico[J].J.Geophys.Res.,2002,107(B10),2226,doi:10.1029/2000JB000099.
[40]Aagaard B T,Hall J F,Heaton T H.Characterization ofnear-source ground motions with earthquake simulations[J].Earthquake Spectra,2001,17(2):177-207.
[41]Andrews D J.Test of two methods for faulting in finite-differ-ence calculations[J].Bull.Seism.Soc.Am.,1999,89:931-937.
[42]Goodman R E,Taylor R L,Brekke T L.A model for the me-chanics of jointed rock[J].Soil Mech.and Found Proc,1968,94:637-658.
[43]Hallquist D,John O.LS-DYNA3D Theoretical Manual[M].Livermore:Software Technology Corporation,1994.
[44]Cescotto S,Charilier R.Frictional Contact Finite ElementsBased on Mixed Variational Principles[J].International Jour-nal for Numercial Method in Engineering,1992,(36):1681-1701.
[45]Peric D,Owen D R.Computational Model for 3-D ContactProblems with Friction Based on the Penalty Method[J].In-ternational Journal for Numercial Method in Engineering,1992,35:1289-1309.
[46]Parsons T.Post-1906stress recovery of the San Andreasfault system calculated from three-dimensional finite elementanalysis[J].J.Geophys.Res.,2002,107(B8):2162,doi:10.1029/2001JB001051.
[47]Parsons T.Tectonic stressing in California modeled fromGPS observations[J].J.Geophys.Res.,2006,111(B03)407,doi:10.1029/2005JB003946.
[48]Masterlark T.Finite element model predictions of static de-formation from dislocation sources in a subduction zone:Sen-sitivities to homogeneous,isotropic,Poisson-solid,and half-space assumptions[J].J.Geophys.Res.,2003,108(B11):2540,doi:10.1029/2002JB002296,.
[49]Ellis S,et al.Simplified models of theAlpine Fault seismic cy-cle:Stress transfer in the mid-crust[J].Geophy.J.Int.,2006,doi:10.1111/j.1365-246X.2006.02917.x.
[50]Ganas A,Parsons T.Three-dimensional model of HellenicArc deformation and origin of the Cretan uplift[J].J.Geo-phys.Res.,2009,114(B06):404,doi:10.1029/2008JB005599.
[51]刘峡,傅容珊,杨国华.用GPS资料研究华北地区形变场和构造应力场[J].大地测量与地球动力学,2006,26(3):33-39.
[52]李红,陈连旺,李红江.广州地区活动断裂的数值模拟[J].大地测量与地球动力学,2008,28(2):39-44.
[53]王凯英,马瑾.川滇地区断层相互作用的地震活动证据及有限元模拟[J].地震地质,2004,26(2):259-272.
[54]王凯英.断块模型中走滑型地震应力触发研究——以青藏高原北部几次强震为例[J].地球物理学报,2009,52(7):1776-1781.
[55]Shi G H.Discontinuous deform ation analysis:a new numeri-cal model for the statics and dynamics of block systems[D].Berkeley:Department of Cilvil Engineering,University of Cal-ifornia,1988.
[56]白武明,林邦慧,陈祖安.1976年唐山大震发生对华北地区各地块运动与变形影响的数值模拟研究[J].中国科学(D辑),2003,33(增刊):99-107.
[57]Liu L.Modeling aseismic fault slips and block deformation innorthern china by DDA[A]∥Proc of the First InternationalForumon Discontinuous Deformation Analysis(DDA)andSimulations of Discontinuous Media[C].Albuquerque:TSIPress,1996:373-383.
[58]自武明,林邦慧,陈祖安.1976年唐山大震发生对华北地区各地块运动与变形影响的数值模拟研究[J].中国科学(D辑),2003,33(增刊):99-107.
[59]蔡永恩,何涛,王仁.1976年唐山地震震源动力过程的数值模拟[J].地震学报,1999,21(5):469-477.
[60]张瑞青,魏富胜,乔成斌.用(DDA+FEM)方法数值模拟1975年海城、1999年岫岩地震发生的过程[J].地震学报,2005,27(3):163-170.
[61]陈祖安,林邦慧,白武明,等.1997年玛尼地震对青藏川滇地区构造块体系统稳定性影响的三维DDA+FEM方法数值模拟[J].地球物理学报,2008,51(5):1422-1430.
[62]陈祖安,林邦慧,白武明,等.2008年汶川8.0级地震孕震机理研究[J].地球物理学报,2009,52(2):408-417.
[2]闻学泽.活动断裂地震潜势的定量评价[M].北京:地震出版社,1996.
[3]薄万举.地壳形变与地震预测[M].北京:地震出版社,2001.
[4]李兴才.断层的震前滑动对唐山地震发生的影响[J].地震学报,1992,14(3):304-308.
[5]周硕愚.断层形变测量与地震预报[J].地壳形变与地震,1994,14(4):90-97.
[6]Sibson R H.Fault rocks and fault mechanisms[J].J.Geol.,1977,133:191-213.
[7]Strehlau J.A discussion of the depth extent of rupture in largecontinental earthquakes[J].Geophys.Monogr.,1986,37:131-145.
[8]Dieterich J H.Earthquake on faults with rate and state-de-pendent friction[J].Tectonophysics,1992,11:115-134.
[9]Gomberg J.Beeler N M.Earthquake triggering by transientand static deformation[J].J.Geophys.Res.,1998,103(B10):24411-24426.
[10]刘桂萍,傅征祥.摩擦状态-速率依从的区域地震触发模型研究[J].地震,2004,24(1):176-183.
[11]王仁.有限单元等数值方法在我国地球科学中的应用和发展[J].地球物理学报,1994,37(增刊):128-138.
[12]王妙月,底青云,张美根.地震孕育、发生、发展动态过程的三维有限元数值模拟[J].地球物理学报,1999,42(2):218-227.
[13]王爱国,袁道阳,梁明剑.兰州盆地最大潜在地震变形数值模拟[J].西北地震学报,2008,30(3):232-238.
[14]章纯.中国东部地区地震活动与构造应力场关系的有限元数值模拟[J].西北地震学报,2007,29(3):230-234.
[15]张彬,杨选辉,陆远忠.地震动态应力触发研究进展[J].西北地震学报,2008,30(3):298-303.
[16]马胜利.模拟断层带摩擦滑动性状与变形特征[J].中国地震,1986,2(2):72-78.
[17]王仁,何国琦,殷有泉.华北地区地震迁移规律的数学模拟[J].地震学报,1980,2(1):32-42.
[18]王仁,孙苟英,蔡永恩.华北地区近700年地震序列的数学模拟[J].中国科学(B辑),1982,8:745-753.
[19]殷有泉,张宏.模拟地震的应变软化的数学模型地球物理学报[J].1982,25(5):414-423.
[20]王继存,续春荣.唐山地震断层破坏及其力学过程的数值模拟地震地质[J].1989,11(4):71-76.
[21]Liu M,Yang Y.Extensional collapse of the Tibetan Plateau:Results of three-dimensional finite element modeling[J].J.Geophys.Res.,2003,108(8):2361.doi:10.1029/2002JB002248.
[22]陆远忠,叶金铎,蒋淳.中国强震前兆地震活动图像机理的三维数值模拟研究[J].地球物理学报,2007,50(2):499-508.
[23]陈连旺,陆远忠,张杰,等.华北地区三维构造应力场[J].地震学报,1999,21(2):140-149.
[24]陈连旺,陆远忠,郭若眉,等.华北地区断层运动与三维构造应力场的演化[J].地震学报,2001,23(4):249-361.
[25]陈连旺,陆远忠,刘杰,等.1966年邢台地震引起的华北地区应力场动态演化过程的三维粘弹性模拟[J].地震学报,2001,23(5):480-491.
[26]陈化然,陈连旺,马宏生,等.川滇地区应力场演化与强震间相互作用的三维有限元模拟[J].地震学报,2004,26(6):567-575.
[27]李平,卢良玉,卢造勋,等.辽宁及邻区地壳构造应力场及其与地震活动关系的三维有限元数值模拟研究[J],地震学报,2001,23(1):24-35.
[28]Melosh H J,Raefsky A.A simple and efficient method for in-troducing faults into finite element computations[J].Bull.Seism.Soc.Am.,1981,71(5):1391-1400.
[29]Melosh H J,Williams C.A Mechanics of graben formation incrustal rocks:A finite element analysis[J].J.Geophys.Res.,1989,94(B10):13961-13973.
[30]Jungels P H.Models of tectonic processes associated withearthquakes[D].Pasadena:California Institute Technology,California,1973.
[31]Jungels P H,Frazier G A.Finite element analysis of the re-sidual displacements for an earthquake rupture:source param-eters for the San Fernando earthquake[J].J.Geophys.Res.1973,78:5062-5083.
[32]Yoshioka S,Tokunaga Y O.Numerical Simulation of Dis-placement and Stress Fields Associated with the 1993Kushi-ro-oki,Japan,Earthquake[J].Pure appl.geophys.,1998,152:443-464.
[33]Hearn E H.What can GPS data tell us about the dynamics ofpost-seismic deformation[J].Geophys.J.Int.,2003,155:753-777.
[34]Sheu S Y,Shieh C F.Viscoelastic-afterslip concurrence:apossible mechanism in the early post-seismic deformation ofthe Mw7.6,1999Chi-Chi(Taiwan)earthquake[J].Geo-phys.J.Int.,2004,159(3):1112-1124.
[35]Buiter J H,Govers Rob,Wortel M J.A modeling study ofvertical displacements at convergent plate margins[J].Geo-phys.J.Int.2001(147):415-427.
[36]Hu Y,et al.Three-dimensionalviscoelastic finite elementmodel for postseismic deformation of the great 1960Chileanearthquake[J].J.Geophys.Res.,2004,109.doi:10.1029/2004JB003163.
[37]Hyodo M K,Hirahara.A viscoelastic model of interseismicstrain concentration in Niigata-Kobe Tectonic Zone of cen-tral Japan[J].Earth Planets Space,2003,55:667-675.
[38]Zhao S,et al.3-D finite element modelling of deformation andstress associated with faulting:effect of inhomogeneous crus-tal structures[J].Geophys.J.Int.,2004,157:629-644.
[39]Dixon T J,Decaix F,Farina K.Seismic cycle and rheologicaleffects on estimation of present-day slip rates for the AguaBlanca and San Miguel-Vallecitos faults,northern Baja Cali-fornia,Mexico[J].J.Geophys.Res.,2002,107(B10),2226,doi:10.1029/2000JB000099.
[40]Aagaard B T,Hall J F,Heaton T H.Characterization ofnear-source ground motions with earthquake simulations[J].Earthquake Spectra,2001,17(2):177-207.
[41]Andrews D J.Test of two methods for faulting in finite-differ-ence calculations[J].Bull.Seism.Soc.Am.,1999,89:931-937.
[42]Goodman R E,Taylor R L,Brekke T L.A model for the me-chanics of jointed rock[J].Soil Mech.and Found Proc,1968,94:637-658.
[43]Hallquist D,John O.LS-DYNA3D Theoretical Manual[M].Livermore:Software Technology Corporation,1994.
[44]Cescotto S,Charilier R.Frictional Contact Finite ElementsBased on Mixed Variational Principles[J].International Jour-nal for Numercial Method in Engineering,1992,(36):1681-1701.
[45]Peric D,Owen D R.Computational Model for 3-D ContactProblems with Friction Based on the Penalty Method[J].In-ternational Journal for Numercial Method in Engineering,1992,35:1289-1309.
[46]Parsons T.Post-1906stress recovery of the San Andreasfault system calculated from three-dimensional finite elementanalysis[J].J.Geophys.Res.,2002,107(B8):2162,doi:10.1029/2001JB001051.
[47]Parsons T.Tectonic stressing in California modeled fromGPS observations[J].J.Geophys.Res.,2006,111(B03)407,doi:10.1029/2005JB003946.
[48]Masterlark T.Finite element model predictions of static de-formation from dislocation sources in a subduction zone:Sen-sitivities to homogeneous,isotropic,Poisson-solid,and half-space assumptions[J].J.Geophys.Res.,2003,108(B11):2540,doi:10.1029/2002JB002296,.
[49]Ellis S,et al.Simplified models of theAlpine Fault seismic cy-cle:Stress transfer in the mid-crust[J].Geophy.J.Int.,2006,doi:10.1111/j.1365-246X.2006.02917.x.
[50]Ganas A,Parsons T.Three-dimensional model of HellenicArc deformation and origin of the Cretan uplift[J].J.Geo-phys.Res.,2009,114(B06):404,doi:10.1029/2008JB005599.
[51]刘峡,傅容珊,杨国华.用GPS资料研究华北地区形变场和构造应力场[J].大地测量与地球动力学,2006,26(3):33-39.
[52]李红,陈连旺,李红江.广州地区活动断裂的数值模拟[J].大地测量与地球动力学,2008,28(2):39-44.
[53]王凯英,马瑾.川滇地区断层相互作用的地震活动证据及有限元模拟[J].地震地质,2004,26(2):259-272.
[54]王凯英.断块模型中走滑型地震应力触发研究——以青藏高原北部几次强震为例[J].地球物理学报,2009,52(7):1776-1781.
[55]Shi G H.Discontinuous deform ation analysis:a new numeri-cal model for the statics and dynamics of block systems[D].Berkeley:Department of Cilvil Engineering,University of Cal-ifornia,1988.
[56]白武明,林邦慧,陈祖安.1976年唐山大震发生对华北地区各地块运动与变形影响的数值模拟研究[J].中国科学(D辑),2003,33(增刊):99-107.
[57]Liu L.Modeling aseismic fault slips and block deformation innorthern china by DDA[A]∥Proc of the First InternationalForumon Discontinuous Deformation Analysis(DDA)andSimulations of Discontinuous Media[C].Albuquerque:TSIPress,1996:373-383.
[58]自武明,林邦慧,陈祖安.1976年唐山大震发生对华北地区各地块运动与变形影响的数值模拟研究[J].中国科学(D辑),2003,33(增刊):99-107.
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[60]张瑞青,魏富胜,乔成斌.用(DDA+FEM)方法数值模拟1975年海城、1999年岫岩地震发生的过程[J].地震学报,2005,27(3):163-170.
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