粘弹性有限元与弹簧滑块耦合模型——断层与地块相互作用的数值模拟
摘要
建立了粘弹性有限元方法和弹簧滑块的耦合模型,模拟了缓慢的大尺度地壳构造运动转化为急剧的小尺度断层失稳的时间过程,展示了地壳块体系统在板块边界作用下的相对运动,断层分配了主要的变形,导致了应力的积累,通过弹簧滑块模型模拟出服从Gutenberg-Richter定律的地震序列。断层摩擦强度的不均匀性控制了地震的发生以及块体的应力状态,地震破裂过程由成核点开始向两端扩展,伴随有应力的触发、应力释放和应力再分配的过程。断层的破裂事件释放了地壳块体的部分应力,靠近断层的地块应力受到局部破裂段的影响,而远离断层的地块应力状态受到断层整体地震活动的控制。
引文
1 马瑾.从断层中心论向块体中心论转变.地学前缘,1999,6(4) :363～369
2 Melosh H J, Raefsky A. A simple and efficient method for introducing faults into finite element computations. Bull Seismol Soc Am, 1981, 71: 1391～1400
3 Melosh H J, Williams C A. Mechanics of graben formation in crustal rocks: a finite element analysis. J Geophys Res, 1989,94: 13961～13973
4 Burridge R, Knopoff L. Model and theoretical seismicity. Bull Seismol Soc Am, 1967, 57(3) : 341～371
5 Cao T,Aki K. Seismicity simulation with a mass-spring model and a displacement hardening-softening friction law. Pure Appl Geophys, 1984, 122: 10～24
6 Brown S R, Scholz C H, Rundle J B, A simplified spring-block model of earthquakes. Geophys Res Lett, 1991, 18: 215～218
7 Carlson J M. Time intervals between characteristical earthquakes and correlations with smaller events: An analysis based on a mechanical model of a fault. J Geophys Res, 1991, 96: 4255～4267
8 Carlson J M, Langer J S. Mechanical model of an earthquake fault. Phys Rev A, 1989, 40: 6470～6484
9 Carlson J M. Two-dimensional model of a fault. Phys Res A, 1991, 44: 6226～6232
10 Cohen S C. Computer simulation of earthquakes. J Geophys Res, 1977, 82: 3781～3796
11 Nussbaum J, Ruina A. A two degree-of-freedom earthquake model with static/dynamic friction. Pure Appl Geophys, 1987,125: 629～656
12 洪汉净.从地震模拟看匀阻段与大震的关系.地震地质,1994,16:109～114
13 Shaw B E. Carlson J M, Langer J S. Patterns of seismic activity preceding large earthquake. J Geophys Res, 1992, 97:479～488
14 Dieterich J H. Modeling of rock friction, 1: Experimental results and constitutive equations. J Geophys Res, 1979, 84:2161～2168
15 Dieterich J H. Modeling of rock friction, 2: Simulation and preseismic slip. J Geophys Res, 1979, 84: 2169～2175
16 Ruina A L. Slip instability and state variable friction laws. J Geophys Res. 1983, 88: 10359～10370
17 Bak P,Tang C. Earthquakes as a self-organized critical phenomenon. J Geophys Res, 1989, 94: 15635～15637
18 Bak P,Tang C, Wiesenfeld K. Self-organized criticality. Phys Rev A, 1988, 38: 364～374
19 Knopoff L J, Landomi A, Abinante M S. Dynamical model of an earthquake fault with localization. Phys Rev A, 1992, 46:7445～7449
20 Cao T,Aki K. Seismicity simulation with a rate-and state-dependent friction law. Pure Appl Geophys, 1986, 124: 487～513
21 Dieterich J H. Time-dependent friction as a possible mechanism for afershocks. J Geophys Res, 1972, 77: 3771～3781
22 马宗晋、张德成、板块构造活动与地震.见:板块构造基本问题.北京:地震出版社,1986． 363～391
23 Byerlee J D. Static and kinetic friction of granite at high normal stress: International Journal of Rock Mechanics and Mining Science. 1970, 7(6) : 577～582
24 Yamashita T.On the dynamical process of fault motion in the presence of friction and inhomogeneous initial stress. I:Rupture propagation. J Phys Earth, 1976, 24: 417～444
25 Ohnaka M. A physical understanding of the earthquake source mechanism. J Phys Earth, 1973, 21: 39～59
26 Ohnaka M. A physical understanding of the earthquake source mechanism. Part Ⅱ. The fault-slip velocity and acceleration. J Phys Earth, 1974, 22: 383～394
27 Ben-Zion Y.Dynamic ruptures in recent models of earthquake faults. Journal of Mechanics and Physics of Solids, 2001, 49:2209～2244
28 Otsuka M. Earthquake magnitude and surface fault formation. J Phys Earth, 1964, 12: 19～24
29 Brace W F, Byerlee J D. Stick-slip as a mechanism for earthquakes. Science, 1966, 153: 990～992
30 Scholz C H. The mechanics of earthquakes and faulting. Cambridge University Press, 1990
31 Byerlee J D. Friction of rocks. Pure Appl Geophys. 1978, 116: 615～629
32 Rice J R, Ruina A L. Stability of steady frictional slipping. J Appl Mech, 1983, 50: 343～349
33 Rice J R, Tse S T.Dynamic motion of a single degree of freedom system following a rate and state dependent friction law. J Geophys Res, 1986, 91: 512～530
2 Melosh H J, Raefsky A. A simple and efficient method for introducing faults into finite element computations. Bull Seismol Soc Am, 1981, 71: 1391～1400
3 Melosh H J, Williams C A. Mechanics of graben formation in crustal rocks: a finite element analysis. J Geophys Res, 1989,94: 13961～13973
4 Burridge R, Knopoff L. Model and theoretical seismicity. Bull Seismol Soc Am, 1967, 57(3) : 341～371
5 Cao T,Aki K. Seismicity simulation with a mass-spring model and a displacement hardening-softening friction law. Pure Appl Geophys, 1984, 122: 10～24
6 Brown S R, Scholz C H, Rundle J B, A simplified spring-block model of earthquakes. Geophys Res Lett, 1991, 18: 215～218
7 Carlson J M. Time intervals between characteristical earthquakes and correlations with smaller events: An analysis based on a mechanical model of a fault. J Geophys Res, 1991, 96: 4255～4267
8 Carlson J M, Langer J S. Mechanical model of an earthquake fault. Phys Rev A, 1989, 40: 6470～6484
9 Carlson J M. Two-dimensional model of a fault. Phys Res A, 1991, 44: 6226～6232
10 Cohen S C. Computer simulation of earthquakes. J Geophys Res, 1977, 82: 3781～3796
11 Nussbaum J, Ruina A. A two degree-of-freedom earthquake model with static/dynamic friction. Pure Appl Geophys, 1987,125: 629～656
12 洪汉净.从地震模拟看匀阻段与大震的关系.地震地质,1994,16:109～114
13 Shaw B E. Carlson J M, Langer J S. Patterns of seismic activity preceding large earthquake. J Geophys Res, 1992, 97:479～488
14 Dieterich J H. Modeling of rock friction, 1: Experimental results and constitutive equations. J Geophys Res, 1979, 84:2161～2168
15 Dieterich J H. Modeling of rock friction, 2: Simulation and preseismic slip. J Geophys Res, 1979, 84: 2169～2175
16 Ruina A L. Slip instability and state variable friction laws. J Geophys Res. 1983, 88: 10359～10370
17 Bak P,Tang C. Earthquakes as a self-organized critical phenomenon. J Geophys Res, 1989, 94: 15635～15637
18 Bak P,Tang C, Wiesenfeld K. Self-organized criticality. Phys Rev A, 1988, 38: 364～374
19 Knopoff L J, Landomi A, Abinante M S. Dynamical model of an earthquake fault with localization. Phys Rev A, 1992, 46:7445～7449
20 Cao T,Aki K. Seismicity simulation with a rate-and state-dependent friction law. Pure Appl Geophys, 1986, 124: 487～513
21 Dieterich J H. Time-dependent friction as a possible mechanism for afershocks. J Geophys Res, 1972, 77: 3771～3781
22 马宗晋、张德成、板块构造活动与地震.见:板块构造基本问题.北京:地震出版社,1986． 363～391
23 Byerlee J D. Static and kinetic friction of granite at high normal stress: International Journal of Rock Mechanics and Mining Science. 1970, 7(6) : 577～582
24 Yamashita T.On the dynamical process of fault motion in the presence of friction and inhomogeneous initial stress. I:Rupture propagation. J Phys Earth, 1976, 24: 417～444
25 Ohnaka M. A physical understanding of the earthquake source mechanism. J Phys Earth, 1973, 21: 39～59
26 Ohnaka M. A physical understanding of the earthquake source mechanism. Part Ⅱ. The fault-slip velocity and acceleration. J Phys Earth, 1974, 22: 383～394
27 Ben-Zion Y.Dynamic ruptures in recent models of earthquake faults. Journal of Mechanics and Physics of Solids, 2001, 49:2209～2244
28 Otsuka M. Earthquake magnitude and surface fault formation. J Phys Earth, 1964, 12: 19～24
29 Brace W F, Byerlee J D. Stick-slip as a mechanism for earthquakes. Science, 1966, 153: 990～992
30 Scholz C H. The mechanics of earthquakes and faulting. Cambridge University Press, 1990
31 Byerlee J D. Friction of rocks. Pure Appl Geophys. 1978, 116: 615～629
32 Rice J R, Ruina A L. Stability of steady frictional slipping. J Appl Mech, 1983, 50: 343～349
33 Rice J R, Tse S T.Dynamic motion of a single degree of freedom system following a rate and state dependent friction law. J Geophys Res, 1986, 91: 512～530
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心