3D dynamic simulations of spontaneous rupture propagation governed by different constitutive laws with rake rotation allowed

In this work we present a 3D Finite Difference numerical method to model the dynamic spontaneous propagation of an earthquake rupture on planar faults in an elastic half-space. We implement the Traction-at-Split-Nodes fault boundary condition for a system of faults, either vertical or oblique, using different constitutive laws. We can adopt both a slip-weakening law to prescribe the traction evolution within the breakdown zone or rate- and state-dependent friction laws, which involve the choice of an evolution relation for the state variable. Our numerical procedure allows the use of oblique and heterogeneous distribution of initial stress and allows the rake rotation. This implies that the two components of slip velocity and total dynamic traction are coupled together to satisfy, in norm, the adopted constitutive law. The simulations presented in this study show that the rupture acceleration to super-shear crack speeds occurs along the direction of the imposed initial stress; the rupture front velocity along the perpendicular direction is slower than that along the pre-stress direction. Depending on the position on the fault plane the orientation of instantaneous total dynamic traction can change with time with respect to the imposed initial stress direction. These temporal rake rotations depend on the amplitude of initial stress and on its distribution on the fault plane. They also depend on the curvature and direction of the rupture front with respect to the imposed initial stress direction: this explains why rake rotations are mostly located near the rupture front and within the cohesive zone.

[1]  J. Rice,et al.  Stability of quasi-static slip in a single degree of freedom elastic system with rate and state dependent friction , 1999 .

[2]  Ares J. Rosakis,et al.  How fast is rupture during an earthquake? New insights from the 1999 Turkey Earthquakes , 2001 .

[3]  J. Virieux,et al.  Dynamic faulting studied by a finite difference method : Bull seismol soc am, V72, N2, April 1982, P345–369 , 1982 .

[4]  M. Cocco,et al.  A thermal pressurization model for the spontaneous dynamic rupture propagation on a three‐dimensional fault: 2. Traction evolution and dynamic parameters , 2006 .

[5]  Ares J. Rosakis,et al.  Laboratory Earthquakes: The Sub-Rayleigh-to-Supershear Rupture Transition , 2004, Science.

[6]  Robert Burridge,et al.  Admissible Speeds for Plane-Strain Self-Similar Shear Cracks with Friction but Lacking Cohesion , 1973 .

[7]  Danilo De Rossi,et al.  Cracks Faster than the Shear Wave Speed , 2022 .

[8]  A. Rosakis,et al.  Cracks faster than the shear wave speed , 1999, Science.

[9]  D. J. Andrews,et al.  A numerical study of tectonic stress release by underground explosions , 1973 .

[10]  D. J. Andrews,et al.  Test of two methods for faulting in finite-difference calculations , 1999 .

[11]  H. Kanamori,et al.  Elastohydrodynamic lubrication of faults , 2001 .

[12]  A. Bizzarri.  Earthquake dynamics and fault interactions , 2003 .

[13]  A. Ruina.  Slip instability and state variable friction laws , 1983 .

[14]  J. Dieterich.  Modeling of rock friction: 1. Experimental results and constitutive equations , 1979 .

[15]  H. Quin.  Dynamic stress drop and rupture dynamics of the October 15, 1979 Imperial Valley, California, earthquake , 1990 .

[16]  M. Takeo,et al.  Determination of constitutive relations of fault slip based on seismic wave analysis , 1997 .

[17]  K. Mair,et al.  Friction of simulated fault gouge for a wide range of velocities and normal stresses , 1999 .

[18]  Elisa Tinti,et al.  Modeling the dynamic rupture propagation on heterogeneous faults with rate- and state-dependent friction , 2005 .

[19]  P. Spudich,et al.  Coseismic temporal changes of slip direction: The effect of absolute stress on dynamic rupture , 1998, Bulletin of the Seismological Society of America.

[20]  E. Tinti,et al.  Estimates of slip weakening distance for different dynamic rupture models , 2004 .

[21]  M. Cocco,et al.  A thermal pressurization model for the spontaneous dynamic rupture propagation on a 3–D fault: Part II – Traction evolution and dynamic parameters , 2005 .

[22]  Terry E. Tullis,et al.  The roles of time and displacement in the evolution effect in rock friction , 1994 .

[23]  D. J. Andrews,et al.  Rupture propagation with finite stress in antiplane strain , 1976 .

[24]  J. Rice,et al.  The growth of slip surfaces in the progressive failure of over-consolidated clay , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[25]  Hideo Aochi,et al.  Selectivity of spontaneous rupture propagation on a branched fault , 2000 .

[26]  Y. Yagi,et al.  Stress-Breakdown Time and Slip-Weakening Distance Inferred from Slip-Velocity Functions on Earthquake Faults , 2003 .

[27]  Kim B. Olsen,et al.  Three-Dimensional Dynamic Simulation of the 1992 Landers Earthquake , 1997 .

[28]  Keiiti Aki,et al.  A numerical study of two-dimensional spontaneous rupture propagation , 1977 .

[29]  Brian Kilgore,et al.  Scaling of the critical slip distance for seismic faulting with shear strain in fault zones , 1993, Nature.

[30]  D. J. Andrews,et al.  Bulletin of the Seismological Society of America , 1985 .

[31]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[32]  M. Ohnaka,et al.  Scaling of the shear rupture process from nucleation to dynamic propagation: Implications of geometric irregularity of the rupturing surfaces , 1999 .

[33]  Mitiyasu Ohnaka,et al.  A constitutive scaling law and a unified comprehension for frictional slip failure, shear fracture of intact rock, and earthquake rupture , 2003 .

[34]  On the inference of absolute stress levels from seismic radiation , 1992 .

[35]  D. J. Andrews,et al.  Solving the dynamic rupture problem with different numerical approaches and constitutive laws , 2001 .

[36]  K. Olsen,et al.  Estimation of the Critical Slip-Weakening Distance: Theoretical Background , 2003 .

[37]  Steven M. Day,et al.  Three-dimensional finite difference simulation of fault dynamics: Rectangular faults with fixed rupture velocity , 1982 .

[38]  M. F. Linker,et al.  Effects of variable normal stress on rock friction: Observations and constitutive equations , 1992 .

[39]  D. Andrews.  Dynamic growth of mixed-mode shear cracks , 1994, Bulletin of the Seismological Society of America.

[40]  Keiiti Aki,et al.  Fault plane with barriers: A versatile earthquake model , 1977 .

[41]  J. Rice.  Spatio‐temporal complexity of slip on a fault , 1993 .

[42]  P. Okubo.  Dynamic rupture modeling with laboratory‐derived constitutive relations , 1989 .

[43]  R. Madariaga,et al.  Rupture dynamics of a planar fault in a 3D elastic medium: Rate- and slip-weakening friction , 1998, Bulletin of the Seismological Society of America.

[44]  S. Day.  Three-dimensional simulation of spontaneous rupture: The effect of nonuniform prestress , 1982, Bulletin of the Seismological Society of America.

[45]  D. Andrews.  A fault constitutive relation accounting for thermal pressurization of pore fluid , 2002 .

[46]  James H. Dieterich,et al.  Time‐dependent friction in rocks , 1972 .

[47]  M. Cocco,et al.  On the slip‐weakening behavior of rate‐ and state dependent constitutive laws , 2002 .

[48]  Yoshiaki Ida,et al.  Cohesive force across the tip of a longitudinal‐shear crack and Griffith's specific surface energy , 1972 .

[49]  Takashi Miyatake,et al.  Dynamical rupture process on a three‐dimensional fault with non‐uniform frictions and near‐field seismic waves , 1978 .

[50]  D. J. Andrews,et al.  Rupture velocity of plane strain shear cracks , 1976 .

[51]  James H. Dieterich,et al.  Modeling of rock friction: 2. Simulation of preseismic slip , 1979 .

[52]  P. Spudich,et al.  What Can Strong-Motion Data Tell Us about Slip-Weakening Fault-Friction Laws? , 2000 .

[53]  Breaking of a single asperity: Rupture process and seismic radiation , 1983 .

[54]  K. Terzaghi,et al.  Soil mechanics in engineering practice , 1948 .

[55]  Steven M. Day,et al.  DYNAMIC RUPTURE IN A LAYERED MEDIUM: THE 1966 PARKFIELD EARTHQUAKE , 1980 .

[56]  M. Cocco,et al.  Slip‐weakening behavior during the propagation of dynamic ruptures obeying rate‐ and state‐dependent friction laws , 2003 .

[57]  Vikas Prakash,et al.  Frictional Response of Sliding Interfaces Subjected to Time Varying Normal Pressures , 1998 .

[58]  R. Madariaga.  Dynamics of an expanding circular fault , 1976, Bulletin of the Seismological Society of America.

[59]  S. M. Day,et al.  Finite element analysis of seismic scattering problems , 1977 .

[60]  Chris Marone,et al.  Frictional behavior and constitutive modeling of simulated fault gouge , 1990 .

[61]  Teruo Yamashita,et al.  A cohesive zone model for dynamic shear faulting based on experimentally inferred constitutive relation and strong motion source parameters , 1989 .

[62]  Karen Mair,et al.  Influence of grain characteristics on the friction of granular shear zones , 2002 .

[63]  A thermal pressurization model for the spontaneous dynamic rupture propagation on a 3–D fault: Part I – Methodological approach , 2005 .