Understanding of dynamic earthquake slip behavior using damage as a tensor variable: Microcrack distribution, orientation, and mode and secondary faulting

Abstract

[1] The importance of the damage effect on dynamic earthquake slip behavior is clarified using the damage tensor variable. Dynamic mode II faults that are embedded in damage-inducing media are assumed to relate to damage effects. This study confirms that the rupture velocity for spontaneous fault tip growth in the damage medium is reduced, being slightly smaller than rupture velocities observed for classical elastic material. Inelastic energy loss resulting in damage is relatively small but nonnegligible to the accumulated fracture energy. Two framework parameters employed in this study determine microcrack orientations and modes of microcracks and provide information on deviations in microcrack distribution between isotropic and nonisotropic ones. Spatial microcrack distribution patterns in isotropic and homogeneous systems are strongly dependent on a parameter related to the damage creation criterion. When considering secondary faulting, two apparently different behaviors, pulverization and branch development, are understood in a single framework, which gives a new insight into fault zone formation. The present results show that damage effect must be treated as a tensor variable rather than a scalar one as employed in many previous studies.Citation: Suzuki, T. (2012), Understanding of dynamic earthquake slip behavior using damage as a tensor variable: Microcrack distribution, orientation, and mode and secondary faulting,

Off-fault long-term damage: A condition to account for generic, triangular earthquake slip profiles

“…Whether those damage zones are formed only by the stress concentrations around the propagating rupture fronts [Scholz et al, 1993] or also include relicts of the longterm fault growth process through segment linkage and quasi-static fault slip [Manighetti et al, 2004] remains unresolved [Dunham et al, 2011a[Dunham et al, , 2011bSavage and Brodsky, 2011]. Furthermore, whether the damage process dominantly includes microcrack activation and/or formation [Lyakhovsky et al, 1997;Yamashita, 2000;Dalguer et al, 2003;Manighetti et al, 2004;Suzuki, 2012], macroscopic shear faulting [Ando and Yamashita, 2007], or plasticity [Andrews, 2005;Ben-Zion and Shi, 2005;Templeton and Rice, 2008;Viesca et al, 2008;Duan and Day, 2008;Ma and Andrews, 2010;Dunham et al, 2011aDunham et al, , 2011bXu and Ben-Zion, 2013;Gabriel et al, 2013] also remains unresolved. Whatever the nature of the cumulative damage around the faults, the across-fault width of the long-term damage zone seems to increase as the fault lengthens laterally over time [Scholz et al, 1993;Manighetti et al, 2004;Kim et al, 2004;Faulkner et al, 2011;Savage and Brodsky, 2011].…”

“…An increasing number of observations support this suggestion, in which significant coseismic failure and strain occurs around large earthquake ruptures [Fialko et al, 2002;Fialko, 2004;Hamiel and Fialko, 2007;Cochran et al, 2009;Fielding et al, 2009]. Experimental and theoretical models have also been developed recently to examine whether off-fault coseismic damage could emerge from the dynamic rupture process [Harris and Day, 1997;Lyakhovsky et al, 1997;Yamashita, 2000;Poliakov et al, 2002;Dalguer et al, 2003;Rice et al, 2005;Andrews, 2005; Ben-Zion and Shi, 2005;Ando and Yamashita, 2007;Bhat et al, 2007;Templeton and Rice, 2008;Biegel et al, 2008;Viesca et al, 2008;Dunham and Rice, 2008;Duan and Day, 2008;Ma, 2008;Sammis et al, 2009;Dieterich and Smith, 2009;Finzi et al, 2009;Bhat et al, 2010;Biegel et al, 2010;Ma and Andrews, 2010;Shi et al, 2010;Hok et al, 2010;Savage and Cooke, 2010;Dunham et al, 2011aDunham et al, , 2011bXu et al, 2012aXu et al, , 2012bNgo et al, 2012;Suzuki, 2012;Xu and Ben-Zion, 2013;Gabriel et al, 2013]. Although they are based on different formalisms, all these models confirm that significant coseismic off-fault damage does develop during the earthquake rupture, with this ...…”

“…Although they are based on different formalisms, all these models confirm that significant coseismic off-fault damage does develop during the earthquake rupture, with this development markedly affecting the mode and properties (i.e., speed and directivity) of the dynamic rupture and the seismic radiation. However, none of these studies have addressed the question of earthquake slip profiles; either the slip distributions that emerge from the experiment or modeling are not examined [Sammis et al, 2009;Hok et al, 2010;Suzuki, 2012;Xu and Ben-Zion, 2013;Gabriel et al, 2013] or they are examined yet found to be different from natural, generic slip profiles [Andrews, 2005;Dunham and Rice, 2008;Templeton and Rice, 2008;Dieterich and Smith, 2009;Savage and Cooke, 2010;Griffith et al, 2010;Dunham et al, 2011aDunham et al, , 2011bXu et al, 2012a].…”

Multiscale Discontinuities Due to Differential Stress around a Pressurized Borehole

“…The DSID model allows predicting directional micro-crack propagation around pressurized discontinuities such as boreholes and fractures. This is a promising feature, because previous damage models used in numerical methods to study hydraulic fracturing were limited to scalar damage (Valko and Economides, 1994) or flat debonded surfaces (which cannot conduct fracture flow -Suzuki, 2012). In addition, the DSID model distinguishes tension and compression damage thresholds, while previous theoretical frameworks were not solving problems related to the non-differentiability (and associated numerical issues) of damage variables depending on absolute values.…”

Modeling of Unilateral Rupture Along Very Long Reverse Faults

“…To confirm the prediction made in the previous section, we conduct a numerical experiment on the spontaneous rupture extension using a staggered grid finite difference method and an inelastic deformation model. At least two types of inelastic deformation model have been proposed: one in which the stress state is restricted to the vicinity of the yield surface, which approximates the Mohr-Coulomb yield criterion (e.g., Andrews, 2005;Dunham et al, 2011;Templeton & Rice, 2008), and one that includes a damage variable whose rate is a function of strain invariants (e.g., Lyakhovsky et al, 1997;Suzuki, 2012Suzuki, , 2013. The former depends on the total stress in the yield function, so it allows consideration of the initial stress dependence.…”