Journal of the Earthquake Engineering Society of Korea (한국지진공학회논문집)

Earthquake Engineering Society of Korea (한국지진공학회)
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Dynamic Similarity in Breakdown Process and Source Time Functions

Breakdown Process의 동적 유사성과 진원 시간 함수

  • 최항 ((주)아이맥스트럭처 ) ;
  • 윤병익 ((주)아이맥스트럭처 )
  • Received : 2024.12.11
  • Accepted : 2025.01.16
  • Published : 2025.05.01
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Abstract

To characterize the breakdown process, we newly introduce and define a dimensionless number called breakdown zone Reynolds number Reb. Reb represents the relationship between shear frictional resistance and inertial force, equivalent to (Vr/Vs)2. Vr and Vs are rupture and shear wave velocities, respectively. Reb also characterizes the energy budget relationship, seismic energy radiation, and its efficiency. Based on Reb, particle motion can be categorized into two cases: a) Reb≪1 and b) Reb ~1 or Reb>1. For case a), since the inertial force is negligible compared to the shear frictional resistance, the particle motion can be viewed as the response of a linear time-invariant system with the stress drop as an input function, and its impulse response function (IRF) is the second type of modified Bessel function with zeroth order supposing linear phase characteristics. The IRF is quite similar to the regularized Yoffe function. The particle velocity spectrum can be characterized with the approximated spectral attenuation slope in the high frequency range of ∝ω-0.6. The attenuation slope, however, would be changed to ∝ω-1.0 if we consider the pre-slip and phase delay of the response. Then, generic omega-square model can model a finite source's source time function (STF). On the other hand, case b) shows that IRF has the same form as Brune's omega-square model, and its STF has steeper spectral attenuation like omega-cube model. This means that the spectral characteristics of STF may change with the rupture velocity. Furthermore, we newly define the ratio of source-controlled fmax to corner frequency fc as Stokes number Sk, a function of Reb and approximately proportional to Reb3/2. Remarkably, Sk delineates a Reynolds number similarity which is comparable to that of isotropic turbulence. The aggregated results of spectral inversion analysis for more than 130 shallow earthquakes occurring in Japan show that the analyzed fmax/fc (=Sk) follow the theoretical relationship, and it is also demonstrated that the non-self-similarity parameter ε proposed by Kanamori and Rivera is related to the scale dependence of Reb. Finally, Reb is compared to the inertial number I, a representative dimensionless number governing the behavior of granular suspension as a model for the interaction between fault gouge and pore-pressure in fault core. As a result, Reb is equivalent to I2. as we consider the differences in length scale and density in each definition. Consequently, I is uniquely linked to Sk by Reb, corresponding to the Stokes number for granular suspension. Hence, it can be asserted that Reb and Sk introduced in this study are representative dimensionless numbers which characterize the whole breakdown process and the behavior of pulverized fault core.

Keywords

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