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 f c as Stokes number Sk, a function of Reb and approximately proportional to Reb 3/2. 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/ f c (=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 I 2 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.

Markov envelope as a theoretical solution of the parabolic wave equation with Markov approximation for the von Kármán type random medium is studied and approximated with the convolution of two probability density functions (pdf) of normal and gamma distributions considering the previous studies on the applications of Radiative Transfer Theory (RTT) and the analysis results of earthquake records. Through the approximation with gamma pdf, the constant shape parameter of 2 was determined regardless of the source distance ro. This finding means that the scattering process has the property of an inhomogeneous single-scattering Poisson process, unlike the previous studies, which resulted in a homogeneous multiple-scattering Poisson process. Approximated Markov envelope can be treated as the normalized mean square (MS) envelope for ground acceleration because of the flat source Fourier spectrum. Based on such characteristics, the path duration is estimated from the approximated MS envelope and compared to the empirical formula derived by Boore and Thompson. The results clearly show that the path duration increases proportionately to ro 1/2-ro 2, and the peak value of the RMS envelope is attenuated by exp (-0.0033ro), excluding the geometrical attenuation. The attenuation slope for ro≤100 km is quite similar to that of effective attenuation for shallow crustal earthquakes, and it may be difficult to distinguish the contribution of intrinsic attenuation from effective attenuation. Slowly varying dispersive delay, also called the medium effect, represented by regular pdf, governs the path duration for the source distance shorter than 100 km. Moreover, the diffraction term, also called the distance effect because of scattering, fully controls the path duration beyond the source distance of 300 km and has a steep gradient compared to the medium effect. Source distance 100-300 km is a transition range of the path duration governing effect from random medium to distance. This means that the scattering may not be the prime cause of peak attenuation and envelope broadening for the source distance of less than 200 km. Furthermore, it is also shown that normal distribution is appropriate for the probability distribution of phase difference, as asserted in the previous studies.

The extended slip-weakening model was investigated by using a compiled set of source-spectrum-related parameters, i.e. seismic moment Mo, S-wave velocity Vs, corner-frequency fc, and source-controlled high-cut frequency fmax, for 113 shallow crustal earthquakes (focal depth less than 25 km, MW 3.0~7.5) that occurred in Japan from 1987 to 2016. The investigation was focused on the characteristics of stress drop, radiation energy-to-seismic moment ratio, radiation efficiency, and fracture energy release rate, Gc. The scaling relationships of those source parameters were also investigated and compared with those in previous studies, which were based on generally used singular models with the dimensionless numbers corresponding to fc given by Brune and Madariaga. The results showed that the stress drop from the singular model with Madariaga’s dimensionless number was equivalent to the breakdown stress drop, as well as Brune’s effective stress, rather than to static stress drop as has been usually assumed. The scale dependence of stress drop showed a different tendency in accordance with the size category of the earthquakes, which may be divided into small-moderate earthquakes and moderate-large earthquakes by comparing to Mo = 1017~1018 Nm. The scale dependence was quite similar to that shown by Kanamori and Rivera. The scale dependence was not because of a poor dynamic range of recorded signals or missing data as asserted by Ide and Beroza, but rather it was because of the scale dependent Vr-induced local similarity of spectrum as shown in a previous study by the authors. The energy release rate Gc with respect to breakdown distance Dc from the extended slip-weakening model coincided with that given by Ellsworth and Beroza in a study on the rupture nucleation phase; and the empirical relationship given by Abercrombie and Rice can represent the results from the extended slip-weakening model, the results from laboratory stick-slip experiments by Ohnaka, and the results given by Ellsworth and Beroza simultaneously. Also the energy flux into the breakdown zone was well correlated with the breakdown stress drop,   and peak slip velocity of the fault faces. Consequently, the investigation results indicate the appropriateness of the extended slip-weakening model.

The slip-weakening model developed by Ohnaka and Yamashita is extended over the breakdown zone by equating the scaling relationships for the breakdown zone and the whole rupture area. For the extension, the study uses the relationship between rupture velocity and radiation efficiency, which was derived in the theory of linear elastic fracture mechanics, and the definition of fmax given in the specific barrier model proposed by Papageorgiou and Aki. The results clearly show that the extended scaling relationship is governed by the ratio of rupture velocity to S wave velocity, and the velocity ratio can be determined by the ratio of characteristic frequencies of a Fourier amplitude spectrum, which are corner frequency, fc, and source-controlled cut-off frequency, fmax, or vice versa. The derived relationship is tested by using the characteristic frequencies extracted from previous studies of more than 130 shallow crustal events (focal depth less than 25 km, MW 3.0~7.5) that occurred in Japan. Under the assumption of a dynamic similarity, the rupture velocity estimated from fmax/fc and the modified integral timescale give quite similar scale-dependence of the rupture area to that given by Kanamori and Anderson. Also, the results for large earthquakes show good agreement to the values from a kinematic inversion in previous studies. The test results also indicate the unavailability of the spectral self-similarity proposed by Aki because of the scale-dependent rupture velocity and the rupture velocity-dependent fmax/fc; however, the results do support the local similarity asserted by Ohnaka. It is also remarkable that the relationship between the rupture velocity and fmax/fc is quite similar to Kolmogorov’s hypothesis on a similarity in the theory of isotropic turbulence.

The phase properties of ground acceleration records from Mw 5.5~6.5 earthquakes are analyzed. The interrelationships between phase properties and significant durations, as well as PGA, are clarified through both of theoretical and empirical approaches. The probabilistic characteristics of phase information is also discussed based on previous studies and it is shown that circular normal distribution is the most appropriate probability distribution for the phase angle and phase difference. Whereas those variates can be modeled by Gaussian random variables. From the survey results on the frequency dependency of the phase statistics, a simple model is introduced, which is possible to express the frequency dependency of phase information. It is also shown that the significant duration can be controlled by appropriately chosen standard deviation of phase difference for 4~8Hz frequency band and additional consideration of phase scattering in higher frequency band through a series of Monte Carlo simulations. The source of phase scattering effect is also pointed out and discussed.

The purpose of this study is to estimate the weighting factor on inspection categories for risk assessment of buildings. For the purpose, survey of practitioners and experts conducted. By A.H.P.(Analytic hierarchy process), relative weighting factor in inspection categories were estimated.

본 연구에서는 특정 대상 시설의 위험도 평가기법을 합리화하기 위하여 기존 특정대상시설 안전등급 평가 메뉴얼을 분석하였으며, 점검항목에 대한 위험도 평가지표를 설정하였다. 합리적인 위험도 평가지표 설정을 위하여 최근 9년간의 인적재난 통계자료를 수집하여 분석하였으며, 주요 재난 발생 원인별 현황 분석을 통해 재난 유형별 각 점검분야의 상대적 가중치를 산정하였다. 또한 최근 9년간 주요사고사례 분석을 통해 체크리스트의 각 점검항목별 중요도를 산정하여, 평가지표의 중요도를 설정하였다. 설정된 점검분야별 상대적 가중치화 점검항목별 중요도를 적용하여 시설물의 위험도를 평가할수 있는 평가모델을 제안하였다.