• Journal of the Earthquake Engineering Society of Korea
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• v.24 no.6
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• pp.253-266
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• 2020

The extended slip-weakening model was investigated by using a compiled set of source-spectrum-related parameters, i.e. seismic moment M_o, S-wave velocity V_s, corner-frequency f_c, and source-controlled high-cut frequency fmax, for 113 shallow crustal earthquakes (focal depth less than 25 km, M_W 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, G_c. 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 f_c 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 M_o = 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 V_r-induced local similarity of spectrum as shown in a previous study by the authors. The energy release rate G_c with respect to breakdown distance D_c 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, ${\tilde{e}}$ and peak slip velocity of the fault faces. Consequently, the investigation results indicate the appropriateness of the extended slip-weakening model.

• Journal of the Earthquake Engineering Society of Korea
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• v.24 no.5
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• pp.219-232
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• 2020

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 f_max 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, f_c, and source-controlled cut-off frequency, f_max, 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, M_W 3.0~7.5) that occurred in Japan. Under the assumption of a dynamic similarity, the rupture velocity estimated from f_max/f_c 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 f_max/f_c; however, the results do support the local similarity asserted by Ohnaka. It is also remarkable that the relationship between the rupture velocity and f_max/f_c is quite similar to Kolmogorov's hypothesis on a similarity in the theory of isotropic turbulence.

• Economic and Environmental Geology
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• v.33 no.1
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• pp.61-75
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• 2000

Through modeling fault network using thin plate finite element technique in the San Andreas Fault system with slip rate over 1mm/year, as well as elevation, heat flow, earthquakes, geodetic data and crustal thickness, we compare the results with velocity boundary conditions of plate based on the NUVEL-1 plate model and the approximation of deformation in the Great Basin region. The frictional and dislocation creep constants of the crust are calculated to reproduce the observed variations in the maximum depth of seismicity which corresponds to the temperature ranging from $350^{\circ}C$ to $410^{\circ}C$. The rheologic constants are defined by the coefficient of friction on faults, and the apparent activation energy for creep in the lower crust. Two parameters above represent systematic variations in three experiments. The pattern of model indicates that the friction coefficient of major faults is 0.17~0.25. we test whether the weakness of faults is uniform or proportional to net slip. The geologic data show a good agreement when fault weakness is a trend of an additional 30% slip dependent weakening of the San Andreas. The results of study suggest that all weakening is slip dependent. The best models can be explained by the available data with RMS mismatch of as little as 3mm/year, so their predictions can be closely related with seismic hazard estimation, at least along faults where no data are available.

• Structural Engineering and Mechanics
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• v.91 no.3
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• pp.239-250
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• 2024

With the aim to provide better predication about fracture behavior, a numerical simulating strategy based on the rigid spring model is proposed for reinforced concrete (RC) structures in this study. According to the proposed strategy, concrete is partitioned into a series of irregular rigid blocks based on the Voronoi diagram, which are connected by interface springs. Steel bars are simulated by bar elements, and the bond slip element is defined at bar element nodes to describe the interaction between reinforcement and concrete. A concrete damage evolution model based on the separation criterion is adopted to describe the weakening process of interface spring between adjacent blocks, while a nonlinear bond slip model is introduced to simulate the synergy behaviour of reinforced steel bars and concrete. In the damage evolution model of concrete, the influence of compressive stress perpendicular to the interface on the shear strength is considered. To check the effectiveness and applicability of the proposed modelling, experimental and numerical studies about a simply-supported RC beam and the two-notched concrete plates in Nooru-Mohamed's experiment are conducted, and the grid sensitivity are investigated.