講演情報
[P12-01]Complex sample-size effect in high-velocity frictiondue to thermoelastic instability inferred by numerical simulation
*野田 博之1 (1. 京都大学 防災研究所)
Tsutsumi and Shimamoto (1997) for the first time reported so-called dynamic weakening in rock friction at coseismic slip rates (~ 0.1 m/s) in lab. experiments. Since then, it has been intensively studied for centimeter-scale samples as summarized by Di Toro et al. (2011). On the other hand, its applicability to larger-scale natural faults hosting large earthquakes remains unclear, partly because the scale dependency of friction has not been understood and evaluated well. Recent experiments by Yamashita et al. (2015) discovered the sample-size effect in the dynamic weakening, and Noda (2023) pointed out it may be driven by thermoelastic instability (TEI, e.g., Barber, 1967; Dow and Burton, 1972). In the present study, a series of simulations for TEI coupled with temperature-weakening friction were conducted to reveal the potentially complex sample-size effect.
In thermoelastic mediums, frictional heat causes expansion around regions of concentrated normal stress, which positively feedbacks to enhance heterogeneity. If it overcomes thermal conduction, which smears out the heterogeneity, then spontaneous growth of the heterogeneity takes place. The critical slip rate Vcr is proportional to the wavenumber and thus reciprocal of the sample size. A larger sample is expected to undergo TEI at a lower slip rate. At such high slip rates, contact time of microscopic asperity may be so short that the time-dependent strengthening (e.g., Dieterich, 1972) is less efficient than the log-t healing. As a result, the temperature-weakening effect conceivably becomes dominant (e.g., Chester, 1994; Noda 2008). If the temperature-weakening friction and TEI are coupled, positive correlation of normal stress and temperature by TEI leads to macroscopic weakening, explaining the observed sample-size dependency at least qualitatively.
Here, TEI is simulated with a spectral method allowing partial opening of the sliding surface. The focus was put on the post-critical behavior. A simple 2-dimensional problem was considered here. Noda (2023) developed a numerical algorithm for calculation of evolving σ based on numerical approximation of spectral boundary integral equation method (SBIEM) by introducing memory variables. The evolving temperature field was calculated with a spectral method with logarithmic wavenumber domain normal to the fault.
A series of simulations revealed that the dynamic weakening occurs at large enough slip if V>Vcr. Specifically, partial opening seems to trigger the dynamic weakening. At larger slip, the friction coefficient is significantly smaller than the low-velocity or low-temperature value, but its dependency on the sample size turned out to be complex. If V is only modestly larger than Vcr, the wavelength of instability is comparable to the sample size, and thus only one contact is developed. As long as the number of contacts is 1, the friction coefficient decreases monotonically with the sample size at a given V and a total displacement. At even larger slip rates, the number of contacts at large slip increases. The increase in the contact number corresponds with the increase in the fraction of contact area to the nominal area of the sliding surface, decreasing the stress concentration factor and local temperature rise. At this stage, the friction coefficient at large slip fluctuates severely with the sample size and becomes difficult to predict, although its level is significantly smaller than the low-temperature value. The simulation results also indicate that the frictional resistance is less sensitive to the sample size if it is larger than about 3 cm than for smaller samples, inferring that the sample-size effect by TEI saturates at large enough samples determined by the wavelength with the maximum growth rate. If this is the case, there may exist an appropriate length scale for homogenization, potentially leading to an upscaling method of lab. experiment to large-scale problems.
In thermoelastic mediums, frictional heat causes expansion around regions of concentrated normal stress, which positively feedbacks to enhance heterogeneity. If it overcomes thermal conduction, which smears out the heterogeneity, then spontaneous growth of the heterogeneity takes place. The critical slip rate Vcr is proportional to the wavenumber and thus reciprocal of the sample size. A larger sample is expected to undergo TEI at a lower slip rate. At such high slip rates, contact time of microscopic asperity may be so short that the time-dependent strengthening (e.g., Dieterich, 1972) is less efficient than the log-t healing. As a result, the temperature-weakening effect conceivably becomes dominant (e.g., Chester, 1994; Noda 2008). If the temperature-weakening friction and TEI are coupled, positive correlation of normal stress and temperature by TEI leads to macroscopic weakening, explaining the observed sample-size dependency at least qualitatively.
Here, TEI is simulated with a spectral method allowing partial opening of the sliding surface. The focus was put on the post-critical behavior. A simple 2-dimensional problem was considered here. Noda (2023) developed a numerical algorithm for calculation of evolving σ based on numerical approximation of spectral boundary integral equation method (SBIEM) by introducing memory variables. The evolving temperature field was calculated with a spectral method with logarithmic wavenumber domain normal to the fault.
A series of simulations revealed that the dynamic weakening occurs at large enough slip if V>Vcr. Specifically, partial opening seems to trigger the dynamic weakening. At larger slip, the friction coefficient is significantly smaller than the low-velocity or low-temperature value, but its dependency on the sample size turned out to be complex. If V is only modestly larger than Vcr, the wavelength of instability is comparable to the sample size, and thus only one contact is developed. As long as the number of contacts is 1, the friction coefficient decreases monotonically with the sample size at a given V and a total displacement. At even larger slip rates, the number of contacts at large slip increases. The increase in the contact number corresponds with the increase in the fraction of contact area to the nominal area of the sliding surface, decreasing the stress concentration factor and local temperature rise. At this stage, the friction coefficient at large slip fluctuates severely with the sample size and becomes difficult to predict, although its level is significantly smaller than the low-temperature value. The simulation results also indicate that the frictional resistance is less sensitive to the sample size if it is larger than about 3 cm than for smaller samples, inferring that the sample-size effect by TEI saturates at large enough samples determined by the wavelength with the maximum growth rate. If this is the case, there may exist an appropriate length scale for homogenization, potentially leading to an upscaling method of lab. experiment to large-scale problems.