3:45 PM - 4:00 PM
[SCG40-17] Thermoelastic instability and temperature-weakening friction cause sample-size dependency of dynamic weakening in high-velocity friction experiments
Keywords:Thermoelastic instability, Sample-size effect, Dynamic weakening of fault, High-velocity friction, Numerical simulation
Scale dependency in friction is crucial in connecting small-scale lab-experimental studies and large-scale natural fault hosting large earthquakes. Since experiments by Tsutsumi and Shimamoto (1997), dynamic weakening in rock friction has been intensively studied in laboratory experiments for centimeter-scale samples of variety of rocks (e.g., Di Toro et al., 2011), and it has been revealed that the rock friction dramatically decreases at coseismic slip rate (~ 0.1 m/s) at which frictional heating becomes important. The weakening is primarily driven by temperature rise T on the sliding surface (e.g., Yao et al., 2016). Yamashita et al. (2015) conducted friction experiments for meter-scale samples and discovered that the dynamic weakening takes place at a smaller slip rate (~ 0.01 m/s), arguing that heterogeneity in the normal stress σ on the frictional surface causes concentration of frictional power and local activation of the dynamic weakening. Recently, Noda (2023) considered a mechanism called thermoelastic instability (TEI, e.g., Barber, 1967; Dow and Burton, 1972) and pointed out that the heterogeneity spontaneously grows at a higher slip rate V than the critical value Vcr, which is inversely proportional to the wavelength of perturbation and thus to the sample size. In the present study, TEI is simulated with a spectral method, and possibility of its operation during laboratory experiments is discussed quantitatively.
A simple 2-dimensional problem same as in Noda (2023) was considered here, consisting of a planer sliding surface with antiplane slip embedded in an infinite linearly-thermoelastic medium. Periodic boundaries were assumed with an interval of W along the surface for approximation of the finite width of sliding surface in experimental rock samples. Noda (2023) developed a numerical algorithm for calculation of evolving σ based on numerical approximation to spectral boundary integral equation method (SBIEM) by introducing memory variables, which is requires less numerical resources and does not suffer from growing memory needed in temporal convolution in SBIEM. The evolving temperature field was calculated with a spectral method with logarithmic wavenumber domain normal to the fault combined with an exponential time-differencing method (Noda and Lapusta, 2010). The numerical solution was validated by comparing with a solution obtained by a standard SBIEM for a short simulation.
Simulations comparable to the experiments by Yamashita et al. (2015) were conducted at the applied, spatially averaged σ of 6.7 MPa, V of 0.01 m/s and the final slip of 0.4 m. W of 0.1 m and 0.01 m leads to V/Vcr of 8.6 and 0.86, respectively, for the constant friction coefficient of 0.7 and physical properties of gabbro. The initial perturbation in σ was given by self-affine distribution with Hurst exponent of 0.81 and standard deviation of 2.5% of the average σ. After 0.4 m of slip, the standard deviation of σ is 3.6 MPa and growing exponentially for W = 0.1 m, while it is 0.86 MPa and approaching to a steady state for W = 0.01 m, as expected from the analyses by Noda (2023) for a single Fourier-mode perturbation. In the case for W = 0.1 m, spatially minimum value of σ becomes negative, requiring implementation of partial opening of the sliding surface. The standard deviation of T is 15 K and 2.4 K for W of 0.1 m and 0.01 m, respectively. Importantly, there is a positive correlation between σ and T, which causes macroscopic weakening when introducing temperature-dependent friction. Numerical simulations with temperature-weakening friction demonstrate dynamic weakening of the sliding surface which depends on the system size. The present simulations indicate that TEI is indeed significant in laboratory experiments and probably responsible for the observed sample-size effect, illuminating the difficulty in application of the experimental results to natural phenomena of different length scale.
A simple 2-dimensional problem same as in Noda (2023) was considered here, consisting of a planer sliding surface with antiplane slip embedded in an infinite linearly-thermoelastic medium. Periodic boundaries were assumed with an interval of W along the surface for approximation of the finite width of sliding surface in experimental rock samples. Noda (2023) developed a numerical algorithm for calculation of evolving σ based on numerical approximation to spectral boundary integral equation method (SBIEM) by introducing memory variables, which is requires less numerical resources and does not suffer from growing memory needed in temporal convolution in SBIEM. The evolving temperature field was calculated with a spectral method with logarithmic wavenumber domain normal to the fault combined with an exponential time-differencing method (Noda and Lapusta, 2010). The numerical solution was validated by comparing with a solution obtained by a standard SBIEM for a short simulation.
Simulations comparable to the experiments by Yamashita et al. (2015) were conducted at the applied, spatially averaged σ of 6.7 MPa, V of 0.01 m/s and the final slip of 0.4 m. W of 0.1 m and 0.01 m leads to V/Vcr of 8.6 and 0.86, respectively, for the constant friction coefficient of 0.7 and physical properties of gabbro. The initial perturbation in σ was given by self-affine distribution with Hurst exponent of 0.81 and standard deviation of 2.5% of the average σ. After 0.4 m of slip, the standard deviation of σ is 3.6 MPa and growing exponentially for W = 0.1 m, while it is 0.86 MPa and approaching to a steady state for W = 0.01 m, as expected from the analyses by Noda (2023) for a single Fourier-mode perturbation. In the case for W = 0.1 m, spatially minimum value of σ becomes negative, requiring implementation of partial opening of the sliding surface. The standard deviation of T is 15 K and 2.4 K for W of 0.1 m and 0.01 m, respectively. Importantly, there is a positive correlation between σ and T, which causes macroscopic weakening when introducing temperature-dependent friction. Numerical simulations with temperature-weakening friction demonstrate dynamic weakening of the sliding surface which depends on the system size. The present simulations indicate that TEI is indeed significant in laboratory experiments and probably responsible for the observed sample-size effect, illuminating the difficulty in application of the experimental results to natural phenomena of different length scale.