5:15 PM - 7:15 PM
[SSS10-P30] Dependence of the rate- and state-dependent friction parameters of metagabbro gouge on normal stress
Keywords:Friction experiment, Gouge, Rate and state dependent friction law, Normal stress dependence
The rate- and state-dependent friction (RSF) law can represent complex frictional slips and is widely used in simulations and modeling of various faulting behaviors. One of the friction parameters, the critical slip distance Dc, is recognized as the distance required for the transition to a new state after a change in the condition of the frictional contact. Laboratory experiments using rock powder as a simulated gouge have demonstrated a positive correlation between Dc and the thickness of the gouge layer or the shear band where the deformation is localized in it (Marone and Kilgore, 1993, Nature). Recently, Yamashita et al. (2024, SSJ meeting) reported that the Dc of metagabbro gouge appears to depend on the fault scale, based on the results of velocity step change experiments on centimeter- and meter-scale laboratory faults. They further suggested that the positive dependence of Dc on normal stress is one of the key factors causing the scale dependence of Dc. However, the normal stresses applied to investigate the normal stress dependence in their study were limited from 3.4 MPa to 20 MPa, leaving it unclear whether the positive dependence persists at higher normal stresses. In addition, for simplicity, only one state variable was assumed when estimating the friction parameters, which may be insufficient to understand the mechanism of the correlation, and a model with multiple state variables may be required. Therefore, we conducted velocity step experiments at higher normal stresses of 30 MPa and 40 MPa and estimated the RSF parameters assuming two state variables.
We used a biaxial friction apparatus at the Central Research Institute of Electric Power Industry (Mizoguchi et al., 2021, EPS), which is the same experimental apparatus as that used by Yamashita et al. (2024, SSJ meeting). The simulated gouge was also the same metagabbro powder (average grain size: 12 µm, maximum grain size: 75 µm), with an initial layer thickness of 3 mm. After applying a normal stress of either 30 MPa or 40 MPa, the velocity step changes were applied between 0.1-1.0-10.0-100.0 µm/s. The current analysis focused on the responses to the velocity increase steps from 10.0 µm/s to 100.0 µm/s and from 1.0 µm/s to 10.0 µm/s, which were identical or close to the conditions of the meter-scale experiments. Assuming that the responses follow the slip law (Ruina, 1983, JGR), the optimal combination of the friction parameters that can best reproduce the observed frictional behavior was determined using a grid search technique. To constrain the search space, we used available information directly from the experimental data: (1) approximating the system stiffness as the increase rate of friction coefficient to the displacement right after the velocity step, (2) determining the minimum value of the parameter a from the constraint that the peak friction coefficient after a velocity step from V1 to V2 does not exceed aln(V2/V1), and (3) determining (a-b1-b2)ln(V2/V1) from the difference between the averaged friction coefficient right before the velocity step and that after the transient response after the step.
Examining the relationship between the normal stress and all friction parameters for the optimal model with a coefficient of determination R2 greater than 0.5 for the experimental data, we found that a-b1-b2 decreases with increasing normal stress up to 10 MPa, beyond which it remains almost constant. Defining Dc1 < Dc2, the average value of Dc1 under all normal stress conditions is on the order of several micrometers, while Dc2 has an average value of several hundred micrometers, both of which show no clear dependence on normal stress. However, focusing on the parameters for the velocity step from 10.0 µm/s to 100.0 µm/s, a, b1, b2 are almost constant independent of normal stress, while both Dc1 and Dc2 tend to increase with increasing normal stress up to 40 MPa. Since the loading rate in the meter-scale experiments was greater than 10.0 µm/s, this normal stress dependence of Dc could become effective and then cause the scale dependence. We will continue to investigate the mechanisms from various aspects, such as observing the microstructures within the gouge layer.
We used a biaxial friction apparatus at the Central Research Institute of Electric Power Industry (Mizoguchi et al., 2021, EPS), which is the same experimental apparatus as that used by Yamashita et al. (2024, SSJ meeting). The simulated gouge was also the same metagabbro powder (average grain size: 12 µm, maximum grain size: 75 µm), with an initial layer thickness of 3 mm. After applying a normal stress of either 30 MPa or 40 MPa, the velocity step changes were applied between 0.1-1.0-10.0-100.0 µm/s. The current analysis focused on the responses to the velocity increase steps from 10.0 µm/s to 100.0 µm/s and from 1.0 µm/s to 10.0 µm/s, which were identical or close to the conditions of the meter-scale experiments. Assuming that the responses follow the slip law (Ruina, 1983, JGR), the optimal combination of the friction parameters that can best reproduce the observed frictional behavior was determined using a grid search technique. To constrain the search space, we used available information directly from the experimental data: (1) approximating the system stiffness as the increase rate of friction coefficient to the displacement right after the velocity step, (2) determining the minimum value of the parameter a from the constraint that the peak friction coefficient after a velocity step from V1 to V2 does not exceed aln(V2/V1), and (3) determining (a-b1-b2)ln(V2/V1) from the difference between the averaged friction coefficient right before the velocity step and that after the transient response after the step.
Examining the relationship between the normal stress and all friction parameters for the optimal model with a coefficient of determination R2 greater than 0.5 for the experimental data, we found that a-b1-b2 decreases with increasing normal stress up to 10 MPa, beyond which it remains almost constant. Defining Dc1 < Dc2, the average value of Dc1 under all normal stress conditions is on the order of several micrometers, while Dc2 has an average value of several hundred micrometers, both of which show no clear dependence on normal stress. However, focusing on the parameters for the velocity step from 10.0 µm/s to 100.0 µm/s, a, b1, b2 are almost constant independent of normal stress, while both Dc1 and Dc2 tend to increase with increasing normal stress up to 40 MPa. Since the loading rate in the meter-scale experiments was greater than 10.0 µm/s, this normal stress dependence of Dc could become effective and then cause the scale dependence. We will continue to investigate the mechanisms from various aspects, such as observing the microstructures within the gouge layer.