[S12P-03] Analyzing short- and long-term friction effects through two-state variable modeling
Introduction
The rate- and state-dependent friction law is a commonly used empirical equation in geophysics to describe the various process of fault slip. The friction coefficient μ of sliding surfaces evolves with the sliding velocity v and internal state variables θ. Though a single state variable can adequately describe the constitutive law with laboratory data in most cases, it is more appropriate to quantify this effect specifically using two state variables. For example, using two state variables to describe the state-variable dominated behavior at high velocities and flow-dominated behavior at low velocities (Reinen et al,1992; Blanpied et al,1998). In this study, we used two state variables to describe two mechanisms with different timescales in the frictional process, short-term and long-term responses. We used the friction obtained by a homemade apparatus (Ma et al., 2023, SSJ meeting) and estimated the friction parameters a, b1, b2, Dc1 and Dc2 with two state variables. We compare our results with those of previous studies using two-state variables RSF law and confirm the feasibility of using two-state variables RSF law.
Experiment methods
We performed velocity step change tests in a double-direct shear apparatus (Ma et al., 2023, SSJ meeting). The loading velocity is controlled by a servo-controlled uniaxial compression tester. We set up three logarithmically increasing velocity steps: 0.01 mm/s, 0.1 mm/s, and 1 mm/s, with each step covering a length of 2 mm slip. In addition, we designed different normal stress between 3.1 MPa and 6.3 MPa, which was achieved by four bolts that tighten a pair of fixed plates. We used metagabbro rock specimen from Tamil Nadu, south India whose nominal contact area is 60 mm long and 20 mm wide.
Results and conclusion
We used the Levenberg-Marquardt method to fit a nonlinear least-squares to experimental data (Skarbek and Savage, 2019, Geosphere). The a-b1-b2 values are estimated between -0.0038 and 0.0109. The Dc1 is estimated between 0.54µm and 20.02µm and the Dc2 values are estimated between 43.49µm and 140.01µm. We compared the values of a-b1-b2, Dc1 and Dc2with previous studies which used two states variable (Reinen et al,1992; Blanpied et al,1998). We found that simply changing the normal stress and slip velocity has little effect on the friction parameters with two state variables, which is consistent with the results using one state variable (Linker & Dieterich,1992, Marone, 1998). The Dc1 value mainly depends on the geometry of contact, which is similar to the characteristic slip distance Dc with one state variable (Scholz,1988). In contrast, the Dc2 value represents the long-term response the distance required to rearrange the fabric on the rock surface (Pozzi et al., 2023). The value of Dc2 is smaller than those by Blanpied et al. (1998) and Reinen et al. (1992). This could be because the total slip of 2 mm in each velocity step might not be sufficient; the long-term effects was not measured with adequate time and distance to evolve to a steady state. We will increase the length of each velocity step and remeasure Dc2 in future work.
The rate- and state-dependent friction law is a commonly used empirical equation in geophysics to describe the various process of fault slip. The friction coefficient μ of sliding surfaces evolves with the sliding velocity v and internal state variables θ. Though a single state variable can adequately describe the constitutive law with laboratory data in most cases, it is more appropriate to quantify this effect specifically using two state variables. For example, using two state variables to describe the state-variable dominated behavior at high velocities and flow-dominated behavior at low velocities (Reinen et al,1992; Blanpied et al,1998). In this study, we used two state variables to describe two mechanisms with different timescales in the frictional process, short-term and long-term responses. We used the friction obtained by a homemade apparatus (Ma et al., 2023, SSJ meeting) and estimated the friction parameters a, b1, b2, Dc1 and Dc2 with two state variables. We compare our results with those of previous studies using two-state variables RSF law and confirm the feasibility of using two-state variables RSF law.
Experiment methods
We performed velocity step change tests in a double-direct shear apparatus (Ma et al., 2023, SSJ meeting). The loading velocity is controlled by a servo-controlled uniaxial compression tester. We set up three logarithmically increasing velocity steps: 0.01 mm/s, 0.1 mm/s, and 1 mm/s, with each step covering a length of 2 mm slip. In addition, we designed different normal stress between 3.1 MPa and 6.3 MPa, which was achieved by four bolts that tighten a pair of fixed plates. We used metagabbro rock specimen from Tamil Nadu, south India whose nominal contact area is 60 mm long and 20 mm wide.
Results and conclusion
We used the Levenberg-Marquardt method to fit a nonlinear least-squares to experimental data (Skarbek and Savage, 2019, Geosphere). The a-b1-b2 values are estimated between -0.0038 and 0.0109. The Dc1 is estimated between 0.54µm and 20.02µm and the Dc2 values are estimated between 43.49µm and 140.01µm. We compared the values of a-b1-b2, Dc1 and Dc2with previous studies which used two states variable (Reinen et al,1992; Blanpied et al,1998). We found that simply changing the normal stress and slip velocity has little effect on the friction parameters with two state variables, which is consistent with the results using one state variable (Linker & Dieterich,1992, Marone, 1998). The Dc1 value mainly depends on the geometry of contact, which is similar to the characteristic slip distance Dc with one state variable (Scholz,1988). In contrast, the Dc2 value represents the long-term response the distance required to rearrange the fabric on the rock surface (Pozzi et al., 2023). The value of Dc2 is smaller than those by Blanpied et al. (1998) and Reinen et al. (1992). This could be because the total slip of 2 mm in each velocity step might not be sufficient; the long-term effects was not measured with adequate time and distance to evolve to a steady state. We will increase the length of each velocity step and remeasure Dc2 in future work.