Microphysically Derived Expressions for Rate-and-State Friction Parameters, a , b , and D c Journal of Geophysical Research: Solid Earth
Microphysically Derived Expressions for Rate-and-State Friction Parameters, a , b , and D c Journal of Geophysical Research: Solid Earth
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速率-状态摩擦（RSF）定律在断层力学中有着广泛的应用，但其经验基础很大程度上反映了对潜在物理机制的有限理解。最近，我们提出了一个微观物理模型，描述了一个粒状断层泥的摩擦行为进行变形的粒状碎屑流伴随着热激活蠕变和粒间滑动的颗粒接触。数值解很好地再现了典型的实验结果。在这里，我们扩展我们的模型，以获得物理上有意义的，分析表达式的稳态摩擦强度和标准RSF参数，a，B，和D c。摩擦强度由晶界摩擦和晶间膨胀摩擦两部分组成。a和B的表达式线性地反映了这两项的速率依赖性。D c与滑移带厚度成比例，仅随速度略有变化。预测的a，B，和D C的值与以前的实验结果显示定量协议，并将其值插入到经典的RSF法律给出模拟摩擦行为，这是与我们的数值实现的模型从稳态小偏离的预测是一致的。对于较大的速度步长，该模型产生福尔斯慢度和滑移定律之间的混合RSF行为，例如，具有中间等效滑移（弱化）距离d 0。我们的模型具有有趣的属性，不仅a和B是速度依赖的，但也D C和D 0规模不同，从经典的RSF模型，可能解释的行为，在许多热液摩擦实验和自然断层摩擦有重大影响。CNS模型对稳态小偏差的预测。预测的标度律D c与以前的实验室实验和自然断层中的地球物理观测结果一致，可能解释了地震学和实验观测结果之间的差异。在另一篇文章中，我们研究了该模型的滑移稳定性，给出了临界刚度的微观物理解释，这与由Kc =（B（cid：1）a）σ n /Dc计算的结果一致。这些都证明了本研究中得到的表达式的有效性。
Rate-and-state friction (RSF) laws are extensively applied in fault mechanics but have a largely empirical basis re fl ecting only limited understanding of the underlying physical mechanisms. We recently proposed a microphysical model describing the frictional behavior of a granular fault gouge undergoing deformation in terms of granular fl ow accompanied by thermally activated creep and intergranular sliding at grain contacts. Numerical solutions reproduced typical experimental results well. Here we extend our model to obtain physically meaningful, analytical expressions for the steady state frictional strength and standard RSF parameters, a , b , and D c . The frictional strength contains two components, namely, grain boundary friction and friction due to intergranular dilatation. The expressions obtained for a and b linearly re fl ect the rate dependence of these two terms. D c scales with slip band thickness and varies only slightly with velocity. The values of a , b , and D c predicted show quantitative agreement with previous experimental results, and inserting their values into classical RSF laws gives simulated friction behavior that is consistent with the predictions of our numerically implemented model for small departures from steady state. For large velocity steps, the model produces mixed RSF behavior that falls between the Slowness and Slip laws, for example, with an intermediate equivalent slip(-weakening) distance d 0 . Our model possesses the interesting property not only that a and b are velocity dependent but also that D c and d 0 scale differently from classical RSF models, potentially explaining behaviour seen in many hydrothermal friction experiments and having substantial implications for natural fault friction. the predictions from the CNS model for small departures from steady state. The predicted scaling law for D c is in-line with previous lab experiments and geophysical observations in natural faults, potentially explaining the discrepancies between seismological and experimental observations. In a companion paper, we investigate the slip stability of the model, giving the microphysical interpretation of critical stiffness, which is consistent with the result calculated from K c = ( b (cid:1) a ) σ n / D c . All of these testify to the validity of the expressions obtained in the present study.