Propagation of a slip transient on a fault with rate- and state-dependent friction resembles a fracture whose near tip region is characterized by large departure of the slip velocity and fault strength from the steady-state sliding. We develop a near tip solution to describe this unsteady dynamics, and obtain the fracture energy G_c, dissipated in overcoming strength-excursion away from steady state, as a function of the rupture velocity v_r. This opens a possibility to model slip transients on rate-and-state faults as singular cracks characterized by approximately steady-state frictional resistance in the fracture bulk, and by a stress singularity with the intensity defined in terms of G_c(v_r) at the crack tip. In pursuing this route, we develop and use an analytical equation of motion to study 1-D slip driven by a combination of uniform background stress and a localized perturbation of the fault strength with the net Coulomb force ΔT. In the context of fluid injection, ΔT is a proxy for the injection volume V_inj. We then show that, for ongoing fluid injection, the propagation speed of a transient induced on a frictionally stable fault is bounded by a large-time limiting value proportional to the injection rate dV_inj/dt, while, for stopped injection, the maximum slip run-out distance is proportional to $V_{\mathrm{inj},\mathrm{total}}^2$.

This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

在断层上具有速率和状态相关的摩擦的滑动瞬变传播类似于断口附近区域的特征，该断口的特征是滑动速度和断层强度与稳态滑动的较大偏离。我们开发了一种近尖端解决方案来描述这种非稳态动力学，并获得了断裂能G _c，它是随着断裂速度v _r的变化而耗散的，该断裂能Gc在克服远离稳态的强度偏移过程中耗散了。这为将速率和状态断层上的滑动瞬变建模为奇异裂纹提供了可能性，奇异裂纹的特征是在裂隙体中具有近似稳态的摩擦阻力，而应力奇异性的强度由G _c（v _r）在裂纹尖端。在这条路线中，我们开发并使用运动解析方程来研究一维滑移，该滑移是由均匀背景应力和故障强度与库仑净力ΔT的局部扰动相结合而驱动的。在流体喷射的情况下，ΔT是喷射体积V _inj的代理。然后，我们表明，对于正在进行的流体注入，在摩擦稳定的断层上引起的瞬变的传播速度受与注入速率dV _inj / d t成比例的长时间限制的限制，而对于停止注入，最大值滑移跳动距离与${\mathrm{伏特}}_{\mathrm{注射}，\mathrm{全部的}}^{\mathrm{2个}}$。

本文是主题主题“固体材料的断裂动力学：从粒子到地球”的一部分。