The onset of frictional motion is mediated by rupture-like slip fronts, which nucleate locally and propagate eventually along the entire interface causing global sliding. The static friction coefficient is a macroscopic measure of the applied force at this particular instant when the frictional interface loses stability. However, experimental studies are known to present important scatter in the measurement of static friction; the origin of which remains unexplained. Here, we study the nucleation of local slip at interfaces with slip-weakening friction of random strength and analyze the resulting variability in the measured global strength. Using numerical simulations that solve the elastodynamic equations, we observe that multiple slip patches nucleate simultaneously, many of which are stable and grow only slowly, but one reaches a critical length and starts propagating dynamically. We show that a theoretical criterion based on a static equilibrium solution predicts quantitatively well the onset of frictional sliding. We develop an efficient Monte-Carlo model by adapting the theoretical criterion and study the variability in global strength distribution caused by the stochastic properties of local frictional strength. The results demonstrate that an increasing spatial correlation length on the interface, representing geometric imperfections and roughness, causes lower global static friction. Conversely, smaller correlation length increases the macroscopic strength while its variability decreases. We further show that randomness in local friction properties is insufficient for the existence of systematic precursory slip events. Random or systematic non-uniformity in the driving force, such as potential energy or stress drop, is required for arrested slip fronts. Our model and observations provide a necessary framework for efficient stochastic analysis of macroscopic frictional strength and establish a fundamental basis for probabilistic design criteria for static friction.

摩擦运动的开始是由类似断裂的滑动前沿所介导的，该滑动前沿局部成核并最终沿着整个界面传播，从而引起整体滑动。当摩擦界面失去稳定性时，静摩擦系数是在此特定时刻施加的力的宏观度量。然而，已知实验研究在静摩擦的测量中表现出重要的分散性。其来源仍然无法解释。在这里，我们研究了具有随机强度的滑动弱化摩擦的界面处的局部滑动的形核，并分析了测得的整体强度的变化结果。通过使用求解弹性动力学方程的数值模拟，我们观察到多个滑片同时成核，其中许多滑片稳定且仅缓慢生长，但达到临界长度并开始动态传播。我们表明，基于静态平衡解的理论标准可以很好地预测摩擦滑动的开始。我们通过适应理论标准来开发有效的蒙特卡洛模型，并研究由局部摩擦强度的随机特性引起的整体强度分布的变化。结果表明，界面上空间相关长度的增加（代表几何缺陷和粗糙度）会导致较低的整体静摩擦。相反，较小的相关长度会增加宏观强度，而其可变性会降低。我们进一步表明，局部摩擦特性的随机性不足以存在系统的前兆滑动事件。对于被制动的滑动前缘，需要随机或系统的驱动力不均匀性，例如势能或应力降。我们的模型和观测结果为有效的宏观摩擦强度随机分析提供了必要的框架，并为静摩擦的概率设计标准奠定了基础。