Based on the assumption that fault slip dominates in the stress relaxation in the brittle crust, Coulomb theory allows for the crustal stress estimation with an empirical frictional coefficient. However, natural variability of fault friction and slip uncertainty exist in the Earth's crust. To address the extent to which heterogeneous frictional slips influence crustal stress and its evolution, we establish a quasi-static, 2D model to represent the fractured crustal rock mass. The model consists of randomly oriented fractures with heterogeneous distribution of frictional coefficients. The global mechanical response is quantitatively related to the cascades of local frictional slips under specific boundary conditions. The temporal evolution of stress is explicitly modeled by an iterative process where a simple slip law is assumed for critical fractures. We particularly illustrate the stress evolution in a normal faulting stress regime, considering different distributions of frictional coefficients. All cases indicate that the decrease in differential stress manifests as a self-organized process, eventually leading to the frictional equilibrium of the fractured rock mass. The final stress state upon equilibrium jointly depends on the orientation and frictional coefficient of all fractures therein. The model informs that the global stress state of a stochastic system can depart substantially from a deterministic estimation via an empirical frictional coefficient. This model quantitatively corroborates and extends the notion of frictional equilibrium, and reveals far more profound influence of system heterogeneity on the local and global stress evolution.

中文翻译：

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通过随机局部库仑摩擦滑移的全局摩擦平衡

基于断层滑动在脆性地壳应力松弛中占主导地位的假设，库仑理论允许使用经验摩擦系数来估计地应力。然而，地壳中存在断层摩擦和滑动不确定性的自然变化。为了解决非均质摩擦滑动对地应力及其演化的影响程度，我们建立了一个准静态的二维模型来表示破裂的地壳岩体。该模型由具有不均匀分布的摩擦系数的随机取向的裂缝组成。全局机械响应与特定边界条件下局部摩擦滑移的级联定量相关。应力的时间演变通过迭代过程明确建模，其中假设临界裂缝的简单滑移定律。考虑到摩擦系数的不同分布，我们特别说明了正断层应力状态下的应力演变。所有情况都表明，微分应力的降低表现为一个自组织过程，最终导致破裂岩体的摩擦平衡。平衡时的最终应力状态共同取决于其中所有裂缝的方向和摩擦系数。该模型表明，随机系统的全局应力状态可以通过经验摩擦系数显着偏离确定性估计。该模型定量证实并扩展了摩擦平衡的概念，