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A Continuum Damage-Breakage Faulting Model and Solid-Granular Transitions

机译：连续破坏破坏断层模型与固体颗粒转变

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摘要

We present a thermodynamically-based formulation for mechanical modeling of faulting processes in the seismogenic brittle crust using a continuum damage-breakage rheology. The model combines previous results of a continuum damage framework for brittle solids with continuum breakage mechanics for granular flow. The formulation accounts for the density of distributed cracking and other internal flaws in damaged rocks with a scalar damage parameter, and addresses the grain size distribution of a granular phase in a failure slip zone with a breakage parameter. The stress-strain relation and kinetics of the damage and breakage processes are governed by the total energy function of the system, which combines the energy of the damaged solid with the energy of the granular material. A dynamic brittle instability is associated with a critical level of damage in the solid, leading to loss of convexity of the solid energy function and transition to a granular phase associated with lower energy level. A non-local formulation provides an intrinsic length scale associated with the internal damage structure, which leads to a finite length scale for damage localization that eliminates the unrealistic singular localization of local models. Shear heating during deformation can lead to a secondary finite-width internal localization. The formulation provides a framework for studying multiple aspects of brittle deformation, including potential feedback between evolving elastic moduli and properties of the slip localization zone and subsequent rupture behavior. The model has a more general transition from slow deformation to dynamic rupture than that associated with frictional sliding on a single pre-existing failure zone, and gives time and length scales for the onset of the dynamic fracturing process. Several features including the existence of finite localization width and transition from slow to rapid dynamic slip are illustrated using numerical simulations. A configuration having an existing narrow slip zone with localized damage produces for appropriate loading conditions an overall cyclic stick-slip motion. The simulated frictional response includes transitions from friction coefficient of ~0.7 at low slip velocity to dynamic friction below 0.4 at slip rates above ~0.1 m/s, followed by rapidly increasing friction for slip rates above ~1 m/s, consistent with laboratory observations.
机译：我们提出了一种基于热力学的公式，用于使用连续损伤破坏流变学对地震脆性地壳中断层过程进行机械建模。该模型将用于脆性固体的连续介质破坏框架的先前结果与用于颗粒流的连续介质破坏机制相结合。该公式用标量损伤参数说明了受损岩石中分布的裂缝和其他内部缺陷的密度，并用断裂参数解释了在破坏滑移区中颗粒相的粒度分布。破坏和破坏过程的应力-应变关系和动力学由系统的总能量函数控制，该函数将受损固体的能量与粒状材料的能量结合在一起。动态的脆性不稳定性与固体中的临界损伤水平相关，导致固体能函数的凸度损失并转变为与较低能级相关的颗粒相。非局部公式提供了与内部损伤结构相关的内在长度尺度，这导致了损伤局部化的有限长度尺度，从而消除了局部模型的不切实际的奇异局部化。变形过程中的剪切加热会导致第二个有限宽度的内部局部化。该公式为研究脆性变形的多个方面提供了框架，包括在演化的弹性模量与滑移局部区域的特性以及随后的断裂行为之间的潜在反馈。该模型具有从缓慢变形到动态破裂的更一般的过渡，而不是与单个预先存在的破坏区域上的摩擦滑动相关的过渡，并且给出了动态断裂过程开始的时间和长度尺度。使用数值模拟说明了一些特征，包括有限局部宽度的存在以及从慢速动态滑移到快速动态滑移的过渡。具有现有的具有局部损坏的狭窄滑动区域的构造在适当的负载条件下产生整体的周期性粘滑运动。模拟的摩擦响应包括在低滑动速度下从〜0.7的摩擦系数到在〜0.1 m / s以上的滑动率下从0.4以下的动摩擦过渡，然后在〜1 m / s以上的滑动率下迅速增加摩擦，与实验室观察一致。

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