Dynamic rupture modeling with laboratory‐derived constitutive relations
Dynamic rupture modeling with laboratory‐derived constitutive relations
复制标题
利用实验室导出的本构关系进行动态破裂建模
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
P. Okubo
中科院分区：
文献类型：
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作者：
P. Okubo
实验室导出的状态变量摩擦本构关系用于面内或 II 型剪切裂纹动态扩展的数值模拟。根据最初由 J. H. Dieterich 提出的这个公式，摩擦阻力随着滑移率的对数以及由 A. L. Ruina 确定的摩擦状态变量的对数而变化。在稳定滑动的情况下，状态变量与（滑移率）−1 成正比。在滑移率突然增加之后，速率和状态依赖性结合起来产生类似于滑移弱化的行为。当在固定破裂速度下人为地强制破裂成核时，在均匀分布的初始应力场中用状态变量摩擦计算的破裂模型与用滑移弱化断层本构关系计算的早期破裂模型非常相似。计算了额外的破裂模型，其中破裂成核是自然实现的，并且对断层的准静态响应进行数值模拟，导致不稳定的动态破裂的发生。当状态变量摩擦定律的破裂成核自然发生时，大部分断层在加速滑移集中在最终成为破裂成核斑块之前加速。伴随这种加速滑移的状态演化导致更高的平均破裂速度或更快速的破裂加速至接近P波破裂速度。破裂模型还针对地震粗糙问题进行了计算，即零应力降区域包围的高应力断层片的破坏。滑移进入零应力降区域的动态超调与简单的能量平衡分析大致一致；破裂的最终尺寸与高应力斑块尺寸的平方成正比。早期的摩擦稳定性分析已经确定了破裂成核的临界断层斑块尺寸。该临界补片尺寸通常不同于根据应用于更简单的滑移弱化定律的裂纹尖端能量平衡考虑确定的临界裂纹长度。在模型计算中，如果起始补片尺寸小于临界补片尺寸，则动态破裂不会成核。这与摩擦稳定性分析一致。因此，这些模型计算表明，遵循状态变量摩擦关系的动态破裂类似于遵循更简单的断层滑动减弱定律的动态破裂。然而，在对断层运动的整个周期进行建模时，状态变量公式中包含的速率相关摩擦响应在与破裂成核相关的低滑移速率下非常重要。适用于滑移弱化断层的临界破裂成核尺寸不能预测状态变量断层的临界破裂成核尺寸。
A laboratory-derived state variable friction constitutive relation is used in the numerical simulation of the dynamic growth of an in-plane or mode II shear crack. According to this formulation, originally presented by J. H. Dieterich, frictional resistance varies with the logarithm of the slip rate and with the logarithm of the frictional state variable as identified by A. L. Ruina. Under conditions of steady sliding, the state variable is proportional to (slip rate)−1. Following suddenly introduced increases in slip rate, the rate and state dependencies combine to produce behavior which resembles slip weakening. When rupture nucleation is artificially forced at fixed rupture velocity, rupture models calculated with the state variable friction in a uniformly distributed initial stress field closely resemble earlier rupture models calculated with a slip weakening fault constitutive relation. Additional rupture models are calculated in which rupture nucleation is achieved naturally, with numerical simulations of the quasi-static response of the fault leading to the onset of unstable, dynamic rupture. When rupture nucleation with the state variable friction law takes place naturally, a large fraction of the fault accelerates before accelerating slip is concentrated in what ultimately becomes the rupture nucleation patch. The state evolution accompanying this accelerating slip leads to higher average rupture speeds or a more rapid rupture acceleration to near P wave rupture speeds. Rupture models are also calculated for the seismological asperity problem, that is, the failure of a highly stressed fault patch surrounded by a region of zero stress drop. Dynamic overshoot of slip into the region of zero stress drop roughly agrees with a simple energy balance analysis; the final size of the rupture is proportional to the square of the size of the high stress patch. Earlier frictional stability analyses have led to the definition of a critical fault patch size for rupture nucleation. This critical patch size is generally different from critical crack lengths determined from crack tip energy balance considerations applied to a simpler slip weakening law. In the model calculations, dynamic rupture does not nucleate if the starting patch size is less than the critical patch size. This is consistent with the frictional stability analyses. Thus these model calculations suggest that dynamic rupture following a state variable friction relation is similar to that following a simpler fault slip weakening law. However, when modeling the full cycle of fault motions, rate-dependent frictional responses included in the state variable formulation are important at low slip rates associated with rupture nucleation. The critical rupture nucleation dimension appropriate for a slip weakening fault does not predict the critical nucleation dimension for a state variable fault.