Analysis of Fault Growth and Linkage Using Work Minimization

为了预测断层的扩展，重要的是要了解剪切作用下的裂纹连锁。如果断层的增长是由最大限度地提高机械效率，断层系统将通过现有断层上的滑动或通过新断层的增长来适应变形，这取决于哪一个在能量上是最容易的。因此，小的缺陷或裂纹是否会连接形成较大的裂纹取决于裂纹有效连接中的能量增益是否超过产生连接裂纹所需的功。利用功最小化原理，本研究项目采用两种方法数值研究了断层如何连接和生长：1）裂纹聚结的参数研究，以测试和校准功最小化的应用; 2）模拟加州南部圣哈辛托断层的演化。第一种方法使用力学模型在一套参数和随机调查，以评估新的故障增长的配置，这将最大限度地提高系统的效率，并积极有利于发展，即工作成本是小于所获得的效率。随机模型将在各种载荷条件下将样本中不同的缺陷分布结合起来，以探索不同程度的各向异性的影响。此外，从实验室到区域尺度的机械效率的缩放调查将促进该项目中采用的第二种方法。第二种方法使用三维模型来研究克拉克断层和狼溪断层之间的跨越的演变，这是圣哈辛托断层在南加州的一部分。数值模型将模拟在此步距解释断层发展的几个阶段，并评估不断变化的机械效率。这项研究将（a）深入了解裂缝生长和合并的机械效率，包括各向异性的影响和模型的比例;和（B）根据功最小化原理，通过两个断层段的生长和连接来分析圣哈辛托断层的发展。地球上的构造板块边界包含许多活动断层，这些断层在破坏性地震中滑动，形成巨大的山脉潜在地震的大小取决于断层的长度;断层越大，潜在地震就越大。虽然断层的行为是了解的，但它们是如何生长的却不清楚。在实验室里，科学家们观察到，在岩石内部，较小的裂缝连接形成断层表面。由于许多岩石已经有大量的小裂缝，但不是所有的岩石都包含断层，我们需要了解有助于裂缝连接和最终断层发展的条件。本计画应用功最小化原理，探讨裂缝如何连结形成断层。这个原则意味着地球是懒惰的。在一个懒惰的地球中，只有当连接裂缝的能量成本小于连接裂缝的能量收益时，裂缝才会连接起来。在地质断层的情况下，好处是连接起来的裂缝可以更容易地容纳滑动，成本是在连接处破碎岩石所需的能量。该项目将开发工具来预测基于工作最小化的裂纹连接。一旦这些工具被开发出来，它们将被应用于加州南部的圣哈辛托断层，该断层最近有两个部分连接的历史。如果模型预测与圣哈辛托断层的解释历史相匹配，则该工具可用于调查世界其他地区并预测未来的断层演化。

To predict fault growth it is important to understand crack linkage under shear. If fault growth is governed by maximizing mechanical efficiency, a fault system will accommodate deformation either via slip on existing faults or via the growth of a new fault, depending on which is energetically easiest. Consequently, whether small flaws or cracks will link to form a larger crack depends on whether the energetic gain in efficient connection of cracks exceeds the work required to create the linking crack. Using the principle of work minimization, this research project numerically investigates how faults link and grow with two approaches: 1) parametric investigation of crack coalescence in order to test and calibrate the application of work minimization and 2) simulation of the evolution of the San Jacinto fault in southern California. The first approach uses mechanical models in a suite of parametric and stochastic investigations to evaluate the configuration of new fault growth that would both maximize efficiency of the system and are energetically favored to develop, i.e. the work cost is less than the efficiency gained. The stochastic models will incorporate different distributions of flaws in a sample under a variety of loading conditions to explore the effect of differing degrees of anisotropy. Furthermore, an investigation of the scaling of mechanical efficiency from the lab to regional scales will facilitate the second approach employed in the project. The second approach uses three-dimensional models to investigate the work associated with the evolution of a stepover between the Clark fault and the Coyote Creek fault, which are part of the San Jacinto fault in southern California. Numerical models will simulate several stages in the interpreted fault development at this stepover and assess the evolving mechanical efficiency. The study will (a) provide insight into the mechanical efficiency of fracture growth and coalescence, including the impact of anisotropy and the scale of the models; and (b) analyze the development of the San Jacinto fault through the growth and linkage of two fault segments based on the principle of work minimization.Tectonic plate boundaries in the Earth contain many active faults that slip in devastating earthquakes and contribute to building large mountain ranges. The size of potential earthquakes depends on the length of the fault; the larger the fault, the bigger the potential earthquakes. While the behavior of faults is understood, how they grow is not. Within the laboratory, scientists observed that within rocks, smaller cracks link to form fault surfaces. Since many rocks already have abundant small cracks but not all rocks contain faults, we need to understand the conditions that contribute to crack linkage and eventual fault development. This project examines how cracks link to form faults by applying the principle of work minimization. This principle implies that the Earth is lazy. Within a lazy Earth, cracks will only link up if the energetic cost of linking the cracks is less than the energetic benefit of having the cracks linked up. In the case of geologic faults, the benefit is that linked up cracks may more readily accommodate slip and the cost is the energy need to break the rock at the linkage. The project will develop tools to predict crack linkage that are based on work minimization. Once these tools are developed, they will be applied to the San Jacinto fault in southern California, which has a recent history of linkage of two segments. If the model predictions match the interpreted history of the San Jacinto fault then this tool may be of use for investigating other regions of the world and predicting future fault evolution.