Analysis of Fault Growth and Linkage Using Work Minimization

为了预测断层的发育，了解剪切作用下的裂纹联系是很重要的。如果断层的生长受机械效率最大化的控制，那么断层系统将通过现有断层的滑动或新断层的生长来适应变形，这取决于哪一种在能量上最容易。因此，小的缺陷或裂纹是否会连接形成更大的裂纹取决于有效连接裂纹的能量增益是否超过产生连接裂纹所需的功。本研究项目利用功最小原理，通过两种方法对断层的连接和生长进行数值研究：1)对裂缝合并进行参数化研究，以测试和校准功最小的应用；2)模拟南加州圣哈辛托断层的演化。第一种方法是在一系列参数和随机调查中使用力学模型来评估新断层生长的配置，这些配置既可以使系统效率最大化，又有利于系统的发展，即工作成本小于所获得的效率。随机模型将在不同的加载条件下纳入试样中不同的缺陷分布，以探索不同程度的各向异性的影响。此外，对从实验室到区域尺度的机械效率比例的调查将促进项目中采用的第二种方法。第二种方法是使用三维模型来研究与克拉克断层和Coyote Creek断层之间的阶梯演化有关的工作，这是南加州圣哈辛托断层的一部分。数值模型将模拟这一阶段解释断层发育的几个阶段，并评估演化的力学效率。该研究将(a)深入了解裂缝生长和聚结的力学效率，包括各向异性和模型规模的影响；(b)基于工作最小化原则，通过两个断层段的生长和联动，分析了圣哈辛托断层的发育。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，并有助于形成大型山脉。潜在地震的大小取决于断层的长度；断层越大，潜在的地震就越大。虽然我们理解了错误的行为，但它们是如何成长的还不清楚。在实验室里，科学家们观察到，在岩石内部，较小的裂缝连接在一起形成断层表面。由于许多岩石已经有大量的小裂缝，但并非所有岩石都含有断层，因此我们需要了解有助于裂缝连接和最终断层发育的条件。本项目通过应用工作最小化原则来检查裂缝如何连接形成故障。这个原理暗示地球是懒惰的。在一个懒惰的地球上，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能更容易容纳滑动，而代价是在连接处打破岩石所需的能量。该项目将开发基于工作量最小化的裂缝连接预测工具。一旦这些工具被开发出来，它们将被应用于南加州的圣哈辛托断层，该断层最近有两段连接的历史。如果模型预测与圣哈辛托断层的解释历史相匹配，那么该工具可能用于调查世界其他地区并预测未来断层的演变。

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.