CMG Research: Analysis and Application of XFEM to dynamic rupture processes in Earthquake physics

CMG 研究：XFEM 在地震物理动态破裂过程中的分析与应用

• 批准号: 0934736
• 负责人: Marc Spiegelman
• 金额: $ 31.7万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-10-01 至 2012-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0934736&HistoricalAwards=false
• 关键词: CMG; Research; Analysis; Application; XFEM

This project will provide both analysis and functioning open-sourcesoftware to evaluate the utility and applicability of the ExtendedFinite Element Method (XFEM) to the problem of dynamic Earthquakerupture on complex non-planar faults. While standard finite elementmethods are applicable to many earthquake physics problems, therequirement that the mesh be conformal to a complex, non-volumeforming network of faults is a fundamental difficulty, particularly in3-dimensions. The XFEM, provides a potentially powerful alternativeby encoding discontinuous basis functions into the approximation spacewithout requiring faults to coincide with mesh edges, an approach thatnaturally fits the earthquake rupture problem.Preliminary work, however, demonstrates several complications thatarise in this application. Standard techniques for frictional failuredo not work with the XFEM, so new weak formulations of failure must bedeveloped. In addition, discrete singularities, which are effectivelyremoved in quasi-static engineering rupture problems, become crucialin dynamic repeated rupture. These discrete problems canfundamentally affect event statistics, and must be avoided.The investigators will address these complications via analysis,computation, and physical intuition. Specifically, they propose twopossibilities for weak failure criteria, and plan to test them with aseries of benchmark problems. Additionally, they propose analysis ofnumerical accuracy of the weak frictional criteria, with the goal ofbetter understanding error in rupture propagation in these discretesystems. In a second component, they plan to derive bounds for theexistence of mesh-fault interaction artifacts. Using these bounds, theywill either determine enrichment schemes that eliminate the artifactsor develop meshing schemes to avoid them. Finally, the above workwill culminate in a proof of concept for the XFEM in repeated ruptureproblems, and they will work to better understand event complexity incomplex fault systems. These problems provide an excellentopportunity for collaboration between computational and appliedmathematicians and earthquake physicists.Broader Significance: Understanding the dynamics and probability ofEarthquakes on realistically complex fault networks is a fundamentalscience and engineering problem that has direct consequences forimproved estimates of Earthquake hazards. Advanced computationalmodels, combined with observations, provide an important tool forexploring and understanding these systems. A critical component ofsuch models, however is the geometric description and accuratemodeling of failure on non-planar faults which poses significantchallenges for traditional finite-element methods. This project willinvestigate an alternative method that allows the description of thefault network to be only loosely coupled to the computational mesh.If this method is successful, it promises to significantly increasethe ease of describing and composing these problems and is bettersuited to exploring the dynamics of fault networks, particularly underthe uncertainty of fault location. The proposed research will alsocontribute to the computational infrastructure for modeling thedynamics of brittle systems and earthquake genesis. The resulting opensource software will be distributed through the ComputationalInfrastructure for Geodynamics (CIG: www.geodynamics.org), and beaccessible to a broad community of researchers with impact beyond theimmediate realm of Earthquake physics.

该项目将提供分析和功能开放源码软件，以评估扩展有限元法（XFEM）对复杂非平面断层上动态地震爆发问题的实用性和适用性。 虽然标准的有限元方法适用于许多地震物理问题，但要求网格与复杂的、非体积形成的断层网络共形是一个基本的困难，特别是在三维情况下。 XFEM提供了一个潜在的强有力的替代方案，通过将不连续基函数编码到近似空间中，而不需要断层与网格边缘重合，这种方法自然适合地震破裂问题。 摩擦失效的标准技术不适用于XFEM，因此必须开发新的弱失效公式。 此外，在准静态工程断裂问题中有效消除的离散奇异性，在动态重复断裂问题中变得至关重要。 这些离散问题会从根本上影响事件统计，必须避免。研究人员将通过分析、计算和物理直觉来解决这些复杂问题。 具体来说，他们提出了两种弱失效准则的可能性，并计划用一系列基准问题来测试它们。 此外，他们提出了弱摩擦准则的数值精度分析，目的是更好地理解这些离散系统中破裂传播的误差。 在第二部分中，他们计划推导出网格故障相互作用工件存在的界限。 使用这些界限，他们将确定消除伪影的丰富方案，或开发网格方案以避免伪影。 最后，上述工作将最终在重复破裂问题的XFEM的概念证明，他们将工作，以更好地理解事件的复杂性在复杂的故障系统。 这些问题为计算和应用数学家与地震物理学家之间的合作提供了一个极好的机会。更广泛的意义：了解现实复杂断层网络上地震的动力学和概率是一个基本的科学和工程问题，对改进地震危险的估计有直接的影响。 先进的计算模型与观测相结合，为探索和理解这些系统提供了重要的工具。 然而，这种模型的一个关键组成部分是几何描述和准确建模的故障上的非平面故障，这对传统的有限元方法提出了重大挑战。 本计画将研究一种替代方法，允许断层网路的描述仅与计算网格松散耦合，如果此方法成功，它将显著增加描述与组合这些问题的简易性，并更适合于探讨断层网路的动态特性，特别是在断层位置不确定的情况下。 这项研究也将为脆性系统动力学和地震成因建模提供计算基础。由此产生的开源软件将通过地球动力学计算基础设施（CIG：www.geodynamics.org）分发，并可供广泛的研究人员社区使用，其影响超出了地震物理学的直接领域。