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A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase-Field Model
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DOI：10.1029/2023JB027143.png)
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Abstract
En 中文
In traditional modeling approaches, earthquakes are often depicted as displacement discontinuities across zero-thickness surfaces embedded within a linear elastodynamic continuum. This simplification, however, overlooks the intricate nature of natural fault zones and may fail to capture key physical phenomena integral to fault processes. Here, we propose a diffuse interface description for dynamic earthquake rupture modeling to address these limitations and gain deeper insight into fault zones' multifaceted volumetric failure patterns, mechanics, and seismicity. Our model leverages a steady-state phase-field, implying time-independent fault zone geometry, which is defined by the contours of a signed distance function relative to a virtual fault plane. Our approach extends the classical stress glut method, adept at approximating fault-jump conditions through inelastic alterations to stress components. We remove the sharp discontinuities typically introduced by the stress glut approach via our spatially smooth, mesh-independent fault representation while maintaining the method's inherent logical simplicity within the well-established spectral element method framework. We verify our approach using 2D numerical experiments in an open-source spectral element implementation, examining both a kinematically driven Kostrov-like crack and spontaneous dynamic rupture in diffuse fault zones. The capabilities of our methodology are showcased through mesh-independent planar and curved fault zone geometries. Moreover, we highlight that our phase-field-based diffuse rupture dynamics models contain fundamental variations within the fault zone. Dynamic stresses intertwined with a volumetrically applied friction law give rise to oblique plastic shear and fault reactivation, markedly impacting rupture front dynamics and seismic wave radiation. Our results encourage future applications of phase-field-based earthquake modeling. Faults are zones of broken and damaged materials, with a fault core region full of fractures. When we simulate earthquakes, we usually simplify these faults to flat planes that experience friction while situated within a host rock. A different way to represent faults in these simulations is using the stress glut method, which models the faults as areas where the earth's crust gives way under stress. However, this method can be problematic, leading to inaccuracies, particularly when a fault crosses a grid cell of the computational domain used for model calculations. We tackle this issue by applying a method that smooths out the stress field using a steady-state phase-field model. We find that our method can recreate realistic earthquake behavior while avoiding the sharp transitions that often occur in traditional models. We test our smooth method by simulating conditions where the fault doesn't align with any grid lines in our model. We notice some key differences in the stress field and earthquake dynamics near the leading edge of the rupture, brought about by the complex behavior of the diffuse fault. Our method retains the simplicity of the stress glut approach, making it easy to incorporate into existing earthquake simulation software. We develop an open-source diffuse interface method based on a phase-field implemented in spectral elementsDynamic earthquake rupture models in a diffuse fault zone differ from discrete fault modelsOur phase-field approach can address the volumetric nature of faulting in physics-based earthquake modeling
Keywords:
earthquake dynamics
computational seismology
dynamics and mechanics of faulting
numerical modeling
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