A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase-Field Model

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.

@article{id3014,
  author = {Hayek, Jorge N. and May, Dave A. and Pranger, Casper and Gabriel, Alice-Agnes},
  doi = {10.1029/2023JB027143},
  journal = {JGR Solid Earth},
  language = {en},
  number = {12},
  pages = {e2023JB027143},
  title = {A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase-Field Model},
  url = {https://doi.org/10.1029/2023JB027143},
  volume = {128},
  year = {2023},
}

%O Journal Article
%A Hayek, Jorge N.
%A May, Dave A.
%A Pranger, Casper
%A Gabriel, Alice-Agnes
%R 10.1029/2023JB027143
%J JGR Solid Earth
%G en
%N 12
%P e2023JB027143
%T A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase-Field Model
%U https://doi.org/10.1029/2023JB027143
%V 128
%D 2023