publication . Preprint . 2020

A unified first order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones

Gabriel, Alice-Agnes; Li, Duo; Chiocchetti, Simone; Tavelli, Maurizio; Peshkov, Ilya; Romenski, Evgeniy; Dumbser, Michael;
Open Access English
  • Published: 02 Jul 2020
Abstract
Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones, here we present a first order hyperbolic and thermodynamically compatible mathematical model for a continuum in a gravitational field which provides a unified description of nonlinear elasto-plasticity, material damage and of viscous Newtonian flows with phase transition between solid and liquid phases. The fault geometry and secondary cracks are described via a scalar function $\xi ...
Subjects
arXiv: Physics::Geophysics
free text keywords: Physics - Geophysics
Funded by
EC| ExaHyPE
Project
ExaHyPE
An Exascale Hyperbolic PDE Engine
  • Funder: European Commission (EC)
  • Project Code: 671698
  • Funding stream: H2020 | RIA
,
EC| TEAR
Project
TEAR
TRULY EXTENDED EARTHQUAKE RUPTURE
  • Funder: European Commission (EC)
  • Project Code: 852992
  • Funding stream: H2020 | ERC | ERC-STG
,
EC| ChEESE
Project
ChEESE
Centre of Excellence for Exascale in Solid Earth
  • Funder: European Commission (EC)
  • Project Code: 823844
  • Funding stream: H2020 | RIA
Communities
FET H2020FET HPC: HPC Core Technologies, Programming Environments and Algorithms for Extreme Parallelism and Extreme Data Applications
FET H2020FET HPC: An Exascale Hyperbolic PDE Engine
Download from
76 references, page 1 of 6

[1] M. Ambati, T. Gerasimov, and L. De Lorenzis. A review on phase-field models of brittle fracture and a new fast hybrid formulation. Computational Mechanics, 55(2):383-405, 2015. (Cited on page 2.) [OpenAIRE]

[2] J.-P. Ampuero. SEM2DPACK, a spectral element software for 2D seismic wave propagation and earthquake source dynamics, v2.3.8, 2012. https://sourceforge.net/projects/sem2d/. (Cited on page 6.)

[3] D.J. Andrews. Rupture velocity of plane strain shear cracks. Journal of Geophysical Research, 81(32):5679-5687, 1976. (Cited on page 1.)

[4] D.J. Andrews. Rupture dynamics with energy loss outside the slip zone. Journal of Geophysical Research: Solid Earth, 110(B1), 2005. (Cited on page 6.)

[5] H. D. Baehr and K. Stephan. Heat and Mass Transfer. Springer, 2011. (Cited on pages 10 and 3.)

[6] M. J. Borden, T.J.R. Hughes, C.M. Landis, and C.V. Verhoosel. A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework. Computer Methods in Applied Mechanics and Engineering, 273:100-118, 2014. (Cited on page 2.)

[7] B. Bourdin, G.A. Francfort, and J.J. Marigo. Numerical experiments in revisited brittle fracture. Journal of the Mechanics and Physics of Solids, 48(4):797-826, 2000. (Cited on page 2.) [OpenAIRE]

[8] H.J. Bungartz, M. Mehl, T. Neckel, and T. Weinzierl. The PDE framework Peano applied to fluid dynamics: An efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids. Computational Mechanics, 46:103-114, 2010. (Cited on page 6.)

[9] S. Busto, S. Chiocchetti, M. Dumbser, E. Gaburro, and I. Peshkov. High order ADER schemes for continuum mechanics. Frontiers in Physiccs, 8:32, 2020. (Cited on pages 3 and 6.) [OpenAIRE]

[10] Y. Cheng, Z.E. Ross, and Y. Ben-Zion. Diverse volumetric faulting patterns in the san jacinto fault zone. Journal of Geophysical Research: Solid Earth, 123(6):5068-5081, 2018. (Cited on page 2.)

[11] F.M. Chester, J.P. Evans, and R.L. Biegel. Internal structure and weakening mechanisms of the San Andreas fault. Journal of Geophysical Research: Solid Earth, 98(B1):771-786, 1993. (Cited on page 1.)

[12] L.R. Chiarelli et al. Comparison of high order finite element and discontinuous Galerkin methods for phase field equations: Application to structural damage. Computers & Mathematics with Applications, 74(7):1542-1564, 2017. (Cited on page 2.)

[13] S. Chiocchetti and C. Müller. A Solver for Stiff Finite-Rate Relaxation in Baer-Nunziato Two-Phase Flow Models. Fluid Mechanics and its Applications, 121:31-44, 2020. (Cited on page 3.)

[14] S. Chiocchetti, I. Peshkov, S. Gavrilyuk, and M. Dumbser. High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension. Journal of Computational Physics, 2020. (Cited on page 2.) [OpenAIRE]

[15] Y. Cui et al. Physics-based seismic hazard analysis on petascale heterogeneous supercomputers. In SC '13: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, pages 1-12, 2013. (Cited on page 2.)

76 references, page 1 of 6
Abstract
Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones, here we present a first order hyperbolic and thermodynamically compatible mathematical model for a continuum in a gravitational field which provides a unified description of nonlinear elasto-plasticity, material damage and of viscous Newtonian flows with phase transition between solid and liquid phases. The fault geometry and secondary cracks are described via a scalar function $\xi ...
Subjects
arXiv: Physics::Geophysics
free text keywords: Physics - Geophysics
Funded by
EC| ExaHyPE
Project
ExaHyPE
An Exascale Hyperbolic PDE Engine
  • Funder: European Commission (EC)
  • Project Code: 671698
  • Funding stream: H2020 | RIA
,
EC| TEAR
Project
TEAR
TRULY EXTENDED EARTHQUAKE RUPTURE
  • Funder: European Commission (EC)
  • Project Code: 852992
  • Funding stream: H2020 | ERC | ERC-STG
,
EC| ChEESE
Project
ChEESE
Centre of Excellence for Exascale in Solid Earth
  • Funder: European Commission (EC)
  • Project Code: 823844
  • Funding stream: H2020 | RIA
Communities
FET H2020FET HPC: HPC Core Technologies, Programming Environments and Algorithms for Extreme Parallelism and Extreme Data Applications
FET H2020FET HPC: An Exascale Hyperbolic PDE Engine
Download from
76 references, page 1 of 6

[1] M. Ambati, T. Gerasimov, and L. De Lorenzis. A review on phase-field models of brittle fracture and a new fast hybrid formulation. Computational Mechanics, 55(2):383-405, 2015. (Cited on page 2.) [OpenAIRE]

[2] J.-P. Ampuero. SEM2DPACK, a spectral element software for 2D seismic wave propagation and earthquake source dynamics, v2.3.8, 2012. https://sourceforge.net/projects/sem2d/. (Cited on page 6.)

[3] D.J. Andrews. Rupture velocity of plane strain shear cracks. Journal of Geophysical Research, 81(32):5679-5687, 1976. (Cited on page 1.)

[4] D.J. Andrews. Rupture dynamics with energy loss outside the slip zone. Journal of Geophysical Research: Solid Earth, 110(B1), 2005. (Cited on page 6.)

[5] H. D. Baehr and K. Stephan. Heat and Mass Transfer. Springer, 2011. (Cited on pages 10 and 3.)

[6] M. J. Borden, T.J.R. Hughes, C.M. Landis, and C.V. Verhoosel. A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework. Computer Methods in Applied Mechanics and Engineering, 273:100-118, 2014. (Cited on page 2.)

[7] B. Bourdin, G.A. Francfort, and J.J. Marigo. Numerical experiments in revisited brittle fracture. Journal of the Mechanics and Physics of Solids, 48(4):797-826, 2000. (Cited on page 2.) [OpenAIRE]

[8] H.J. Bungartz, M. Mehl, T. Neckel, and T. Weinzierl. The PDE framework Peano applied to fluid dynamics: An efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids. Computational Mechanics, 46:103-114, 2010. (Cited on page 6.)

[9] S. Busto, S. Chiocchetti, M. Dumbser, E. Gaburro, and I. Peshkov. High order ADER schemes for continuum mechanics. Frontiers in Physiccs, 8:32, 2020. (Cited on pages 3 and 6.) [OpenAIRE]

[10] Y. Cheng, Z.E. Ross, and Y. Ben-Zion. Diverse volumetric faulting patterns in the san jacinto fault zone. Journal of Geophysical Research: Solid Earth, 123(6):5068-5081, 2018. (Cited on page 2.)

[11] F.M. Chester, J.P. Evans, and R.L. Biegel. Internal structure and weakening mechanisms of the San Andreas fault. Journal of Geophysical Research: Solid Earth, 98(B1):771-786, 1993. (Cited on page 1.)

[12] L.R. Chiarelli et al. Comparison of high order finite element and discontinuous Galerkin methods for phase field equations: Application to structural damage. Computers & Mathematics with Applications, 74(7):1542-1564, 2017. (Cited on page 2.)

[13] S. Chiocchetti and C. Müller. A Solver for Stiff Finite-Rate Relaxation in Baer-Nunziato Two-Phase Flow Models. Fluid Mechanics and its Applications, 121:31-44, 2020. (Cited on page 3.)

[14] S. Chiocchetti, I. Peshkov, S. Gavrilyuk, and M. Dumbser. High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension. Journal of Computational Physics, 2020. (Cited on page 2.) [OpenAIRE]

[15] Y. Cui et al. Physics-based seismic hazard analysis on petascale heterogeneous supercomputers. In SC '13: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, pages 1-12, 2013. (Cited on page 2.)

76 references, page 1 of 6
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