Bayesian Inversion for Anisotropic Hydraulic Phase-Field Fracture
arXiv:2007.16038 · doi:10.1016/j.cma.2021.114118
Abstract
In this work, a Bayesian inversion framework for hydraulic phase-field transversely isotropic and orthotropy anisotropic fracture is proposed. Therein, three primary fields are pressure, displacements, and phase-field while direction-dependent responses are enforced (via penalty-like parameters). A new crack driving state function is introduced by avoiding the compressible part of anisotropic energy to be degraded. For the Bayesian inversion, we employ the delayed rejection adaptive Metropolis (DRAM) algorithm to identify the parameters. We adjust the algorithm to estimate parameters according to a hydraulic fracture observation, i.e., the maximum pressure. The focus is on uncertainties arising from different variables, including elasticity modulus, Biot's coefficient, Biot's modulus, dynamic fluid viscosity, and Griffith's energy release rate in the case of the isotropic hydraulic fracture while in the anisotropic setting, we identify additional penalty-like parameters. Several numerical examples are employed to substantiate our algorithmic developments.
References in corpus (4)
- A phase-field modeling approach of fracture propagation in poroelastic media
- Phase-field modeling of fluid-driven dynamic cracking in porous media
- Phase field modeling of hydraulic fracture propagation in transversely isotropic poroelastic media
- ParaDRAM: A Cross-Language Toolbox for Parallel High-Performance Delayed-Rejection Adaptive Metropolis Markov Chain Monte Carlo Simulations