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Virtual multi‐dimensional internal bonds model with fracture energy conservation for three‐dimensional numerical simulation of laboratory scale fluid pressurized fracturing
Author(s) -
Huang Kai,
Zhang Zhennan,
Ghassemi Ahmad
Publication year - 2021
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.3263
Subject(s) - dissipation , fracture mechanics , mechanics , finite element method , fracture (geology) , strain energy release rate , discrete element method , materials science , softening , structural engineering , representative elementary volume , geotechnical engineering , engineering , composite material , physics , thermodynamics
Strain‐softening models have proved effective in treating fracturing under mechanical load. However, these models tend to suffer from mesh‐size dependency due to failure in preserving the fracture energy. The Virtual Multi‐Dimensional Internal Bond Model (VMIB) is derived from a particle‐based constitutive law at the micro scale that is implemented in a 3D Finite Element Method (FEM), in which material softening and energy dissipation occur in the “representative elementary volume”. However, according to the classic fracture mechanics theory, energy dissipation is due to the creation of new fracture surfaces instead of homogenized softening within the volume element. Therefore, the dissipated strain energy has to be consistent with the fracture energy during failure process. We present an improved VMIB model to bridge the energy storage in a volume and dissipation over a fracture surface. This is accomplished by developing a 3D virtual bond potential that incorporates the material fracture energy and eliminates the mesh‐size sensitivity. The virtual bond potential considers both the critical fracture energy and element size. The 3D model is calibrated and verified simulations of a group of three‐point‐bend tests. Then, by incorporating the coupled three‐dimensional element partition method, the model is applied to a series of laboratory scale fluid pressurized fracturing experiments. Multiple fracture propagation from closely‐staged cluster from a laboratory test is simulated. The comparisons between numerical and experimental results indicate that the model captures the fractures growth influenced by the stress boundary conditions and the stress shadow. The predicted breakdown pressure reasonably agrees with the experiment data.