A phase-field model of frictional shear fracture in geologic materials

Fei, Fan; Choo, Jinhyun

doi:10.1016/j.cma.2020.113265

Cited by 77 publications

(107 citation statements)

References 94 publications

Supporting

Mentioning

103

Contrasting

Order By: Relevance

“…Following Fei and Choo [34], the orientation of a failure plane is defined by its slip direction and its normal , where the vector pairs are of unit length ( = = 1) and orthogonal ( = 0). Given the stress state at a point, the normal stress is defined by…”

Section: Stiffness Degradation Due To Damage On a Failure Planementioning

confidence: 99%

“…where = , as given by Fei and Choo [34]. No shear stress is supported parallel to a crack face in the absence of friction, and hence this stress contribution must be removed from a damaged region, as shown in equation (2).…”

Section: Stiffness Degradation Due To Damage On a Failure Planementioning

confidence: 99%

“…) and crack opening ( < 0) can be found in the phase field context in Fei and Choo [34,45], with more advanced criteria proposed by Bryant and Sun [53].…”

Section: Stiffness Degradation Due To Damage On a Failure Planementioning

confidence: 99%

“…A range of methods and models have been proposed for modelling brittle and ductile crack opening problems: continuum-based models such as the finite element method (FEM) [2], the extended finite element method (XFEM) [2,4], the phase field method [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], damage models [21][22][23][24][25], the numerical manifold method [26] and the material point erosion method [27]. Closed crack problems for modelling brittle materials in compression range from the finite-discrete element method (FDEM) [28] to damage models [29][30][31][32][33], phase field models [34][35][36][37][38] as well as particle-based models [39][40][41][42] and plasticity models [37]. The main advantage of phase field and damage models is that no complex interface tracking is necessary to determine the crack path.…”

Section: Introductionmentioning

confidence: 99%

“…Reproduction of this angle in a representative simulation is therefore an important measure of its efficacy. Recently Fei and Choo [34,45,46] have made important progress in this area in the context of the phase field method, and are the first to clearly demonstrate that they can reproduce the expected frictional crack angle in biaxial compression tests. This is achieved through the implementation of an anisotropic elastic degradation model.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A damage model for the frictional shear failure of brittle materials in compression

Gill¹

2021

Preprint

View full text Add to dashboard Cite

Damage models have been successfully employed for many decades in the modelling of tensile failure, where the crack surfaces separate as a crack grows. The advantage of this approach is that crack trajectories can be computed simply and efficiently on a fixed finite element mesh without explicit tracking. The development of damage models for shear failure in compression, where the crack faces slide over each other subject to friction, is a non-trivial extension of this approach. A major difference is that part of the material stiffness in the damaged region must be retained to avoid interpenetration of the crack faces. This problem is resolved here by employing an anisotropic modification to the elastic stiffness tensor in the damaged region. This has the benefit of driving frictional cracks into the correct orientation, according to the Mohr-Coulomb failure criteria, but three issues remain. The first is that the shear discontinuity introduces some spurious stress perturbations around crack regions that are narrow (less than 3-4 elements wide). This is ameliorated by Helmholtz smoothing to allow efficient simulation on a coarse mesh. The second is that the complementarity of shear stress means that the shear stiffness is removed normal to the crack interface as well as parallel to it, and the third is that there are two potentially active failure planes at each point. Both these latter two issues are resolved by the introduction of a novel failure plane selection variable, which regulates either single plane or dual plane failure, and prevents the growth of erroneous cracks normal to the crack face. Both local and non-local models are investigated for linear and exponential strain softening responses. Unlike the non-local model, the local model demonstrates some mesh-size dependence, but it still retains some properties of interest, in that it supports narrower cracks and more rapidly forms a preference for the growth of a single crack when there are a number of competing cracks. The model is implemented in commercial finite element package COMSOL Multiphysics v5.5 and validated against two benchmark simulations: biaxial compression and the failure of a 45 o slope. The correct crack angles, stipulated by the Mohr-Coulomb friction angle, are correctly reproduced, as is the postfailure residual frictional force in biaxial compression. The effect of the shear fracture energy on the force-displacement response is investigated, demonstrating the successful simulation of the range of material behaviour expected in geological samples, from broad ranged gradual collapse to sharp, almost instantaneous failure.PREPRINT: A damage model for the frictional shear failure of brittle materials in compression PREPRINT: A damage model for the frictional shear failure of brittle materials in compression they "…are computationally efficient and thus suitable for large-scale engineering simulations, phase field methods are quite demanding and therefore currently limited to small-scale problems." [47]. As such, it is an objective of ...

show abstract

Section: Stiffness Degradation Due To Damage On a Failure Planementioning

confidence: 99%

Section: Stiffness Degradation Due To Damage On a Failure Planementioning

confidence: 99%

“…) and crack opening ( < 0) can be found in the phase field context in Fei and Choo [34,45], with more advanced criteria proposed by Bryant and Sun [53].…”

Section: Stiffness Degradation Due To Damage On a Failure Planementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A damage model for the frictional shear failure of brittle materials in compression

Gill¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

A modified damage and fracture phase field model considering heterogeneity for rock‐like materials

Chen,

Qin

2023

Deep Underground Science and Engineering

View full text Add to dashboard Cite

Damage and fracture are the most extensive failure modes of rock materials, which may easily induce disaster and instability of engineering structures. This study developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks. The modified phase field model introduced the heterogeneity of fracture parameters and modified the governing equations. Meanwhile, the free energy was constructed by the elastic strain energy sphere‐bias decomposition and the plastic strain energy. As for the numerical implementation, the three layers finite elements method structure was used in the frame of the finite element method. The ability of the modified phase field model has been illustrated by reproducing the experiment results of rock samples with pre‐existing cracks under compression.

show abstract

Phase‐field modeling of rock fractures with roughness

Fei

Choo

Liu

et al. 2022

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

Phase-field modeling-a continuous approach to discontinuities-is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the existing phase-field models, however, incorporates the impact of surface roughness on the mechanical response of fractures-such as elastic deformability and shear-induced dilation-despite the importance of this behavior for subsurface systems. To fill this gap, here we introduce the first framework for phase-field modeling of rough rock fractures. The framework transforms a displacementjump-based discrete constitutive model for discontinuities into a strain-based continuous model, without any additional parameter, and then casts it into a phase-field formulation for frictional interfaces. We illustrate the framework by constructing a particular phase-field form employing a rock joint model originally formulated for discrete modeling. The results obtained by the new formulation show excellent agreement with those of a well-established discrete method for a variety of problems ranging from shearing of a single discontinuity to compression of fractured rocks. It is further demonstrated that the phase-field formulation can well simulate complex crack growth from rough discontinuities.Consequently, our phase-field framework provides an unprecedented bridge between a discrete constitutive model for rough discontinuities-common in rock mechanics-and the continuous finite element method-standard in computational mechanics-without any algorithm to explicitly represent discontinuity geometry. K E Y W O R D Sphase-field modeling, rock fractures, rock discontinuities, roughness, rock masses, shearinduced dilation INTRODUCTIONRock fractures are pervasive in natural and engineered subsurface systems. The mechanical behavior of rock fractures not only controls the performance of many geotechnical structures such as slopes and tunnels (e.g., [1][2][3] ), but it plays an important role in the operation of subsurface energy technologies such as hydraulic stimulation, nuclear waste disposal, enhanced geothermal systems, and geologic carbon storage (e.g., [4][5][6][7][8] ).

show abstract

A phase-field model of frictional shear fracture in geologic materials

Cited by 77 publications

References 94 publications

A damage model for the frictional shear failure of brittle materials in compression

A damage model for the frictional shear failure of brittle materials in compression

A modified damage and fracture phase field model considering heterogeneity for rock‐like materials

Phase‐field modeling of rock fractures with roughness

Contact Info

Product

Resources

About