Numerical modeling of fracture coalescence in a model rock material

Abstract

The crack pattern, as well as crack initiation, -propagation and -coalescence observed in experiments on gypsum specimens with pre-existing fractures in uniaxial, biaxial, and tensile loading are satisfactorily predicted with the numerical model presented in this paper. This was achieved with a new stress-based crack initiation criterion which is incorporated in FROCK, a Hybridized Indirect Boundary Element method first developed by Chan et al. (1990). The basic formulation of FROCK is described, and the code verified for both open and closed pre-existing fractures either with only friction or with friction and cohesion. The new initiation criterion requires only three material properties: σcrit, the critical strength of the material in tension; τcrit, the critical strength of the material in shear; r0, the size of the plastic zone. The three parameters can be determined with the results from only one test. Predictions using this model are compared with experiments on gypsum specimens with pre-existing fractures loaded in uniaxial and biaxial compression performed by the authors. Specifically, wing crack and shear crack initiation, crack propagation, coalescence stress and -type as well as the crack pattern up to coalescence can be modeled. The model can also duplicate experimental results in compression and tension obtained by other researchers. These results show that stress-based criteria can be effectively used in modeling crack initiation and crack coalescence.

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Bobet, A., Einstein, H.H. Numerical modeling of fracture coalescence in a model rock material. International Journal of Fracture 92, 221 (1998). https://doi.org/10.1023/A:1007460316400

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  • Displacement discontinuity method
  • brittle material
  • crack initiation criterion
  • crack coalescence modeling
  • uniaxial compression
  • biaxial compression