Laboratory-scale modelling of rock failure processes

Fracture propagation in a FEMDEM simulation of a heterogeneous Brazilian disc test.

Experimental research shows that the failure process in brittle rocks under compression is characterized by complicated micro-mechanical processes, including the nucleation, growth and coalescence of microcracks, which lead to strain localization in the form of macroscopic fracturing. The evolution of microcracking, typically associated with the emission of acoustic energy, results in a distinctive non-linear stress-strain response, with macroscopic strain softening commonly observed under low-confinement conditions. Furthermore, unlike other materials (e.g., metals), rocks exhibit a strongly pressure-dependent mechanical behaviour. A variation of failure mode, from axial splitting to shear band formation, is indeed often observed for increasing confining pressures. This variation in failure behaviour is reflected in a non-linear failure envelope and in a transition from brittle to ductile post-peak response.

Using Geomechanica’s Irazu FEMDEM software several of the characteristics mentioned above can be captured as emergent properties of a numerical model whereby crack initiation and propagation are explicitly modelled according to the principles of non-linear elastic fracture mechanics. Material heterogeneity (e.g., different mineral phases and micro-cracks) can be directly incorporated into the model as well as stiffness and strength anisotropy. Experimental validation indicates that the model can quantitatively reproduce the macroscopic mechanical response of the sample (e.g., elastic behaviour, overall strength, post-peak brittle failure), as observed in laboratory studies.

Furthermore, the FEMDEM software allows simulating the acoustic activity associated with the rock progressive breakdown. Taking advantage of the discrete material representation and the dynamic solver, seismic information, including source location, mode of fracture, initiation time, and event energy, can be extracted based on internal monitoring of node motions. In agreement with laboratory results, numerical results highlight the stochastic self-similarity of the microfracturing process in terms of frequency-magnitude distribution of acoustic events (Gutenberg-Richter relationship), spatial distribution of hypocenters (i.e., fractal character), and time evolution of AE rate (Omori’s law).

Further Reading:

  • Lisjak A, Liu Q, Zhao Q, Mahabadi OK and Grasselli G (2013). "Numerical simulation of acoustic emission in brittle rocks by two-dimensional finite-discrete element analysis". Geophysical Journal International. (DOI: 10.1093/gji/ggt221)
  • Mahabadi OK (2012). "Investigating the influence of micro-scale heterogeneity and microstructure on the failure and mechanical behaviour of geomaterials". Ph.D. Thesis, University of Toronto. Toronto, Canada (URL )
  • Mahabadi OK, Randall NX, Zong Z and Grasselli G (2012). "A novel approach for micro-mechanical characterization and modelling of geomaterials incorporating actual material heterogeneity". Geophysical Research Letters. 39(L01303) (DOI: 10.1029/2011GL050411)
  • Lisjak A, Tatone B, Grasselli G and Vietor T (2012). "Modelling of the strength and deformation anisotropy of an argillaceous rock (Opalinus Clay) at the laboratory scale". In Proceedings of the 46th US Rock Mechanics / Geomechanics Symposium. Chicago. 24-27 June, 2012.
  • Mahabadi OK, Cottrell BE and Grasselli G (2010). "An example of realistic modelling of rock dynamics problems: FEM/DEM simulation of dynamic Brazilian test on Barre granite". Rock Mechanics and Rock Engineering. 43(6), 707-716. (DOI: 10.1007/s00603-010-0092-7)
  • Mahabadi OK, Lisjak A, Grasselli G, Lukas T and Munjiza A (2010). "Numerical modelling of a triaxial test of homogeneous rocks using the combined finite-discrete element method". In Proceedings of the European rock mechanics symposium (EUROCK) 2010. Lausanne, Switzerland. 15-18 June, 2010.
  • Mahabadi OK, Grasselli G and Munjiza A (2009). "Numerical modelling of a Brazilian Disc test of layered rocks using the combined finite-discrete element method". In Proceedings of 3rd Canada-US (CANUS) Rock Mechanics Symposium (RockEng09). Toronto, Canada. 9-14 May, 2009.
Simulation highlights

  • Elastic models including isotropic and transversely isotropic
  • Isotropic and anisotropic strength model
  • Micro-scale heterogeneity with arbitrary number of stiffness and strength properties
  • Material mapping for exact mineralogy
  • Bedding and layering
  • Time-varying loading conditions
  • Acoustic emission recording function (even magnitude, source location, and mode of failure)

UCS test on a heterogeneous rock sample. Time evolution of AE source locations and associated magnitude during a unconfined compression test on a Stanstead Granite sample.

UCS test on a heterogeneous rock sample.