The Underground Research Laboratory (URL) was a revolutionary test site in Canada operated by Atomic Energy of Canada Limited (AECL) from 1985-2003 to study deep geological repositories for nuclear waste. Perhaps the most cited study from the URL is by Martin (1997) documenting the observed excavation damaged zone (EDZ) of a 3.5-m-diameter Mine-by Experiment (MBE) tunnel in Lac du Bonnet granite. The shape of the failure zone was spalling in the roof and floor of the tunnel, ultimately resulting in a V-shaped notch in the regions of the maximum tangential stress (σ1 = 60 MPa, σ3 = 11 MPa oriented 11° measured counter-clockwise from the horizontal and vertical axes, respectively).
Pivoting to the numerical modelling space, the study by Martin (1997) is often considered when verifying constitutive models for brittle rocks. Vazaios et al. (2018) used Irazu FDEM (i.e., using cohesive element approach) to simulate the EDZ of the MBE and successfully replicated the observed location and depth of failure.
Alternatively, studies utilizing continuum codes such as FLAC2D/3D (Hajiabdolmajid et al., 2002; Rafiei Renani and Martin, 2018) to simulate the EDZ of the MBE require the use of elasto-plastic constitutive models. Specifically, the use of a post-yield cohesion weakening-friction strengthening (CWFS) model (shown below), whereby as the plastic strain accumulates, cohesion decreases and friction mobilizes, is required to produce the observed failure. From a physical viewpoint, the CWFS model implicitly captures some fundamental aspects of brittle failure in rocks, such as tensile cracking preceding shear failure and delayed frictional strength mobilization due to the delayed development of internal normal stress. Recently, strain softening and hardening models were implemented in Irazu FEM, thus allowing a similar CWFS phenomenon to be captured.
For comparison with Irazu FEM (i.e., without using the cohesive element approach), the material properties used for the simulation were taken from the studies of Hajiabdolmajid et al. (2002) and Rafiei Renani and Martin (2018). As shown below, the Irazu FEM modelled a plastic zone consisting of a V-shaped notch that closely replicates the observed failure at the MBE tunnel (red line), as well as the simulation results obtained using FLAC2D reported by Hajiabdolmajid et al. (2002) and FLAC3D by Rafiei Renani and Martin (2018). Furthermore, the tensile failure simulated in the sidewalls corresponds well with the locations of acoustic emission measurements at the MBE tunnel site. Note that there is overprediction by the numerical models of the depth of failure in the floor of the tunnel because of the lack of consideration of the stronger granodiorite in this region.
All in all, the versatility of Irazu in its FEM capabilities is greatly enhanced with the addition of strain softening and hardening models. Furthermore, it still remains fully capable of using the FDEM to explicitly simulate brittle fracturing and obtain realistic simulation results.
References
Diederichs, M.S., 2017. The 2003 Canadian Geotechnical Colloquium: Mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling. Canadian Geotechnical Journal 44(9), 1082–1116.
Hajiabdolmajid, V., Kaiser, P., Martin, C.D., 2002. Modelling brittle failure of rock. International Journal of Rock Mechanics and Mining Sciences 39, 731–741.
Martin, C.D., 1997. Seventeenth Canadian Geotechnical Colloquium: The effect of cohesion loss and stress path on brittle rock strength. Canadian Geotechnical Journal 34, 698–725.
Rafiei Renani, H., Martin, C.D., 2018. Cohesion degradation and friction mobilization in brittle failure of rocks. International Journal of Rock Mechanics and Mining Sciences 106, 1–13.
Vazaios, I., Vlachopoulos, N., Diederichs, M.S., 2019. Mechanical analysis and interpretation of excavation damage zone formation around deep tunnels within massive rock masses using hybrid finite–discrete element approach: case of Atomic Energy of Canada Limited (AECL) Underground Research Laboratory (URL) test tunnel. Canadian Geotechnical Journal 56(1), 35–59.