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Applicability of Polyaxial Rock Peak Strength Criteria in Numerical Modeling
Roostaei, Roozbeh (University of Toronto) | Harrison, John P. (University of Toronto)
Abstract This paper aims to address the potentially inappropriate application of triaxial rock strength criteria to the polyaxial stress states calculated during 3d numerical analysis. We review some existing well-known polyaxial criteria, and discuss the advantage and disadvantage of each. Smoothness and convexity, 3d geometrical representation, the strengthening effect of σ2, and ease-of-use are some of the major requirements that are examined here. We show that accuracy may be achieved at the expense of mathematical complexity and advanced laboratory testing. However, such testing has not yet been accepted as a feasible common practice in rock engineering. 1 Introduction Determining the peak strength of rock has always been an essential problem in characterization of material behaviour in rock engineering practice. The most common approach in measurement and prediction of peak strength is to utilize a generally accepted strength criterion, such as the well-known triaxial Mohr-Coulomb and Hoek-Brown criteria. Although the conventional triaxial strength criteria perform well in certain circumstances, they suffer from neglecting the simultaneous influence of all three principal stress components. That is mainly because of the triaxial nature of their empirical derivation methods, and thus being written in terms of σ1 and σ3, and not taking into account the intermediate principal stress σ2. Studies on the effect of the intermediate principal stress started by conducting triaxial compression and triaxial extension tests on same materials. These results show that the peak strength of the rock in a triaxial extension stress state (σ1= σ2> σ3) is slightly higher than that in triaxial compression (σ1> σ2= σ3) (Figure 1.b). This testing was followed, after appropriate advances in testing equipment, by the true triaxial or the so-called ‘polyaxial’ tests on different rock types. Results from polyaxial tests show that when the stress state deviates from triaxial compression (σ1> σ2= σ3) to polyaxial (σ1> σ2> σ3), the strength of the rock reaches a peak before it falls to a value in the triaxial extension stress state (σ1= σ2> σ3) that is slightly higher than that in triaxial compression (Figure 1.a). This confirms the earlier results of triaxial compression versus triaxial extension tests.
- Europe (0.29)
- North America > Canada > Ontario > Toronto (0.16)
Simulating the Mechanical Re-Compaction of the EDZ in an Indurated Claystone (Opalinus Clay)
Lisjak, Andrea (Geomechanica Inc.) | Tatone, Bryan S. A. (Geomechanica Inc.) | Mahabadi, Omid K. (Geomechanica Inc.) | Grasselli, Giovanni (University of Toronto) | Vietor, Tim (National Cooperative for the Disposal of Radioactive Waste (NAGRA)) | Marschall, Paul (National Cooperative for the Disposal of Radioactive Waste (NAGRA))
Abstract This study aims at strengthening the understanding of the mechanical sealing process of the excavation damaged zone (EDZ) in Opalinus Clay, an indurated claystone currently being assessed as the host rock for a deep geological repository in Switzerland. To achieve this goal, hybrid finite-discrete element method (FDEM) simulations are applied to the HG-A experiment, an in-situ test carried out at the Mont Terri underground rock laboratory to investigate the hydro-mechanical response of a backfilled and sealed microtunnel. The mechanical re-compaction of the EDZ is analyzed by accounting for an increase of swelling pressure from the bentonite backfill onto the rock. Simulation results indicate an overall reduction of the total fracture area around the excavation as a function of the applied pressure, with locations of ineffective sealing associated with self-propping of fractures. 1 Introduction In the field of underground nuclear waste disposal, the excavation damaged zone (EDZ) is defined as a zone with hydro-mechanical and geochemical modifications inducing significant changes in flow and transport properties of the rock mass. A sound understanding of the processes involved in the EDZ formation and temporal evolution is necessary to increase the confidence in performance and safety assessment calculations of deep geological repositories. In the short-term, the EDZ is typically associated with an increase of flow permeability of one or more orders of magnitude. In the long-term, the EDZ will experience complex, time-dependent thermo-hydro-mechanical-chemical processes due to the interaction between the rock mass, buffer materials and heat-producing waste. Experimental data from laboratory and in-situ testing clearly show that sealing mechanisms occur in argillaceous rocks, including Opalinus Clay, leading to a reduction in the effective hydraulic conductivity of the EDZ with time (Bock et al. 2010). In this study, the mechanical re-compaction of the EDZ in response to radial stress acting on the excavation walls caused by swelling of the saturated bentonite buffer was numerically investigated. With its explicit consideration of fracturing processes, a hybrid finite-discrete element (FDEM or FEMDEM) simulation approach was applied to the HG-A experiment. The HG-A in-situ experiment was carried out at the Mont Terri underground rock laboratory (URL) to investigate the hydro-mechanical response of a backfilled and sealed microtunnel (Marschall et al. 2006).
- Europe (0.90)
- North America > Canada (0.70)
- North America > United States > California (0.28)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Mineral > Silicate > Phyllosilicate (0.84)
Statistical Calculation of Mean Stress Tensor using both Euclidean and Riemannian Approaches
Gao, Ke (University of Toronto) | Harrison, John P. (University of Toronto)
Abstract Stress is an important parameter in rock mechanics. As it is represented by a second-order tensor, the usual statistical methods for scalars and vectors strictly are not applicable. As a result, the correct method for calculation of a mean stress tensor is still not clear. Here, and using recent results from the field of diffusion tensor imaging (DTI), we examine two calculation approaches for the mean tensor – based on Euclidean and Riemannian geometries – and discuss their similarities and differences. We apply both methods to back-calculate the mean field stress around a circular opening, and conclude that the approaches give similar results. We go on to examine interpolation between stress tensors, and show that the Euclidean and Riemannian approaches can differ significantly. We conclude that it is currently not possible to identify which of these two approaches is most appropriate for engineering applications. 1 Introduction Stress is an important parameter in rock mechanics. As it is represented by a second-order tensor, the usual statistical methods for scalars (e.g. classical statistics) and vectors (e.g. directional statistics) strictly are not applicable. As a result, the correct method for calculation of a mean stress tensor – i.e., one that is faithful to its tensorial nature – is still not clear. Here, and using recent results from the field of diffusion tensor imaging (DTI), we examine two calculation approaches for the mean tensor – using Euclidean and Riemannian geometries – and discuss their similarities and differences. Customarily in rock mechanics, stress magnitude and orientation are processed separately (Figure 1). Examples of this are found in the many publications concerning the relationship between stress magnitude/orientation and burial depth (e.g. Brown & Hoek 1978, Martin 1990). Other examples are where each principal stress has been considered separately as a vector (e.g. Markland 1974, Lisle 1989, Ercelebi 1997). All these methods violate the tensorial nature of stress and may yield unreasonable results (Gao & Harrison 2014). As a way of being faithful to the tensorial nature of stress, several researchers (e.g. Hyett et al. 1986, Hudson & Cooling 1988, Walker et al. 1990) have suggested use of a common Cartesian coordinate system when calculating the mean stress tensor. From a geometrical point of view, this approach calculates the Euclidean centroid in Euclidean space (Bhatia 2007).
- North America > United States (0.47)
- North America > Canada > Ontario > Toronto (0.16)