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A failure envelope that ignores the intermediate principal stress is typically adequate for the design of rock structures. To obtain the complete envelope, the rock cylinders should be tested using confined compression as well as confined extension tests. While confined compression tests are common, confined extension tests are rarely carried out. Current techniques available to test rocks under confined extension conditions require shaping the cylindrical specimens to a dog-bone geometry. The limited data available in the literature indicates that the results from these dog-boned shaped tests produces strengths that are considerably greater than the confined triaxial tests carried out on traditional cylindrical specimens. Whether this increased strength is real or simply an artifact of the stress path for triaxial confined extension tests (intermediate principal stress equal to the maximum principal stress) versus confined compression tests (intermediate principal stress equal to the minimum principal stress) is unknown. We propose here a new methodology to test rocks under confined extension condition with zero intermediate principal stress. We used the flattened Brazilian test and calculated the major and minor principal stresses from the strain on the surface of the specimens. To test the rock under increased confined conditions, we tested specimens with increasing depth of flattening. We derived equations to calculate the major and minor principal stresses in a flattened Brazilian specimen considering the bi-modularity in the stress-strain equations. We tested Lac du Bonnet granite specimens for major principal stress range 15-37% of its UCS and observed that the minor principal stresses remains in the range of Brazilian strength of the material (11.6 MPa). The results suggest that the nonlinear Hoek-Brown failure criterion based on only compressive triaxial results provides a reasonable estimate of the tensile strength. [ABSTRACT FROM AUTHOR]

Unlike metals, rocks show bi-modularity (different Young’s moduli and Poisson’s ratios in compression and tension). Displacements monitored during the Brazilian test are used in this study to obtain the Young’s modulus and Poisson’s ratio in tension. New equations for the displacements in a Brazilian test are derived considering the bi-modularity in the stress–strain relations. The digital image correlation technique was used to monitor the displacements of the Brazilian disk flat surface. To validate the Young’s modulus and Poisson’s ratio obtained from the Brazilian test, the results were compared with the values from the direct tension tests. The results obtained from the Brazilian test were repetitive and within 3.5% of the value obtained from the direct tension test for the rock tested. [ABSTRACT FROM AUTHOR]

Numerical modelling is playing an increasing role in the interpretation of geological observations. A similar phenomenon is occurring with respect to the interpretation of the stress–strain response of intact rock measured in laboratory tests. In this research, the three-dimensional (3D) bonded particle model (BPM) with flat-jointed (FJ) contact was used to investigate the impact of stress paths on rock failure. The modified FJ contact model used for these studies numerically captured most of the intact rock behavior of Lac du Bonnet granite observed in the laboratory. A numerical simulation was used to track the behavior of this rock for different stress paths, starting with uniaxial tension and compression loading conditions. The migration from uniaxial tension to triaxial compression is challenging to simulate in physical laboratory tests but commonly observed around underground excavations. The numerical modelling methodology developed for this research tracks this stress path and the impact of the intermediate stress on peak strength at low confinements, commonly found around underground excavations. [ABSTRACT FROM AUTHOR]

The flat-jointed (FJ) contact model implemented in the particle flow code resolves the long-standing issue of the code producing unrealistically low ratios of uniaxial compressive strength (UCS) to direct tensile strength. Despite the improvements introduced with the FJ model, an FJ sample calibrated to the UCS still produces a crack initiation stress much lower than the expected value of approximately 0.4 UCS, as commonly observed in laboratory compression tests for most rocks. In this study, we investigated the role of initial crack volume on the crack initiation stress of a rock. We found that the microcracks among the mineral grains and their associated void space played a major role in controlling the stress magnitude associated with crack initiation. We also observed that the closure of these cracks between mineral grains was the primary driver of the crack closure phase in the compression test, and the elastic bimodularity was due to the crack density. We developed a methodology to incorporate the initial microcracks using the FJ contact model to match the crack closure stress and bimodularity of a laboratory rock sample. By introducing microcracks and voids among the mineral grains, we automatically capture the crack initiation stress of Lac du Bonnet granite measured at approximately 40% of the UCS. [ABSTRACT FROM AUTHOR]