Abstract
We present stress concentration factors at the edges of 3D voids in uniaxial compression. Variations in these stress concentration factors due to Poisson's ratio of the host material, void shape, and void-void proximity are explicitly quantified. Voids loaded by a vertical compressive stress are hypothesised to fail in one or two ways: (1) tension crack development due to tensile stress concentrations at the void poles; or (2) compressive stress concentrations at the void sides causing the void wall to fail in shear. The stress concentration factors in this study are found using the numerical displacement discontinuity method. Equations are provided to assess the proximity of a void to the two hypothesised modes of failure. For 3D voids thinned in an axis that lies parallel to the compressive stress these have increasingly high stress concentrations at their sides. Changes in stress concentrations due to the Poisson's ratio of the matrix are minor, apart from for the intermediate stress at the void sides. Void shape, void separation, and void alignment are critical factors in the concentration of stresses. This suggests a significant departure from strength predictions for porous material that are based solely on scalar values of porosity.
Highlights
Natural and manmade voids, cavities, pores, and cracks are ubiquitous in rocks within the Earth's brittle upper crust
Recent studies of porous material strength that quantified aspects of void topology within the rock, have shown that it is not porosity that exerts a control on bulk rock strength (Meille et al, 2012; Bubeck et al, 2017): both pore shape and pore orientation have been shown to change the bulk strength of a rock (Bubeck et al, 2017)
Maximum tensile and compressive stress concentrations for the void poles and sides are plotted in Fig. 7 as a function of Poisson's ratio
Summary
Cavities, pores, and cracks are ubiquitous in rocks within the Earth's brittle upper crust. In Fig. 1b) the radial length az of voids is no longer the shortest axis, fractures tend to link the most spherical shaped voids within the core (either from the void side or poles). Fractures in this case align approximately with the core long axis. Poisson's ratio is calculated as the axial strain in an axis perpendicular to an applied force divided by the strain measured in the axis parallel to the applied force This describes the amount a material will extrude in a direction perpendicular to the applied compression.
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