Dependence of rock properties on the Lode angle: Experimental data, constitutive model, and bifurcation analysis
Résumé
The overwhelming majority of experimental tests on rocks have only been conducted for a single value of the Lode angle θ corresponding to the axisymmetric compression (AC). There are now sufficiently extensive data sets from both AC and axisymmetric extension (AE) tests (corresponding to two extreme θ values) for two materials, synthetic rock analogue material, GRAM1, formed of bonded rigid particles (Nguyen at al., 2011) and Solnhofen Limestone (Heard, 1960). These data cover a wide range of the confining pressure (from brittle faulting to ductile flow). Very recently the data from true 3-D tests (for different θ) also covering both brittle and ductile fields were published for Castlegate (Ingraham et al., 2013) and Bentheim (Ma and Haimson, 2013) Sandstone as well. By processing all these data we constrain a 3-invariant initial yield function (YF). The whole YF also depends on inelastic strain. This dependence was constrained for GRAM (as well as for two limestones) for AC, which allowed to relate the YF and plastic potential in a simple manner (Mas, Chemenda, IJRRMS, 2015) and thereby to close the constitutive formulation/model. The bifurcation analysis with this model revealed that the θ-dependence of the properties encourages the strain localization. The brittle-ductile transition under AE occurs at the mean stress, σ, 1.5 times greater than under AC, meaning that under AE the material is more prone to fracture development. The angle between the most compressive stress and the forming deformation localization bands is systematically higher for AE than for AC for the same σ. All these predictions are confirmed by the experimental data. The theoretical results also show that the θ-dependence can cause the failure (deformation band) plane to deviate from the intermediate stress direction.