Experimental data from triaxial compression and extension tests on a weak sandstone (Red Wildmoor) are analysed. This rock exhibits stress-dependent elasticity, damage, friction hardening, cohesion softening and dilatancy which are modelled within the frame of a coupled elastic-plastic theory. The constitutive model is described and calibrated on experimental data. Validation is done through back analysis of the triaxial tests and comparison of the simulation with actual data.
Des essais triaxiaux de compression et d'extension sur un grès faible (le grès rouge de Wildmoor). Cette roche presente des modules elastiques qui dependent de l'etat de contraintes, de I'endommagement, un ecrouissage en frottement, un radoucissement en cohesion et de la dilatance. Ces phenomènes sont modeliser dans Ie cadre d'une theorie elastoplastique couplee. Dans cet article, on decrit Ie modèle constitutif et on l'etalonne sur les donnees experimentales, Le modèle est valide par la simulation des essais triaxiaux et la comparaison aux donnees reelles.
Experimentelle Ergebnisse von dreiaxialen Kompressions- und Extensionversuchen an einem weichen Sandstein (Red Wildmoor) sind bearbeitet. Der' Fels weist spanungsabhangige Elastizitat, Reibungsvervestigung, Kohesionsentfestigung und Silatanz auf, welche im Rahmen einer gekoppelten elastoplastishen Theorie beschrieben sind. In dieser Arbeit wird das konstitutive Model beschrieben und auf der experimentellen Basis kalibriert. Der Modelnachweis erfolgt durch die Simulation von Dreiaxialversuchen und durch der Vergleich der theoretishen Ergenissen mit dem experiment.
The behaviour of a weak sandstone (Red Wildmoor) is studied here on the basis of the an extensive experimental program of axisymmetric triaxial compression and extension tests (Papamichos et al I996a). Starting from their elasticity, the experiments Confirmed that Red-Wildmoor sandstone elasticity is not only stress-dependent but also coupled to the plasticity. Stress dependency of the elastic moduli can account for an initially convex upward stressstrain curve in uniaxial compression, which is, from a micro-mechanical point of view, attributed to closing of micro-cracks. Mathematically this effect can be modelled by assuming an appropriate complementary energy density function, which plays the role of an elastic strain potential and leads to a hyperelastic model. In addition, rock elasticity degrades in due course of deformation due to microcrack generation. This phenomenon can be described mathematically by introducing plastic strain as an additional internal variable into the appropriate state function (e.g. the free energy). Within the frame of plasticity theory, the experimental data clearly support a mixed hardening/softening model. Past the state of initial yield, friction is mobilised as a function of plastic shear strain and reaches saturation at some given peak value. On the other hand, in due course of deformation new microcracks may be activated and/or new ones may form. We therefore assume that all deviator softening must be attributed to micro-cracking, which leads to a decrease of the tensile strength. This softening mechanism may be active during all stages of the straining processes. However it becomes more pronounced when the material looses its capacity to mobilise additional friction resistance. Thus for simplicity we assume that during the friction hardening phase all tensile strength softening is negligible and it becomes noticeable only past the peak of the mobilised friction. Above assumption is corroborated by acoustic emission (AE) data. AE in sandstones under triaxial compression usually starts to increase gradually at about 60% of peak deviator. The maximum rate of AE events is recorded in the deviator-softening regime, and is followed by a decrease of the rate of AE events. Such an observation indicates that past the point of maximum rate of AE the size of the actual localised softening zone is already a small fraction of the specimen size, with a decreasing tendency as the global deformation continues. Thus the point of maximum AE must correspond to the point of observable localised failure.