Material stability analysis of rock joints

Abstract

SUMMARYFor prediction of rockfalls, the failure of rock joints is studied. Considering these failures as constitutive instabilities, a second-order work criterion is used because it explains all divergence instabilities (flutter instabilities are excluded). The bifurcation domain and the loading directions of instabilities, which fulfill the criterion, are determined for any piecewise linear constitutive relation. The instability of rock joints appears to be ruled by coupling features of the behavior (e.g., dilatancy). Depending on the loading parameters, instabilities can lead to failure, even before the plastic limit criterion. Results for two given constitutive relations illustrate the approach. Some given loading paths are especially considered. Constant volume (undrained) shear and -constant paths are stable or not depending on the link between the deviatoric stress and strain along undrained paths, as found for soils. Some unstable loading paths are illustrated. Along these paths, failure before the plastic limit criterion is possible. The corresponding failure rules are determined. Copyright © 2012 John Wiley & Sons, Ltd. Rock slopes present different types of defects at all scale. We call rock joints the discontinuities (e.g., in mechanical properties) at macroscopic scale, and we assume that rock joints have the greatest influence on the stabilities of rock slopes. This is why geomechanical stability analyses need to represent accurately rock joints' failures. We thus focus on the mechanical behavior of such joints, and in the framework of a 2D assumption, only four scalar variables will be used to describe the corresponding mechanical state. Two stress components are considered: one normal, denoted (considered positive in compression), and one tangential, denoted . On the other hand, relative displacements occurring along the joint are considered, with a normal component u (positive in compression) and a tangential component .We define here, as in the general plasticity theory, that failure is obtained when relative displacements along the joint (that we can call 'deformation', from a general point of view) go on under a constant loading, by the existence of limit stress states. Failure of rock joint is obtained for example during constant normal load shearings, defined by a constant value of , once reaches a peak or a plateau [1][2][3][4]: under these conditions, increases continuously, whereas stresses are constant. This situation in a rock slope would trigger rockfalls. Such analysis of failure introduces directly the concept of limit stress states, for which stresses do not vary anymore, E d D .d , d / D E 0, whereas relative displacements still evolve, E

Revisiting the existence of an effective stress for wet granular soils with micromechanics

“…Indeed, the nonassociativity of granular materials leads to a second possible reason for numerical results dispersion through bifurcated behaviors when the loading path is not controllable() or, equivalently, does correspond to a potentially unstable direction showing a negative second‐order work. ()…”

“…Indeed, the nonassociativity of granular materials leads to a second possible reason for numerical results dispersion through bifurcated behaviors when the loading path is not controllable 28,29 or, equivalently, does correspond to a potentially unstable direction showing a negative second-order work. [30][31][32] For further discussion, the same triaxial compression is repeated 3 times: a classical mixed loading path (d 1 > 0; dΣ 2 = dΣ 3 = 0) is imposed on dense or loose packings during 3 runs of the same simulation. Runs #2 and #3 consider the exact same individual particles obtained after one unique run of the sample generation procedure; whereas run #1 makes use of another-either dense or loose-packing obtained after another run of the generation procedure.…”