Institute of Fundamental Technological Research

The present technical note extends the previous work by the authors concerned with formulation of a constitutive model of elastoplastic response of sands (Superior sand model) and its application to the analyses of static liquefaction and instability states in triaxial compression and extension occurring in the undrained deformation of saturated granular materials. To account for time-dependent behavior and strain rate effects, an elastic, viscoplastic extension of the model to triaxial compression is proposed. The constitutive equations derived are used to predict the model response in different loading histories. In particular, strain rate and stress rate effects and undrained creep deformation for specified stress components are discussed in detail. Comparison of model predictions with available experimental data also is provided.Key words: saturated sand, constitutive model, elastic–viscoplastic behavior.

A general, three-dimensional formulation of the elastoplastic refined Superior sand constitutive model is presented. The model is aimed at realistic simulation of liquefaction phenomena occurring in loose saturated granular materials under monotonic static loading. The isotropic hardening/softening is related to plastic deformation and distance to a reference yield surface. The nonassociated flow rule is used with the closed yield surface introduced previously in the Superior sand model. The refined model accounts for the different response of materials with different deposition densities. The model prediction of drained and undrained plane-strain compression is presented and compared with the response in triaxial compression/extension loading. Static and kinematic instability states also are discussed.

The response of the elastoplastic refined Superior sand constitutive model in undrained triaxial compression and extension tests is presented. The model is aimed at realistic simulation of liquefaction occurring in loose, saturated, granular materials under monotonic static loading. The yield surface introduced previously in the original Superior sand model is modified, and a non-associated flow rule is used. The isotropic hardening–softening is related to plastic deformation and distance to a reference yield curve. The refined model accounts for the different response of materials with different deposition densities. The model prediction of undrained triaxial compression and extension tests is compared with experimental results. The higher tendency for liquefaction response in extension is well described. Instability and phase-transformation states also are discussed, and the energy of liquefaction is quantified.Key words: static liquefaction, constitutive model, triaxial tests, liquefaction energy.

This paper presents a theoretical analysis of the process of burst of a rock pillar. The analysis is based on a one-dimensional model of a pillar-roof system in which, due to mechanical softening of pillar rock and elastic unloading of roof rock, internal instability may occur. Instability results in a dynamic process, which is treated in the paper using both discrete and continuous approaches. In the latter case, instability of the system produces generation of an unloading stress wave in the roof. Equations for the velocities and accelerations of the bursting pillar, and for the time duration of the burst are derived. Assuming a simplified stress-strain relationship for the pillar rock, closed-form solutions for both discrete and continuous approaches are presented. Comparison of the above solutions is made, and numerical values for the maximum kinetic burst energy and its time duration are given for a wide range of mechanical constants for rocks.

The Paper reports experiments on optically sensitive granular material consisting of crushed glass partices. The pattern of principal stress trajectories occurring at large plastic deformations was directly observed by shearing the material and viewing it in circularly polarized light. The trajectories were compared with principal strain-increment directions, computed from incremental displacement fields. The experiments show significant deviation between principal axes of stress and strain-increment. The results are also employed in verifying some of the existing perfectly plastic flow reules for granular meterials. The results confirm those previously obtained for an assembly of optically sensitive discs.

A static solution is presented for the case of compression of short circular cylinders between rough, rigid plates. It is assumed that the material is perfectly plastic, satisfying the Coulomb yield condition and the associated flow law. The stress state is calculated for the edge régime of the Coulomb hexagon for which the Haar-Kármán hypothesis is satisfied. The solution is obtained for several height-diameter ratios, various friction conditions at the cylinder-plate interface and for various angles of internal friction. Results of theoretical solutions are compared with available experimental data. The analysis may be useful in experimental determination of the angle of internal friction and cohesion by compressing short cylinders between rigid plates.

Depending on the stress state, a bulk solid, regarded as the elastic-plastic material, can exhibit workhardening, worksoftening or perfectly plastic properties. During continuing motion, the solid flow can be assumed as incompressible, and the stress field satisfies a condition of critical state which can be identified with the Coulomb yield condition. The model of Coulomb material is introduced; such material satisfies the Coulomb yield condition and the flow law associated with this condition by the plastic potential rule. In general, the Coulomb material is stronger than the considered bulk solid in the critical state. The kinematic approach and the familiar upper bound theorem are applied in order to determine lower bounds on pressure exerted by the flowing material on bin walls and to determine flowability criterion. In the latter section, the flow induced by a horizontally moving rough plate is analyzed and two flow patterns are considered.

Flow (Dynamics), Plasticity, Bulk solids, Coulombs, Critical points (Physics), Stress, Surface roughness, Motion, Theorems (Mathematics), Pressure

This paper aims at analyzing the response of the elasto-viscoplastic model Superior sand proposed by Boukpeti et al. for describing rate effects in undrained loading of loosely-packed granular deposits. The equations governing the model in triaxial compression are solved for three loading histories: constant strain rate, constant stress rate, and creep. The resulting stress-strain-time curves are discussed in the light of material instability states in relation to static liquefaction. It is shown that the classical second-order work rate instability criterion is no longer valid, and a new criterion based on the deformation acceleration is presented.