Keywords: prediction, numerical analysis, constitutive model, hollow cylinder, stress-strain behaviour.

Laboratory experiments have shown that real soil behaviour is not ideal and simple. On the contrary, soil behaves in a highly non-linear way as strength and stiffness characteristics depend on stress and strain magnitudes. In order to describe material behaviour in a realistic way complex and accurate constitutive models that can be implemented in numerical analysis procedures are required. This paper evaluates the predictive capabilities of an effective soil model through comparison with experimental results of tests on a fine-medium sand. Comparison is made at various densities, mean effective consolidation stresses and drainage conditions. The model used for the analysis is Lade's double hardening model [1] which is an elasto-plastic constitutive model based on concepts from non-linear elasticity and isotropic work hardening/softening plasticity theories. The model consists of two intersecting yield surfaces and is especially designed for the simulation of the behaviour of granular soils.

The current investigation focuses on the prediction of the stress paths and stress-strain behaviour using experimental data from the hollow cylinder apparatus. The sand under consideration is a quartzitic sand that consists of angular to sub-angular grains with D₅₀=0.28mm. The minimum and maximum densities are e_min=0.526 and e_max=0.860, respectively. All specimens were formed by pluviation through water and have been isotropically consolidated to various mean effective stress levels. The specimens at a relative density D_r=37.4% do not show any brittleness under undrained monotonic torsional loading and after an initial contractant phase during which the shear stress steadily increases to a peak value, mobilized at the maximum rate of excess pore pressure accumulation, and remains nearly constant for shear strains up to about 2%. This contraction phase is halted by each effective stress path reaching the point of phase transformation where contraction ceases and dilation begins. Eventually, the effective stress path follows the sand's failure envelope. The tendency to contract reduced significantly for D_r=62.9% but it requires much denser specimens in order to eliminate it. The behaviour of the sand specimens under drained monotonic torsional loading is initially contractive for the same strain range as their undrained counterparts. With increasing initial confining pressure the specimens show higher contraction tendencies and a reduced rate of dilation while subsequent loading leads to a decrease in the maximum stress ratio. The slope of the phase transformation line is uniquely determined for both monotonic undrained and drained torsional loading conditions. It is also independent of variations in density of the specimens at least in the range of relative densities studied herein. However, the angle of shearing resistance is higher for the drained tests.

Numerical analyses were performed using the Imperial College Finite Element Program (ICFEP) [2]. The behaviour of medium density Ham river sand specimens can be accurately predicted for torsional shearing under drained loading conditions. The use of the same model parameters for the prediction of the response of the specimens under undrained loading conditions resulted in less accurate simulation of the material behaviour (effective stress paths, stress-strain and excess pore water pressure against strain curves), especially regarding the stress-strain response. However, the prediction of the soil behaviour improves with increasing density. It should be emphasized that the constitutive model was based on triaxial testing while the tests performed in this study are torsional shear tests on hollow cylinder specimens.

1

P.V. Lade, "Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces", Int. J. Solids Struct., 13, 1019-1035, 1977. doi:10.1016/0020-7683(77)90073-7

2

D.M. Potts, and L. Zdravkovic, "Finite element analysis in geotechnical engineering", Thomas Telford Publishing, London, 1999.

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