A Constitutive Model For Sandy Soils Based On A Stress-dependent Density Parameter

Abstract

The results of drained and undrained hollow cylinder tests on clean sand and sand with fines content of 10-15 % by weight constitute the basis for an investigation of the behaviour of sandy soils. An elastic-plastic constitutive model, which account for the combined influence of density and effective stress in a unique way, is developed.

The study addresses many important issues relevant to sandy soil behaviour and represents a unite experimental and theoretical effort to develop a constitutive model for sandy soils comprising balanced features of accuracy, simplicity and versatility. Particular attention in both experimental and theoretical considerations is given to the effects of density and effective stress as well as their combined influence on the sandy soil behaviour.

In general, two series of tests are performed, drained torsional shear tests and undrained torsional shear and torsional simple shear tests. Both series include monotonic and cyclic tests. The results of the drained torsional shear tests illustrated the effects of density and mean effective stress on the stress-strain and volume change behaviour of sandy soils and indicated that this behaviour is related to the relative initial state of the soil. The significance of the combined effects of density and effective stress is most profoundly illustrated by the measured identical stress-strain characteristics for quite different initial states including combinations of loose sand at low effective stress and dense sand at high effective stress. Another interesting observation is that stress-strain behaviour for the initial states above the threshold void ratio that indicates zero undrained residual strength, is practically independent of both density and effective stress. Thus, the threshold void ratio associated to zero undrained residual strength indicates the softest drained stress-strain behaviour for a given soil and initial fabric.

Based on the experimental evidence obtained from the drained torsional shear tests, a plastic stress-strain relation with density-stress dependent parameters is developed. The parameters of this relation are expressed as functions of an index parameter established in the framework of the steady state of deformation concept. The parameter employed in the relation is the State Index I, which characterizes the sandy soil behaviour by accounting for the combined effects of density and effective stress related to a given initial fabric. The validity and the efficiency of the state index for representing drained sandy soil behaviour over a wide range of densities and effective stresses is assessed.

The proposed stress-strain relation is a modified hyperbolic relation with the initial plastic modulus defined as a function of the plastic strain. Thus, it accounts for the greater nonlinearity than that provided by the two-constant hyperbolic relation and improves the accuracy of the stress-strain representation over the entire range of strains. The proposed stress-strain relation is characterized by a single set of coefficients for the entire range of densities and stresses. An elastic-plastic constitutive model is developed in the framework of the incremental theory of plasticity. The model is defined in a stress space that enables to account for the rotation of principal stresses and comprises: very small, in fact, 'point' yield surface with purely kinematic hardening rule; failure surface which incorporates the effects of density, effective stress and initial anisotropy, and which serves as bounding hardening surface and plastic potential; a set of four hardening surfaces in the memory with a rule for evaluation of the current hardening surface based on an assumption for mixed hardening; and plastic potential formulation providing noncoaxial and nonunique flow for all stress states except for those at failure.

The accuracy and effectiveness of the elastic-plastic constitutive model is assessed through a comparison of the measured and predicted behaviour of sand in monotonic and cyclic, drained and undrained shear tests. The applicability of the model to seismic response analysis is demonstrated through blind-prediction of a seismic response of level ground model obtained from centrifuge test. Results of the element test simulations and blind-prediction of the response in the centrifuge tests have shown that the model is capable of representing drained and undrained, monotonic and cyclic behaviour with high degree of accuracy. Yet, that can be achieved with a single set of strength and deformation parameters over a wide range of densities and effective stresses.