Formulation of a unified constitutive model for clays and sands

Abstract

This paper presents a new generalized e!ective stress model, referred to as MIT-S1, which is capable of predicting the rate independent, e!ective stress}strain}strength behaviour of uncemented soils over a wide range of con"ning pressures and densities. Freshly deposited sand specimens compressed from di!erent initial formation densities approach a unique condition at high stress levels, referred to as the limiting compression curve (LCC), which is linear in a double logarithmic void ratio, e, mean e!ective stress space, p. The model describes irrecoverable, plastic strains which develop throughout "rst loading using a simple four-parameter elasto-plastic model. The shear sti!ness and strength properties of sands in the LCC regime can be normalized by the e!ective con"ning pressure and hence can be uni"ed qualitatively, with the well-known behaviour of clays that are normally consolidated from a slurry condition along the virgin consolidation line (VCL). At lower con"ning pressures, the model characterizes the e!ects of formation density and fabric on the shear behaviour of sands through a number of key features: (a) void ratio is treated as a separate state variable in the incrementally linearized elasto-plastic formulation: (b) kinematic hardening describing the evolution of anisotropic stress}strain properties: (c) an aperture hardening function controls dilation as a function of &formation density'; and (d) the use of a single lemniscate-shaped yield surface with non-associated #ow. These features enable the model to describe characteristic transitions from dilative to contractive shear response of sands as the con"ning pressure increases. This paper summarizes the procedures used to select input parameters for clays and sands, while a companion paper compares model predictions with measured data to illustrate the model capability for describing the shear behaviour of clays and sands.

Factors affecting seismic response of submarine slopes

“…As a result, sand models do not capture the key elements of soil behavior for this problem. Other models that are applicable to both sands and clays (Pestana and Whittle, 1999) are relatively complex and entail the complete numerical implementation in a generalized stress state.…”

On generalization of constitutive models from two dimensions to three dimensions

“…The rotation hardening proposed by Sekiguch and Ohta (1977) is widely used in geomechanics and is also adopted for this research (e.g., Pestana and Whittle, 1999;Gajo and Muir Wood, 2001). According to Sekiguchi-Ohta's proposal, during rotational hardening all the deviatoric components of a stress state are decreased by γ p′ , where γ is the rotational hardening parameter tensor, meanwhile the value of the mean effective stress remains unchanged.…”

A unique Critical State two-surface hyperplasticity model for fine-grained particulate media

“…Thus a number of extensions to the MCC plasticity model have been proposed to represent this directional bias. These introduce some form of plastic anisotropy through rotation and/or shearing of the yield surface (for example see Belokas and Kavvadas (2010); Dafalias (1986); Gajo and Wood (2001); Karstunen and Koskinen (2008); Karstunen et al (2005); Pestana and Whittle (1999); Sivasithamparam et al (2010); Wheeler et al (2003); Whittle and Kavvadas (1994)). …”

“…12 Previous extensions to the MCC model, such as the single-surface formulations of Karstunen et al (2005) and Wheeler et al (2003) require 8 constants whereas the more sophisticated two-surface models of Whittle and Kavvadas (1994) and Pestana and Whittle (1999) require 15 and 13 constants respectively. The recently proposed model of Sivasithamparam et al (2010) requires 10 constants, however it has no LAD or control over the shape of the ellipsoidal yield surface, leading to strength over-predictions for both non-compressive load paths and over-consolidated soil states.…”