A fabric-based sand plasticity model with reversal surfaces within anisotropic critical state theory

Abstract

The paper describes the formulation and capabilities of a new constitutive model that accounts for the effects of fabric anisotropy on the response of granular materials under monotonic loading. It is developed within the framework of bounding surface plasticity in conjunction with the concept of (stress) reversal surfaces, i.e., the use of the last stress reversal point as projection center for defining the image stress on the bounding surface. A key constitutive ingredient is the fabric anisotropy variable A, relating the fabric tensor to the plastic strain rate direction, that acquires the value A = 1 as the third requirement for critical state according to the anisotropic critical state theory. This A is used in the definition of dilatancy, the plastic modulus and the evolution equation of the fabric tensor, thus simulating experimental results that show more dilative and stiff response when the loading is applied along the direction of the fabric. Model performance is verified against a large database of monotonic shearing tests on samples of Toyoura sand prepared with three different methods, as well as similar tests on samples whose (initially horizontal) deposition plane was rotated by up to 90 degrees. All simulations are performed with a single set of constants, thus validating the efficiency of the model to account for density, stress level and, most importantly, fabric anisotropy effects on the monotonic shearing response. The paper shows that considering dependence of strength and dilatancy on Lode angle θ and state parameter ψ does not suffice for simulating fabric anisotropy effects on sand response. It ends with a discussion of how fabric effects on sand response are more pronounced under undrained, versus drained conditions.