A critical state sand plasticity model accounting for fabric evolution

Abstract

SUMMARY Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three‐dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by Li & Dafalias [2012], in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void‐based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non‐coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data. Copyright © 2013 John Wiley & Sons, Ltd.

Modelling non-coaxiality and strain localisation in sand: The role of fabric and its evolution

“…This paper presents a general three-dimensional critical state sand plasticity model with full account of the effect of fabric and its evolution recently developed by the authors (Gao et al 2014). The model has been developed within the Anisotropic Critical State Theory proposed by Li & Dafalias (2012).…”

Constitutive modelling of fabric anisotropy in sand

“…An important inclusion in the yield function in Equation (1) is a fabric anisotropy variable A that is defined by the following joint invariant of F ij and n ij , Gao et al 2014 ij ij A F n  (3) where F ij is a symmetric traceless tensor whose nor m F=(F ij F ij ) 0.5 is referred to as the degree of fabric a nisotropy. For convenience, F ij is normalized such th at in critical state, F is unity.…”

“…Since əf/ər ij consists of two parts with one being coaxial with r ij (or equivalently σ ij itself) and the other involving F ij which is attributed to fabric anisotropy and is in general noncoaxial with r ij (Gao et al 2014), the flow rule expressed by Equations (12) and (13) naturally address the non-coaxiality issue in soil modelling.…”

“…The model parameters are listed in Table 1 and the initial degree of anisotropy F 0 is set to be 0.45. The procedure for parameter determination is discussed in Gao et al (2014). Figure 1 shows the model simulations for the anisotropic sand behaviour under undrained torsional loading with constant intermediate principal stress vatiable b=0.25.…”

“…In this setting, it is convenient to use the model to explain the non-coaxiality in the z-θ plane (Gao et al 2014). To elaborate on this point and motivated by the approach in Dafalias et al (2004), we plot in Figure 2 the variation with deviatoric strain of the difference of the angle α(σ) between the direction of the major principal stress σ 1 and the vertical direction, from the angle α(ε) that the major principal strain ε 1 forms with the vertical direction.…”