A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution

Abstract

Soil fabric and its evolving nature underpin the non-coaxial, anisotropic mechanical behaviour of sand, which has not been adequately recognized by past studies on constitutive modelling. A novel three-dimensional constitutive model is proposed to describe the non-coaxial behaviour of sand within the framework of anisotropic critical state theory. The model features a plastic potential explicitly expressed in terms of a fabric tensor reflecting the anisotropy of soil structure and an evolution law for it. Under monotonic loading, the fabric evolution law characterizes a general trend of the fabric change to gradually become co-directional with the loading direction before the soil reaches the critical state. When a sand is subjected to rotation of principal stress directions, the fabric evolves with the plastic strain increment which is further dependent on the current stress state, the current fabric and the direction of stress increment. During its evolution, the fabric rotates towards the loading direction and reaches a final degree of anisotropy proportional to a normalized stress ratio. With the incorporation of fabric and fabric evolution, the non-coaxial sand behaviour can be easily captured, and the model response converges to be coaxial at the critical state when the stress and fabric are co-directional. The model has been used to simulate the mechanical behaviour of sand subjected to either monotonic loading or continuous rotation of principal stress directions. The model predictions agree well with test data.

SANISAND‐FN: An evolving fabric‐based sand model accounting for stress principal axes rotation

“…The simplicity of the KH as the only hardening mechanism is in contrast to the extra loading mechanism for the specific loading condition associated with stress PA rotation that had to be introduced in other models without KH. 19,28 Moreover, the model maintained the capabilities of the already developed bounding surface (BS) sand models within ACST for conventional radial loading paths, such as the SANISAND-F model. The SANISAND-FN model is in fact an extension of this last model accounting for the effect of noncoaxiality, hence the symbol N on its name, in particular under continuous stress PA rotation.…”

“…As explained in Section 1, this led Li and Dafalias 34 to introduce a third loading mechanism associated with Lode angle change, also adopted by Gao and Zhao. 28 However, in this work, we want to maintain the simplicity and efficiency of the kinematic hardening (KH) with the small yield surface (YS) formulation adopted in the SANISAND family of models, without adding any additional loading mechanism, and maintain the model's capabilities for proportional and radial loading, in addition to loading under stress PA rotation. To this extent, some of the constitutive ingredients have to be reformulated for accurate results.…”

Bayesian model selection for sand with generalization ability evaluation

“…Usually two kinds of internal parameters have to be considered: (a) one or several scalar parameters characterizing the density state with respect to a critical density, such as the evolution of e/e c in considered models of this study, which is a usual way to define the isotropic internal state, and (b) one or several tensorial parameters characterizing the anisotropic internal state, such as the critical state considering fabric anisotropy. [77][78][79][80][81] In complex loading paths, experimental studies have indicated that the behaviour of a granular soil under shear is predominantly anisotropic. Such anisotropic behaviour of sand can be effectively modelled by incorporating the fabric tensor and its evolution.…”

Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule

“…However, the associated flow rule does not work for most geomaterials (Lade et al, 1987;Collins and Houlsby, 1997). Therefore, the non-associated flow rule is usually used (Lu et al, 2016;Gao and Zhao, 2017). There are two approaches to obtaining the desired plastic strain increment direction n: (i) constructing a plastic potential function g to determine n by orthogonality as shown in Fig.…”