A hypoplastic model for granular soils incorporating anisotropic critical state theory

Abstract

Summary It is well known that soil is inherently anisotropic and its mechanical behavior is significantly influenced by its fabric anisotropy. Hypoplasticity is increasingly being accepted in the constitutive modeling for soils, in which many salient features, such as nonlinear stress‐strain relations, dilatancy, and critical state failure, can be described by a single tensorial equation. However, within the framework of hypoplasticity, modeling fabric anisotropy remains challenging, as the fabric and its evolution are often vaguely assumed without a sound basis. This paper presents a hypoplastic constitutive model for granular soils based on the newly developed anisotropic critical state theory, in which the conditions of fabric anisotropy are concurrently satisfied along with the traditional conditions at the critical state. A deviatoric fabric tensor is introduced into the Gudehus‐Bauer hypoplastic model, and a scalar‐valued anisotropic state variable signifying the interplay between the fabric and the stress state is used to characterize its impact on the dilatancy and strength of the soils. In addition, fabric evolution during shearing can explicitly be addressed. Modifications have also been undertaken to improve the performance of the undrained response of the model. The anisotropic hypoplastic model can simulate experimental tests for sand under various combinations of principle stress direction, intermediate principal stress (or mode of shearing), soil densities, and confining pressures, and the associated drastic effect of different principal stress orientations in reference to the material axes of anisotropy can be well captured.

Non‐coaxial hypoplastic model for sand with evolving fabric anisotropy including non‐proportional loading

“…During the loading process, the fabric always evolves toward the loading direction characterized by a unit‐norm deviatoric tensor n . Following Li and Dafalias 26 and Yang et al., 38 the definition of the fabric evolution law can be expressed as follows: where m is a positively valued parameter that controls the pace of fabric evolution. The loading direction is characterized by a second‐order deviatoric unit‐norm tensor n , whose expression will be given in the later section of the paper.…”

“…To reflect the recent deformation history and improve the model performance in the small‐strain range, the hypoplastic model was enhanced by the intergranular strain concept (Niemunis and Herle 37 ). More recently, the ACST was incorporated into the hypoplastic model by Yang et al 38 . and Liao and Yang 39 to simulate anisotropic sand behavior under both monotonic and cyclic loading.…”

“…Different from recent ACST‐based hypoplastic models (Yang et al. ; 38 Liao and Yang 39 ), the fabric tensor is further incorporated into the hypoplastic flow, enabling the model to produce the non‐coaxial deformation. Furthermore, the hypoplastic potential surface is modified to have a Lode‐angle‐dependent shape, such that the three‐dimensional stress‐strain behavior of sand can be simulated satisfactorily.…”

A simple hypoplastic model for overconsolidated clays

“…1, the hypoplastic model (1) predicts an effective stress path directed toward left from an isotropic stress state. Some attempts have been made to remedy this shortcoming [16,22,26,49]. We proceed to multiply the nonlinear term in model (1) with a function f u , which vanishes for isochoric strain rate to give…”

A coupled SPFEM/DEM approach for multiscale modeling of large‐deformation geomechanical problems

“…14). After finding the acceleration, the velocity and the displacement are updated with the velocity Verlet time integration, which corresponds to a special case of the Newmark scheme with = 1∕2 and = 0 in Eqs (2) and (3). The velocity Verlet scheme possesses second-order accuracy but is only conditionally stable, so that the time step increment has to be set sufficiently small to satisfy the CFL condition.…”