Formulation and implementation of an elastoplastic constitutive model for sand‐fines mixtures

Abstract

Sand‐fines mixtures are commonly used engineered materials, and their mechanical behavior is significantly affected by density, confining pressure, as well as fines content. Although many laboratory tests have been performed on sand‐fines mixtures, few works have been conducted on its constitutive law. To adequately describe the mechanical behavior of sand with different fines content, a novel elastoplastic constitutive model was developed for sand‐fines mixtures by incorporating an equivalent granular state parameter into Rowe's stress‐dilatancy equation, plastic modulus, and in conjunction with the correlation between the critical state and fines content. Subsequently, the Runge‐Kutta schemes with automatic error control are adopted for the proposed model and implemented in a finite element code. The performance of the fines‐state‐dependent model with the Runge‐Kutta schemes, in terms of accuracy, efficiency and convergence, is verified by analyzing element scale tests and boundary value problems. The comparisons of simulated and experimental results demonstrate that the fines‐state‐dependent model can effectively capture the strain hardening (or softening) and contraction (or dilatancy) behaviors of sand‐fines mixtures under drained conditions. In addition, the key features under undrained conditions, such as flow, limited flow, and non‐flow behaviors can also be reasonably reproduced.

Modified unified critical state model for soils considering over-consolidation and cyclic loading behaviours

“…Existing numerical implementation schemes of the constitutive models are generally classified as backward Euler 51 – 54 and forward Euler 55 – 57 schemes. The backward Euler scheme with the return-mapping technique is accurate because the resulting stress automatically satisfy the yield function to a specified tolerance.…”

General friction law for velocity‐stress dependent phase transition in granular flow

“…In this flow regime, the rheological behavior and the constitutive law are dictated by the inertial number 6,33,55,57 . In geomechanics, constitutive modeling 58–60 for granular soil or rock becomes more complicate when considering loading path, 61–63 water content, 62,64 and particle breakages 40,58 …”

“…In this flow regime, the rheological behavior and the constitutive law are dictated by the inertial number. 6,33,55,57 In geomechanics, constitutive modeling [58][59][60] for granular soil or rock becomes more complicate when considering loading path, [61][62][63] water content, 62,64 and particle breakages. 40,58 Until now, most simulations for plane shear flow have focused mainly on the dimensional analysis and less on the velocity-stress conditions.…”

Constitutive model for soil-rock mixtures in the light of an updated skeleton void ratio concept

“…SRMs are widely encountered in geotechnical engineering, such as natural slopes [6], waste rocks and tailings from mining [8], clay-aggregate mixtures in rockfill dams [12] and tunnels [14]. The soil content (sc) is one of the most important factors governing the mechanical behavior of SRMs [3,26,29,33,36]. In recent years, many field tests, laboratory tests and numerical simulations have revealed that sc greatly affects the shear strength [4,16,23,37], failure modes [5,15,17], stress-dilatancy [4,33], and critical state parameters of SRMs [25,33].…”

“…Although some pioneering works has been done on the constitutive modelling of SRMs [7,17,26], properly modeling the behavior of this kind of complex heterogeneous materials remains an open challenge [35,39,40]. Predicting the mechanical properties SRMs for varying sc remains a widely open issue.…”