Review of Proposed Stress-dilatancy Relationships and Plastic Potential Functions for Uncemented and Cemented Sands

Abstract

Stress-dilatancy relationship or plastic potential function are crucial components of every elastoplastic constitutive model developed for sand or cemented sand. This is because the associated flow rule usually does not produce acceptable outcomes for sand or cemented sand. Many formulas have been introduced based on the experimental observations in conventional and advanced plasticity models in order to capture ratio of plastic volumetric strain increment to plastic deviatoric strain increment (i.e. dilatancy rate). Lack of an article that gathers these formulas is clear in the literature. Thus, this paper is an attempt to summarize plastic potentials and specially stress-dilatancy relations so far proposed for constitutive modelling of cohesionless and cemented sands. Stress-dilatancy relation is usually not the same under compression and extension conditions. Furthermore, it may also be different under loading and unloading conditions. Therefore, the focus in this paper mainly places on the proposed stress-dilatancy relations for compressive monotonic loading. Moreover because plastic potential function can be calculated by integration of stress-dilatancy relationship, more weight is allocated to stress-dilatancy relationship in this research.

Stress–Dilatancy Relationship of Erksak Sand under Drained Triaxial Compression

“…The linear stress ratio-plastic dilatancy relationships for various shear phases of Toyoura sand under undrained triaxial compression conditions were also obtained [16]. The most well-known stress-dilatancy relationships were collected by Rahimi [17]. The micro mechanics approach also gives linear stress-dilatancy relationships for granular materials [18,19].…”

“…The complex stress-plastic dilatancy relationship can be obtained by differentiating the plastic potential function proposed in classical elastoplastic models [17]. Recently the stress-dilatancy relationship was obtained by use of fractional order derivatives of plastic potential or yielding function with respect to loading path [20][21][22][23].…”

Stress–Dilatancy Behaviourof Fibre-Reinforced Sand

“…The stress–dilatancy relationship is commonly used as the basis for the development of constitutive models for soils [ 18 , 19 , 20 ]. The best known are the stress–dilatancy relationships of Rowe [ 21 ] and Bolton [ 22 ].…”

Stress–dilatancy behaviour of remoulded Fujinomori clay

“…For structured and highly overconsolidated clays, however, the Cam-clay model's stress-dilatancy relationships should be modified. By differentiating the plastic potential functions of the classical elasto-plastic model, various stress-plastic dilatancy relationships can be obtained [9]. Szypcio [13] developed a general stress-plastic dilatancy relationship for soils based on the Frictional State Concept (FSC).…”