Non-orthogonal elastoplastic constitutive model with the critical state for clay

Abstract

A non-orthogonal elastoplastic model for clay is proposed by combining the non-orthogonal plastic flow rule with the critical state concept and presented from the perspective of the magnitude and direction of the plastic strain increment. The magnitude is obtained based on the improved elliptical yield function and the plastic volumetric strain dependent hardening parameter. The direction is determined by applying the non-orthogonal plastic flow rule with the Riemann-Liouville fractional derivative to the yield function without the necessity of additional plastic potential function. The presented approach gives rise to a simple model with five parameters. All parameters have clear physical meaning and can be easily identified by triaxial tests. The model performance is shown by analyzing the evolution process of the yield surface, the hardening rule and the plastic flow direction.The capability of the proposed model to capture the mechanical behaviours of clay with different stiffness is also confirmed by predicting test results from the literature.

Non-orthogonal elastoplastic constitutive model for sand with dilatancy

“…There are seven independent material parameters in the proposed model, i.e., λ, κ, ν, φ, φf, β determine β-value based on the method proposed by Lu et al [19,40] . Parameter ξ is called the spacing ratio [21,30] . It can also be used to describe the change of the void ratio ΔΠ of sand between the initial state and the phase transition state under triaxial compression conditions under p=const.…”

“…It can also be used to describe the change of the void ratio ΔΠ of sand between the initial state and the phase transition state under triaxial compression conditions under p=const. The change of the void ratio has been derived and expressed as ΔΠ=(λ−κ)•ln(px/px0) [21] , where px0 and px are the equivalent mean principal stresses for the initial state and the phase transition state, respectively.…”

“…As an alternative, the plastic flow direction can also be directly achieved by applying the nonorthogonal plastic flow rule to the yield function [18][19][20] . The non-orthogonal plastic flow rule has been used to model the dilatancy behaviours of soil under triaxial compression conditions [20][21][22][23] .…”

“…A proper hardening parameter is still needed in describing the contractive-dilative behaviour of sand. If hardening rule stems only from volume change, just as the models for normally consolidated clay [21,[24][25][26] , once the critical state of zero incremental dilation is reached, the ultimate plastic deformation occurs and hardening stops [17] . Obviously, the plastic volumetric strain is not suitable for direct use as a hardening parameter to predict the dilative behaviour of sand.…”

Nonlinear damage creep model based on variable-order fractional theory for rock materials

“…Qu et al developed a fractional plastic flow model to characterize volumetric compression/dilation transition state [21]. And based on fractional theory, Lu et al introduced 3-D fractional plastic flow rule into characteristic stress space and presented a new fractional elastoplastic model for soil [22,23]. Sun et al applied fractional-order dilatant equation to capture state-dependent stress-dilatant behavior of fine sand [24].…”