A Constitutive Model with a Historiotropic Yield Surface for Sands

Constitutive anamnesis model (CAM) for fine‐grained soils

“…Its size in the effective stress space is described by the scalar state variable $$p_B$$, defining the isotropic part of the back stress tensor $${\bm \sigma }_B$$ and the inclination of its bisector with the deviatoric structural tensor Ω defining the deviatoric part of $${\bm \sigma }_B$$: $$\begin{equation} {\bm \sigma }_B=p_B{\left(-\mathbf {1}+\bm{\Omega }\right)}. \end{equation}$$The proposed flow surface is similar to the one proposed in Grandas‐Tavera et al 50 . for sand and reads: $$\begin{equation} F({\bm \sigma },{\bm \sigma }_B)=\rm w:\rm w-\dfrac{2}{3}M_{\rm w}^{2}\underbrace{{\left[1-{\left(\dfrac{p^{\prime }}{p_B}\right)}^{c_B}\right]}}_{D} \underbrace{{\left[1-\sqrt {\dfrac{3}{2}}\dfrac{\sqrt {\bm{\Omega }:\bm{\Omega }}}{M_{\bm{\Omega }}}\right]}^2}_{G} \end{equation}$$whereby $$\rm w$$ is a deviatoric tensor capturing the position of the current stress with respect to the major axis of the flow surface: …”

“…The adopted dilatancy description (Equations (47)–(49)) was established in Tafili et al 59 . according to extensive experimental evidence on fine‐grained soils 7,10,11,50 and the attentive reader is referred to these works for comprehensive details.…”

“…Figure 12 contains the characteristic friction angles $$\varphi _c$$, $$\varphi _{peak}$$ and $$\varphi _{ptl}$$ as functions of the normalized void ratio $$e/e_c$$ for Kaolin and for a sand provided in Grandas‐Tavera et al 50 . Notice the different values of this parameter for clays in comparison to sands $$n_{peak}=2$$ 50 . Figure 12 shows the difference in the shape of the peak friction angle of sands and clays as well.…”

“…Figure 12 shows the difference in the shape of the peak friction angle of sands and clays as well. $$\varphi _p$$ of clays has a vertex and varies exponentially between $$e/e_c=$$ 0.8 and 1.2, whereas $$\varphi _p$$ of sands 50 is almost a linear function of $$e/e_c$$ in the range between 0.8 and 1.4.…”

“…The model has been proposed for viscous and non‐viscous clays, but it is not limited only to fine‐grained soils. Moreover, Grandas et al 50 . proposed a model using similar tools to describe the behaviour of sands.…”