## Nomenclature  
\(e_{0}\)initial void ratio  
\(e_{cs}\)critical state void ratio  
\(e^{*}\)equivalent intergranular void ratio (Equation (18))  
\(e_{min}\)minimum void ratio (see Section 3.3)  
\(e_{max}\)maximum void ratio (see Section 3.3)  
\begin{tabular}{l l} \(\Delta e^{e}\) & elastic void ratio increment \\ \(\Delta e^{p}\) & plastic void ratio increment \\ \(\lambda\) & slope of the straight CSL \\ \(\overline{\lambda}\) & slope of the curved CSL \\ \(\overline{\lambda_{t}}\) & tangential slope of the proposed CSL (Equation (5)) \\ \(\overline{\lambda_{s}}\) & secant slope of the proposed CSL (Equation (6)) \\ \(\kappa\) & slope of the unloading-reloading line from the isotropic compress test \\ \(\
u\) & [PERSON]'s ratio \\ \(E\) & [PERSON]'s modulus \\ CSL & critical state line \\ RCL & reference control line \\ NCL & normally consolidation line \\ \(\Gamma\) & apparent maximum void ratio (fitting parameter in Equations (2) and (3)) \\ \(\alpha\) & half-slope of the straight portion of the proposed CSL (fitting parameter in Equation (3)) \\ \(\theta\) & curvature index (fitting parameter in Equation (3)) \\ \(p_{ref}\) & reference pressure (fitting parameter in Equation (3)) \\ \(\xi\) & fitting parameter for a power function in Equation (2) \\ rc & average roundness of sand \\ rf & average roundness of fines \\ r & ratio of the average roundness = rc/rf \\ \(SR\) & particle size ratio = D10/d50 \\ D10 & effective size of the sand \\ d50 & mean size of fines \\ \(R\) & radius of the Extended Mises cone \\ \(FC\) & fines content \\ \(FCh\) & threshold fines content (Equation (22)) \\ \(\beta\) & fines influence factor (Equation (19)) \\ \(\beta_{0}\) & fitting parameter (Equation (20)) \\ \(M_{c}\) & stress ratio at the critical state \\ \(M_{f}\) & maximum stress ratio during shearing \\ \(M_{c}(0)\) & \(M_{c}(FC)\) stress ratio at the critical state for FC = 0 and FC > 0 (Equation (23)) \\ \(M_{c}(FCth)\) & stress ratio at the critical state for FC = \(FCh\) \\ \(\Delta M_{c}\) & difference between \(M_{c}(FC_{th})\) and \(M_{c}(0)=M_{c}(FC_{th})-M_{c}(0)\) \\ \(\chi\) & initial state variable for loose sand in Equations (12) and (13) \\ \(\Psi\) & state variable for dense sand = \(e-e_{cs}\) \\ \(\Omega\) & state variable (see Section 3.3) \\ \(I_{\rm D}\) & relative density (see Section 3.3) \\ \(\sigma_{ij}\) & ordinary stress tensor \\ \(\widetilde{\sigma}_{ij}\) & transformed stress tensor (Equation (24)) \\ \(p\) & ordinary mean effective stress \\ \(\widetilde{p}\) & transformed mean effective stress \\ \(p_{0}\) & initial mean effective stress \\ \(p_{cs}\) & critical state mean effective stress \\ \(\widetilde{q}\) & transformed deviator stress \\ \(\eta\) & ordinary stress ratio = \(q/p\) \\ \(\widetilde{\eta}\) & transformed stress ratio = \(\widetilde{q}/\widetilde{p}\) \\ \(\mathfrak{s}_{ij}\) & ordinary deviatoric stress tensor \\ \(\mathfrak{s}_{ij}\) & transformed deviatoric stress tensor \\ \(de_{ij}\) & strain increment tensor \\ \(de^{\epsilon}_{ij}\), \(de^{\epsilon}_{ij}\) & elastic and plastic portions of the strain increment tensor \\ \(de^{\epsilon}_{v}\) & volumetric plastic strain increment \\ \(\Lambda\) & proportionality constant \\ \(H\) & hardening parameter \\ \(\widetilde{H}\) & hardening parameter in the transformed stress space \\ \(n_{b}\) & fitting parameter in Equation (17) \\ \end{tabular}