The strain paths of cement stone in the deviatoric and meridian planes under the constant Lode angle loading path (true triaxial stress state) are analyzed. The amount of volumetric and shear strains first increases and then decreases with the intermediate principal stress coefficient. Owing to the generation of plastic volumetric strain and plastic shear strain in the direction of deviatoric stress, the strain path exhibits nonlinearity in the meridian planes. The deviation of the strain path from the constant Lode angle arises from the accumulation of plastic shear strain along the Lode angle direction. In the framework of fractional plasticity, a three-dimensional elastoplastic constitutive model incorporating Lode angle is proposed, including yield function, potential function, and fractional flow rule. The yield surface evolves in both meridian and deviatoric planes, allowing the yield function to precisely characterize the stress state. Since the plus-minus sign in the flow direction of the yield surface is opposite to that in the flow direction of cement stone, a simple elliptic function incorporating Lode angle serves as the potential function. The procedure for the determination of fractional order based on the entirety of the deformation process is proposed, including variable and constant fractional order. The comparison between the experimental result and the analytical solution of constitutive model confirms its accuracy and validity. Furthermore, the difference between variable and constant fractional order on deformation is analyzed. The comparison results indicate that the variable fractional order can provide a more accurate description of deformation than the constant fractional order.

Overconsolidated (OC) clays are commonly encountered in geotechnical engineering and are subjected to threedimensional (3D) stress conditions. This study proposes a unified plastic potential function for triaxial and 3D general stress conditions, by incorporating the overconsolidation parameter and intermediate principal stress parameter. This function can effectively capture the coupling influence of the overconsolidation degree and intermediate principal stress on the dilatancy characteristics of OC clay. Additionally, it possesses a simple form and clear physical significance, making it easily applicable in constitutive models. Then, a simple bounding surface model in triaxial stress conditions is established by adopting the dilatancy relation and the model is extended to general 3D stress conditions by the transformed method based on spatially mobilized plane (SMP) strength criterion. Finally, the performance of the proposed model is validated through various triaxial shearing tests under a wide range of overconsolidation ration (OCR) and the simulation results of the proposed model are compared with those of the SANICLAY model. The comparative analysis indicates that the proposed model effectively describes the complex characteristics of OC clays by simple theory and it demonstrates significant advantages in deformation and pore water pressure simulation due to the advanced dilatancy relation.

A comprehensive three-dimensional elastoplastic constitutive model is presented to characterize the stress-strain behavior of cement stone under the true triaxial stress state. This constitutive model incorporates a threedimensional yield function and a three-dimensional potential function. The three-dimensional yield function is designed to accurately represent the true triaxial stress state during hardening. The three-dimensional potential function is devised to depict the plastic flow direction under true triaxial stress state. The yield and potential functions include parameters that control the shape of the deviatoric and meridian planes, and these parameters vary with the plastic internal variable. Consequently, the yield function can accurately describe the stress state, and the potential function can precisely capture the variations in plastic flow direction. Additionally, a detailed procedure for determining the parameters of the yield function and potential function is proposed based on the full deformation process. The constitutive model is presented in the form of analytical solution. The comparison of experimental data with the constitutive model confirms its accuracy and validity. A sensitivity analysis of the deviatoric and meridian parameters in the potential function is performed, shedding light on their impact on the model behavior. Furthermore, the significance of incorporating Lode angle dependence into the potential function is discussed, emphasizing its essential role in accurately capturing strain in the direction of the intermediate principal stress.