A Variable-Order Dynamic Constitutive Model for Clay Based on the Fractional Calculus

To accurately describe the deformation characteristics of clay under long-term cyclic load, based on fractional calculus theory, elastoplastic theory and the basic element model, a variable-order fractional dynamic model designed to predict accumulative strain of clay was exhibited. Firstly, the cyclic load was separated into static and alternating load in accordance with cyclic load characteristics, and the strain of clay under static and alternating load was analyzed. Then, on the basis of the variable-order Abel dashpot model, rheological theory and elastoplastic theory, the expressions of the rheological constitutive model and strain response were both obtained. Finally, in combination with the undrained dynamic triaxial testing of Zhan Jiang clay and Tian Jin soft clay, a series of analyses was carried out on the effectiveness and parameter sensitivity of the model when subjected to long-term cyclic loading. By comparing the dynamic constitutive model with pre-existing models, the superiority of the dynamic constitutive model is revealed. The results show that the dynamic constitutive model can characterize properly the deformation characteristics of clay under the action of long-term cyclic loading, especially in its accelerating stage. The parameter sensitivity of the model exhibits a growing trend with the increment of loading duration.