A fractal order creep-damage constitutive model of silty clay

Silty clay has a remarkable creep effect due to its high moisture content, strong compressibility, and low shear strength. Studying the long-term creep characteristics of soft clay and analyzing its creep damage mechanism is of great engineering value and practical significance for evaluating displacement stability and preventing excessive foundation displacement. In this paper, a series of triaxial consolidation drainage creep tests were performed to investigate the creep behavior of the silty clay interlayer. The test results show that the sample exhibits attenuation creep when the stress level is low; otherwise, it exhibits non-attenuation creep. Based on the fractal derivative theory, a fractal derivative viscoelastic plastic creep model considering the effect of damage is proposed and the analytical solution of the model is also given. By identifying the model parameters, it is found that the fitting curves under different stress levels agree well with the test results, especially in the accelerated stage, which cannot be described by the classical model, demonstrating that the proposed model can well characterize the entire three-stage creep process of silty clay. According to sensitivity analyses of the model parameters, fractal derivative order and damage factor are critical parameters for characterizing the creeping type. In comparison with the classical widely used creep model, the proposed model has the advantages of fewer parameters, higher simulation precision, and higher calculation efficiency, making it more applicable in investigating soil creep properties. The results can provide a precious theoretical reference for the creep characteristic analysis and damage prediction of soil in soft areas.