Fractional viscoelastic-plastic constitutive model for frozen soil based on microcosmic damage mechanism

Abstract

Frozen soil is a kind of composite geotechnical material with significant creep properties. To develop a creep constitutive model that can consider the composite properties and internal microcosmic damage mechanism of frozen soil, it is first conceptualized as a binary medium material containing both bonded elements and frictional elements, and the creep breakage mechanism of frozen soil is analyzed. Then, the relationship between micro-strain and macro-strain is established based on the homogenization theory. The creep constitutive relations of bonded elements and frictional elements are established, respectively, based on the creep breakage mechanism and the fractional calculus theory. In addition, the breakage ratio is defined as a function of creep time. Finally, a new fractional constitutive model with a composite structure is established. The three-dimensional model is also derived to facilitate its extensive application. Reasonable agreement is achieved comparing the model prediction results with the creep experimental results, and the proposed model can accurately capture the creep deformation characteristics of each phase. The results of the parameter sensitivity analysis further demonstrate the applicability of the definition of composite structure for the frozen soil.