An elasto-visco-plastic model based on stress functions for deformation and damage of water-saturated rocks during the freeze-thaw process

A schematic drawing of strain-time curves during freeze-thaw cycles and the curve fitted by the elasto-visco-plastic model, which shows the deformation and damage of water-saturated rocks. [Display omitted] •A new elasto-visco-plastic model based on stress functions is proposed.•The characteristics of plastic strain show a unique process of damage development of saturated rocks.•The data of strain-time relationship of sandstone are well fitted by the new model. Rocks can be used as building materials. In this study, based on the effect of freeze-thaw cycles (FTC) on the properties of water-saturated rocks and the theory of rheology, an elasto-visco-plastic model based on stress functions is proposed, which consists of the elastic, viscoelastic and viscoplastic submodels. The elastic strain shows obvious time dependence and is different from the traditional one in the theory of creep. Although the Kelvin model can be used to fit the relationship between elastic strain and time during the freezing process, but not suitable for thawing process. A threshold element obtained by improving the classical plastic element in rheology is applied to improve the Kelvin model to simulate the viscoelastic behavior of rocks, which only has the action of a valve without any plastic flow and does not work during the thawing process. The viscoelastic strain will be generated after the frost heave stress is greater than σftev, after thawing, it will not recover until time tends to infinity. The viscoplastic strain will be developed when the frost heave stress exceeds σftvp, which can be divided into two substages during the freezing process, namely the substages of stress growth (tvp⩽t⩽tcf) and stress constancy (tcf⩽t⩽tn). The viscoplastic strain will continue to develop until the frost heave stress is reduced to σftvp after thawing. Thus it can be seen that the characteristics of viscoplastic strain show a unique process of damage development of water-saturated rocks during the freeze-thaw (FT) process. Finally, the model is simplified by a piecewise linear function and adopted to fit the strain-time data of water-saturated red sandstone samples during the freezing process.