Study of constitutive model of frozen sandstone damage based on Weibull distribution

Abstract: The deformation and destruction characteristics of frozen rock is a basic mechanical problem encountered during the construction using the freezing method. Under the action of load, the mechanical characteristics and deformation characteristics are greatly different for the rock with different freezing temperatures, which significantly affects the safety and stability of the freezing wall. Therefore, the study of the damage constitutive relation of the frozen rock is significant for instructing the freezing method design and construction. In order to analyze the whole process of the frozen rock deformation and destruction under load action, the Weibull distribution was adopted to describe the heterogeneity of rock materials. On the basis of the Drucker-Prager destruction principle, the rock damage constitutive model under triaxial stress state was established. In combination of the triaxial compression test of freezing sandstone, the change relations among the homogeneity coefficient m, average strength F₀ and the freezing temperature as well as peripheral pressure in the constitutive relation were focused on in the analysis; the damage constitutive equation was corrected, and the damage evolution regularity of the frozen sandstone was studied based on this model. As indicated by the study, according to the monoaxial and triaxial compression tests of the frozen sandstone, under the same peripheral pressure, as the freezing temperature drops, the sandstone strength peak was significantly increased; the strain peak was reduced; the strength was decreased at the compaction stage; the slope was increased at the elastic deformation stage. The brittle destruction characteristics of the rock were significant. Under the same freezing temperature, there was no significant change in homogeneity coefficient m and average strength F₀ with the rising peripheral pressure. However, with the decreased freezing temperature, m and F₀ showed exponential growth and linear growth respectively. Accordingly, as the freezing temperature dropped, the sandstone was frozen better, and both the ratio of the ice formed in the internal free water and the ice strength enhancement were higher, which was especially significant in 0 to −10℃. The freezing effect increased the homogeneity and average strength of sandstone. The damage constitutive equation of the sandstone with different freezing temperatures was corrected based on the mechanical characteristics and deformation regularity of the sandstone with different freezing temperatures. On the basis of the corrected constitutive model study, the damage evolution curves can well reflect the compaction, linear elasticity, yield deformation and deformation characteristics of each stage of the strain softening in the frozen sandstone compression test, verifying the rationality of the model. The study result provided useful reference for the rock-mechanics characteristic study under low-temperature environment and the underground freezing engineering design and construction.