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The constitutive model of the frozen soil-structure interface is a critical component of frozen soil mechanics research, and the surface roughness plays a significant role in determining the interaction between the soil and structure. Most of the previous research about the interface roughness mechanical behavior is based on numerical simulations, and these methods mainly depend on empirical and semi-empirical approaches to determine parameters. However, there is a lack of sufficient research on the internal mechanisms of micro-mechanical deformation of the contact surface based on roughness. To elucidate the impact of roughness on the deformation mechanism and mechanical behavior of frozen soil, a series of cryogenic direct shear tests and a binary medium model based on the interface of frozen soil-structure were conducted. The test was carried out at −4 °C under different normal load and roughness conditions. The test results showed that the shear curve of the specimen interface presented brittle failure, and the stress peak was evident at this temperature. Moreover, the shear zone was introduced to explain the change of roughness on the mechanical behavior of the samples. A binary medium constitutive model was established to depict the overall mechanical behavior of the interface during prepeak shear with different roughness. The simulated roughness, displacement, and shear stress are in good agreement with the measured data. The effectiveness of the model is evaluated by correlated factors, and it is verified that the model can properly depict the change of roughness on the mechanical characteristics of the interface. • Established an improved roughness algorithm that considers various factors. • The relationship between the surface roughness and the shear stress is analyzed. • A binary medium constitutive model considering the effect of roughness is proposed. [ABSTRACT FROM AUTHOR]