Fractal Strength Criterion and Improved Statistical Damage Constitutive Model for Freeze–Thaw-Impacted Soils

The degradation of macroscopic mechanical properties in soils associated with freeze–thaw (FT) cycles is predominantly driven by the evolution of their microscopic pore structures. Although previous studies have provided valuable qualitative insights, quantitative analyses explicitly linking the macro- and microscale responses remain limited. Furthermore, most existing constitutive models for FT-impacted soils fail to capture strain-softening behavior, which is critical for reliably characterizing progressive failure in geotechnical structures. In this study, the stress–strain responses of two FT-impacted soils (Ningming clay and Nanjing clay) were systematically investigated through unconfined compression tests, and mercury intrusion porosimetry (MIP) tests were conducted to characterize the evolution of microscopic pore structures. A quantitative relationship between shear strength and surface fractal dimension derived from MIP tests was established and termed the fractal strength criterion. Building on this criterion, an improved statistical damage constitutive model incorporating the strain-softening effect was developed to describe the stress–strain behavior of FT-impacted soils. The model was validated using both experimental results from this study and published literature data. The results demonstrate that the proposed fractal strength criterion and the improved statistical damage constitutive model provide a robust framework for characterizing the macro–micromechanical behavior of FT-impacted soils, offering practical value for predicting the long-term stability of geotechnical structures such as slopes, embankments, and foundations in seasonally frozen regions.