An improved statistical damage constitutive model for warm frozen clay based on Mohr–Coulomb criterion

There are many microdefects distributed randomly in frozen soil, which will lead to great uncertainty and randomness of mechanical properties and behaviors under applied load, therefore, it is more scientific to study stress–strain relationship of frozen soil by stochastic method instead of deterministic way. For the warm frozen clay and warm ice-rich frozen clay, a stochastic damage constitutive model has been proposed on the foundation of a large number of experimental data, in which the axial strain is regarded as random variable. In this paper, according to these experimental data under three temperature conditions (− 0.5 °C, − 1.5 °C and − 2.0 °C) and the above research results, the strength of soil element is selected as random variable and an improved statistical damage constitutive model is deduced, and in this new model, the Mohr–Coulomb failure criterion is also used to judge whether the soil element is damaged. Finally, compared with original model, it is found that the new improved model can better describe the experimental data and reflect deformation characteristics. Especially, when the stress reaches its peak value, the experimental data and new theoretical curves overlap with each other.