Study on damage statistical constitutive model and stochastic simulation for warm ice-rich frozen silt

► The strength distribution and confidence intervals for warm ice-rich frozen silt are given. ► A damage statistical constitutive model is presented. ► A stochastic model is established to describe the random characteristics of the frozen silt. ► The stochastic simulation is conducted by the way of Monte-Carlo technique. ► The stochastic simulation can describe the random characteristics of test curves quite well.