Mechanical damage model and brittleness index of frozen rocks based on statistical damage theory

The establishment of mechanical model and brittleness index of frozen rocks can provide crucial guidance to the construction of rock mass engineering in permafrost area or artificial freezing engineering with water-rich soft rocks. The exponential function of strain difference is established for initial compacted stage and linear elastic stage in the stress–strain curve, thereby yielding the statistical damage model and damage evolution equation of frozen rock according to statistical damage theory, Hoek–Brown criterion and the strain difference function. The novel damage model is proposed to well simulate the whole failure process of frozen rocks, and based on that a novel brittleness index of frozen rocks is derived using energy method. Hence, a series of triaxial tests of saturated red sandstones under different low temperature are conducted. Confining pressure and low temperature have significant influences on the mechanical properties and brittleness of frozen rocks, and Hoek–Brown criterion is appropriate for expressing the nonlinear relation between principal stresses of frozen rocks. In addition, the rationality of the proposed damage model is proved by comparing with the test curve, and the superiority of the novel damage model compared with the existing ones is proved by two evaluation methods. Furthermore, the variation of damage evolution shows that confining pressure can enhance the rock ductility and low temperature can improve the rock brittleness, which is further verified by the novel brittleness index. The feasibility of the novel brittleness index is demonstrated by comparing that with the existing brittleness indexes. Eventually, the physical significance of parameters S 0 and β for the damage model curves and brittleness index of frozen rocks are discussed. Consequently, the proposed damage model and novel brittleness index are suitable for the application of frozen rock engineering.