Damage constitutive model and strength criterion of cemented paste backfill based on layered effect considerations

The concepts of initial damage, loaded damage, and total damage were introduced for cemented paste backfills (CPBs) with stratified structures. Based on these, the damage evolution model, damage constitutive model, and strength criterion of CPB with stratified structures were formulated based on damage theory and the total differential rule. Finally, compression experiments and numerical simulations of CPBs were conducted with three-dimensional particle flow code with the layer numbers of 0, 1, 2, and 3, a solid content of 75% and a cement–sand ratio of 1:4. The theoretical curves of the damage constitutive model and strength criterion of the layered CPB closely matched the curves generated based on experimental tests and numerical simulations. This finding verified the correctness of the model. The initial increase of the damage fits closely to a quadratic polynomial as a function of the layer number, the total damage rate first increased and then decreased, while the maximum of the total damage rate increased.