Creep hardening damage constitutive model of coal with fracture proppant

Fracture is the flow channel of gas (fluid) body in the exploitation of coalbed methane and other energy sources. It has a great influence on gas (fluid) production and work efficiency. Creep results in the proppant embedded in the coal seam leading to fracture damage, reducing fracture permeability. However, there are few studies on a creep model considering proppant embedding in fractures. In this paper, a creep test of proppant embedment in a fracture of a coal seam is carried out, and a creep model considering the damage to proppant embedment is established. The results show that with an increase of closure stress, the range of strain rate first increases and then decreases, and the mean value of strain rate increases slowly and then increases rapidly when the closure stress levels increases in the stable creep stage. During the creep of coal with a fracture proppant, there is not only the hardening and damage of coal, but there is also the damage to proppant embedding. A creep hardening damage model considering the viscosity damage factor of coal, the stress hardening model, the elastic-plastic damage factor, proppant compaction and the embedded viscosity loss factor is established. The creep hardening damage model can better describe the whole process of decelerating creep, stable creep and accelerating creep of coal with proppant fracture.