Study on Bingham fractional damage model of backfill material under different moisture content conditions

Filling mining technology is an important representative technology to realize green and low-carbon mining. The backfill materials have distinct rheological characteristics under the long-term action of formation loads and groundwater seepage. In order to study the creep characteristics of backfill materials under different moisture contents and reveal their aging-mechanical properties, based on the Riemann-Liouville fractional calculus and damage mechanics theory, the fractional element and damage variables are introduced to improve the traditional Bingham model, and the fractional Bingham creep damage model is proposed. Based on the experimental data of gangue cemented backfill under different moisture content, the parameters of the creep model are obtained by using user-defined function fitting and the least square method. The results show that the improved Bingham fractional creep damage model can describe the whole creep process of backfill materials under different moisture contents, and the rationality of the model is verified. Compared with the traditional Bingham model, the fitting degree of the Bingham fractional creep damage model is higher, which solves the problem that the traditional Bingham model cannot describe the nonlinear creep stage. Model parameter α and ξ increase with the increase of axial stress and moisture content. Under the same moisture content, η gradually increases with the increase of axial stress. This work has a certain reference significance for studying the mechanical properties and creep constitutive model of backfill materials containing water.