Trans-scale relationship analysis between the pore structure and macro parameters of backfill and slurry

The characteristics of the porous structure of backfill are directly related to the macro parameters of the flowability of the filling slurry and the mechanical features of the backfill, which are fundamental to the study of multiscale mechanics of backfill. Based on the geometry and fractal theory, scanning electron microscopy images of backfill were analysed by image analysis methods such as OTSU and box counting. The fractal dimension of the pore structure was calculated. By quantitatively characterizing the pore structure, the trans-scale relationships between the fractal dimension of the pore structure and the macro parameters of the filling slurry were established in terms of equilibrium shear stress (ESS) and equilibrium apparent viscosity (EAV). In addition, the correlations between the fractal dimension and macro parameters of backfill were obtained in terms of uniaxial compressive strength (UCS), water content (WC) and porosity. The influence of the microstructure on the macro parameters was discussed. The results show the following: (i) the fractal dimension of the backfill pore structure can characterize the complexity of the structure; (ii) the fractal dimension of the pore structure is negatively correlated with the ESS and EAV of the filling slurry. The UCS of the backfill is positively correlated with the flowability parameter; (iii) the fractal dimension of the pore structure has a certain correlation with some macro parameters of the backfill, i.e. the fractal dimension is negatively correlated with the UCS and positively correlated with the WC and (iv) the linear correlations between the pore fractal dimension and UCS and WC are established. The correlation coefficient between the fractal dimension and UCS has an R(2) value of −0.638, while the corresponding value of the fractal dimension and WC is 0.604. UCS and WC can be predicted by the fractal dimension of pores.