Objective Investigating grout diffusion patterns and predicting the grouting range hold great significance for coal gangue grouting and filling engineering in goaves. Specifically, they are significant for designing grouting hole and row spacing, guiding grouting construction, determining the grouting filling degree, and further ensuring grouting effects.

Methods Using crushed rocks as the medium to be grouted and coal gangue-based grout as the grouting materials, this study conducted grouting experiments under different particle sizes of crushed rocks and varying mass fractions of grout. Accordingly, it investigated the flow patterns of gangue-based grout in goaves.

Results and Discussion Under a mass fraction of 50%, the diffusion distances of the grout in crushed rocks with particle sizes of 3-5, >5-7, and >7-9 mm were determined at 5.0, 5.5, and 6.2 cm, respectively, with a maximum difference in the diffusion distance of 1.2 cm. When the mass fraction of the grout was reduced to 40%, the diffusion distances increased to 10.2, 14.5, and 18.0 cm, respectively, with the maximum difference in the diffusion distance expanding to 7.8 cm. When the mass fraction further decreased to 30%, the diffusion distance exhibited a nonlinear growth, reaching 20.5, 28.0, and 34.0 cm, respectively. In this case, the maximum difference in the diffusion distance surged to 13.5 cm. Overall, the diffusion distance increased with both decreasing grout mass fraction and increasing particle size of the crushed rocks, with variations in grout mass fractions producing more significant impacts on the diffusion distance than changes in particle sizes of crushed rocks. The coal gangue-based grout experienced three flow stages in crushed rocks, i.e., rapid grouting, stable grouting, and blockage, which were prolonged with a decrease in the grout mass fraction. The diffusion distance of coal gangue-based grout in crushed rocks increased with a decrease in grout mass fraction. Furthermore, with an increase in the particle size of the crushed rocks, the grout mass fraction produced more significant impacts on the diffusion distance of coal gangue-based grout, as evinced by the nonlinear characteristics of the fitting coefficient (m). Through analyses of the impacts of both the particle size of crushed rocks and the grout mass fraction on the diffusion distance of grout, the basic relationship between the diffusion distance and mass fraction was determined. In combination with the basic relationship between the particle size and mass fraction, a dimensional analysis was further conducted. As a result, a dual-parameter equation for predicting grout diffusion distance that can be applied to coal gangue grouting filling in goaves was established. These findings were applied in the design of surface filling engineering in goaves via coal gangue grouting within a certain coal mine in northern Shaanxi, providing full-chain technical support for large-scale coal gangue grouting filling in goaves. The results of this study offer a valuable reference for the collaborative disposal of solid waste in mines. This will contribute to the achievement of the goals of peak carbon dioxide emissions and carbon neutrality.