Mining induced subsidence can significantly affect mining costs where major surface facilities and natural environment need to be protected. Overburden grout injection is a technology used to control coal mine subsidence by injecting the mine waste material extracted from the coal back into the inter-burden rock during longwall mining. The flowing slurry is here categorised as a nonlinear viscous cohesive (Bingham plastic) fluid. During longwall mining the grout slurry is pumped into the separated beds of the rock mass through a central vertical borehole, which is drilled deep into the inter-burden rock strata above the coal seam. However, a blockage can occur in the injection system when the slurry velocity falls below a certain critical threshold velocity, indicating a material phase change from cohesive-viscous to cohesive-frictional. In situ field injection tests through boreholes have been simulated at a smaller scale at the CSIRO laboratory in Brisbane by pumping the slurry through a radial disk (gap = 4 mm) from its centre. Laboratory experiments indicate a general, nonlinear, cohesive, viscous, frictional model for shear behaviour of the slurry, in which the material shear parameters are functions of the disk radial distance. Complete dimensional and dimensionless analytical solutions have been developed based on an approach related to Bingham-Herschel-Bulkley fluid mechanics. The derived formulae include relations for minimum pump pressure, local pressure and pressure gradient, wall shear stress, volume rate, velocity and velocity gradient. The theoretical results match the experimental measurements. The experiments covered slurries with maximum particle sizes of 0.5 to 2 mm with about 50% being larger than 100 μm. The viscosities at the various solids concentrations were measured with a standard torsion viscometer. This study differs from the previous research in several distinct aspects, namely, consideration of the variable shear parameters rather than fixed values, inclusion of total nonlinear behaviour, and implementation of a friction function to mimic behaviour of the deposited and consolidating stiff slurry, which can cause a significant pressure rise as a result of the increased shear resistance.