The paper concerns simulation of fully developed and axially-symmetrical turbulent flow of coarse-dispersive slurry if all solid particles have similar size and shape with particles diameter from 1 mm to 5 mm, solid density from 1045 kg/m^3 to 3000 kg/m^3, and solid concentration by volume from 20% to 40%. The author examines the influence of particle diameter on additional shear stress due to the ‘particles-wall’ interactions for moderate and high solid concentration. The mathematical model was developed using Bagnold's concept,  and assumes that the total wall shear stresses are equal to the sum of ‘liquid-wall’ and ‘particles-wall’ shear stresses. The mathematical model was successfully verified with own measurements of frictional head loss in vertical coarse - dispersive slurry flow, named: ‘sand-water’, ‘polystyrene-water’ and ‘pvc-water’, , . The mathematical model can predict ‘particles-wall’ shear stress, pressure drop and friction factor for coarse-dispersive turbulent slurry flow in a pipe, . The aim of the paper is to present qualitative and quantitative dependence of solid particle diameter, solid particle density, solid concentration, and Reynolds number for carrier liquid phase on the ‘particles-wall’ shear stress. It is demonstrated that the solid particle diameter plays crucial role in its dependence on the ‘particles-wall’ shear stress. It was proved that in particular flow conditions the ‘particles-wall’ shear stress is much higher compared to the carrier liquid wall shear stress.