Solid-liquid suspension flows are widely encountered in industrial applications. In many of these flows, the carrier fluid exhibits shear-thinning behaviour and the solids have a broad size distribution. Shear-thinning suspensions can occur in laminar or weakly turbulent regimes due to their high viscosity. This paper presents a DNS-DEM model for weakly turbulent coarse-particle suspension flows. Although our interest is in shear-thinning suspensions, we aim firstly to develop a liquid-solid model in a Newtonian fluid to remove the uncertainty in particle-fluid interaction in non-Newtonian suspensions. Matching experiments were conducted for validation. The predicted mixture velocity and concentration profiles are in good agreement with experiments, and discrepancies are mostly less than 10%. The mean velocity profiles are significantly damped by coarse particles and particle phase generally exhibits a higher fluctuation. This DNS-DEM modelling approach is viable for simulating these flows and will form the basis of future work on shear-thinning suspension flow. (C) 2020 Elsevier B.V. All rights reserved.