In this study, 2D and 3D numerical models based on the Smoothed Particle Hydrodynamics (SPH) approach have been developed to simulate turbulent open channel flows over a fixed rough bed. Both models were then used to simulate free surface turbulent flow over a rough boundary, including the free surface dynamic behaviour. The numerical code is based on the open source code SPHysics (http://www.sphysics.org) and during this study significant improvements have been made to this code on the modelling of turbulence and rough bed treatment. A modified sub-particle-scale (SPS) eddy viscosity model is proposed to reflect the turbulence transfer mechanisms and drag force equations are included into the momentum equations to account for the existence of roughness elements on the bed and on sidewalls. The computed results of flow velocity, shear stress and free surface elevations have been compared with detailed laboratory measurements under different flow conditions. The comparison has demonstrated that the modified SPH models can accurately simulate the free surface flows over a fixed rough bed. It was found that the modified 3D model is more accurate than the modified 2D model in predicting the flow velocity, shear stress profiles and the dynamic behaviour of the free surface. The capabilities and limitations of each model to simulate such free surface flow are highlighted and discussed.