The paper presents numerical simulations of particle-laden fully developed turbulent channel flows performed in a stochastic Lagrangian framework. The particle inertia is large in order to neglect the effect of the turbulent gas motion on the particle dispersion. In contrast the inter-particle collisions are important and accounted for by using Direct Simulation Monte-Carlo (DSMC) method. The comparison of the Monte-Carlo results with those obtained by Discrete Particle Simulation (DPS) shows that the stochastic collisions algorithm is able to predict accurately the particle statistics (number density, mean velocity, second- and third-order velocity moments) in the core flow. More, the paper analyses the number sections needed for accurate predictions. In the very near-wall region, the Monte-Carlo simulation fails to account for the wall shelter effect due to the wall-normal unbalanced inter-particle collisions influence induced by the presence of the wall. Then, the paper shows that DSMC permits to assess the closure approximations required in moment approach. In particular, the DSMC results are compared with the corresponding moment closure assumptions for the third-order correlations of particle velocity, the correlations between the drag force and the velocity and the inter-particle collision terms. It is shown that at the opposite of the standard DSMC, the moment approach can predict the wall shelter effect. Finally, a model for the mean transverse force is proposed for taking into account wall shelter effect in DSMC. (C) 2018 Elsevier Ltd. All rights reserved.