The classical sediment transport models based on shallow water equations (SWE) describes the hydro-morphodynamic process without horizontal velocity shear along the vertical and considers that the fluid velocity is equal to sediment velocity. The classical shear shallow water (SSW) with friction and topography source terms assumes that the fluid density is uniform in all the space. Nevertheless, for the coastal flows with sediment transport we are interested in it seems essential to consider these shear effects, the phase lag effect and the nonhomogenous ness of fluid density. In this paper, we develop new sediment transport models incorporating the shear velocity along the vertical, the phase lag effect and the spatial variation of the fluid density. The starting point is the 2D equations for the evolution of mixing quantities and sediment volume rate. These equations describe the motion of fluid mixing in a domain bounded by a dynamical water surface and water bed. Contrary to the classical sediment transport models, the second-order vertical fluctuations of the horizontal velocity are considered. Considering the kinematic conditions on the moving surfaces, we apply an average along the depth on the three-dimensional equations to obtain simplified equations. The resulting model has a wider range of validity and integrates the morphodynamic processes proposed in the literature. The proposed mathematical derivation is in the context of recent developments with the additional presence of sediment and a dynamic bed.