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This paper is concerned with extending the stratigraphic model previously introduced by Eymard et al. (Int. J. Numer. Methods Eng. 60(2):527–548 2004) and subsequently studied by Gervais and her coauthors for the simulation of large-scale transport processes of sediments, subject to an erosion constraint. Two major novelties are considered: (i) the diffusion law relating the flux of sediments and the slope of the topography is now nonlinear and involves a p-Laplacian with p > 2 in order for landscape evolutions to be more realistic; (ii) the sediment transport is now intertwined with the water flows due to lakes and rivers via a direct coupling at the continuous PDE level, which avoids empirical algorithms at the discrete level such as MFD (multiple flow directions) at the price of additional p-Laplacians. Aimed at enriching the capabilities of IFPEN's simulator, these sophistications entail the construction of a new finite volume scheme, the details of which are supplied. The physical model is validated through several test cases. Finally, a further extension of the model to the case of multiple lithologies is presented, along with numerical results. [ABSTRACT FROM AUTHOR]