The main objective of this talk is to present some geophysical applications that can be studied with two-layer or two-phase shallow models. Namely, applications on avalanches and sediment transport problems. Firstly, several models will be presented, by studying the relations between them. Actually, all the models considered in this talk include a source term corresponding to a Coulomb friction law. One of the difficulties of this term is that it is multi-evaluated for the case of a material at rest. The second part of the presentation focus on an unified formulation to approximate numerically these models, taking into account the difficulty introduced by multi-evaluated source terms.
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