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We present a rigorous homogenization approach to modelling piping ow erosion in a spatially heterogeneous soil. The aim is to provide a justication to a formal homogenization approach to piping ow erosion with deposition in a spatially heterogeneous soil. Under the assumption that the soil domain is perforated periodically with cylindrical repeating microstructure, we begin by proving that a solution to the proposed set of microscopic equations exist. Two-scale convergence is then used to studydoi:10.9734/jamcs/2020/v35i330256 fatcat:ko4oerhuebesvfsunkkaj2u6py