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A large part of Ghana’s population reside in locations that are prone to flooding. A regular method of protection against radical floods is the adoption of flood defence systems. Collapse of flood defence are due to in- adequate height and inadequate strength of the defence system. The later is attributed to an internal process termed piping which mostly takes place in hydraulics structures. In this study a model is developed to simulate the piping erosion phenomena with deposition in a heterogeneous periodi- cally perforated soil. Flow diversion phenomena due to deposition of fines in the pore spaces was also included in the modelling process. Because it is an extremely difficult problem to study the properties of a micro non- homogeneous medium, the problem was attacked by applying asymptotic analysis which immediately leads to the concept of homogenization and two scale convergence. The asymptotic behaviour of the solutions to the micro problem was studied and a homogenized model with effective co- efficients void of oscillations called macro problem capable of simulating the piping flow erosion phenomena with deposition in a spatially hetero- geneous soil was derived. A strong observation from the numerical sim- ulations performed was that soil particle concentration in the water/soil mixture decreases but at a decreasing rate. Also soil particle deposition increases at regions with increasing amount of particle concentration in the flow which in turn causes a reduction in bare pore spaces across the soil domain with higher observations towards the outflow region in the soil domain. The increase in the deposition process becomes slower with time.