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Classical theories for two-body abrasion have been applied in a new numerical simulation model. The statistical approach preserves the simplicity of the classical model but increases its versatility by treating the case of multiple abrasive groovings in a surface of realistic topography created by this abrasion. The influence of grit size, load and workpiece hardness on wear rate, specific energy, number of contacting particles and wear surface topography, are predicted. The validity of the model is demonstrated by extensive comparisons with the experimental results of other investigators. The statistical nature of the model is expected to increase the general understanding of abrasive wear and grinding by, for example, providing a basis for separation of geometrical and materials parameters.