This work starts from the hypothesis that spatial dynamics and the functions (cover or use) of geographical objects could be, partly, explained or anticipated by the history of their functions and colocalizations changes. Hence, an approach relying on association rules mining for the extraction of explicative/predictive models of territorial evolution is proposed. In order to deal with the asymmetry of the used learning data, we proposed to adapt the supports assignment process for the MSApriori and we also proposed a new multiple minimum support based algorithm called BERA. Applied on study cases from the Corine Land Cover database between 1990 and 2012, the proposed mining methods proved their worth in the management of data imbalance and the generated rules highlight realistic urban dynamics.