The final publication is available at Springer via http://dx.doi.org/10.1007/s00603-020-02142-y This paper addresses the problem of the stability of structures on calcareous rocks due to long-term weathering processes. The case study consists of a building resting on a calcarenite rock formation where two abandoned man-made caves exist directly under the structure. The boundaries of the caves were exposed to a slightly acidic environment inducing time-dependent weathering. Analyses were performed following a semi-decoupled approach, where the weathering process, driven by a reactive transport mechanism, was first solved and its results were fed to the mechanical problem which hence accounted for the spatial and temporal evolution or rock damage. For the mechanical problem, a nonlocal constitutive model was employed for the objective simulation of localised deformations. Relevant outcomes are obtained regarding the evolution of the structure’s stability and about the importance of regularising the finite element solution in the presence of brittle materials. Peer Reviewed