In recent years, a multiphysics model that represents the complex physical phenomena that influence the accumulation of rust in the storage tunnels (alveoli) has been numerically implemented in the finite element method (FEM) software Cast3M. Seeking to estimate the thermo-hygro-corrosive properties of the alveoli at long time scales, recent (and ongoing) works on improving the execution time of the resolution algorithm were undertaken. However, for a FEM numerical model to be considered as a rigorous engineering/scientific tool, error bars must be associated to all computational results; therefore, the careful quantification of the plethora of modeling uncertainties is primordial. To undertake such an endeavor, multiple issues must first be tackled, begininning with an improvement of the physical representativity of the multiphysics model, following with an improvement of the computational performance of the numerical model, and ending with rigorous sensitivity studies of the implemented model. Work on computational performance is necessary, so as to render program execution fast enough to ensure that the large sets of numerical experiments required run in reasonable times.