In this work, the mathematical-numerical model of carbonation process in reinforced concrete (RC) structures, which has been developed by the authors, is applied to different cases of study to take into account the probabilistic nature of durability assessment procedure even if within the framework of a rough and ready approach. In particular, the aim of this Part I of the work is to study how the variability of the parameters defining the differential equations in the model influence the assessment of the corrosion initiation time of RC structure. Comparison with experimental results and numerical simulations are undertaken in Part II of this work.