In this paper, supplementary cementitious materials are used as a substitute for cement to decrease carbon dioxide emissions. A by-product of the iron manufacturing industry, ground granulated blast-furnace slag (GGBS), known to improve some performance characteristics of concrete, is used as an effective cement replacement to manufacture mortar samples. Here, the influence of curing conditions on the durability of samples including various amounts of GGBS is investigated experimentally and numerically. Twelve high-strength Portland cement CEM I 52.5 N samples were prepared, in which 0%, 45%, 60%, and 80% of cement were substituted by GGBS. In addition, three curing conditions (standard, dry, and cold curing) were applied to the samples. Durability aspects were studied through porosity, permeability, and water absorption. Experimental results indicate that samples cured in standard conditions gave the best performance in comparison to other curing conditions. Furthermore, samples incorporating $45\%$ of GGBS have superior durability properties. Permeability and water absorption were improved by $17\%$ and $18\%$, respectively, compared to the reference sample. Thereafter, data from capillary suction experiments were used to numerically determine the hydraulic properties based on a Bayesian inversion approach, namely the Markov Chain Monte Carlo method. Finally, the developed numerical model accurately estimates the hydraulic characteristics of mortar samples and greatly matches the measured water inflow over time through the samples.