A combined data-driven, experimental and modelling approach for assessing the optimal composition of impregnation products for cementitious materials

The effectiveness of sol-gel based treatments for the protection of concrete depends on their capacity to penetrate into the material pores. Optimization of sol formulation to achieve maximum penetration depth is not a straightforward process, as the influence of different physical properties of the sol varies with the pore size distribution of each concrete. Thus, a comprehensive experimental programme to evaluate this large number of materials would require a significant number of experiments. This manuscript describes an approach, using combined computational and experimental approach to design tailor-made impregnation products with optimized penetration depth on concrete or cementitious materials with different pore size distributions. First, a process-based numerical model, calibrated experimentally for one sol composition and several cementitious material samples with different pore structures is developed. The model calculates the penetration depth for a specific pore structure. The optimization process utilizes the probabilistic and non-parametric Gaussian Processes regression method Gaussian Processes at two steps; first to make the choice of the optimal experimental design, and second to make predictions of physical properties based on the obtained training points. In the final step, the penetration depth is calculated for each mix combination in defined parameter range. The effectiveness of this approach is demonstrated on three cases. In the first instance, we optimized the impregnation product for the maximum penetration depth without any restrictions. With another two cases, we impose the restrictions on the gelation time, i.e. the time in which the sol reacts to gel. The validation of the procedure has been made by the use of a blind validation and shows promising results. The impregnation product penetrated significantly deeper with a product selected by using the described procedure compared to the considered best product before this optimization. The proposed procedure can be applied to a wide range of cementitious materials based on their pore size distribution data. This offers significant advantage compared to purely experimental approaches, where a set of experiments is required for each considered material.