Hierarchical meta-modelling for fast prediction of the elastic properties of stone injected with CNT/cement mortar

This paper presents an innovative hierarchical meta-modelling approach for predicting the effective elastic properties of stone injected with composite cement grouts containing Carbon NanoTubes (CNTs) for structural rehabilitation purposes. The study first addresses the homogenization of the nano- and micro-scales through numerical representative volume elements. The first numerical model focuses on the cement matrix doped with randomly oriented CNTs, while the second model represents the porous stone with CNT/cement grout filling the pores. However, the computational burden associated with these models poses a significant limitation when analysing large-scale macrostructural elements. To overcome this challenge, a hierarchical meta-modelling approach based on two nested Kriging surrogate models is proposed. This approach offers a fast and accurate alternative to bypass the time-consuming numerical homogenization process. The first surrogate model establishes a connection between the microstructural characteristics of the CNTs and cement and the effective elastic properties of the composite grout. Subsequently, a second meta-model expands over the first one by introducing two additional variables: the elastic modulus of the stone and the porosity, allowing for estimation of the overall elastic properties of CNT/cement/stone composites. The accuracy and efficiency of the proposed hierarchical meta-model is demonstrated through detailed parametric analyses. To showcase its potential for optimizing rehabilitation interventions, the paper is closed with its application to a benchmark case study of a stone column injected with CNT/cement grout. •Composite CNT/cement grouts are investigated for the first in the literature.•A novel nested surrogate modelling approach is proposed for multi-scale composites.•Fast stiffness estimates of porous stone injected with CNT/cement grout are obtained.•The proposed approach is used to assess the performance of grout injected columns.