Effective mechanical properties of eco-concretes reinforced with bio-sourced calcium carbonate nanoparticles: Free vibration analysis of simply supported slabs

Bio-sourced calcium carbonate-rich wastes, such as eggshells, fish bones, animal bones, and snail shells, represent promising raw materials for producing calcium carbonate nanoparticles after suitable processing, such as grinding, calcination, or chemical precipitation. In this study, the effective mechanical properties and free vibration response of simply supported eco-concrete slabs reinforced with bio-sourced calcium carbonate nanoparticles are investigated. The effective elastic properties of the concrete composite are evaluated using the Hashin–Shtrikman homogenization model for a two-phase isotropic system composed of concrete as the matrix and nano-CaCO₃ particles as the reinforcement. Reinforcement volume fractions of 10% and 20% are considered. The free vibration behavior of the reinforced slabs is then analyzed using First-Order Shear Deformation Theory (FSDT) and Higher-Order Shear Deformation Theory (HSDT). The governing equations are derived using the principle of virtual work, and Navier’s analytical solution is adopted to satisfy the simply supported boundary conditions. The obtained results show that the addition of nano-CaCO₃ improves the effective stiffness of concrete. The Young’s modulus increases from 20 GPa for ordinary concrete to 22.81 GPa and 25.88 GPa for 10% and 20% nano-CaCO₃ reinforcement, respectively. The fundamental dimensionless frequency of the square slab increases from 0.0921 for ordinary concrete to 0.1277 and 0.1287 for 10% and 20% nano-CaCO₃, respectively. These results indicate that 10% nano-CaCO₃ provides a significant improvement in stiffness and vibration performance, while the additional gain beyond this fraction remains limited. The HSDT formulation shows better agreement with reference results than FSDT and is therefore adopted for the parametric analysis.