Prediction of Dielectric Constant of Polyurethane Grouting Materials Based on Fractal Characteristics

The microstructure of polyurethane (PU) grouting material is the key determinant of its macroscopic dielectric properties. In this study, based on its microscopic fractal characteristics and combined with effective medium theory and the Menger sponge structure, an n-stage fractal dielectric model was constructed. This model correlates the material’s dielectric response with its fractal dimension and porosity. The fractal dimensions of PU specimens with densities ranging from 0.29734 g/cm3 to 0.41817 g/cm3 were calculated using the box-counting method. Within this density range, the fractal dimension of the PU specimens showed no significant variation, with a calculated value of approximately 2.7355. By approximating the microscopic unit as an n-stage fractal cube based on the Menger sponge structure and incorporating series-parallel dielectric models, an analytical expression for the dielectric constant was derived. A comparison with experimental data shows that the model’s predictions are in good agreement with the measured values, with a mean relative error (MRE) of only 4%.