Quantitative Relationship Between Strength and Porosity of Nano-Silica-Modified Mortar Based on Fractal Theory

Nano-silica (NS) is an ideal modifier for mortar materials, and exploring the evolution of the fractal dimension of the pore structure in NS-modified mortar is crucial for elucidating the mechanism by which NS enhances mortar strength. In this study, NS reinforced mortar was prepared using an NS sol solution, which inhibited the aggregation of NS particles. The relationship between the strength and pore structure of NS-modified mortar was quantitatively analyzed based on fractal dimension theory and gray correlation degree. The experimental system evaluated the mortar strength, pore structure distribution, and micro-morphology. Based on this evaluation, the fractal dimension of the mortar pore volume was calculated in detail. Subsequently, models for mortar strength and NS content were further established using grey analysis. The results indicate that NS significantly enhances the strength of mortar while also increasing its porosity due to reduced fluidity. NS can improve the compressive strength of mortar by up to 35%. The curve fitting of volume fractal dimension and box dimension is effective and can accurately reflect the complexity of the pore structure. The calculation of the grey correlation analysis model shows that the impact of varying silica content on the mechanical properties of mortar specimens is not linear; the distribution and quantity of bubbles are the main factors affecting the strength of the specimen.