Grouting Mechanism of Weathered Sandstone Based on Fractal Theory

Water-rich weathered sandstones of tunnel, water conservancy, mining, and other engineering constructions, being exposed to water, are highly porous, strongly permeable, and have well-developed fissures posing significant safety threats during construction. Emphasizing the disorder and random uncertainty characteristics of sandstone fractures, this study explores the relationship between hydraulic conductivity and fractal dimension of sandstone based on fractal theory. Subsequently, considering the injectability of particulate slurry in fractures, a fractal model for cement dosage in grouting weathered sandstone is established. The study reveals cement dosage variations with fractal dimensions under one-dimensional and two-dimensional flow conditions. Three physically meaningful grouting zones namely the “hydraulic fracturing zone,” the “normal grouting zone,” and the “microfine fracturing zone” are defined based on the relationship curve between cement dosage and hydraulic conductivity. The field verification by data from the Qingdao metro project indicated that the measured data aligns with the theoretical patterns proposed in this study. The results indicate that the established relationship between hydraulic conductivity and cement dosage, and the defined grouting zones, are accurate and can be used to streamline engineering projects, involving weathered sandstone.