Fractal-based model for maximum penetration distance of grout slurry flowing through soils with different dry densities

Existing penetration models for grouting slurry seldomly consider the relationship between dry density and complexity of soil. A novel penetration model, in which the complexity of the flow path in soil was described by fractal theory, has been proposed for quantifying the maximum penetration distance of grout slurry flowing through soils with different dry densities. The relationship among dry density, fractal dimension and fractal tortuosity of flow path was identified by SEM analysis, showing that fractal tortuosity increases but fractal dimension is almost unchanged with increase of dry density. The results calculated by the penetration model were validated against experimental results for different soils under various pump pressures and volume flow rates. The analysis results show that the grout slurry tends to penetrate to a long distance under high pump pressure, low flow rate, low consistency factor and low fluidity index. High dry density and small average particle size of soil reduce the penetration distance. The proposed model is helpful to achieve a better design in soil ground stabilization via grouting.