Calculation of rising height of capillary water based on fractal model for grain-size distribution

The rising of capillary water, which is driven due to the pressure difference at both sides of the meniscus caused by surface tension, causes the phenomenon of mud boiling and mud seepage in the silt roadbed. The rising height of the capillary water is the key to preventing and controlling the mud boiling and mud seepage in the roadbed. A method for calculating the rising height of the capillary water based on the grain-size distribution is proposed, which overcomes the test defects in measuring the height of the capillary water. By using the sieving tests to calculated the grain-size distribution and fractal of silt, a fractal model is established to analyze the effects of the fractal dimension, air-entry value, porosity, the maximum rising height of the capillary water and saturated permeability coefficient on the rising height and velocity of the capillary water. The calculated results show that the rising height of the capillary water is positively correlated with the time as a power function, increases with the fractal dimension, air-entry value, the maximum rising height of the capillary water and saturated permeability coefficient, and decreases with the porosity. The rising speed of the capillary water is only related to the fractal dimension of the grain-size distribution and increases with the increase of the fractal dimension of the grain-size distribution but not related to the porosity, air-entry value and the saturated permeability coefficient.