A model of capillary water rise based on fractal theory and experimental validation

As to the roadbed projects in coastal areas, capillary water rise can produce roadbed diseases and affect the safety and durability of road operation. It is important to study the capillary water rise height. The article regards capillary water rise as a kind of unsaturated soil seepage phenomenon, and introduces fractal dimension to unsaturated soil permeability coefficient modification. A capillary water rise height model based on fractal theory is proposed to obtain the capillary water rise height curve with time. Then a vertical tube method capillary water rise height test was conducted on a mainline roadbed soil sample in Nantong, with the control test of changes in the dry density of the soil sample and the fractal dimension of the initial particle size distribution. The results show that: the capillary water rise presents a rapid increase at the beginning, and then slowly increases, and finally stabilizes. The larger the fractal dimension of the particle size distribution of soil sample, the greater the capillary water rise height; the smaller the dry density of the soil sample, that is, the greater the porosity, the greater the capillary water rise height. In the capillary water rise height model, the capillary water rise height is related to the sample porosity, saturated permeability coefficient, capillary water rise height corresponding to the inlet value, fractal dimension, etc. In the theoretical model, the variation of fractal dimension only changes the capillary water height corresponding to the inlet value, not the saturated permeability coefficient; while the dry density change, i.e., the porosity change, only leads to the saturated permeability coefficient change, does not affect the intake value corresponding to the height of capillary water, the results from theoretical model are consistent with those from the test, verifying the effectiveness of the theoretical model. This study provides theoretical guidance for the prevention and control of road-base capillary water disease.