Spontaneous imbibition is a capillary-driven flow phenomenon that exists widely in nature and is important for several industries. Recently, Tolman length has been introduced to improve the classical Lucas-Washburn imbibition model, in order to alleviate the deviations in calculating the capillary pressure. However, imbibition experiments to measure Tolman length have been scarce. In addition, the fluid-wall friction has a considerable impact on the imbibition process, while it is often ignored. In this work, imbibition experiments under specific conditions are carried out to measure the values of Tolman length, and the fluid-wall friction is taken into consideration in the equilibrium equation. The water uptake model in fractures is adopted to make corrections to the rise of water level. The experimental results show that Tolman length decreases first and then rises with the increasing curvature radius of liquid-gas interface. The data reveal that the Tolman length-based model can better describe the real imbibition processes than the classical Lucas-Washburn model.

Water uptake in rock fractures caused by rainfall plays a significant role in slope stability analysis. Since the fracture network system has complicated structures and multiple scales, the models based on the averaged system cannot account for these properties. On the other hand, a model describing a single fracture with fractal characteristics and surface roughness fails to deal with the case of multiple fractures at spatial scales. In this study, a fracture-network model is established to account for the complex structures and multiple scales of fractures. By considering the connectivity between fractures and the limited area of aquifer, capillary pressure formulations in different fractures are derived based on the Young-Laplace equation, and the final water level under specific rainfall conditions is also obtained. The cross-section shapes and exhaust conditions of rainwater infiltration have important influences on the final water level. The results indicate that the final water level is proportional to the ratio of perimeter to cross-section area when the fracture is a cylinder, and a circular pipe can reduce water level elevation in the fracture system.