A calculation method for capillary force considering particle size and liquid bridge volume

Deformation of earth dams subjected to unsaturated seepage correlates with capillary cohesion between wet particles. The calculation of capillary force for water in the form of liquid bridge between wet particles has contributed to recognize mechanism of capillary cohesion. From particle size and liquid bridge volume, wet particles can be simplified unequal-sized sphere particles. A dataset of numerical solutions to the Young-Laplace equation was firstly obtained according to liquid bridge geometry. Based on ellipses approximation of the liquid bridge geometry between equal-sized wet particles, analytical expressions were derived by the use of the equivalent radius for the rupture distance and the capillary force in terms of liquid volume and separation distance for small volumes (VLB *≤1×10-3) and solid-liquid contact angles θ ≤20°, which is also verified using the published test data of capillary force for small liquid bridge volume. Based on the dataset of numerical solutions of the Young-Laplace equation for a wide range of liquid bridge volumes, a curve-fitting expression of the rupture distance was also developed well-adapted for large liquid bridge volume (VLB *> 1×10-3). An improved fitting expression for the capillary force by the proposed expression was finally validated against the dataset of numerical solutions. The results of deviations show that it is superior to other previous expressions for a wide range of volume (VLB*≤0.13) as well as various particle radius ratios in the range of 1~128, solid-liquid contact angles θ≤40° and separation distances before rupture. The proposed calculation method can be embedded in micro-structural elastic-plastic model for the typical wet particulate materials to analyze the deformation and stability of earth dams during rapid drawdown of water level. © 2021, China Water Power Press. All right reserved.