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

1 1 1 2 3
ZHANG Zhao ，CHENG Jingxuan ，LIU Fengyin ，QI Jilin ，XU Zengguang
（1. Institute of Geotechnical Engineering，Xi’an University of Technology，Xi’an 710048，China；
2. College of Civil and Transportation Engineering，
Beijing University of Civil Engineering and Architecture，Beijing 100044，China；
3. State Key Laboratory of Eco-hydraulics in Northwest Arid Region，Xi’an University of Technology，Xi’an 710048，China）

Abstract：Deformation of earth dams subjected to unsaturated seepage correlates with capillary cohesion be⁃
tween 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 ap⁃
proximation of the liquid bridge geometry between equal-sized wet particles，analytical expressions were de⁃
rived 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 （V * ≤1×10 ） and solid-liquid contact angles θ≤20°，
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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 vol⁃
umes， a curve-fitting expression of the rupture distance was also developed well-adapted for large liquid
bridge volume （V * ＞1×10 ） An improved fitting expression for the capillary force by the proposed expres⁃
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sion 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 （V * ≤0.13） as well as various parti⁃
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cle 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 draw⁃
down of water level.
Keywords：wet particulate material；capillary cohesion；liquid bridge tensile；capillary force

（责任编辑：耿庆斋）

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