考虑颗粒粒径和液桥体积的毛细力计算方法  

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

作　　者：张昭[1] 程靖轩 刘奉银[1] 齐吉琳 许增光[3] ZHANG Zhao;CHENG Jingxuan;LIU Fengyin;QI Jilin;XU Zengguang(Institute of Geotechnical Engineering,Xi’an University of Technology,Xi’an 710048,China;College of Civil and Transportation Engineering,Beijing University of Civil Engineering and Architecture,Beijing 100044,China;State Key Laboratory of Eco-hydraulics in Northwest Arid Region,Xi’an University of Technology,Xi’an 710048,China)

机构地区：[1]西安理工大学岩土工程研究所,陕西西安710048 [2]北京建筑大学土木与交通工程学院,北京100044 [3]西安理工大学省部共建西北旱区生态水利国家重点实验室,陕西西安710048

出　　处：《水利学报》2021年第4期442-460,共19页Journal of Hydraulic Engineering

基　　金：国家自然科学基金项目(41877278,51679198,51922088);国家留学基金项目(201908610043);陕西省教育厅重点实验室科研计划项目(18JS71);西安理工大学省部共建西北旱区生态水利国家重点实验室项目(QNZX-2019-07,2019KJCXTD-12)。

摘　　要：土坝在非饱和渗流作用下的变形过程与湿颗粒间的细观毛细黏聚作用密切相关,因此对湿颗粒间形如液桥的水分的毛细力进行计算分析有助于认识这种作用机理。从颗粒粒径和液桥体积出发,将湿颗粒简化为不等径球体颗粒,先结合其间液桥的几何特征构建了Young-Laplace方程数值解的数据组。其次,将固-液接触角θ≤20°范围内的小体积液桥(V^(*)_(LB)≤1×10^(-3))表面形状假定为椭圆弧,依据颗粒等效半径推得液桥断裂距离及其毛细力关于液桥体积和颗粒间距的解析公式,并采用已有文献中不等径球体颗粒间小体积液桥的毛细力实测值验证了解析公式的有效性。再次,依据液桥体积变化更广范围内Young-Laplace方程数值解的数据组,引入颗粒半径比构建了适用于大体积液桥(V^(*)_(LB)>1×10^(-3))的断裂距离拟合公式,并将其嵌入已有不等径湿颗粒间液桥的毛细力拟合公式中进行改进。最后,采用Young-Laplace方程数值解的数据组评价了已有的与改进的毛细力拟合公式适用性,通过对比预测误差发现:改进公式对半径比在1~128范围内的湿颗粒间不同体积液桥(V^(*)_(LB)≤0.13)在固-液接触角θ≤40°且颗粒间距不超过液桥断裂距离范围内的毛细力预测效果优于已有公式。将本文提出的毛细力计算方法嵌入典型湿颗粒材料的微细观弹塑性本构模型时,可用于水位骤降时土坝的变形分析及其稳定性评价。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^(*)_(LB)≤1×10^(-3))and solid-liquid contact anglesθ≤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 vol⁃umes,a curve-fitting expression of the rupture distance was also developed well-adapted for large liquid bridge volume(V^(*)_(LB)>1×10^(-3)).An improved fitting expression for the capillary force by the proposed expres⁃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^(*)_(LB)≤0.13)as well as various parti⁃cle radius ratios in the range of 1~128,solid-liquid contact anglesθ≤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.

关 键 词：湿颗粒材料 毛细黏聚 液桥拉伸 毛细力 

分 类 号：TU43[建筑科学—岩土工程]