粗颗粒间液桥毛细力演化规律的动态计算方法

水力特性是非饱和土力学理论与工程的重要课题之一，土样水力特性的变化过程本质上可反映为土颗粒间毛细力的演化规律。为此，以粗颗粒为研究对象，将其简化为一对不等径球体颗粒，而其间的水分形态可视为形如圆环的液桥，不考虑颗粒重力和浮力的影响。以Young-Laplace方程为基础，先推得计算液桥毛细力的控制方程组，再结合液桥的无量纲体积最大、最小值及其外曲率半径的割线迭代算法提出求解毛细力的动态计算方法，进而研究毛细力与颗粒间距、颗粒半径比和液桥体积的无量纲关系，结果表明：当颗粒间距一定时，液桥的毛细力随其体积和颗粒半径比增大均呈递增趋势；当液桥体积一定时，其抗拉刚度随颗粒间距增大呈递减趋势。最后，利用已有文献中液桥毛细力与颗粒间距的实测关系，验证了该动态计算方法在表征液桥从形成至断裂时毛细力演化规律的有效性。

A dynamic calculation method for evolution law of capillarity forces of liquid bridge between coarse particles

Hydraulic behavior plays a significant role in unsaturated soil mechanics. The changing process in this behavior of the soil specimen can be essentially reflected as the evolution of capillary forces for the liquid bridge between soil particles. Focused on coarse particles, they can be simplified as a pair of uneven-sized sphere particles, water form between the particles can be characterized by annular liquid bridge. The effects of gravity and buoyancy on particles will be neglected. Based on Young-Laplace equation, governing equations are first derived to calculate capillary forces for the liquid bridge. A dynamic calculation method is then proposed by taking into account the maximum and minimum dimensionless volumes and the secant iterative procedure for the calculation of the external radius of curvature for the liquid bridge, so as to study the evolution of capillarity forces with inter-particle spacing, ratio of particle radius, and liquid bridge volume. It can be observed that the capillary force increases as the liquid bridge volume and ratio of particle radius increase with a fixed inter-particle separation; the tensile stiffness is a decreasing function of the inter-particle separation with a fixed liquid bridge volume. Finally, this dynamic calculation method is validated against the published test data of capillary forces versus inter-particle separation in the process from liquid bridge formation to rupture.