黏土片与球状颗粒间范德华作用的简便计算方法
An easy method to calculate van der Waals interaction between clay plate and spherical particle
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摘要: 黏粒(黏土片)与非塑性粉粒间相互作用是控制粉质黏土/黏质粉土这一大类土体力学特性的关键因素之一,范德华力是两种颗粒间最主要的相互作用形式,也是饱和土真黏聚力的来源。然而,在土体宏微观关联理论分析、离散元模拟等研究中尚难以得到该力的解析解。为此,提出一种简便计算方法,其基本思想是将粉粒视为球体,将黏土片视为由规则排列的基本立方体构成,将问题转变为可实现的基本立方体与球状颗粒间的范德华作用求解。首先采用蒙特卡罗模拟,计算得到不同空间排列方式下基本立方体与球状颗粒间范德华作用力;随后,训练一个三层人工神经网络模型用于高精度拟合范德华力与两种颗粒空间关系参数的函数关系;最后采用叠加法即可简便求得黏土片与球状颗粒间范德华作用的合力与合力矩。结果表明,提出的简便计算方法准确性高、计算速度快,且拟合的模型参数适用于黏土片与土体中大于1
的球状颗粒间范德华作用计算。 Abstract: The interaction between clay plate and non-plastic silty particle is one of the key factors determining the mechanical behavior of silty clay and clayey silt, which form a major category of soil in geotechnical engineering. The van der Waals force is the most important interaction between clay plate and non-plastic silty particle, which is also the origin of true cohesion in saturated clay. However, it is extremely difficult to obtain the analytical solution for this force to be applied in micro-macro cross-scale correlation and discrete element method simulation of soil. An easy method is proposed in this study for this purpose. The basic idea is to view the non-plastic silty particle as the spherical particle and to divide the cubic clay plate into basic cubes. Then, the problem is simplified to obtain the van der Waals interaction between the basic cube and the spherical particle, which can be solved in the following way. First, the Monte Carlo simulation is used to collect the data of van der Waals interaction of the basic cube and the sphere with a wide range of relative position. Then, an artificial neuro network was trained to fit the function between the van der Waals force and the relative position of the two objects with high accuracy. Finally, the total force and torque applied on the clay plate are summed up over all the basic cubes constituting the clay plate. It is found that the proposed easy method has strength in both accuracy and efficiency. The model-fitting parameters can be used to calculate the van der Waals interaction between the clay plate and the spherical particle with a diameter greater than 1 m.