An easy method to calculate van der Waals interaction between clay plate and spherical particle

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.