Particle Model Methods for Stress Analysis of Soil (I)

On Static Particle Model System and Numerical Analysis

Abstract

The purpose of this study is to develop the method for stress analysis of the material as soil, by which we are able to previously calculate the performance for traction or cultivation of field machinery.
This paper introduces the static particle model system defined by 5 conditions, which is one of the idealizations of microscopic mechanical structure of the material as soil.
The numerical method for stress analysis of this model system is developed. This method is in the category of Finite Element Method, if FEM is interpreted in a broad sense. However, it has the following advantages in comparison to the FEM in a narrow sense.
(a) This method is easily applied to the problems including material non-linearity, geometrical noninearity, or plasticity.
(b) It is easily applied to the problems generating cracks.
(c) It is easily applicable, by easy extension, to the dynamic pobleme including (a) and (b).
Alternatively, this method has a weak point that it is difficult to know the correspondence of model system to a real system. This system is nonlinear and non-conservative, therefore we can hardly find the correspondence analytically. We must rely on numerical evidences to find the model to real correspondence.
A numerical evidence equivalent to a uniaxial compression test is tried in this paper. The model used has simple and regular arrangement of particles as shown in Fig. 4. Consequently, the following results are obtained in the macroscopic mechanical character of the model system.
(1) Several yielding points are found on the curve of axial force vs. axial strain.
(2) A hysteresis phenomenon appears on the curve.
From these results, it can be estimated that the relationship of axial force vs. axial strain as in Fig. 8. is obtained, if the system contains many enough particles, and the values of C_i are scattered.