A Distinct Element Modeling with Spring Parameters-Elastic Constants Relation and its Numerical Application

When applying numerical techniques to problems of deformation of rocks, the body to be analyzed is divided into small portions and is represented by a system of points linked together with the neighboring points. In the so-called distinct element modeling, the particles in the system are directly connected by springs and a contact law is used to specify forces on the particles to simulate the mechanical behavior of the body. The relation between the spring stiffness and commonly measured material properties, such as the Young’s modulus and the Poisson’s ratio, should be known a priori. For the general case of a random packing of particles, the relation is found by means of a process in which a system of particles and set of parameters are prepared to simulate a set of specimen-size test and then the input parameters are chosen to match the measured material properties. The validity of the numerical result is only demonstrated by comparison model behaviors with the measured responses. The process includes trial-and-error manner, therefore, no model is complete to reproduce the mechanical properties. In this paper, a relation between the spring stiffness and the elastic constants; the Young’s modulus and the Poisson’s ratio, is introduced to a three-dimensional distinct lattice spring method. Two simple numerical examples will be presented to demonstrate the performance of the method with the procedure for the determination of the spring stiffness.