Entropy in the phenomenon of granular media displacement

Abstract

The displacements of a loose medium in the gravitational field are discussed regarding it as a discrete medium. For the given boundary conditions the elements of this medium may form various configurations in the course of the displacements Boltzmann's concept of entropy has been adopted in the form of a functional depending on the density function of the medium elements in the configurations that are being formed. For the boundary conditions assumed in the form of the so-called Dirac's function the maximum value of entropy has been determined which corresponds to the greatest probability of the occurrence of configurations of the elements forming the discrete medium. It can be found that the density function satisfying this condition has the form of Gauss function. The measurements of displacements of a loose medium confirm this result. These displacements satisfy Boltzmann's universal principle according to which during the displacements of a loose medium there are formed configurations in which the entropy attains its maximum value. This accounts for the wide application of Oauss function as the so-called fundamental solution in the integral formulae describing the displacements of the carth's crust in regions where it underwent destruction as a result of underground mining exploitation.