Entropy and Granular Materials: Experiments

Experiments on circular disks supported on a horizontal air table and enclosed in an initially square frame that provides simple shear, constant area, and constant pressure external conditions are reported. Each test was performed on disks of one size; disks of 2.54, 1.27, and 0.64 cm (1, 1/2, and 1/4 in.) diameter were used. The excitation of the system was caused by changing the angle of the frame either monotonically or side to side. The arrangements of the disks were photographed from above at various stages in each experiment. Twenty-one experiments were conducted in which the initial state of the disks, the disk size, the friction between the table and disks, and the external conditions were altered. The number of contacts for each disk was counted, and the frequency of occurrence of states with the same number of contacts was obtained. Similarly, the number of disks about each void was counted, and the frequency of each number was determined. These two counts allowed the contact and void entropies to be calculated. The presentation of these entropies showed that they approached limiting values as excitation increased and that the values depended on the external conditions and not on the friction condition. The behavior of the arrays was random and not chaotic. These results supported the use of information entropy in the geometric description of granular materials and the validity of Jaynes's maximum entropy procedures.