Entropy and granular materials: Experiments

Experiments on circular disks supported on a horizontal air table and enclo sed in an initially square frame that provides simple shear, constant area, and constant pressure external conditions are reported. Each test was perf ormed 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 chan ging the angle of the frame either monotonically or side to side. The arran gements of the disks were photographed from above at various stages in each experiment. Twenty-one experiments were conducted in which the initial sta te of the disks, the disk size, the friction between the table and disks, a nd the external conditions were altered. The number of contacts for each di sk was counted, and the frequency of occurrence of states with the same num ber of contacts was obtained. Similarly, the number of disks about each voi d was counted, and the frequency of each number was determined. These two c ounts allowed the contact and void entropies to be calculated. The presenta tion of these entropies showed that they approached limiting values as exci tation increased and that the values depended on the external conditions an d 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 ma ximum entropy procedures.