ABSTRACT
A simple conjecture, which provides a fundamental principle for the study of both fluctuations and propagation of forces, has been put forward by Edwards years ago (Edwards & Oakeshott 1989). The idea is to consider all “jammed” configurations equally likely. A priori, there is no justification for this ergodic hypothesis, but its application to models of jamming and compaction has been rather successful (Makse & Kurchan 2002). Its extension to forces in granular packings is in principle straightforward: sets of forces belonging to all mechanically stable configurations have equal probability. However, in an ensemble of stable granular packings, two levels of randomness are generally present (Bouchaud 2003). First, the force geometry clearly depends on the underlying geometrical contact network, which is different in different packings. Secondly, randomness in the values of the forces is present even in a fixed contact network, since the forces are not necessarily uniquely determined from the contact network. Instead of considering both levels of randomness simultaneously, a natural first step is thus to obtain the averages for a fixed contact geometry, and then possibly average over the contact geometries.
