  We consider a spring-block model with both dry and viscous frictions,
subjected to a periodic driving allowing mechanically stable configurations to
be sampled. We show that under strong driving, the scaling of the correlation
length with the energy density is incompatible with the prediction of Edwards
statistical approach, which assumes a uniform sampling of mechanically stable
configurations. A crossover between the Edwards scaling and the non-standard
high energy scaling is observed at energy scales that depend on the viscous
friction coefficient. Generalizing Edwards thermodynamics, we propose a
statistical framework, based on a sampling of marginally stable states, that is
able to describe the scaling of the correlation length in the highly viscous
regime.
