  The dynamics of an elastic interface profile h(x,t) under a driving force
increasing at rate c, a restored force -epsilon h, and disorder is
investigated. Using perturbation theory and functional renormalization group
the phase diagram and the scaling exponents, up to the first order in 4-d, are
obtained. The model is found to be critical in the double limit epsilon->0$ and
c/epsilon->0$ and belongs to a different universality class as that of constant
force models. It is shown that undirected sandpile models with stochastic rules
and linear interface models with extremal dynamics belong to this new
universality class.
