A two-species model of a two-dimensional sandpile surface: a case of   asymptotic roughening
  We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is flat on average, so that there is no bias due to gravity. We find anomalous scaling: the expected logarithmic smoothing at short length and time scales gives way to roughening in the asymptotic limit, where novel and non-trivial exponents are found. 
Bandan Chakrabortty and Anita Mehta
cond-mat.stat-mech