Loss of criticality in the avalanche statistics of sandpiles with dissipative sites

To account for the dissipative mechanisms found in nature, non-conservative elements have been incorporated in the energy redistribution rules of sandpiles and similar models of hazard phenomena. In this work, we found that incorporating non-conservation in the form of spatially-distributed sink sites affect both the external driving and internal cascade mechanisms of the sandpile. Increasing sink densities result in the loss of critical behavior, as evidenced by the gradual evolution of the avalanche size distribution from power-law (correlated) to exponential (random). For low density cases, we found no optimal configuration that will minimize the risk of producing large avalanches. Our model is inspired by analogs in natural avalanche systems, where non-conservative elements have an inherent spatial distribution.