One-dimensional sandpile model with avalanche probability

We propose a one-dimensional sandpile model with avalanche probability. The simulation is performed with the cellular automata method. As the local slope closes to the critical slope sands avalanche with a probability, the avalanche size and the average local slope are studied at different avalanche probabilities. The self-organized critical (SOC) behavior is studied at critical exponent α=1.50 ± 0.02 as the avalanche probability is between 0.05 and 0.98. The average local slope descends with the increase of collapse probability. A sharp transition occurs between the trival behavior and SOC behavior in this model. The SOC phenomenon in one-demensional rice-pile experiment is well explained.