Self-organized criticality in one-dimensional sandpile model with avalanche probability included

Proposed an one-dimensional sandpile model which include avalanche probability, and performed computer simulation by cellular automata method. The results show that there are two critical points p(1) and p(2) when avalanche probability p transits from 0 to 1. The self-organized criticality (SOC) behavior can be found in the model when p(1) < p < p(2). There is a sharp transition between the trivial behaviour and the SOC behaviour in the model. When there is SOC, the SOC behaviour is universal, the two critical exponents are 1.50 +/- 0.02 and 1.58 +/- 0.15. With the model, the SOC phenomenon appearing in the experiment of one-demensional rice-pile is well explained.