Application of gambler’s ruin model to sediment transport problems

This study applies the gambler’s ruin model to simulate sediment transport. First, the model is mathematically formulated to determine the probability of reaching the maximum state of the sediment carrying capacity, and the mean time spent in transient states before reaching the maximum sediment carrying capacity. Experimental data are used to model the sediment movement process given the bedload and the suspended load particles in the water column. The impact of different parameters is discussed under varying flow conditions and varying sediment particle characteristics. The model shows that, as the maximum number of particles increases, the probability that the flow can carry the particles decreases. A smaller particle size is normally associated with a higher probability of reaching the maximum sediment carrying capacity under the same flow condition. It is also found that as the time a particle spends in the water column increases, the probability of the flow maintaining the same number of particles after several sediment particle transitions into different states increases.