Application of gambler's ruin model to sediment transport problems

- A gambler's ruin model of particle interaction between channel bed and flow is developed.
- The probability of reaching the maximum allowable particle number in flow is calculated.
- The effective risk of the treatment plant failing to handle the turbidity can be estimated.
- Variability in the effective risk of exceeding the maximum reservoir carrying capacity is quantified.

SummaryThis 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.In the second case study, the effective risk of a given number of sediment particles in the water column reaching the maximum capacity of the water treatment plant in the Shihmen Reservoir Basin in 2008 is modeled. The Xia Yun hydrologic station is selected for the simulation because it is a fully comprehensive hydrologic station and is located near the Shihmen Reservoir. Moreover, a novel approach is used to incorporate uncertainty analysis in the gambler's ruin model: the Perturbance Moments Method (PMM). Results of expected value and one-standard-deviation interval in the number of sediment particles in the water column are acquired.