Three-State Continuous-Time Markov Chain Model for Mixed-Size Sediment Particle Transport

In this study, transport of mixed-size sediment particles under steady flow is described using the continuous-time Markov process. The continuous behavior of particle movement among the immobile bed material, bedload, and suspended load layer is modeled using a three-state continuous-time Markov process. Therefore, the probability of particles staying in each layer can be obtained by the proposed model, which can then be used to quantify the number of particles, and the bedload and suspended load transport rate, respectively. In addition, since the finer particles are more likely sheltered by coarse particles on the bed, mixed-size particles are considered in this paper to account for such an effect. The influence of dimensionless effective shear stress on the mean transient rates, representing the average rate of particle transitions among the immobile bed material, bedload layer, and suspended load layer, is quantified and discussed. The proposed model is verified against the experimental data with both bedload and suspended load particles. The modeling results of both bedload and suspended load transport rate show a reasonable agreement with laboratory measurements.