A multiple-state discrete-time Markov chain model for estimating suspended sediment concentrations in open channel flow

Transport processes of uniform size sediment particles in steady and uniform flow are described by a multi-state discrete-time Markov chain. The multi-state discrete-time Markov chain is employed to estimate the suspended sediment concentration distribution versus water depth for various steady and uniform flow conditions. Model results are validated against available measurement data and the Rouse profile. Moreover, the proposed model is used to quantify the average time required to reach dynamic equilibrium of particle deposition and entrainment processes. Firstly, suspended sediment concentrations under three different flow conditions are discussed. As the Rouse parameter decreases, the difference between the suspended sediment concentration estimated by the Markov chain model and the Rouse profile becomes more significant, and is larger for higher relative height from the bed. It is speculated that the use of the terminal settling velocity in the transport process can lead to underestimation of the residence probability and overestimation of the deposition probability. Secondly, laboratory experiments are used to validate the proposed model. It is observed that as the Rouse parameter decreases, more time is required for the sediment concentration to reach a dynamic equilibrium. The flow depth is found to have an impact on the time spent to reach the concentration dynamic equilibrium. It is recognized that the performance of the proposed model relies heavily on the knowledge of the vertical distribution of the turbulence intensity. Also, for lower Rouse parameters, concentrations estimated by the Markov chain model exhibit larger variation compared to those estimated by the Rouse profile.