The occurrence of piping failures in earth structures demonstrates the urgency and importance of studying piping. With this

intention, a new piping model was developed in the framework of continuum mixture theory. Assuming that porous media are

comprised of solid skeleton phase, fluid phase and fluidized fine particles phase, the fluidized fine particles phase is considered

to be a special solute migrating with the fluid phase. The three phases interact while being constrained by the mass conservation

equations of the three phases, and a sink term was introduced into the mass conservation equation of the solid skeleton phase to

describe the erosion of fluidized fine particles, then a new continuum fluid-particle coupled piping model was established and

validated. The validation indicates that the proposed model can predict the piping development of complicated structures under

complex boundary and flow conditions, and reflect the dynamic changes of porosity, permeability and pore pressure in the

evolution of piping.

Due to the nonlinear relationship between storage and discharge existing in the nonlinear forms of the Muskingum model, the model parameters and outflow cannot be directly determined. The traditional routing procedure has been widely applied to model calibration and flood routing. However, most studies have focused only on the accuracy of parameter estimation methods which adopt the traditional routing procedure, ignored the correctness and effectiveness of routing procedure itself. In this study, three routing schemes of traditional routing procedure are evaluated by simulation experiment and the results demonstrate that the routing scheme 1 is the best, and scheme 3 is followed, the worst one is scheme 2. But the scheme 1 and 3 yield parameters estimates and corresponding outflow hydrographs lead to violation of the routing equations in terms of residuals. The scheme 2 is legitimate, however, the accuracy is not high enough. As an alternative, a new routing procedure based on iterative method is proposed for parameter estimation and flood routing of the nonlinear Muskingum models. The proposed routing procedure is applied to model calibration and flood routing for three examples involving single-peak, multi-peak, and non-smooth hydrographs. The results show that the proposed routing procedure is not only satisfying the routing equations for all time stages in the routing process, but also superior to the routing scheme 2. Therefore, it can confidently be applied to parameter estimation and flood routing for the nonlinear Muskingum models.