Simulation of the Riprap Movement Using the Continuous-Time Random Walking Method

Chengpeng Lu,Maomei Wang,Gang Zhao,Hongguang Sun,Longcang Shu,Zhipeng Li,Yuzhu Lin

doi:10.3390/w13192669

Chengpeng Lu, Maomei Wang + Show 5 more

Open Access

https://doi.org/10.3390/w13192669

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Abstract

During the implementation of the riprap project, the underwater migration process of the stones is quite uncertain because of its difficulty to observe. The process of stone transportation is discrete, which makes it unsuitable to be described by a continuous differential equation. Therefore, considering the distribution of stone jumping and waiting, a continuous-time random walk (CTRW) model is established. Based on the actual engineering data, five schemes simulate the one-dimensional motion of riprap underwater and further discuss the spatial distribution and particle size of the riprap. The results show that the CTRW model can effectively predict the riverbed elevation change behavior caused by the riprap project. The suitability of the model for the prediction of riprap movement decreases first and then increases with the increase in the selected width. This indicates that the randomness of the motion of the riprap causes the width of the observation zone to have a significant effect on the overall behavior of riprap movement. When the width is large enough, the influence of the randomness of the motion can be reduced by the average movement behavior within the observation zone. While the observation time of riprap movement is from a short to long time scale, the transport behavior changes from subdiffusion to normal diffusion behavior.

Highlights

Riprap is one of the most common materials used to protect the stability of riverbeds and revetments, bridge abutments and pier foundations from scouring [1]
The continuous-time random walking theory (CTRW) extends the assumption of a fixed step size and fixed waiting time to the jump step size and a waiting time dominated by probability density distribution on the basis of the random walking theory
Numerical Simulation Based on the Field Investigation Varied by Different Widths of

Summary

Introduction

Riprap is one of the most common materials used to protect the stability of riverbeds and revetments, bridge abutments and pier foundations from scouring [1]. The transport of riprap is similar to the bedload in the broad sense. In the condition of an underlying water surface, these methods used for riverbanks are no longer applicable [2]. The stability evaluation of riprap adopts Monte Carlo simulation, inertia analysis, the Faroson blue point estimation method and others to calculate the riprap under the flow conditions [3,4]. Numerical simulation methods are usually used to simulate the changes in water flow, wind, waves and riverbed morphology caused by the implementation of stone dumping projects. The existing software is generally used for two-dimensional or three-dimensional simulation, and PFC software is commonly used [5,6], namely River2D [7,8], or the discrete element method is used to simulate the conditions and hydrodynamic methods to establish aggregation models, such as the DEM-SHP model [9], DEM-CFD model [10]

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