Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Trajectory Prediction of Falling Riprap Stones based on CFD-DEM Coupling Analysis
Zheng Huang1, Jie Yang 2, Jian Zhou1, Yanbo Liu1*
1 College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China
2 CCCC Shanghai Dredging Co.Ltd , Shanghai, China

ABSTRACTto be exponential.

Underwater riprap has been commonly used for protection of riverbeds,
banks and offshore structures against damage from scouring. Riprap isusually placed by dropping stones from the surface or certain depth of
the water. However, in the case of water flow present in the construction
site, the trajectory of riprap stones is difficult to predict. In this paper,
CFD-DEM coupling simulations are implemented for investigating thedrifting trajectory of riprap stones dropped in groups. The results of thesimulations show that median value of drifting distance is logarithmic to
the flow velocity. The drifting distances of the stones follow normaldistribution. The results of the simulated contact points of the stones tothe bottom are in good agreement with the reported results fromexperiments.

In experimental researches, Han (2002) applied an indoor test in watertank to investigate the empirical relationship between the drift distanceof mixed thrown riprap during the settling process. The relationshipbetween the distribution of riprap beds in dynamical flow field and the
median particle size is investigated in the indoor test as well. Li (2017)
investigated group throwing conditions of different stones and thrownvolume through water tank experiment. The relationships between thedistribution of group thrown stones and the thrown volume of riprap,
average particle size, Froude number on the surface flow, verticalvelocity distribution, and water depth are also investigated in theexperiment.
Two-phase flow theory (TPM) or discrete phase theory (DPM) arecommonly employed methods to numerically simulate water flows
containing particle phases. TPM is based on Euler analysis which is notable to accurately simulate the interaction between the discrete phase andfluid phase. DPM is based on Euler-Lagrangian analysis which canaccurately calculate the interactions between discrete phase and fluid
phase but does not include the interactions between particles. For
investigating the interactions between particles, the CFD-DEM coupling
method is adopted in this paper. Collisions between stones during riprap
placement is a process of contact, compression, and rebound; therefore
DEM is a more appropriate approach for stone collision simulation. As
the comprehensive DEM algorithm is included in the CFD-DEM method,
the interactions between each particle are considered in the simulations.
The relationship between the median value of drifting distances and flow
velocity in group threw riprap working conditions is investigated. The
distribution of the contact point of stones to the bottom is also
investigated in this paper.

KEY WORDS: Riprap; Trajectory; CFD-DEM; Hertz-Mindlincontacts; Koch-Hill model

INTRODUCTION
Underwater riprap is a common reinforcement approach adopted forprotection of river bed and submarine pipelines from scouring damages.
During the process of settlement, stones usually drift due to the force
applied by the water flow. In addition, interactions between stones (i.e.
collision and friction) also affect the drift trajectory of the stones. Thedrift distance of riprap in flow direction is regarded as an importantparameter in during underwater riprap placement. However, as it isinfluenced by multiple factors, the trajectory of underwater riprap during
settlement is difficult to be accurately predicted.
Considering the the morphology of stones used in underwater riprap andcomplex flow situation in the construction site, various empirical orsemi-empirical formulas have been developed to estimate the drift
distance of underwater riprap in previous researches. With the averagevelocity and average settlement velocity as the parameters of a simplified
drifting model, Liang (1978) developed the drift distance formula of theunderwater riprap by motion balance equation considering the
propulsive force of water flow and the inertial force. Zhan(1992)
proposed an empirical formula to calculate the drift distance ofunderwater riprap by assuming the vertical distribution of flow velocity

CFD-DEM THEORYThe CFD-DEM coupling method was first applied in the simulation ofparticle-containing fluid engineering by Tsuji et al. (1992). The inviscid
joint surge fluidization process of one-dimensional horizontal pipe isinvestigated by this method. In the CFD-DEM coupling method, thefluid is regarded as a continuous medium following the Navi-Stokes
equation with volume fraction solved through the finite volume method.

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