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

Numerical Analysis of Dry Bulk Cargo Load in a Cargo Hold Due to Ship Vertical Acceleration
Fuminori Yanagimoto, Kei Sugimoto, Kinya Ishibashi
Hull Rules Development Department, Nippon Kaiji Kyokai (ClassNK)
Chiyoda-ku, Tokyo, Japan

Daisuke Yanagihara
Dept. Marine System Engineering, Kyushu University
Fukuoka-shi,Fukuoka,Japandecreases and it degree is not clarified because above measurement
during actual voyage usually included uncertainty.
Numerical method and small scaled experiment are effective to clarify
the above phenomenon. Ishibashi et al. already presented their small
scaled experiments to simulate vertical load of granular cargoes. Theseexperiments showed that strain of a bottom plate of an experimental tankcompared to strain calculated using above CSR formulation, indicatingthat the value of 𝐶𝐶𝑏𝑏𝑏𝑏 is lower than 1.0. However, the cause of such
reduction has been unclear (Ishibashi et al., 2021).
To investigate the detail of granular cargo behavior and the cause of theload reduction, numerical method is a useful approach. In particular,Discrete Element Method (DEM) is frequently employed to model
granular materials. DEM has been also employed to analyze granularmaterial behavior in cargo hold of a bulk carrier. They mainly dealt withliquefaction due to moist bulk cargo and movement of the cargo(Chen etal., 2018; Ju et al., 2017, 2018; Spandonidis & Spyrou, 2013; Wang etal., 2020) and only a few studies tried to evaluate bulk cargo load on thehull structure (Song et al., 2018; Toh et al., 2018).
Song et al. developed procedure to map internal load obtained by DEM
analyses to finite element model, but did not note the feature of theinternal load due to granular cargoes (Song et al., 2018). Internal load
due to roll motion of a ship was studied considering DEM-FEM coupling
analysis by Toh et al. (Toh et al., 2018). This study calculated granularmaterial load on inner hull during ship roll motion.
Following above previous studies, the authors employed DEM-FEMcoupling analysis to calculate internal load caused by granular cargo load
during ship vertical motion. A commercial CAE software LS-Dyna wasemployed to simultaneously model DEM-FEM interaction. Explicitanalysis, which is usually adopted in DEM simulation, was employed forthis study.

ABSTRACT.
To understand inertial load due to dry bulk cargo on the inner bottom ofbulk carriers, DEM-FEM coupling analysis was employed to model
granular material behavior and evaluate granular material loading on thebottom plate. According to the results, the load around the center of thebottom plate is smaller than the average value and that near the edge islarger than the average value when the bottom plate deforms. This
nonuniform distribution is caused by the interlocking between theparticles to form ‘arch’. The amplitude of ‘arch’ is determined by theheight of cargo and width of the cargo hold.

KEY WORDS: Dry bulk cargo; Discrete Element Method; Coupling
analysis; Granular material; Design load; Arching effect; Bulk carrier

NOMENCLATURE
𝐵𝐵: width of the tank [mm]𝐻𝐻: height of particle aggregate [mm]INTRODUCTION

Dry bulk cargo is one of the most common cargo carried by bulk carriers.
Its internal load on the inner hull structure due to ship motion is a factor
to determine scantling of ship parts, especially inner bottom plates.
Dynamic pressure on the inner hull due to granular cargoes is defined as
below;
𝑃𝑃𝑑𝑑 = 𝐶𝐶𝑏𝑏𝑏𝑏 𝑎𝑎𝑥𝑥 (𝑥𝑥 − 𝑥𝑥𝐺𝐺 ) + 𝐶𝐶𝑏𝑏𝑏𝑏 𝑎𝑎𝑦𝑦 (𝑦𝑦 − 𝑦𝑦𝐺𝐺 ) + 𝐶𝐶𝑏𝑏𝑏𝑏 𝑎𝑎𝑧𝑧 (𝑧𝑧 − 𝑧𝑧𝐶𝐶 )Coefficients, 𝐶𝐶𝑏𝑏𝑏𝑏 , 𝐶𝐶𝑏𝑏𝑏𝑏 and 𝐶𝐶𝑏𝑏𝑏𝑏 are set to 0.25,0.25, and 1.0 in IACS
CSR-B&T. The values of 𝐶𝐶𝑏𝑏𝑏𝑏 and 𝐶𝐶𝑏𝑏𝑏𝑏 smaller than 1.0 are attributed tofriction between the granular cargoes and ship inner hull plates. On theother hand, although 𝐶𝐶𝑏𝑏𝑏𝑏 is set to 1.0 in CSR B&T, Kuramoto et al.
indicated that 𝐶𝐶𝑏𝑏𝑏𝑏 was lower than 1.0 according to their measurement ofan ocean going bulk carrier (Kuramoto et al., 1987). Tanaka et al
estimated 𝐶𝐶𝑏𝑏𝑏𝑏 = 0.75 from the measurement by Kuramoto et al (Tanakaet al., 1999), but such phenomenon to reduce granular cargo load due tovertical acceleration has not been clarified and whether the load

METHODThe numerical model is shown in Fig. 1. Considering the numerical cost,
the authors did not model the actual size of a cargo hold and employed asmall scaled model tank. The dimensions of the tank were set to the samevalues of the small scaled experiment although depth was set to 130mm,
which was shorter than the actual model size and periodic boundary

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