Modelling the stability of iron ore bulk cargoes during marine transport
Graphical abstract
Introduction
A subject of particular importance to the resources industry concerns the safe trans-oceanic transport of large tonnages of iron ore [1]. It is most important that the stability of the loaded bulk cargo be guaranteed under all dynamic conditions due to the rolling and pitching motion of the vessel induced by waves. Historically, many vessels transporting iron ore bulk cargoes have listed or capsized, with cargo shift being the suspected cause [2], [3], [5], [6]. Therefore, safety precautions are urgently required during shipping the iron ore bulk materials. As shown in Fig. 1, there are two main failure modes that result in cargo shift, namely, liquefaction and cargo slip [7], [8].
Liquefaction occurs due to the cyclic motion of the ship and may lead to the loss of shear strength, and subsequent cargo shift [4], [9]. Liquefaction of an iron ore bulk cargo is a process where the bulk material flows in a manner resembling a liquid under the monotonic or cyclic ship motion. Under the regulation of the International Maritime Solid Bulk Cargo Code (IMSBC Code) [10], a Transportable Moisture Limit (TML) test shall be conducted on all eligible iron ore fines commodities to determine the upper moisture threshold for safe maritime transport. If an iron ore cargo is eligible for a TML, the gross water content of the material on board the vessel must not exceed the TML value to eliminate the risk of liquefaction.
In comparison, cargo slip involves a portion of the surcharge zone within the stockpile, and it is often argued that it poses less danger to the stability of the vessel [11]. The failure mechanism is predominantly related to the material's stress state under dynamic ship motion [12]. The cargo slip phenomenon alters the vessel's metacentre leading to instability of the bulk carrier. Kirby [13] suggests a circular shear failure surface for cohesive iron ore fines on the basis of the classic slope stability theory in soil mechanics. Recent studies [14] have investigated the motion experienced by various vessel classes, which provides further details to better predict and assess the cargo stability.
Based on the forgoing comments, the study presented in this paper aims to address the cargo slip phenomenon during maritime transport of iron ore using analytical and numerical methods to predict cargo slip and assess post-failure stability.
Section snippets
Cargo slip modelling — bulk solids flow theory
Generally, an iron ore bulk cargo is constrained on five boundaries with only the top surface free. The load profile is dependent on the shape of the hold, the hatch arrangement and the degree of fill, while the surface of the bulk material is often rilled to form a surcharge angle (θs). It is assumed that the moisture content of the bulk material is below saturation level and, therefore, the bulk solid can be described as a Coulomb friction, cohesive material [15]. Fig. 2 shows typical
Cargo slip model — the slope stability theory
Kirby [13] utilised the classical theory for slope stability in soil mechanics to model the cargo slip phenomenon. Considering a cohesive iron ore cargo shown in Fig. 7 (a), modelling was performed by considering the effect of gravity to shift the cargo when it is at a rolling level. The material burden is deemed to fail along a circular surface when the gravitational force due to rolling exceeds the resistant shear force. Despite that this method and the flow property theory were both
Dem modelling of the cargo stability
Discrete element modelling (DEM) is an ideal tool to study cargo stability post slip by analysing the post failure material redistribution. The DEM code used in this study was LIGGGHTS [21]. The Hertz-Mindlin model (Cundall & Strack, [22]) was used to compute the particle-particle and particle-wall contacts. The contact force between two particles includes a normal force (Fn) component and a tangential force (Ft) component,where
- •
Fn is the normal contact force,
- •
F
Cargo slip modelling comparison
The cargo slip model using the bulk solids flow property theory and the slope stability theory (Kirby [13]) is compared based on the Handy size cargo geometry in the forgoing discussion. The iron ore sample with material properties shown in Fig. 2 and Fig. 4 are also utilised. For Kirby's model, the cargo geometry yields a slope length of 6 m for a nominal stockpile surcharge angle of 30°. Following the assumption that the maximum roll angle is 20°, comprising of 15° static roll angle and 5°
Conclusion
The study presented in this paper investigated the load stability of iron ore cargoes during maritime transport. Two analytical approaches and a numerical method were compared with the results yielding the following major conclusions:
- •
The bulk solids flow property theory can be utilised to model cargo slip during maritime transport of iron ore.
- •
The cargo slip predicted using the classic slope stability theory and bulk solids flow property theory provide similar results.
- •
The cargo slip predicted
Reference (35)
- et al.
Effect of saturation on liquefaction resistance of iron ore fines and two sandy soils
Soils Found.
(2016) - et al.
On uniaxial compression and Jenike direct shear testings of cohesive iron ore materials
Powder Technol.
(2017) - et al.
Assessment of rolling resistance models in discrete element simulations
Powder Technol.
(2011) - et al.
Rolling friction as a technique for modelling particle shape in DEM
Powder Technol.
(2012) - et al.
On the numerical calibration of discrete element models for the simulation of bulk solids
Comput. Aided Chem. Eng.
(2006) - et al.
Investigation into calibration of discrete element model parameters for scale-up and validation of particle–structure interactions under impact conditions
Powder Technol.
(2011) - et al.
A methodical calibration procedure for discrete element models
Powder Technol.
(2017) - et al.
Calibration of discrete element parameters and the modelling of silo discharge and bucket filling
Comput. Electron. Agric.
(2009) - et al.
Rolling friction as a technique for modelling particle shape in DEM
Powder Technol.
(Feb. 2012) P1097 — Systematic Evaluation of Transportable Moisture Limit Measurement Methods for Iron Ore Fines Bulk Cargoes — Public Final Report
(2014)
Marine Safety Investigation Report 34: Loss of Bulk Carrier Melete
The impact of bulk cargoes liquefaction on ship's intact stability
UPB Sci. Bull.
Influence of Ore Physical Properties on the Transportable Moisture Limit for Barged Materials
Investigating the susceptibility of iron ore to liquefaction
Safe transport at sea of bulk mineral cargoes
Bulk Solids Handl.
“A Commentary on the Application of Bulk Solids Strength and Flow Properties to the Evaluation of the Conditions for the Safe Transport of Bulk Coal by Ship,” ACARP Report R5-85-4138
Cited by (22)
Numerical investigation of dry bulk cargo load during ship vertical motion
2022, Ocean EngineeringParameter calibration of discrete element method modelling for cohesive and non-spherical particles of powder
2021, Powder TechnologyCitation Excerpt :Hu et al. focused on the minimum and maximum critical angles in the first avalanche and reported that these critical angles were applicable for parameter calibration [18]. In addition to the static and dynamic angles of repose, indirect calibration procedures using shear box tests [19] and drawdown tests [20] have also been investigated. In the case of a single test, however, there exist an infinite number of combinations of parameters that can reproduce the experiment.
Calibration of cohesive DEM parameters under rapid flow conditions and low consolidation stresses
2020, Powder TechnologyCitation Excerpt :Discrete Element Method (DEM) has emerged as a reliable tool to simulate various processes and bulk solids handling equipment [1–4].