The physical mechanisms of capsizing of ships in carriage of [620256]

Ocean Engineering
Manuscript Draft

Manuscript Number: OE -D-16-00929

Title: The physical mechanisms of capsizing of ships in carriage of
nickel ores

Article Type: Full leng th article

Keywords: clay lateritic nickel ore; viscous liquid; liquefaction; shear
stress; collapse; capsizing

Abstract: In the past five years, the capsizing of considerable bulk
carriers with nickel ores in South China Sea has made shipping indu stry
shocked. Clay lateritic nickel ore is characterized by liquefaction on
the surface under the influence of waves or long time engine vibrations
during transportation. However, the existing methods based on the
calculation of GM values fail in explainin g the capsizing of the bulk
carriers during shipment. Our initial investigation into the incident
shows that the blending liquid (not pure water) after liquefied is highly
viscous and can generate non -free surface. In contrast to the prevailing
theories of ship stability, this non -free surface may create negative
influence on ship's stability. Therefore, we speculate that the viscosity
coefficient may play a critical role in the processes of ship's
capsizing. Here we take advantage of mathematical modeling to make a
thorough analysis to the physical mechanisms of capsizing. The conclusion
has been made that the imbalance of the shear force has led to a shift of
the liquefied cargoes when the inertial force of the liquid cargoes is
greater than that of the sh ear stress, thus caused an abrupt loss of
stability.

Highlight

1. Liquefaction of the nickel ores during shipment has led to numerous ships capsizing and
sinking
2. The collapse of the viscosity sheer force may play a critical role,
3. Numerical simulations have demonstrated that the sloshing of the cargo after liqu efied
increases the heeling moments
4. The collapse of the viscosity sheer force is significantly associated with the frequency and
amplitude of the wave
5. A plausible solution to the capsizing has been suggested. *Highlights (for review)

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65 The physical mechanisms of capsizing of ships
in carriage of nickel ores
Youjia Zou1 and Xiangying Xi2
1(Merchant Marine College, Shanghai Maritime University, Shanghai, China )
2(Faculty of Management, Wuhan University of Technology, Wuhan, China )
(E-mail: [anonimizat])

【Abstract】 In the past five years, the capsizing of considerable bulk carriers with
nickel ores in South China Sea has made shipping industry shocked. Although a
number of countermeasures have been taken by ship owners, it doesn’t seem to
prevent the ships from incident, possibly implying that we may not yet fully
understand some fundamental aspects of the incident. Clay lateritic nickel ore is
character ized by liquefaction on the surface under the influence of waves or long time
engine vibrations during transportation. However, the existing methods based on the
calculation of GM values fail in explaining the capsizing of the bulk carriers during
shipment . Our initial investigation into the incident shows that t he blending liquid
(not pure water) after liquefied is highly viscous and can generate non-free surface. In
contrast to the prevailing theories of ship stability, this non -free surface may create
negative influence on ship’s stability, sometimes may result in a severe consequence
of capsizing. Therefore, we speculate that the viscosity coefficient may play a critical
role in the processes of ship’s capsizing. Here we take advantage of mathematical
modeling to make a thorough analysis to the physical mechanisms of capsizing. The
conclusion has been made that the imbalance of the shear force which is mainly
determined by the viscosity coefficient has led to a shift of the liquefied cargoes when
the iner tial force of the liquid cargoes is greater than that of t he shear stress, thus
caused an abrupt loss of stability. Finally the increasing external moments result in a
capsizing and sinking .

【Key Words 】clay lateritic nickel ore, viscous liquid, liquefacti on, shear stress,
collapse, capsizing

1. Introduction
Five years ago, t he bulk carriers in carriage of nickel ores with great viscosity after
liquefied were very few, therefore the dynamic characteristics of the liquefied cargoes
are not well described in the literature. The study on the properties of the liquefied
cargoes remains little known. Nowadays there is an increasingly need in the study on
the processes of liquefaction of this special bulk cargo with a gr eat deal of casualties
during shipment pushed by the huge demand of Chinese market (Lei Hai, 2011) . The
maritime statistic databases show that there have been 13 bulk carriers capsizing and
over one hundred seafarers have lost their lives since 2009. Parti cularly, there were 5
casualty ships in a very short period from 21 October to 25 December 2010, with 52 *Manuscript
Click here to view linked References

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65 lives lost or missing. However, the situation seemed improved in 2012 and 2014, but
the alarm was raised again in 2015, with M/V “Jupiter” and “Alam Ma nis” capsizing
off Vietnam and south of Taiwan, respectively, 3 dead and 16 missing. See Table 1.

Table 1. Recent c asualties related to liquefaction of bulk cargo
Date of incident Vessel ’s name Cargo loaded Type of incident Location of incident
08/2009 Hodasco 15 Iron ore Capsize Off Malaysia
09/09/2009 Black Rose Iron ore Capsize Off Paradip Port (India)
17/07/2009 Asian Forest Iron ore Capsize Mangalore (India)
21/10/2010 Jian Fu Star Nickel ore Capsize West of Taiwan
10/11/2010 Nasco Diamond Nickel ore Capsize East of Taiwan
22/11/2010 Haixin g Nickel ore Capsize Off Lianyungang(China)
03/12/2010 Hong Wei Nickel ore Capsize South of Taiwan
25/12/2010 Vinalines Queen Nickel ore Capsize South China Sea
21/11/2011 Bright Ruby Iron ore Capsize South of Taiwan
17/02/2013 Harita Bauxite Nickel ore Capsize South China Sea
08/04/2 013 Changhang R uihai Nickel ore Heavy listing Off Fujian Coast (China)
14/08/2013 Trans Summer Nickel ore Capsize Off Hong Kong
01/01/2015 Jupiter Nickel ore Capsize Off South of Vietnam
17/07/2015 Alam M anis Nickel ore Capsize South of Taiwan

Obviously, the capsizing of the bulk carriers is closely associated with the properties
of this special cargo which is listed by the International Maritime Solid Bulk Cargoes
Code (IMSBC) issued by IMO . Some studies on the nickel ores indicate that the
nickel ores usually stored in open fields normally contain a moisture content of
30~40%, some are much more higher if it is in a rainy season. The nickel ores with
high moisture could liquefy under the influence of waves or long time engine
vibrations, and become very viscous (Popek, 2010 ). The viscosity of liquid cargo was
thought by the traditional theories of ship stability to have positive effects on ship’s
stabil ity because it can prevent the cargo from moving when a ship experiences a
rolling. But this conclusion doesn’t seem always right. Our investigation, however,
reveals that t he viscosity of liquid cargo has negative effects on ship’s stability when
an unfav ourable situation is enco untered, for example, cross winds and waves,
sometimes can lead to significant catastrophic consequences to ship and crew,
challenging the classic theories. Although the risks of those special solid bulk cargoes
(total 58) during s hipment are qualitatively pointed out by IMO (Wang, et al., 2010 ),
how those solid bulk cargoes exactly affect ship’s stability still remains unexplainable.
More and more evidence manifest that when a ship with nickel ores experiences cross
waves and winds , the ship will roll with waves in a similar period. The solid bulk
cargoes will liquefy at the upper layers first after a few hours, but the liquefied
cargoes still remain relatively static to ship at the initial stage because the inertial
force is insuff icient to drive the cargoes to shift. However, the liquefied cargoes start
to slide to one side of the ship abruptly as the inertial force (variable with the period
and amplitude of rolling ) of the liquefied cargoes is greater than that of its friction

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65 shear stress (fixed, mainly determined by the viscosity coefficient) when the rolling
becomes unfavourable (eg, prolonging period or growing amplitude), leading to an
unusual heeling angle, in turn a capsizing and sinking of the vessels. See Fig.1a -b.

Fig 1 .schematic map of forces acting on a ship and cargo . a, forces exerting on a ship and cargo
when t = nT+T/4 ; b, forces exerting on a ship and cargo when t = nT+3T/4. When a collapse of the
friction shear force occurs, the cargo will abruptly shift to one side of the ship, leading to an unusual
heeling angle, in turn a capsizing. T represents period.

2. Study methods
Continuous casualties imply that we may not yet really understand some fundamental
aspects of the capsizing although tremendous endeavours have been made by owners
and ship masters to prevent ships from capsizing. To test our hypotheses, we do
experiments in laboratory by using a six DOF platform to observe t he processes of
liquefaction and then use the mathematical model to simulate the sloshing of liquefied
cargoes in a tank.

2.1 Processes of liquefaction in laboratory
The experiments are carried out by using a six DOF platform which can create
motions in six d irections to simulate the real environment at sea (Chen and Nokes,
2005) . The simulated ship is a bulk carrier with a deadweight of 55,000 m/t. We adopt
a scale of 1:45 to cargo hold No.3 to make a tank with a size of L:0.86m, B:0.62m,
and D:0.42m (Guan, e t al., 2014 ). The tank is transparent and filled with nickel ore of
38% (volume ratio), containing 35% moisture (upper limit value recognized by
IMO).

Before experiment, we connect a torque sensor with the bearing to sense the heeling
moments during moving. The experiments show that the development of the
liquefaction can be divided into three stages. At the first stage, the fine particles
compact each other because of air and moisture stored in the fine grained cargo, in
turn water seeps out in the s urface of the cargo after 2h42m, and more and more water
can be observed with time and motions of the tank. At the second stage, water in the
surface mixes with mud, resulting in a layer of slurry after 6h28m. At the final stage,
the slurry steadily aggreg ates and finally remains at a stable condition, leading to a
thick layer of muddy slush at the upper layer of the cargo but a layer of compact
nickel ore at the bottom after 34h48m (assuming that the motions of the tank remain

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65 same at the amplitude and fre quency throughout the processes although both of them
may vary from time to time in realistic regimes ).

2.2 Heeling moment of the liquefied cargo
The experiments indicate that the liquefied cargo regularly sloshes with the tank
together without relative m ovement to the tank when the rolling amplitude is at 5
degrees , but the sloshing start to become furious and irregular, and a small relative
movement to the tank has been observed, and the heeling moment steadily increases
when the rolling amplitude is at 15 degrees. A strong sloshing and a large relative
movement to the tank have been observed when the rolling amplitude reaches 18~20
degrees (critical value, may vary from cargo to cargo, mainly depending on the
viscosity coefficient of the liquefied cargo ) with a period of 3.3s. The dynamic
heeling moment abruptly hits the record subsequently. See Fig 2.

Fig 2. The dynamic heeling moment in different stages with a period of 3.3s. R/A represents rolling
angle.

2.3 Numerical simulations
To further examine the hypotheses, a numerical simulation method has been
employed to simulate the motions of aforesaid bulk carrier. When a bulk carrier is
sailing with liquefied cargo under the influence of cross winds and waves, usually
there is a ship rolling and sloshing of liquefied cargo. In particular, the motions of the
fluid surface is characterized by strong nonlinear as the amplitude of the sloshing is
huge.

Ship motion in irregular waves may be described by non -linear equations of motion
written in a non-inertial reference system (Krata, 2010). For a motion of
incompressible viscous fluid with a 2 -dimension free surface, the governing equations
of fluid field consist of continuity equation:
0V 
(1)
And momentum transport equation:
2 11 dVg f p Vdt
       
(2)
Where

is the density of the fluid ,
0 2 4 6 8 10 12 14 16 18 20-40-30-20-10010203040
t/sMoment N.m

R/A 15°
R/A 10°
R/A 5°

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pis pressure,
f
is the generalized volume force,
g
is the acceleration of gravity,

is the fluid dynamic viscosity coefficient,

The volume force
f
can be expressed as (Das, et al., 2010) :
[ 2 ( )]G
GGdr df a r rdt dt          
(3)
Where
a
is the mean acceleration of the particle “o” to the fixed coordinate system,

is the angle velocity of ship rolling,
Gr
is the radius vector from point “o”。

Fig 3 . a 3-dimension coordinate system of cargo hold.

The sloshing of fluid in the cargo hold is characterized by strong nonlinear,
particularly when approaching the resonant zone, possibly involving broken wave s,
jet flow s, splash es and shock wave s, etc. however, it is not possible to consider all
factors. Furth ermore, it is not necessary to take into account all of those factors
because some of them are not of significant values to this study. Therefore, the
boundary of fluid surface can be expressed as a single function, and the boundary
condition of fluid surf ace can be written as (Kim, et al., 2004) :
( z) 0ut   
(4)

is the height of fluid surface ，
u is the velocity vector.

2.4 Level -set method and equation s
One of the most difficulties in study on the sloshing of the fluid cargo is how to
exactly determine the elevation of the fluid surface, or track the surface. The current
methods in dealing with this issue can be grouped into two types: front capturing and
front trac king. The front capturing includes continuity transpor t method, volume
tracing method, level -set and phase field method, etc. The front tracking involves
moving mesh method , MAC, wave function method and particle method . Here we use

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65 level -set method to tra ck the fluid surface and solve the N -S equations by combining
the SIMPLE algorithm and Superbee -TVD format. The N -S equations are discretized
by combining differential formats of Leap Frog and DuFort -Franke l in MAC
staggered mesh es.

To construct a functio n
(x, t) ,which meet s the requirement that the fluid surface
(t)
is exactly the zero equivalent surface of the function
(x, t) at any time ,
  (t) : (x,t) 0 x    
(5)
The initial value of
 must be monotonic in normal direction near the
(0) ,and zero
in
(t) . Usually, the value of
(x, t) can be the range from the point x to su rface
(0)
(Colicchio, et al., 2005 ):
1
2(x, (0)) x
(x, t) 0 (0)
(x, (0)) xd
x
d 
 
  
(6)
Where
1
and
2 represent the different media zone, respectively, in both sides of the
boundary. The initial value of
 must be one and only.

To ensure that the zero value surface of the function
 is the active interface,

must meet the governing equations (Popov, et al., 1993 ):
0dvdt t   
(7)
In order to meet the requirement of range function ,
(x, t) must be reinitialized by
solving the initial values of following equations:
0( )(1 )
(x,0) 0tsign  
   
(8)
Where
0()sign
is a symbol function,
0
is a value obtained last time .

2.4.1 Smooth process of some physical parameters
Huge density ratio near the interface may make the calculations instable because the
algorithmic domain is solved by using unified governing equations, possibly leading
to a large error of frequency diffusion and non -physical oscillation. In an effort to
overcome this shortcoming, a convenient method is adopted by applying a smooth
process to the den sity in a narrow area near the interface (Fang, et al., 2007 ).

(9)
a
is a short range (normally 1.5~2.5 times of th e grid breadth). the fuzziness of the

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65 interface cannot spread because the interface fixing is prior to the smooth process.
The viscosity coefficient can be processed in a similar manner.

2.4.2 Solving the governing equations of fluid field
We solve the governing equations of fluid field by the finite differential method based
on the SIMPLE algorithm . The N -S equations are discretized by combining
differential formats of Leap Frog and DuFort -Franke l (unconditional stable ) in MAC
staggered mesh es. The form at of the discretized momentum equations in X direction
can be expressed as (simplified as homogenous grids ) (Fang, et al., 2007 ):

(10)
Where , are the generalized mass force and viscosity force, respectively.

(11)

( )

(12)

(13)

(14)

(15)
(16)

Where , .

2.4.3 Solving the equations of Level -set function
For one dimension equations, a format of Superbee -TVD has been used to solve the
equations (Zhu, et al., 2008 ),
(17)
Assuming ,we integrate the volume cell in
temporal and spatial domain s, resulting in:

(18)
The mean integrate in a defined spatial domain :

,
The mean integrate in a defined temporal domain :

, , (19)
The (19) can be discretized by approximating eige nvalues as:

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,
(20)
For a 2-dimension equation , a step -by-step method can be applied by solving the
along the direction of x first, then the along the direction of y.

2.5 The motion equations of ship rolling
Assuming a periodical perturbation is given to a ship by waves and winds （in practice,
winds may vary irregularly in a short period ）, the perturbation moment can be
expressed as:
sin( )pM M t   
(21)
The motion equations of a ship is:
2
2
sin( ) sin( ')tJ B Ctt
M t M t
        
    
(22)
Where
J
is the ship inertia l force and additional mass inertia l force to ship’s ordinate ,

is the angle of ship rolling ,
B
is damping coefficient,
C
is the restoring moment,
M
is the perturbation moment induced by each frequency of waves and winds ,

is the phase of perturbation,
tM
is the amplitude of moment,
'
is the angle of phase lag

3. Analysis of results
4. The liquefaction usually takes time under the influence of cross waves and engine
vibrations. In order to achieve the results in a limited time, we set the moisture
content at 38.2% for the sampled nickel ore, which is greater than that (35. 7%)
recommended by The International Maritime Organization’s (IMO) Code of Safe
Practice for Solid Bulk Cargoes (BC C ode), but very close to that one being carried
by the incident vessels. The kinematic viscosity at room temper ature varies ranging
from 0.00343 m2/s to 0.00742 m2/s with the change of its states (from near solid to
mixture), and the R eynolds number varies fr om 3,892 to 1,830 ( )
accordingly, but we choose the mixture state as the worst condition for our
simulations. The boundary condition is no -slip on the wall. The initia l excitation
amplitude , A, is and the initial excitation frequency, ω, is 0.0758 rad/s.
5.
We use a ship with the deadweight of 55,000 m/t, 181.5m in length, 30.5m in breadth
and 16.8m in depth for the simulations. The simulations indicate that the pressure on
the side wall remains quasi -periodical when the rolling angle is at

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65 , but the pressure becomes slightly irregular
when the rolling angle is set at .

Fig 4. The history of pressure on the side wall when the rolling angle is at .

We gradually increase the excitation amplitude to , an abrupt growth of the
pressure on the side wall, nearly 10 to 13 times of the normal condition, has been
observed , implying the shift of the liquefied cargoes. See Fig 5.

Fig 5. The history of pressure on the side wall when the rolling angle varies from to .

In almost all capsizing casualties , a phenomenon worth notin g is that the incident
vessels finally developed a list against the waves and winds rather than along with
them (this information is obtained from narration of survivals, and some are from an
investigation into ships with a heavy list but not capsizing or sinking), inconsistent
with our intuition. The existing theories remain unexplainable. Our understanding is
that the restoring moment acquired by a ship is closely associated with waves and
winds. During the rolling motion of a ship from t = nT + 0 to t = nT + T/4 (see Fig.1 ),
there always has a chance that the ship can gain the maximum restoring moment
while the phases of waves are exactly in line with that of winds. However, the phases
of waves may be not consistent with , even opposite to, that of winds during the rolling
motion of the ship from t = nT + T/4 to t = nT + 2T/4 (see Fig.1 ) owing to the
behaviour of the unsteadiness and gustiness of winds , therefore leading to an
opportunity for the ship to obtain a maximum restoring acceleration after the

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65 wind -induced heeling moment superimposed on the ship is removed (out of phase) ,
and resulting in a huge inertial force which is much bigger than the friction shear
force, in turn a cargo shifting against waves and winds and ship capsizing.

6. Conclusion
An experiment in laboratory has been done by using a six DOF platform for observing
the processes of the liquefaction of the nickel ore . A numerical simulation has been
developed by using the Level -set method for the sloshing motions of fluid cargo.
following conclusions can be made:
●the moisture content is an important factor inducing the liquefaction of the cargoes,
●the processes of the liquefaction of the nickel ore have three stages. Th e state of the
nickel ore develop s in different stages. However, t he liquefied cargoes can mix with
mud and form a steady layer of glutinous thick slurry at the last stage.
●the wind -induced heeling moment varies irregularly rather than constantly and
steadily, can result in an excessive righting moment, leading to a cargo shift against
the winds and waves.
●the viscosity coefficient plays a critical role in contributing to a capsizing of vessels.
When the inertial force is greater than the friction shear force, a collapse of shear
force may occur, leading to a shift of liquefied cargoes, in turn a loss of ship stability,
and a capsizing.
●the value of the viscosity coefficient is mainly determined by the moisture content,
state, and the physical properties of the cargo .

7. The way in the future
In view of the special properties of some cargoes listed in IMSBC code, masters
should carefully take into account the possible risks inv olved in carrying those
cargoes. The certificates must be issued by a third party with license and presented by
the consigner before loading. Ship masters should never start loading operations prior
being in possession of certificates of Moisture Content a nd Transport able Moisture
Limit . In many cases, however, the certificates are issued by a n unreliable source in
Southeast Asia. Sometimes, even if the certificates are issued by a competent agency ,
but the cargoes stored in open fields may be different from that stated in the
certificates. In case the cargoes in the field s are consistent with that in the certificates,
this cannot guarantee that all cargoes are safe for shipment because the sample test by
the agencies is usually confined on the surface of the cargo, the inner cargo may still
be in excess of TML . All in all, there is no reliable source for the issue of the
certificate in Southeast Asia.

Although a number of ideas in curbing these marine casualties have been proposed,
none of them are reall y applicable. For example, an introduction of l ongitudinal hold
divisions can reduce considerably the risks of cargo shift (Andrei and Pazara, 2013 ),
but it may cause other problems, such as affecting loading or unloading operations,
specializing the bulk carriers, and reducing the chances of carrying other cargoes in
the future, etc. Besides, this technique is for new ships only, modification for existing

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65 ships may be not approved by owners due to huge costs involved . In order to
effectively prevent any po ssible fraudulent or irresponsible behavio ur in moisture
content, A practical and plausible solution is to develop a smart portable infrared
device mounted in each cargo hold, recog nized by IMO and class society, which can
conveniently sense the moisture c ontent of the nickel ore throughout the loading
operation . Masters and duty officers must monitor the device which can give alarm in
sound and light once the moisture content is over the limit set. Masters should stop
and reject the loading at any time if an alert is raised . This method is much more
reliable with low cost, and is likely to be accepted by all related parties, and can
greatly enhance the safety of all bulk carriers in carriage of nickel ores or similar
cargoes. I strongly suggest that the MSC of the IMO start to discuss my suggestion as
soon as possible in order to prevent more unnecessary casualties from happening. We
are able to do so, why not start ea rlier?

Reference

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65 laterite, China Nonferrous M etals, 2, 74 –76.