431
1 INTRODUCTION
Ship stability primarily depends on the position of its
center of gravity relative to the transverse metacenter.
The presence of partially filled tanks or free surfaces
within cargo holds can severely compromise stability,
potentially leading to vessel instability or capsizing[1],
[2]. Liquefaction of cargo, where wet granular bulk
cargoes transform into a fluid-like state, poses
significant risks during transportation [3]. PMNs, due
to their nature and moisture content, are susceptible to
liquefaction under certain conditions.
Between 1988 and 2015, 24 suspected liquefaction
incidents were reported, resulting in 164 fatalities and
the loss of 18 vessels [3] pp – 1. Apart from several
other reasons which put ships in danger, as argued by
the International Association of Classification Societies
[4], cargo liquefaction remains one of the most
significant threats to ship safety.
While bulk carriers generally exhibit favourable
intact stability margins, they may become particularly
vulnerable to stability issues under specific conditions,
as highlighted by Krata et al. [5] due to significant
corrections to the transverse metacentric height caused
by free surfaces. These corrections, illustrated in Fig. 1,
highlight the influence on FSC values with respect to
the displacement of bulk carriers.
From this perspective, the aforementioned
considerations result in modifications to a vessel's
seakeeping properties, primarily characterized by the
following phenomena[6]-[8]
− Decrease transverse metacentric height (GM).
− Increased angle of heel.
− Reduced righting arms (GZ).
Stability Analysis of a Bulk Carrier under Damage
Scenarios during the Loading of Polymetallic Nodules
in the Clarion–Clipperton Zone
P. Kacprzak
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: A potential consequence of loading polymetallic nodules (PMNs) in a marine environment is
liquefaction. During loading operations in the Clarion–Clipperton Zone (CCZ), the ship is exposed to cyclic
rolling and pitching, which increases the risk of cargo liquefaction. This phenomenon poses a particular danger
when PMNs liquefy under certain conditions. Combined with cargo shifting, liquefaction can significantly
compromise the vessel's transverse stability —even when it occurs in a single cargo hold. Due to the limited
operational experience in transporting PMNs, this study investigates the key risk factors affecting ship stability.
The research discusses the likelihood of liquefaction, the influence of wind lever arms, and critical roll amplitudes
under conditions where the weather criterion is not fulfilled. These aspects are analyzed through three
representative damage scenarios. The findings indicate that, for the vessel analyzed, flooding in a single
compartment does not result in overall stability failure. However, strict monitoring of cargo moisture content in
relation to the transportable moisture limit (TML) remains essential to mitigate risks. The study concludes with
practical recommendations to assist ship operators in managing these challenges effectively.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 2
June 2025
DOI: 10.12716/1001.19.02.12
432
− Decreased dynamic stability.
− Change in the roll period of the ship.
Figure 1 Stability corrections (FSC) based on analysis,
developed using data from [5]
1.1 Description of PMNs
From a transportation perspective, the mass of PMNs
and their liquefaction parameters are crucial for
assessing the safety of bulk cargo transportation.
Several studies [9]–[11] have evaluated their physical
properties in the context of deep-seabed characteristics.
The density of PMNs ranges from 1.75 to 2.40 kg/m³,
while water content varies significantly between 39%
and 66%. Using pycnometric techniques[11], the
specific density of PMNs was determined to average
3.31 kg/m³. These findings emphasize that PMNs must
be treated as heavy cargo.
1.2 PMNs Properties and Associated Risks
Analyses conducted by Bureau Veritas for Blue
Nodules demonstrated that PMNs could be classified
as "Manganese Ore," a cargo type included in the 2020
release of the International Maritime Solid Bulk
Cargoes (IMSBC) [13]. According to the IMSBC, the
bulk density of manganese ore ranges from 1.450 to
3.200 kg/m³, with a typical moisture content up to 15%.
However, research [14] indicates that the free moisture
content of well-drained PMNs can reach 20%,
exceeding IMSBC values. Additionally, studies [15],
suggest that even low-moisture cargo could still lead to
liquefaction, necessitating stricter moisture control.
During maritime transportation and loading in open
seas, a combination of cyclic loading, fine particles, and
moisture content can cause liquefaction [2]. This may
result in the bulk carrier listing or capsizing. External
factors, such as rain and monsoon conditions, can
exacerbate moisture levels in the cargo without visible
signs [16] Admittedly, comprehensively
understanding the behavior of granular materials
remains extremely challenging, as these materials
exhibit significant variation under differing
environmental and experimental conditions [17].
1.3 Influence of Grain Size on Liquefaction
As argued by Oldendorrf company grain size of cargo
directly influences the risk of liquefaction [18]. In
general, the size of nodule particles before extraction
varies between 3–4 cm [19] as shown in Fig.2.
The particle size of PMNs, as tested in reliability
analyses of mining systems, showed that
hydrodynamic lifting motors and pumps undergo
repeated impeller blade impacts and fragmentation,
altering particle sizes within limits ranging from 1 mm
to 15 mm [20], This variability poses an increased risk
of liquefaction, especially in scenarios involving long
vertical hydraulic pipeline lengths that have not yet
been adequately tested.
Figure 2. Cumulative proportions of the number and mass of
nodules in different particle sizes [18, p. 7]
1.4 Challenges in Ship Stability
Current ship stability criteria are insufficient to reliably
assess the risks associated with transportation of wet
bulk cargoes, especially with the transport of PMNs.
However, the research by Kacprzak [21] showed that,
in intact conditions, the current model for assessing
ship stability is sufficiently reliable, even when
compared with roll motion predictions. Nevertheless,
specific cargo implications highlight the need for
updated stability assessments tailored to bulk carriers
transporting liquefiable cargo. It is crucial that ships
are made aware of the risks associated with loading
PMNs as cargo. Despite existing studies on ship
stability and liquefaction, no comprehensive
assessment has yet addressed PMN-specific loading
scenarios under offshore environmental conditions.
1.5 Aim and Objective of the study
The aim of this study is to assess the risk of ship
stability failure during cargo liquefaction scenarios
involving the flooding of a single cargo hold in a bulk
carrier, with a primary focus on directly addressing
whether liquefaction in one hold will result in the
failure to meet regulatory criteria. The analysis focuses
on the loading phase, during which the calculated
righting arm (GZ) values may reach their minimum in
the simulated sequence — while still remaining
positive — potentially representing the most
vulnerable intact stability condition. Under such
circumstances, liquefaction may be initiated by the
cumulative effect of repeated roll and pitch motions,
which compress the cargo and force pore water out.
Currently, operational experience with transporting
potentially liquefiable materials (PMNs) under
offshore conditions remains limited.
The specific objectives of this study are as follows:
− To analyze the stability of a bulk carrier under a
flooding scenario involving one cargo hold filled
with potentially liquefiable material.
− To assess vessel stability in accordance with IS Code
(weather criterion).
− To identify critical roll amplitudes beyond which
the vessel fails to meet the weather criterion
− To evaluate the impact of varying wind lever arms
on ship stability and roll behavior.
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− To propose practical recommendations for
enhancing the safety of bulk carriers transporting
PMNs.
2 RESEARCH METHOD
2.1 Vertical and transverse shifts of VCG due to
liquefication and cargo shift
The free surface correction (FSC) is a mathematical
approach used to consider the effect of the additional
heeling moments caused by liquids during roll and
heeling. These effects are typically represented as a
virtual rise in the vertical center of gravity (KG),
resulting in a corrected KG’ value, as shown in Eq. (1)
[21]. This approach reduces the ship’s righting arm
curve (GZ) to reflect the destabilizing influence of the
free surface.
KG KG FSC=
+
(1)
Free surface moment (FSM) may be calculated
using methods presented in [22]. However, a widely
used approach simplifies the process by basing the
calculation on the moment of inertia of the tank
horizontal projection. This method is typically applied
during the calculation of initial stability and is
expressed by Eq. (2), where Ib ρ represents FSM
b
I
FSC
D
=
(2)
where: Ib – lateral moment of inertia based on
dimensions of the ships hold [m
4
], ρ – density of fluid
[t/m
3
], D – displacement of ship [t].
In general, Eq. (2) for correcting KG is applicable
only for relatively small angles of heel. Despite this
limitation, it is commonly used worldwide due to its
simplicity [5]. FSC is particularly significant in
scenarios involving partially filled tanks or cargo
holds. While the method has some recognized
limitations, it often represents the worst-case moment,
irrespective of the tank’s or cargo holds filling level.
Notably, a study by Krata [5] found that the highest
values of FSM occur when the tank is filled between 40
and 60% of its volume, as illustrated in Fig. 3.
Figure 3. FSM in function of tanks filling level – developed
based on data from [5]
Research conducted by S. Ferauge [23] uses an
alternative approach to the calculation of Free FSM
correction for fluidized cargo, emphasizing its
applicability to high-density materials such as PMNs.
Given the unique physical properties of PMNs,
including their high density and AOR, this method
offers improved accuracy in modeling stability
scenarios. The formula for FSC under such conditions
is expressed by Eq. (3)
( )
3
tan
12
c
v
LB
G AOR
D
=
(3)
δGv – correction to KG due to fluidized cargo [m], L,B –
main dimensions of ships hold [m], tan(AOR) – tangent
of Angle of Repose ρc – density of cargo [t/m
3
]
Eq. (3), unlike the classical FSC method, includes
the tangent of the angle of repose (AOR), which reflects
the geometry of the cargo surface in the hold. This
allows for a more accurate representation of the free
surface effect for materials such as PMNs. Although
Eq. (3) does not explicitly depend on the filling ratio,
the expected variability of FSM with tank filling — as
shown in Fig. 3 — can be used to estimate its relative
influence. Therefore, the formulation used in this study
combines the material-specific advantage of AOR with
a conservative approach to FSM magnitude.
Building on this formulation, the effect of the
fluidized cargo is incorporated into the stability
analysis through a correction to the ship’s vertical
center of gravity (KG), calculated as follows:
The KG of the ship is corrected by δGv as calculated
using Eq. (4):
v
KG KG G
=
+
(4)
Finally, the corrected GZ curve, adjusted for the δGv
is expressed by Eq. (5):
( ) ( )
sinGZ lk KG
= −
(5)
where: lk – cross curves of stability [m], φ – angle of
heel [°]
In this study, the corrected GZ curve will be utilized
as the basis for further stability analysis, using Eqs. (4)
and (5) to model scenarios involving PMNs
liquefaction effectively. From an engineering safety
perspective, simplifying assumptions and
overestimation are preferred to ensure that worst-case
scenarios are adequately captured. Major accidents
often follow an unforeseen sequence of events, this
constitutes a scenario gap [24], [25]. In this research, the
unknown risks associated with potential liquefaction
of PMNs are addressed by applying the worst-case free
surface moment, regardless of the cargo hold's filling
level. Therefore, in this study, FSC is calculated using
Eq. (3), as it represents the worst-case scenario
appropriate for modeling the potential liquefaction of
PMNs.
The issue of cargo shift onboard a ship in waves has
been extensively studied by [26] – [28] Then the
transverse center of gravity (YG) deviates from zero
(i.e., YG ≠ 0), the vessel develops a static list. In such
scenarios, the GZ curve must be corrected to account
for the shift using the following Eq. (6) [29].
( ) ( ) ( )
11
cosG Z GZ YG
= −
(6)
where: ΔYG – transverse shift of centre of Gravity [m].
These corrections are crucial for proper assessment
in flooding scenarios. The above equations are
formulated based on methodologies presented in the
434
literature [21], [29]–[33]. The corrected G1Z1 curve thus
serves as the basis for conducting a detailed stability
analysis in accordance with the weather criterion
outlined in the IS Code. However, the impact of free
surface on the ship stability is discussed in detail in [8].
2.2 Stability assessment by IS Code
The formulation of the Weather Criterion is based on
empirical relationships developed many years ago for
vessels that do not necessarily represent modern ship
designs with large superstructures [34]. In [35]–[38]
various approaches to stability assessment are
discussed, including alternative calculation methods
permitted under the assumptions of the Second-
Generation Intact Stability Criteria (SGISC).Many
authors argue that current stability assessments, which
rely on the standard assumptions of the IS Code, may
be insufficient. Therefore, more detailed analyses — as
proposed under SGISC — are recommended. The
International Maritime Organization (IMO) has
introduced SGISC, which incorporates five different
failure modes, in response to recurring incidents linked
to inadequate stability. In this study, we focus on
damage stability based on Dead Ship Condition mode.
However, it should be emphasized that this
research does not attempt to modify the existing
Weather Criterion. All calculations — particularly
those involving the Weather Criterion — are
performed strictly in accordance with the standard IS
Code, but the criterion is further extended in this study
to determine the specific roll amplitudes at which the
vessel fails to meet statutory stability requirements.
3 RESULTS
3.1 Ship used in simulation
To calculate ship stability under a specific flooding
scenario involving a single hold, a B517 series vessel
[39] was utilized. The detailed characteristics of the
ship are presented in Tab. 1
Table 1. Principal Dimensions and Specifications of Bulk
Carrier BCS-1
Bulk carrier B517
Length between perpendiculars LBP [m]
185.00
Moulded breadth B [m]
24.40
Design draught T [m]
11.011
Deadweight DWT [t]
33390
In this study, the ship's stability is analyzed using
the loading sequence method B, as developed in the
author’s work[40]. The analyzed bulk carrier has
favorable stability characteristics due to its design,
which incorporates both long and short holds. The
short holds are specifically used for carrying heavy
cargo. In the case of liquefaction, the transverse
moment of inertia in short holds is approximately 38%
lower compared to long holds of this ship. Moreover,
shorter holds have a lower volume capacity, which
increases the height of the cargo, raising the vertical
center of gravity (VCG) in each hold. This, in turn,
reduces the transverse GM which results in a decrease
of roll accelerations. On the other hand, an increase in
cargo volume correlates with the expected FSM, as
discussed before and shown on Fig. 2.
3.2 GZ curves during loading simulation in intact
condition
Large stability margin during loading simulation is
observed, which decreases during last loading stages
Fig. 3 presents the GZ curves during the loading
simulation. Based on Fig. 3, it can be observed that
from the beginning of the loading process (stage 0),
there is a significant increase in GZ values. After
loading stage 1, the GZ values start to decrease,
reaching their lowest point at the final loading stage.
Figure 3. GZ curves for each loading stage
In general, this ship, under intact conditions,
maintains positive stability throughout the loading
process. However, since this analysis considers the
worst-case scenario with respect to weather criteria, the
last loading stages should be regarded as unfavorable,
due to the largest mass of loaded nodules PMNs and
maximum number of cyclic pitch and roll motion and
lowest values of GZ arms.
3.3 Stability Failure Scenarios and the impact on GZ
Curves
The transverse shift of cargo toward the starboard side
is examined under three distinct damage scenarios.
The transverse cargo profiles within the hold are
illustrated in Figs. 4, 5, and 6. The cross-sectional areas
of the cargo profiles are identical, indicating that the
total amount of cargo remains constant across all
scenarios.
In this study, cargo hold No. 1 of Bulk Carrier B517
is analysed. The damaged condition corresponds to
internal flooding due to liquefaction of cargo within
this hold. The permeability factor is included to
indicate the proportion of the cargo hold volume
available for internal flooding due to liquefaction. It is
used here only for descriptive purposes and does not
refer to flooding caused by hull breach. Relevant
parameters are listed in Table 2.
Table 2. Parameters of the flooded hold resulting from
liquefaction
Parameter
Hold no. 1 of Bulk Carrier B517
Hold length [m]
21.00
Hold Breadth [m]
24.40
Hold Height [m]
15.70
Flooded volume [m³], % of hold
2316.7, 48 %
Permeability factor [-]
0.529
The resulting ship static list is based on a
hypothetical shift of cargo, with the corresponding
values as follows:
− Damage scenario 1: φc = 10[°], VCGc = 6.38 [m], ∆YG
= 0.283 [m](see Fig. 4),
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− Damage scenario 2: φc = 16.5[°], VCGc = 6.56 [m],
∆YG = 0.461 [m] (see Fig. 5),
− Damage scenario 3: φc = 22[°], VCGc = 6.79 [m], ∆YG
= 0.569 [m] (see Fig. 6)
where: φc – angle of list of cargo [°], TCGc – Transverse
centre of gravity of cargo [m], ∆YG – Difference of
transverse ships center of gravity [m]
Figure 4 Cargo Profile within Hold under Damage scenario 1
Figure 5. Cargo Profile within Hold under Damage
scenario 2
Figure 6. Cargo Profile within Hold under Damage
scenario 3
The combined effects of liquefaction (FSC
correction) and cargo shift (∆YG correction) on the GZ
curves in intact condition are illustrated in Fig. 7, which
presents the final G1Z1 curves impacted by all
aforementioned factors.
Figure 7. Influence of liquefaction and cargo shift on Final GZ
Curves in three damage scenarios
In damage scenario 1, G₁Z₁ is reduced by 58%, while
in damage scenario 3, the reduction reaches up to 67%
in comparison to the intact condition. Under damage
conditions, the angle of the maximum righting arm is
reduced by an estimated 10°. This indicates that cargo
shift associated with liquefaction significantly
decreases the stability margin. The static list of the ship,
resulting from the combined effect of liquefaction and
cargo shift, is shown in Fig. 8. The cargo list φC is
correlated with the ship's static list φ0. An increase in
the cargo list in the hold does not cause a proportional
increase in the ship's static list. This indicates that the
greater the cargo heel, the smaller its impact on the
ship's heel, suggesting a nonlinear effect, as shown in
Fig. 8
Figure 8. Relation between cargo list in hold to ship list
considering all corrections to GZ
3.4 Stability analysis based on weather criterion
According to the assumptions of the IS Code, with a
static wind pressure of P = 504 Pa, a range of roll motion
amplitudes leading to noncompliance with the
statutory weather criterion was determined using the
authors’ proprietary software.
The G1Z1 curves were described by polynomial
functions, which facilitate a precise analysis. The areas
under the G1Z1 curve were calculated using Simpson’s
rule, a standard method widely accepted in naval
engineering. This method of integration is commonly
used in naval architecture [41] and is recommended in
ship loading manuals as a technique for determining
the b/a ratio. The b/a ratio is an important factor in
assessing the ship's stability under rolling motion,
where a value of b/a < 1 indicates the threshold at
which the vessel may become unstable [22]. By
analyzing the b/a ratio in relation to roll amplitudes,
critical roll amplitudes that lead to the failure of the
weather criterion (b/a = 0.999) were identified. The
values of roll motion leading to non-fulfillment of the
weather criteria are as follows:
− Damage scenario 1 φ₁ (b/a = 0.999) = 34.7[°]
− Damage scenario 2 φ₁ (b/a = 0.999) = 27.8[°]
− Damage scenario 3 φ₁ (b/a = 0.999) = 23.6[°]
The relationship between the b/a ratio and roll
amplitudes under the three damage scenarios is
illustrated in Fig. 9.
Figure 9. b/a ratio as a function of roll amplitudes for the
investigated damage scenarios (standard wind lever arms).
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3.5 Critical roll amplitudes influenced by wind levers
An increased wind levers alters the static heel induced
by steady wind action; thus, the enhanced wind effect
reduces the amplitude of roll motions, leading to a
failure to meet the weather criterion.
Fig.10, 11, and 12 present the influence of varying
roll motion amplitudes on the b/a ratio for several
configurations of wind lever arms under Damage
scenarios 1,2 and 3.
Figure 10. b/a ratio in damage scenario 1 for different set of
wind levers
Figure 11. b/a ratio in damage scenario 2 for different set of
wind levers
Figure 12. b/a ratio in damage scenario 3 for different set of
wind levers
As shown in Fig. 13, increasing the wind lever arm
(lw1) causes a noticeable decrease in the roll
amplitudes at which the weather criterion is no longer
satisfied (i.e., when b/a < 1).
Figure 13. Limiting roll amplitudes as a function of wind
lever arms causing non-fulfillment of the weather criteria.
The above analysis showed that the critical roll
amplitude is reduced by:
− 14.1% for damage scenario 1,
− 18.3% for damage scenario 2,
− 20.4% for damage scenario 3.
This progressive reduction indicates a strong
sensitivity of the system to external wind lever arms.
The trend confirms that even moderate increases in
wind lever arms can significantly diminish the vessel’s
safety margins under roll-inducing conditions.
4 DISCUSSION
The analysis conducted highlights the dynamic
interplay between cargo configuration and damage
scenarios that affect ships stability. The simulation
results for the B517-series bulk carrier indicate that,
under intact conditions, the vessel maintains a
satisfactory stability margin throughout the loading
process. However, this margin notably decreases
during the final loading stages, when the accumulation
of cargo mass and increased pitch and roll amplitudes
pose a greater risk of liquefaction.
The impact of liquefaction and transverse shift of
cargo in the analyzed damage scenarios indicates a
gradual deterioration of the ship’s transverse stability.
Although the ship’s heel does not increase
proportionally with the heel of the liquefied cargo, the
observed nonlinearity suggests that at higher cargo
heel angles, its influence on the overall ship heel
decreases. For increasing severity of the damage
scenarios, the critical roll amplitude required to reach
the failure threshold (b/a = 0.999[-]) decreases
significantly— from 34.7° in damage scenario 1 to just
23.6° in damage scenario no 3. These results reinforce
the need to assess liquefaction-prone cargoes not only
through static stability margins but also in the context
of dynamic responses during realistic sea states.
Additionally, the study demonstrates that increased
wind lever arms reduce the allowable roll amplitudes
before violating the weather criterion. Increasing the
static wind lever arms resulted in a reduction of the roll
amplitudes at which the vessel fails to meet the
weather criterion—by 14.1%, 18.3%, and 20.4% for
damage scenarios 1, 2, and 3, respectively. This trend
indicates that the effect of changing wind lever arms on
critical roll amplitudes is approximately linear.
This finding underscores the amplifying role of
aerodynamic forces in stability failure and suggests
437
that wind effects must be integrally considered in
operational risk assessments.
Although cargo liquefaction in a single hold does
not directly cause capsizing, it can significantly
contribute to the risk under certain conditions. Based
on the analysis, roll amplitudes exceeding 30° result in
non-fulfillment of the weather criterion, which may
lead to capsizing. This risk is heightened by the fact
that the angle of repose (AOR) of polymetallic nodules
is 33°, meaning that any roll motion exceeding this
value may cause cargo shifting within each hold, even
if the cargo is in a dry state. If shifting occurs in
additional holds beyond the initially liquefied one, the
cumulative effect may lead to a complete loss of
stability and eventual capsizing According to weather
statistics for the Clarion–Clipperton Zone (CCZ) the
most common wave characteristic periods range
between 6 and 10 seconds. As shown in the short-term
prediction model of B517 bulk carrier in investigated
loading simulation by Kacprzak [40] the highest roll
amplitudes fall within this wave period range. These
findings are valid under the assumption of constant
wave parameters over a short duration. Additionally,
it should be noted that, due to its ship geometric
characteristics, the investigated vessel is expected to
operate within an unfavorable wave period range,
which corresponds to conditions that induce the
highest expected roll motions.
However, a more realistic assessment should
incorporate long-term prediction models. Given that
the proposed ship is expected to operate year-round, a
long-term model of exploitation is more appropriate,
and it is likely to predict higher maximum roll
amplitudes over the vessel’s service life.
These findings continue previous research and
suggest that, even under seemingly moderate sea
conditions, dynamic effects related to liquefaction may
lead to critical degradation of ship stability, and this
kind of assessment should be delivered also for the
master on board, with clear statement that flooding in
one hold will not cause capsizing of the ship but will
lead to a condition state of significantly reduced safety
margin.
Based on the simulation results and stability
assessment presented in this study, the following
practical recommendations are proposed for vessels
involved in the loading and transport of PMNs:
− Continuously monitor cargo moisture content,
especially during loading, to prevent conditions
leading to liquefaction.
− Perform loading operations only in calm sea states,
as even moderate rolling can accelerate liquefaction.
Once water is observed within one hold, this
situation will not lead to vessel capsizing.
− Use onboard systems such as MRUs to monitor roll
amplitudes and accelerations in real time, allowing
early detection of critical dynamic conditions.
− Properly trim and evenly distribute the cargo. Since
the angle of repose of PMNs is about 33°, roll
motions beyond this threshold may cause cargo
shift and transverse instability.
− Implement onboard emergency protocols for
single-hold liquefaction, including rapid
assessment of stability and clear guidance on when
safety margins or weather criteria are exceeded
5 CONCLUSIONS
Polymetallic nodules (PMNs) are a cargo type not yet
fully verified in terms of maritime transport safety.
Their liquefaction behavior remains insufficiently
understood, particularly given that mining and
transshipment are expected to occur simultaneously
under offshore conditions. Laboratory testing does not
fully replicate the dynamic environment of real
operations. This study assumes an idealized, fluid-like
behavior of PMNs during liquefaction; however, in
reality, the transition between granular and fluid states
may be non-uniform and spatially variable. This
warrants further experimental investigation.
This research evaluated whether liquefaction
during the loading process poses a significant threat to
vessel stability. The findings indicate that liquefaction
in a single cargo hold does not cause global stability
failure under low sea state conditions. Even when
combined with transverse cargo shift, the effect
remains limited—provided that liquefaction is
confined to only one hold.
The analysis was carried out within the framework
of the International Stability Code (IS Code),
supplemented by second-generation intact stability
criteria (SGISC), allowing for a broader and more
realistic treatment of the vessel’s dynamic behavior.
Based on this framework, the study also developed
practical recommendations for the safe handling and
transport of PMNs.
Future research should focus on the development of
systems capable of accurately monitoring vessel
conditions during offshore operations to mitigate
potential hazards. The proposed stability assessment
model represents a preliminary step toward a more
comprehensive evaluation framework. These results
emphasize the importance of real-time onboard
monitoring—particularly during marginal sea states—
and may contribute to the development of future
guidelines for PMN classification under the IMSBC
Code.
ACKNOLEDGEMENT
This work was supported by a project funded by the Gdynia
Maritime University (No.WN/PI/2025/07)
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