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1 INTRODUCTION

The competitiveness of railway transport can be

maintained by means of the introduction of combined

transport systems in operation. As known, one of the

most promising and widespread one is container

transportation.

The efficiency of container transportation can be

improved by means of designing promising container

structures intended for transportation of a wide range

of freight. The designing of such containers requires

taking into account the potential loads that affect the

containers during their transportation by rail, road, air,

sea, and also if they are included in combined trains

transported by train ferries (Fig. 1). Such combined

transportation has developed when the transport

corridor New Silk Road connecting Ukraine and China

was put into operation, which has made it possible to

transport combined trains by ferries.

Therefore, the issue of designing new container

structures with improved technical and operational

characteristics and calculating the loading on them if

they are included in combined trains requires thorough

investigation.

The designing of new container structures requires

taking into account a wide range of potential loads in

operation. These loads depend not only on the

operational conditions but also on types of freight they

transport: package, bulk, pallet freight, etc.

Research of Loading of a Hopper Container During Sea

Transportation by a Train Ferry

J. Gerlici & A. Lovska

University of Zilina, Zilina, Slovak Republic

ABSTRACT: The efficiency of freight transportation can be improved by the use of hopper containers. If required

they can be equipped with lift-off roofs, which makes it possible to transport the freight requiring protection from

weather. The possibility to transport these containers by sea was studied through their loading. The research

included the case when a hopper container was part of the combined train and transported by the train ferry. It

was taken into account that the container was loaded with bulk freight. The pressure to the container walls was

determined with the Coulomb method. The value of the pressure from the bulk freight was included in the

strength calculation. It was found that the maximum equivalent stresses in the container structure did not exceed

the allowable values. The study also included the determination of the container stability relative to the flat wagon

frame during sea transportation. It was found that with consideration of the typical diagram of interaction

between the container and the flat wagon frame the equilibrium stability of the container was provided at the

rolling angles up to 26°.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 4

December 2025

DOI: 10.12716/1001.19.04.31

1322

Figure 1. Train ferry transportation. a) Train ferry

Heroes of Odessa [1]; b) Rolling Wagons onto a Train

Ferry [2]

The special features of designing containers to

transport long freight are described in article [3]. The

strength calculation for the bearing structures of a

container at the loads on the container walls from the

tubes was made with the finite element method.

However, the authors of the study mentioned did not

discuss the issue of how to determine the pressure from

the bulk cargo to the container walls.

The introduction of containers for fruit and

vegetable transportation is substantiated in article [4].

It describes the main requirements for such containers.

The results of strength calculation for the container

frame at the operational loading modes were

presented. However, the authors did not determine the

pressure from the freight transported to the container

walls.

The effect of the container weight to the metacenter

height of the train ferry is studied in [5]. The algorithm

to assess the effect of the location of the container

weight center on the container carrier stability was

proposed. But the authors did not study the container

stability when transported by the train ferry.

The value of the pressure from the bulk cargo to the

walls of an open car transported by the train ferry is

determined in study [6]. The dynamic loading causing

an additional effect to the sidewall of the car body was

determined by means of differentiation of the law of

sea wave motion. However, the authors did not study

the pressure to the container walls during its sea

transportation.

The effect of the bulk freight to the walls of a car

body is assessed in [7]. The loading on the body was

studied with the method of mathematical and

computer modelling. But the author did not determine

the pressure from the bulk freight to the container

walls during train ferry transportation.

The techniques for loading and fastening steel rolls

in containers for their train ferry transportation are

studied in work [8]. The authors substantiated the

implementation of the solutions proposed for ensuring

the container stability during sea transportation.

However, it should be noted that the authors did not

study the stress state of the containers transported by

sea.

Research into the dynamic loading on transport

means, including containers as part of combined trains

transported by sea, is presented in [9, 10]. The study

provides the safety requirements for transport facilities

during sea transportation. However, the determination

of the stress state of transport means did not include

the pressure from the bulk freight transported.

The analysis of the literature makes it possible to

conclude that the issue of determination of the

container loading is very important and requires

further consideration to improve the operational

efficiency.

The objective of the article is determination of the

hopper container loading placed on the flat wagon

transported by a train ferry. This will help to improve

the safety and environmental friendliness of cargo

transportation by the sea.

The following tasks were set to achieve the

objective:

− a determination of the strength of a hopper

container placed on the flat wagon during train

ferry transportation; and

− a determination of the stability of a hopper

container relative to the flat wagon frame during

train ferry transportation.

2 PRESENTATION OF THE MAIN MATERIAL OF

THE ARTICLE

Higher efficiency of freight transportation can be

achieved by means of hopper containers (Fig. 2).

A special feature of the container is its end walls at

an angle of 30° to the vertical axis. Therefore, it can be

discharged due to the gravity characteristics of the

freight through the hatch doors (fig. 3). The container

can be equipped with the lift-off roof for the freight

requiring weather protection (fig. 4).

The transportability of the container by sea was

studied by means of its loading. The research was

made for the case if the container was included in the

combined train and transported by the train ferry.

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Figure 2. Hopper container. a) general view; b) framework

The stresses on the bearing structure of the

container were determined with the finite elements in

SolidWorks Simulation. The Mises criterion (the theory

of energy transformation) was used as the design

criterion [11, 12].

Figure 3. Diagram of the container discharge

The design diagram of the container is given in fig.

5. It was taken into account that the vertical load Рv and

the pressure from the bulk freight Рр affected the

container. The calculation was made for grain as the

bulk freight because it is one of the most widespread

types of bulk cargo transported in containers. Besides,

the design model included the reactions Рf occurring in

the container fittings to the dynamic loading during

rolling. These reactions were applied to the fixed

fittings on the side of the roll of the container.

Figure 4. Lift-off roof of the container

Figure 5. Design diagram of the container

The pressure to the container walls was determined

with the Coulomb method [6]

sin( )



  

−

=

+−

(1)

where

G is the weight of the prism of a freight shift;

ϑ is the plane inclination angle to the horizontal line;

ρ is the internal friction angle (for ideal bulk

environment it equals the natural slope angle);

δ is the friction angle between the freight and the wall.

It should be noted that the maximum pressure

would correspond to the direction of the sliding plane.

The value of the maximum pressure could be found

with the method proposed by V. V. Synelnykov [6],

according to which the variable ϑ – the plane

inclination angle – should be replaced in the maximum

pressure condition (dp/dϑ) = 0 with some variable x (in

the research it is α = θ); in the general case it can be

found analytically. Considering this condition, the

formula for determination of the pressure from the

bulk freight has the form

cos ( )

sin sin ( )

1 cos

cos





  



−

=  



  −





(2)

where

γ is the volume weight of the freight, kN/m

;

h is the height of the open car body, m.

The design diagram of the container is given in

Figure 6.

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Figure 6. Design diagram for determination of the pressure

from the bulk freight to the container walls

The angular displacements of the container relative

to the longitudinal axis include the dynamic loading

because it additionally affects the freight and the

container walls. Therefore, the pressure from the bulk

freight to the container walls was determined with the

following formula:

cos ( )

sin sin ( )

1 cos

cos

p h F





  



−

=   +



  −





(3)

where

Fa is the additional pressure conditioned by the

dynamic loading to the bulk freight.

The value of the dynamic loading to the container

and the bulk freight was determined by the method

presented in [10]. For the case without displacements

of the container relative to the flat wagon frame, the

value of acceleration to it accounted for 0.25g. The

calculation included a rolling angle of 12.2°

conditioned by the static action of wind to the above-

water projection of the ferry. As far as the value Fa was

4.26 kPa, the total pressure from the bulk freight

equalled 11.6 kPa.

The finite element model of the container consisted

of isoparametric tetrahedrons [13 – 17]. A graph-

analytical method was used to determine the optimal

number of grid elements [18 – 22]. The number of

elements in the model was 112714, and the number of

units – 37005. The maximum element size was 120 mm

and the minimum – 24 mm.

The container was fixed in the zones of its

interaction with the flat wagon. Low-alloyed Steel

09C2Cu was taken as the structural material. The

calculation also included that the allowable stresses

were equal to the yield limit of the material, i.e. 345

MPa. The results of the calculation are given in Figure

Figure 7. Stress state of the container

The maximum equivalent stresses in the container

were recorded in the bottom side sill and were 294.2

MPa, which were lower than the allowable values [23]

(Fig. 8). Thus, the strength of a container transported

by sea and included in the combined train was

ensured.

Figure 8. Maximum equivalent stresses in the container

The research also included the determination of the

equilibrium stability of the container with

consideration of the typical diagram of interaction with

the flat wagon transported by the sea. The results of the

calculation are given in Figure 9.

Figure 9. Design diagram for determination of the container

stability

The container stability must meet the condition:

( )

)

(

( )

cos sin

sin

rest

br f br c

c br c

Р n М g

p Мg

  



  +    + 

=



 +   + 

(4)

1325

where

Мov is the value of restoring moment;

Мrest is the value of overturning moment;

Мbr is the gross mass of the container;



is the acceleration to the container at angular

displacements relative to the longitudinal axis;

Рbr is the gross weight of the container;

Bc is the container breadth;

nf is the number of fixed fittings at which the container

is supported at angular displacements relative to the

longitudinal axis;

hf is the height of a fixed fitting.

And the stability threshold reaches if the restoring

moment equals the overturning moments, i.e. if kс = 1.

The results of the calculation are given in Figure 10.

Figure 10. Dependency of the stability coefficient of the

container on the rolling angle

It has been found that the container stability with

consideration of the typical diagram of interaction with

the flat wagon is provided at the rolling angles up to

26°.

The subject of this study is quite new, because the

issue of transportation of combined trains by the sea

has not received sufficient attention. This type of

transportation entered operation in 2017 and it was a

link in the route from Ukraine to China (the New Silk

Road). Therefore, a comparative analysis of the

achieved results with already known studies is not

provided within the framework of this work.

It is important to note that the proposed calculation

algorithm can also be used to study the loading of a

container filled with another type of bulk cargo. In

subsequent works, the authors will pay attention to

this issue.

Further, as subsequent tasks being planned to solve

by the authors within the framework of this study is an

experimental assessment of the strength of a hopper

container during transportation by the sea. Due to the

difficulty of manufacturing an original design of such

a container with real dimensions, it is assumed that

full-scale tests will be carried out on a reduced-scale

sample. Such a task can be implemented using the

similarity method.

An equally important task in this area is to ensure

the efficiency of the wagon braking system during their

transportation by the sea. It is known that the braking

system of the wagon coupling is connected to a special

pneumatic system on a train ferry during

transportation of wagons by the sea. When passing

dangerous places in the water area, the coupling is

braked by a pneumatic system. This allows increasing

the safety of wagon transportation by the sea.

3 CONCLUSIONS

The research deals with determination of the strength

of a hopper container placed on the flat wagon

transported by the train ferry. The maximum

equivalent stresses were recorded in the bottom side

sill of the container and amounted to 294.2 MPa, which

were lower than the allowable values. Thus the

strength of a container included in the combined train

transported by sea was ensured.

The research also includes determination of the

stability of a hopper container relative to the flat wagon

frame transported by the train ferry. It has been found

that with consideration of the typical diagram of

interaction between the container and the flat wagon

frame the equilibrium stability of the container is

provided at the rolling angles up to 26°.

ACKNOWLEDGEMENTS

This publication was supported by the Cultural and

Educational Grant Agency of the Ministry of Education of the

Slovak Republic under the project KEGA 024ZU-4/2024:

Deepening the knowledge of university students in the field

of construction of means of transport by carrying out

professional and scientific research activities in the field. It

was also supported by the Slovak Research and Development

Agency of the Ministry of Education, Science, Research and

Sport under the project VEGA 1/0513/22: Investigation of the

properties of railway brake components in simulated

operating conditions on a flywheel brake stand. Funded by

the EU NextGenerationEU under the Recovery and

Resilience Plan for Slovakia under the project No. 09I03-03-

V01-00131.

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