Heavy lift semi-submersible barge: A new tool for caissons...

International Marine and Offshore Engineering Conference (IMOC 2014)

Heavy lift semi-submersible barge: A new tool for caissons conceptual design

A.Radwan, A.Aly, M.Osama

Copyright © 2013 Arab Academy for Science, Technology and Maritime Transport – All Rights Reserved.

Abstract – The rapidly expanding offshore industry worldwide and the introduction of

dry towing since 1975, lead to an increase in demand for heavy lift transport. The fleet of

semi-submersible ships/barges expanded through an addition of 19 newly built or

converted ships/barges during 2006 to 2012. Although, the design of stability columns

(Caissons) represents the corner stone that affects the intact and damage stability

specially at submerging processes, there is no sufficient data available in the literature.

Therefore, the aim of the present study is to introduce a new tool for caissons conceptual

designs to achieve the stability standards specified by the regulation authorities for intact

stability.

A mathematical model was developed using (MATHLAB) to determine the caissons

preliminary dimensions for any barge based on its particulars and required submerged

depth. Furthermore, the model was validated through a case study of a 100 m barge and

submerged depth of 7 m, using a computer package (MAXSURF). The model results were

found to meet the harshest stability standard specified by regulation authorities and

classification societies. Hence, this model represents an innovative tool for any barge

caissons conceptual design.

Keywords: semisubmersible barge, caissons design, stability standards, Maxsurf,.

Nomenclature

AW The windage area

B Breadth

BML Vertical distance between longitudinal

metacentric height and center of buoyancy

BMT Vertical distance between transverse metacentric

height and center of buoyancy

CB Block coefficient

Cs Center of water plane area at desired submerged

depth

CW Aerodynamic resistance coefficient

D Depth

ds Submerged depth measured from main deck

F Caissons free board

GML Longitudinal metacentric height

GMT Transverse metacentric height

GZ Hydrostatic righting arm

H Caissons height from main deck

hW Windage area centroid

HW The vertical center of hydrodynamic resistance to

the wind force

I Second moment of water plane area

KB Center of buoyancy above the keel

KG Center of gravity above the keel

KML Longitudinal metacentric above the keel

KMT Transverse metacentric above the keel

L Length

LV The wind heeling moment arm

PW Wind pressure

RB Average ratio of fwd caisson breadth to aft

caisson breadth

RL Average ratio of fwd caisson length to aft caisson

length

T Draught

Vw Wind speed

X Desired distance in longitudinal direction

between caissons and barge bow / stern

Y Desired distance in transverse direction between

caissons and barge port / starboard side

∇ Displaced volume

ρ Density

𝜟 Vessel displacement

Subscript M Submerging condition to main deck

S Submerging condition to required submersible

depth

x Longitudinal direction

y Transverse direction

1 Aft caissons

2 Fwd caissons

B Barge



1. Introduction

For over a century, all kinds of floating cargo such as

drilling rigs, floating dry docks, dredging equipment

have been towed across the world’s oceans on its own

keel [1], [2] . Where, the safety of towing is largely

dependent on the link between the towed object and the

tug. Parting of this towline frequently ended in

significant accidents [3].

In the early 1960’s, towage companies realized that if

awkwardly shaped floating objects could be moved on a

barge, this would have the significant advantage of being

much faster and safer than the traditional ‘wet’ tow. At

the end of the 60’s, loading of floating cargo on board a

cargo barge was affected. Thus, the ‘dry tow’ was born.

Subsequently, specialized semi-submersible barge were

built for this purpose [2] .

In 1976, semi-submersible barge ‘ocean servant 1’ had

been introduced with one of the most innovative features,

which had installed buoyancy caissons at four corners,

enabling barge to submerge horizontally without the

bottom reaction necessary for conventional barges. As a

result the water depth for submerging was not limited

and the deck could be kept parallel to the keel of the

cargo [2]. An example of such barges are ‘POSH GIANT

1’,’ BOABARGE 20, 22 , 29 , 30 , 33 , 34, 35 , 36’ and

‘TERAS 002’.

At the same centaury, the first semi-submersible

heavy-lift ships had been introduced by Docklift 1 in

1972 [4], followed by open deck Super Servant 1 in 1979

[4]. Many ships followed, some of which were copies of

the Super Servant 1 such as the DanLifter and Dan

Mover (later renamed Super Servant 5 and 6) or larger

ships of similar design, such as the Mighty Servant1, 2

and 3 introduced in 1983 [4].

Some of the existing heavy-lift ships were modified

over the years. In 1999, Mighty Servant 1 was extended

by 30 m in length and widening by 10 m to reach a total

of 50 m width. Its submersion draft was also increased to

26 m (at aft caissons), resulting of 14 m over its deck [4].

Fig.(1) [4],shows the development of semisubmersible

ships (excluding the dock ships and yacht carriers) since

2000. A total of 19 new ships were added to the fleet

between 2006 and 2012, almost tripling the fleet of 2005.

Figure 1: The development of semi-submersible ships through 2000 to

2012.

Semisubmersible barges could have four or two

caissons either fixed or removable. The four caissons

semisubmersible barges submerging their main deck

horizontally to certain depth using its ballasting tanks,

allowing the bottom of the floating cargo to make

uniform contact with the deck as the deck rise [1],[5]. If

necessary, one of these caissons could be removed

according to the loaded cargo size.

A two caissons semisubmersible barge is a bottom

reaction barge, having only Aft or FWD caissons and it

has to lay on the sea bed to reach equilibrium during

submerging process. The main advantage of such type,

that it has a free deck allowing the operation of float in or

out and load out much easier. However, its main

disadvantages that it requires a prepared sea bed and

limited water depth. Also, the contact between barge

main deck and cargo occurs at line which requires a

special structural to ensure the ability of performing the

required job successfully without any possible structural

damage.

Caissons design represents the corner stone that affects

the intact and damage stability of semisubmersible

barges especially at submerging process. The caissons

should be as small as possible while complying with the

stability functional standpoints. This minimizes wave

loading on the upper caisson part, enables more free deck

area and reduces manufacturing cost. Therefore, the aim

of the present paper is to introduce a new tool for

caissons conceptual designs to achieve the stability

standard specified by the regulation authorities for intact

stability.

2. Semi-submersible stability philosophies

and standards

Many research papers were published immediately

after the loss of the Alexander L. Kielland and Ocean

Ranger in the nineties of the past century to established

intact stability standards for semisubmersible barges.

Such standards have been developed as a result of a long



historical process. They have been completely successful

for expected operating conditions to avoid capsizing [5].

Therefore, a review of stability theory, methods and

standards applied to semi-submersible barges was

undertaken. In addition to a comparison between the five

significant regularity authorities, known to have been

active in developing mobile and offshore units. These

regularities are:

The Norwegian Maritime Directorate (NMD) [6].

The Canadian Coast Guard (CCG) [7].

The International Maritime Organization (IMO) [8].

The American Bureau of Shipping (ABS) [9].

Det Norske Veritas (DNV) [10].

It worth noting that Lloyd’s Register of Shipping was

excluded in the comparison, since it specifies no

particular stability standards for semisubmersible barges.

But LR Committee is willing to advise on such matters

although it cannot assume responsibility for them [11].

The metacentric height (GM), has been used for many

years as a measure of any conventional floating vessel’s

initial stability at small angle of heel. The semi-

submersible has a unique feature due to the change of

water plane area during submerging condition at main

deck where, the second moment of water plane area

about its centroids (y, x) would decrease leading to a

sudden loss in GML and GMT respectively (condition M).

GML suddenly decreased about one hundred meters

and the corresponding longitudinal righting moment

causes trim to grow. GMT value is relatively small

compared to GML because of small breadth to vessel

length. Its value can’t be less than one meter in operating,

transit and survival condition and not less than 0.3 meter

in intermediate temporary condition (condition M to S)

[10] .

For large angle of heel, GZ curve is the measuring

criteria for intact stability. The established methods for

assessing intact stability from the view point of semi-

submersible designer are categorized as follows [12] :

Static stability method based simply on minimum

righting moment requirement, ignoring all dynamic

effects such as wind and wave loads. Therefore, its

main disadvantage that they don’t give indication of

safety margins.

Moment and Energy Balance method based on

taking account of the steady wind heeling moment

and righting moment. As, the vessel absorb energy a

sudden wind gust, causing it to heel down from an

initial angle. Energy balance methods involve

comparing areas under the wind heeling moment and

righting moment curves as shown in figure (2).These

requirements considering only the total work done by

a steady wind moment as the vessel heels, and

ignoring any pre-existing motions, wave-induced roll,

damping and changes in the righting moment

associated with the wave. These dynamic effects are

taken into account through overall safety factors, such

as the1.3 factor applied to the area ratio for semi-

submersibles as stated in regularity standards.

Figure (2), shows typical heeling and righting

moment arm curves, together with parameters considered

during a conventional intact stability analysis [13] .

The ratio of areas under the heeling and righting moment

curves has to satisfy the criterion:

𝐴 + 𝐵 ≥ 1.3 (𝐵 + 𝐶)

Where: the areas A, B and C are integrated up to an

angle 𝜃R (which is either the second intercept angle 𝜃2, or

minimum down flooding angle 𝜃D, whichever is smaller).

Figure 2: Wind heeling and righting moment arm curves, and

parameters used in an intact stability analysis.

Static angle of heel is the angle of heel where the

righting lever curve intercepts the heeling lever curve for

the first time. Only the CCG and NMD authorities which

require the static heel angle to be less than 15⁰, 17⁰

respectively. Other authorities specify no limits on either

the static heel angle or second intercept angle.

Second intercept angle 𝜃2 is the angle of heel where

the righting lever curve intercepts the heeling lever curve

for the second time. NMD is the only authority which

requires the second intercept angle to be greater than 30⁰.

Downflooding angle 𝜃D is the minimum heel angle where

an external opening without watertight closing.

The wind heeling moment arm (LV) can be calculated

along heel angle using the following equation [14] :

𝐿𝑉(𝜃) =𝑃𝑊∗𝐴𝑊(ℎ𝑊+𝐻𝑊) cos2 𝜃

𝑔∗ 𝛥 , 𝐻𝑊 =

𝑇

2

Where:

PW, is the wind pressure, AW is the windage area with

centroid at height hW measured from water line, HW is the

vertical center of hydrodynamic resistance to the wind

force which is assumed to be half-draught as shown in

figure (3) , g is gravity acceleration and 𝜟 is vessel

displacement .



Figure 3: Wind heeling arm

The wind pressure PW is a function of speed Vw and

could be calculated as follows:

𝑃𝑊 =1

2∗ 𝑐𝑤 ∗ 𝜌 ∗ 𝑉𝑊

2

Where:

CW is aerodynamic resistance coefficient which depends

on the form and configuration of the sail area. An

average value for CW is 1.2 and ρ is density of air.

For intact stability analysis, there is a general agreement

according to authorities’ requirement on wind speed. A

wind speed of 100 knots (51.5 m/s) is used to represent

the extreme storm or survival condition. 70 knots

(36m/s) is used when assessing stability in transit, normal

operational and intermediate conditions. Finally, a

reduced wind speed of 50 knots (25.8 m/s) is used when

assessing stability in the damaged condition.

Most existing intact stability standards, for all types of

vessels including semi-submersibles, specify moment

and energy balance requirements, together with a

minimum range of angles over which the vessel is stable.

Some also specify a minimum value of GM, thus

retaining one feature of earlier righting moment criteria.

These standards are summarized and compared as shown

in table (2). [6-10]

Table (1): Comparison between different regularity standards.

CCG NMD IMO &

ABS DNV

Ratio of the

area under

GZ curve

to wind

curve

≥ 1.3 ≥ 1.3 ≥ 1.3 ≥ 1.3

Static angle

of heel due

to wind

≤ 15⁰ ≤ 17⁰ Not

specified

Not

specified

Angle of

heel

(second

intercept)

Not

specified ≥ 30⁰

Not

specified

Not

specified

Min

imu

m G

MT

Op

erati

ng,

tran

sit

&

surviv

al

con

dit

ion

≥ 1 m

≥ 1 m

Not specified

≥ 1 m

Inte

rm

ed

iate

tem

porary

co

nd

itio

n

≥ 0.3 m

≥ 0.3 m

Not

specified

≥ 0.3 m

Min

imu

m R

igh

tin

g m

om

ent

GZ

Up to 𝜃D or

max. GZ, or

up to 15 ° , whichever is

least to:

𝐺𝑍 ≥ 0.5 ∗𝐺𝑀0 ∗ sin 𝜃

GM0 is min. permissible

GMT

Positive over

range

from upright to

second

intercept

Positive over

range

from upright to

second

intercept

Positive

GZ curve shall be

min.

15° in conjunctio

n with a

height of not less

than 0.1 m

within this range

GZMax

≥ 70

In addition to previous intact stability criteria, a

reserve buoyancy ratio is an important requirement for

caissons design. It is defined as the reserve buoyancy

divided by the volume displacement of the vessel at

maximum submerged draught with no trim [6]. The IMO

committee concluded that the intended effect of having

reserve buoyancy was to provide a margin of righting

lever and righting energy. This would be a better way to

comply with the requirements of reserve buoyancy.

Based on the above mentioned stability philosophy

and standers, a mathematical model is developed as a

new tool for caissons conceptual design for any

submersible barge based on its main particulars.

3. Mathematical model

The model was constructed to determine AFT and

FWD stability caissons dimensions to achieve stability

standards for any semisubmersible barge at required

depth.

3.1. Mathematical Model inputs

The present mathematical model uses a minimum

input data as follows:

1. Main Barge particulars:

Barge overall length (LB), breadth overall (BB), depth

(DB), block coefficient (CB) and the required

submerged depth measured from main deck (ds)

2. Caisson locations:

Aft and FWD locations on board barge deck (X1, Y1,

X2, Y2), as shown in figure (3).

3. Stability requirements:

Longitudinal and transverse metacentric height at

requires submerged depth (GML)S , (GMT)S.



Figure 4: Barge main deck general arrangement.

3.2. Model assumptions

The model assumptions are based on the critical

stability condition which occurs when the barge is at

fully submerged depth. Therefore, assumptions are :

1- During submersing process the values of barge

trim and heel are equal zero.

2- Center of buoyancy above the keel, at submerging

condition to main deck (𝐾𝐵𝑀) is equals to half of

barge depth.

𝐾𝐵𝑀 =𝐷𝐵

2 (1)

3- Since it is difficult to locate center of gravity at

submerging condition for loaded or unloaded

barges owing to the multiple variables

dependency ( barge light weight , cargo mass

distribution , ballast water distribution) , therefore:

Center of gravity above the keel at submerging

condition to main deck (KGM)

𝐾𝐺𝑀 =2

3∗ 𝐷𝐵 (2)

FWD and AFT caissons are ballasted to the

same required submerging depth (ds) to achieve

required depth.

4- Based on historical data, the approximate ratios of

FWD caissons length and breadth to those of AFT

caissons are 1.35, 0.67 respectively.

𝑅𝐿 =𝐿2

𝐿1= 1.35 (3)

𝑅𝐵 =𝐵2

𝐵1= 0.67 (4)

5- According to DNV [6] ,the ratio of reserve

buoyancy shall not be less than 1.5% for the FWD

and AFT end buoyancy structures considered

separately.

3.3. Mathematical model equations:

The mathematical model is based on group of

equations which calculate AFT and FWD caissons

dimensions to fulfill the specified longitudinal and

transverse metacentric height ((GML)S, (GMT)S) at

required submersible depth .

The value of transverse metacentric at required

submersible depth (KMT)S is a function of (GMT)S ,

(KBS) , (KGS), (BMT)S , Where:

(𝐾𝑀𝑇)𝑆 = (𝐺𝑀𝑇)𝑆 + 𝐾𝐺𝑆 (5)

(𝐾𝑀𝑇)𝑆 = 𝐾𝐵𝑆 + (𝐵𝑀𝑇)𝑆 (6)

In the same analogy, for longitudinal metacentric

above the keel at required submersible depth (KML)S is :

(𝐾𝑀𝐿)𝑆 = (𝐺𝑀𝐿)𝑆 + 𝐾𝐺𝑆 (7)

(𝐾𝑀𝐿)𝑆 = 𝐾𝐵𝑠 + (𝐵𝑀𝐿)𝑆 (8)

Center of buoyancy above the keel at the required

submersible depth (KBs) can be calculated as follows:

𝐾𝐵𝑆 ∗ 𝛻𝑆 = 𝐾𝐵𝑀 ∗ 𝛻𝑀 + 2 ∗ (𝐷𝐵 + .5 ∗ 𝑑𝑆) ∗(𝛻1 + 𝛻2) (9)

𝐾𝐵𝑆 ∗ 𝛻𝑆 = (𝐶𝐵 ∗ 𝐿𝐵 ∗ 𝐵𝐵 ∗𝐷𝐵

2

2) + 2 ∗ (𝐷𝐵 + .5 ∗

𝑑𝑆) ∗ (𝐿1 ∗ 𝐵1 ∗ 𝑑𝑆 + 𝐿2 ∗ 𝐵2 ∗ 𝑑𝑆) (10)

As the change of center of buoyancy from submerging

condition at main deck (KBM) to required submersible

depth (KBS) is equal to the change of (KGM) to (KGS)

then, (KGS) can be calculated by add the value of (KBS –

KBM) to (KGM) as follows :

𝐾𝐺𝑠 = 𝐾𝐺𝑀 −𝐷𝐵

2+ 𝐾𝐵𝑠 (11)

At required submersible depth, the second moment of

water plane area is dependent only on caissons

dimension. Therefore, by taking the second moment of

water plane area about its y and x axes (IY, IX), the values

of (BML)S and (BMT)S at required submersible depth

could be calculated as follows:

(𝐵𝑀𝐿)𝑆 =𝐼𝑌

𝛻𝑆 (12)

(𝐵𝑀𝑇)𝑆 =𝐼𝑋

𝛻𝑆 (13)

Where:

𝐼𝑋 = 2 ∗ [𝐵2

3∗𝐿2

12+ 𝐿2 ∗ 𝐵2 ∗ (. 5 ∗ 𝐵2 + 𝑌2 − .5 ∗ 𝐵𝐵)2] + 2 ∗

[𝐵1

3∗𝐿1

12+ 𝐿1 ∗ 𝐵1 ∗ (. 5 ∗ 𝐵1 + 𝑌1 − .5 ∗ 𝐵𝐵)2] (14)

𝐼𝑌 = 2 ∗ [𝐿2

3∗𝑊2

12+ 𝐿2 ∗ 𝐵2 ∗ (. 5 ∗ 𝐿2 + 𝑋2 + 𝐶𝑆)2] + 2 ∗

[𝐿1

3∗𝑊1

12+ 𝐿1 ∗ 𝐵1 ∗ (. 5 ∗ 𝐿1 + 𝑋1 − 𝐿𝐵 + 𝐶𝑆)2] (15)



𝐶𝑆 =(2∗𝐿2∗𝐵2)∗(𝑋2+0.5∗𝐿2)+(2∗𝐿1∗𝐵1)∗(𝐿𝐵−𝑋1−0.5∗𝐿1)

2∗𝐿2∗𝐵2+2∗𝐿1∗𝐵1 (16)

The AFT and FWD caissons height ( H ) can be

calculated according to reserve buoyancy ratio specified

by DNV as follows:

𝛻𝑆 ∗1.5

100= 𝐿1 ∗ 𝐵1 ∗ 𝐹1 (17)

𝐻1 = 𝑑𝑆 + 𝐹1 (18)

𝛻𝑆 ∗1.5

100= 𝐿2 ∗ 𝐵2 ∗ 𝐹2 (19)

𝐻2 = 𝑑𝑆 + 𝐹2 (20)

The above equations (12), (13), (14), (15) were found

to be third degree. Only one solution from eight is logical

and could be considered. Therefore, a computer code

written in MATLAB was used to solve these equations

numerically. Meanwhile, a correlation had been created

to demonstrate the effect of each parameter on caissons

dimensions as follows:

𝐿1 ∝ 𝐺𝑀𝑇 ∗ 𝐿𝐵 ∗ 𝐷𝐵 ∗ 𝐶𝐵 ∗ 𝑌1 ∗ 𝑑𝑆 ∗ 𝑌2

𝐺𝑀𝐿 ∗ 𝐵𝐵 ∗ 𝑋1 ∗ 𝑋2 ∗ 𝑅𝐿 ∗ 𝑅𝐵

(21)

𝐵1 ∝ 𝐺𝑀𝐿 ∗ 𝐵𝐵 ∗ 𝐶𝐵 ∗ 𝑑𝑆 ∗ 𝑋1 ∗ 𝑋2 ∗ 𝑅𝐿

𝐺𝑀𝑇 ∗ 𝐿𝐵 ∗ 𝐷𝐵 ∗ 𝑌1 ∗ 𝑌2 ∗ 𝑅𝐵

(22)

The current model was constructed to calculate the

AFT and FWD caissons dimensions for a submersible

barge. Three existing different barges were selected as

shown in table (2), to study the effect of barge

parameters variation on caissons dimensions at specified

longitudinal and transverse metacentric heights. Added to

that, the effect of changing transverse metacentric height

on caissons dimensions for the same barge was also

studied.

Table 2: Selected barges main particulars.

PMS 42 OCEAN

ORC FJORD

LB (m) 100.5 141.02 155.15

BB (m) 30.4 36 45.5

DB (m) 6.096 8.7 9

CB 0.95 0.95 0.95

ds (m) 7 8 11

L *B *D 18624.4 m3 44167.4 m3 63533.9 m3

L / B 3.3 3.9 3.4

L / B *D 20 34 30.7

4. Model Results and Discussions

The Model was applied for each barge in table (2) at

transverse metacentric height (GMT) of 1, 2, 3 m and

different longitudinal metacentric heights (GML). Aft and

FWD caissons locations were selected to be in the most

corners extremity (i.e.: X1=Y1=X2=Y2=0). The obtained

AFT caissons dimensions at each individual (GMT) were

grouped and represented graphically in figure (4).

Figure 5: Effect of barge size variations on AFT caissons dimensions

at different GMT

Figure (4), show that for specific barge and constant

(GMT), upon increasing of (GML) the caissons length and

width are found to be there inversely proportional.

The (GML) to (GMT) ratio below 20 lead to

unacceptable caissons length. While, ratios above 30 lead

to caissons width larger than barge width. From this we

can conclude that the optimum ratio lie between 20 to 30.

The optimum (GML) to (GMT) ratio were found to be

lie between 20 to 30. Ratios below 20 lead to

unacceptable caissons length. While, ratios above 30 lead

to caissons width larger than barge width.

Figure (4), the FJORD barge caissons dimension curve

lay between the two other curves at the three different

transverse metacentric height chart. That proves that the

different main particulars of barge have the same effect

on caissons dimension at different transverse metacentric



height. Therefore, it can be concluded that the caissons

dimensions are dependent on the result from (L / B * D)

more than the result from ( L * B * D) or (L / B).

Although, the FJORD semisubmersible barge is the

largest one; it was found that its curve lies between the

PMS 42 and OCEAN ORC. This indicates that the

caissons dimensions aren’t dependent on barge

displacement.

The effect of changing transverse metacentric height

on caissons dimensions for a specific barge was studied

and presented as shown in figure (5). The figure shows

that at constant (GML), the increase of (GMT) is

associated with an increase of caissons length and a

decrease in their corresponding width.

Figure 6: Effect of changing GMT on caisson dimensions for PMS 42.

From figure (4), caissons preliminary dimensions

could be determined for a semi-submersible barge

through selection of required GMT . Generally, the value

of GMT shouldn’t be less than 0.3 meter at any loading

condition. The larger value of GMT increases the cargo

loading capacity. The appropriate curve is selected

according to barge main particulars (L / B * D). Then,

AFT caissons dimensions could be determined at

specified optimum (GML) to (GMT) ratio. The FWD ones

are calculated based on assumption (no.4) and by

applying equations (16 -19) for reserve buoyancy criteria.

5. Model verification:

Barge PMS-42 was selected for mathematical model

verifications using a computer package called

“MAXSURF”. Caissons were assumed to be at extreme

corners onboard deck (i.e.: X1=Y1=X2=Y2=0).

Five values for GMT and GML were proposed to

generate the corresponding KGs and caissons dimensions

from the developed mathematical model and figure (4).

Each set of data represents a separate case study to

validate the mathematical model, as shown in table (3).

Table 3: Proposed case studies.

Case

1

Case

2 Case 3 Case 4 Case 5

GM T (m) 1 1 1 2 3

GM L (m) 30 35 40 40 40

AF

T c

ais

son

s

Dim

en

sio

n

(m)

length 8 7.4 7.2 12.4 18.9

Width 9.1 11.3 13.3 8.9 7

Height 10.8 10.3 9.9 9.6 9.2

FW

D c

ais

son

s

Dim

en

sio

n

(m)

length 10.8 10 9.7 16.7 25.5

Width 6.2 7.6 9 6.02 4.75

Height 11.2 10.6 10.2 9.8 9.4

KGS (m) 4.7 4.8 4.9 5 5.3

Each case in Table (3) was modeled using RHINO and

MAXSURF, as shown in figure (6). Then, intact stability

was evaluated by importing MAXSURF file to

HYDROMAX module. Upright hydrostatics was used to

verify the proposed GMT and GML values. Then, GZ

curves for large angle stability were generated to verify

compliance with stability standers specified by regulation

authorities at required submerged depth.

Figure 7: Semi-submersible barge modeled in Rhino and Hydromax .

As shown in table (4), calculations of upright

hydrostatics reveals that the MAXSURF output values of

GMT and GML are very close to proposed ones at the

required ds.

Table 4:Percent diffrence between MAXSURF output values and

proposed (GMT and GML ) at ds= 7m.

Case 1 Case 2 Case 3 Case 4 Case 5

Proposed GMT 1 1 1 2 3

Cal. GMT 1.093 0.986 1.023 1.973 2.658

diffrence (%) 9.3% -1.4% 2.3% -1.4% -11.4%

Proposed GML 30 35 40 40 40

Cal. GML (m) 29.56 33.08 38.22 37.77 37.11

diffrence (%) -1.4% -5.4% -4.4% -5.5% -7.2%



Upright hydrostatics also reveals the dramatic change

of GMT and GML at submerging condition to main deck.

Figure (7), shows the abrupt decrease of GM at 6 m draft

(condition M). The values of GMT rapidly decreased

from 12.5 to 1 m , also GML from 151.66 to 29.5 m, this

is due to the change of water plane area on barge deck.

This sudden change could be overcome by submerging

with small trim which increase the water plane area. The

slope change in vessel displacement plot reflects the TPC

values at different drafts. TPC values also rapidly

decreased from 31.4 to 3.25 t/cm at submerging

condition to main deck due to change of water plane area

and remained constant to required dS.

Figure 7: Change of GMT , GML and displacement at different draft.

To generate GZ curve at the required submerged depth

using HYDROMAX, a load case is required. Therefore,

it is assumed that the barge displacement is equal to the

summation of weights at required submerging depth. Its

longitudinal location coincide on (LCB) since, there is no

trim. Its vertical location equal to calculated (KGS).

Finally, wind speed was selected to be 70 knots at

transient, normal operational and intermediate conditions

for all cases. The wind heeling moment and GZ curves

for each case were generated and presented as shown in

figure (8).

From figure (8), it could be depicted that all cases

meet area ratio requirements of 1.3 with percent margin

of approximately 140 % at GMT=1. This percent is

directly proportional with GMT (case 3, 4 & 5) and

inversely proportional with GML (case 1, 2 & 3).

Furthermore, the intact stability results for all cases were

tested under the harshest standards as specified by

regularity authorities as shown in Table (5). All cases

succeeded to meet values for GZ at 15⁰, angles of heel at

first and second intercept, maximum GZ and vanishing

stability. Upon increasing GMT values, cases 4 & 5 were

found to have the largest margin values compared to the

other cases, comply with the stability standards and have

maximum loading capacity and KG limits. However,

they are not considered cost effective solution owing to

the high infrastructure cost of caissons and limited deck

area. On the other hand, case 1 was found to be the

optimum design solution with the smallest GMT value

of 1 m and GML/GMT = 30.

Figure 8: Generated GZ and wind heeling curve of each case.



Table 5: Intact stability results under the harshest standards.

6. Conclusions

Semisubmersible barges are a large growing industry

and expected to continue. Caisson design features is a

complicated issue that isn’t broadly investigated.

Comparison between different intact stability

standards reveled that in spite of they are outwardly

similar, the effect of variation limiting angle, GZ values

on stability margins can’t be predicted.

A mathematical model was developed to determine

caissons dimensions for any semisubmersible barge and

to provide the most practical caisson design. The

optimum (GML) to (GMT) ratio were found to be situated

between 20 to 30.

RHINO and MAXSURF aided mathematical model

verification, proved high matching between the proposed

and generated values of GMT and GML .

The abrupt change of GMT and GML at the submerging

process could be overcome by ballasting with a small

trim to increase the water plane area..

Testing intact stability results for all cases under the

harshest standards specified by regularity authorities

further verified the developed model.

Minimum GMT and GML are required for optimum cost

effective design to reduce the structure cost, abrupt

change in heel during operation, steady tilt and low

frequency motion.

7. Citations and References

1. Hoorn, Frank Van, 2004: Ship Design & Construction , Society of

Naval Architects and Marine Engineers.

2. Hoorn, Frank Van: Semi-Submersible Heavy-lift Ships in Operation , in Society of Naval Architects and Marine Engineers.

3. Hoorn, Frank Van and Wijsmuller Transport B. V., 1991: Design

criteria for self-propelled heavy-lift transports and how theory correlates with reality, in Society of Naval Architects and Marine

Engineers.

4. Hoorn, Frank Van, 2008: Heavy-Lift Transport Ships - Overview of Existing Fleet and Future Developments, in Marine perations

specialty symposium : National University Of Singapore.

5. BMT Fluid Mechanics Limited, 2006: Review of issues associated with the stability of semi-submersibles

6. Norwegian Maritime Directorate, 1992.: Regulations for Mobile Offshore Units.

7. Transport Canada Marine Safety, undated: Standards Respecting

Mobile Offshore Drilling Units, ref.TP6472E,. 8. International Maritime Organization (IMO), 1995: Code on Intact

Stability for all Types of Ships Covered by IMO Instruments,

Resolution A.749 (18) 9. American Bureau of Shipping, 1997: Rules for Building and

Classing Mobile Offshore Drilling Units, Part 3: Hull Construction

and Equipment. 10. Det Norske Veritas 'DNV', July 2012: Rules For Classification Of

Ships, Part 5 Chapter 7.

11. Lloyd’s Register of Shipping, 1996.: Rules and Regulations for the Classification of Mobile Offshore Units

12. H. Bird, and A. Morrall, 1986: Research Towards Realistic

Stability Criteria,, in The SAFESHIP Project : London. 13. Fjelde, Sindre, 2008: Stability and motion response analyses of

transport with barge, University of Stavanger

14. Biran, Adrian , 2003: Ship Hydrostatics and Stability. Butterworth-Heinemann, 351 pp.

Authors’ information 1 Cap., CEng, Phd in Naval Architecture and Marine Eng, EG.navy 2 Prof., Dr., Head of the Department of Naval Architecture and Marine

Engineering, Arab Academy for Science and Technology and Maritime

Transport 3 Demonstrators of Naval Architecture and Marine Engineering, Arab

Academy for Science and Technology and Maritime Transport.

The group is very interesting in the fields of ship design. The group is interested in using CAD ,calculating stability and resistance for ships of

complex hull forms.

intact stability standards

authorities requirement

Cases No.

1 2 3 4 5

(A+B)/ (B+C)

≥1.3 3.13 2.64 2.59 3.74 3.92

Static angle of heel due to wind

≤ 15⁰ Acc. to CCG

4.5⁰ 4.8⁰ 4.5⁰ 2.4⁰ 1.7⁰

Angle of heel at the second intercept

≥ 30⁰ Acc. to NMD

41⁰ 36⁰ 36⁰ 40⁰ 34⁰

Min. GM+ ≥ .3 m 1.09 0.9 1.0 1.9 2.6

Angle at which max. GZ occurs

≥7⁰ Acc. to

DNV 20⁰ 18⁰ 17⁰ 14⁰ 11⁰

Angle of vanishing stability

≥15⁰ Acc. to DNV

44⁰ 40⁰ 41⁰ 43⁰ 38⁰

GZ value at 15⁰ heeling angle (m)

≥0.1 m Acc. to

DNV 0.31 0.28 0.27 0.45 0.49

Heavy lift semi-submersible barge: A new tool for caissons...

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