FE Simulation of a Double-bottom Grounding on a Conical Rock

8/11/2019 FE Simulation of a Double-bottom Grounding on a Conical Rock

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HELSINKI UNIVERSITY OF TECNOLOGYShip Laboratory / Kristjan Tabri

FE simulation of a double-bottom grounding on a conical rock

Report


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CONTENTS:

1. INTRODUCTION .......................................................................................................................................4

2. MODELING OF THE DOUBLE-BOTTOM............. ............ .............. ............. .............. ............ .............. 43. SIMULATION PROCEDURE............ ............. ............. ............. .............. ............. ............ .............. ........... 8

4. DATA PROCESSING ............................................................................................................................... 11

5. RESULTS AND DISCUSSION ................................................................................................................ 11


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ABSTRACT

Current simulations are a part of a research project FSAKARI. The objective of the

simulations is to investigate how double-bottoms with different designs behave in case of a

grounding on a conical rock. To evaluate the effect of the different factors like double-bottom

construction and rock penetration to the double bottom five different double-bottom designs

are modeled. The simulations are carried out with different rock penetrations. After post-

processing the simulation data will be used in FSA analysis. Simulations are carried out in the

Ship Laboratory of the Helsinki University of Technology. For FE simulation explicit finite

element code LS-Dyna is used.


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1. Introduction

To estimate the risks in a case of a ship grounding on a rock it should be possible to estimate

how the ship behaves in grounding event. (As there is straight connection between the ship

and its double-bottom behaviour, also behaviour of the double-bottom should be known. To

investigate the behaviour of the double-bottom several FE simulations, where a rigid obstacle

(rock) penetrates to the double-bottom, are carried out. As it is too laborious to carry out a FE

simulation for the whole double-bottom of the ship only a small part of the ship is modelled.

During the simulation the model is fixed on the sides and is not moving, but the rock has a

horizontal and a vertical displacement. By the simulation, contact force and extent of the

damage are determined for the model. Based on that information forces and extent of the

damage can also be estimated for the whole ship. In current simulations main interest are on

the following points: How the depth of the rock penetration affects the contact force and the damage

Rock penetration needed for tearing

Average contact force

Extent of the tearing in outer and inner bottom plating

Force history during the contact event

This report includes descriptions of the different double-bottom models and FE simulation

process. Resulting data is presented for every simulation.

2. Modeling of the double-bottom

For the simulation five different double-bottom models are created. For modelling and three-

dimensional meshing FE program LS-Ingrid is used. LS-Ingrid is also used as a translator to

convert a database into LS-Dyna input file. Part of the ship is modelled according to the

structural drawings for a RO-RO vessel.

Main particles of the vessel are:

LWL: 150.47 [m]

LPP: 146.27 [m]

B: 25.35 [m]

T: 7.35 [m]


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Main particles of the double-bottom of the ship:

Girder spacing: 4.26 [m]

Floor spacing: 2.4 [m]

Height: 1.6 [m]

For the simulation, a small part from the middle of the ship is modeled (Figure 1). The model

included 4 floors and 3 girders, and its length was 12 meters and width 17 meters. Height of

the model depends on a particular case and varies from 1.6 [m] to 2.4 [m]. Altogether five

different double-bottom designs were used. The basic case is denominated as a case A. Cases

B, C, D are created by changing only one parameter in the case A. Case E has a different

designs than other cases. In the case E model has longitudinal girders instead of longitudinal

stiffeners and also transversal floors are removed. General picture of the cases A, B, C and Dis given in figure 2 and for the case E in figure 3.

Figure 1. Modeled part

Main parameters and particles for the different double-bottom models:

1. CASE A

Length 12 [m]

Breath 17 [m]

Height 1.6 [m]

Thickness:

floors 11 [mm]

girders 11 [mm]

Modeled part


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external plating 12 [mm]

internal plating 17 [mm]

Rock radius 1.1 [m]

Mass of the bottom model 75.7 [ton]

2. CASE B (db height)

Height of the double-bottom increased by 50% 1.62.4 [m]

Rock radius 1.1 [m]


3. CASE C (plating)

Bottom plating thickness increased by 50 % 12 18 [mm]

Rock radius 1.1 [m]


4. CASE D (stiffeners)

Bottom stiffeners moment of inertia increased by 90 % 2477 4720 [cm4]

Moment of inertia is increased by changing cross-

sectional area of the stiffener. Stiffener type is

changed from HP 260x10 to HP 300x13.

Rock radius 1.1 [m]


5. CASE E (girders)

Longitudinal stiffeners are replaced by longitudinal girders. Transversal floors are removed.

Longitudinal girders:

Thickness 10 [mm]

Girder spacing 710 [mm]

Rock radius 1.1 [m]


6. CASE A2

Same as the case A, but rock radius is 2 metres


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7. CASE A3

Same as the case A, but rock radius is 3 metres

The model depending on a particular case has 70,000- 85,000 elements. The size of the

prevailing element is 10x10 [mm2]. For the precise simulation of tearing, fracture criteria for

the prevailing element size is calculated. For that we modelled a specimen and carried out

several tensile tests and looked for correct failure criteria by comparing real and calculated

stress curves. The model had boundary conditions at both ends and on both sides (Figure.2),

where all degrees of freedom are fixed.

Figure 2.Double-bottom model (Cases A, B, C, D)

As it can be seen from the figure 2, x-axis points to longitudinal direction and z-axis points to

vertical direction. Same notifications are later used in appendices with time-histories.

Longitudinal direction,

boundary conditions

Breath,

boundary conditions

Floor

Centre girder

Tank-top (inner plating)

Outer plating

X

Z


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Figure 3.Double-bottom model (Case E)

3. Simulation procedure

To simulate the grounding event a conical rock is modelled. Cone angle is 45 and radius ofthe top cone of the rock is 1.1 meters for the cases A, B, C and D, and 2 and 3 meters for the

cases A2 and A3. In figure 4, modelled rock is shown graphically. The rock is given a

horizontal and a vertical displacement as a function of time as follows (figure 5):

vertical displacement =15t

horizontal displacement = MAXPt

0.026-0.24

026.0cos1

2

1

where

t -time

PMAX -maximum (final) rock penetration to the double-bottom

0.026 -time when rock starts to penetrate to the double-bottom

0.24 -time when rock attains its final penetration

As forces close to boundary conditions may cause some disturbances and inaccuracy, the rock

starts to penetrate the double-bottom not exactly at the first end of the model but 0.39 [m]


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(t=0.026 [s]) from it. In the same reason longitudinal displacement of the rock terminates 2.4

[m] before the end of the model. Total longitudinal displacement of the rock is 9.6 [m]

(tTOTAL=0.64 [s]). The simulations are carried out for 7 different rock penetrations- from 0.5 to

3.5 [m] with 0.5 [m] spacing. In every case the rock attained final penetration value 3.6

meters (t=0.24 [s]) from the first end of the model. Centre of the rock is always moving along

the centre girder. Horizontal velocity of the rock is 15 [m/s], but as the force calculation

process is quasi-static, velocity of the rock does not have any effect to the force values. In

figure 5 rock movements with corresponding temporal values are presented graphically.

The double-bottom model, the shape and the movements of the rock are described in input file

for LS-Ingrid. For the simulation initial input file is converted into input file for explicit finite

element code LS-Dyna. In LS-Dyna calculations contact force between rock and the double-

bottom is calculated by usingpenalty method. In thepenalty methodnormal interface springs

are placed between all penetrating nodes and surfaces, and forces are calculated by using

springs. Better description of thepenalty methodand other matters concerning the simulation

procedure are given in LS-Dyna theoretical manual [1].Computer used for simulation is dual

195 MHz processor Silicon Graphics Octane2 UNIX Workstation with 512 MB memory.

Operation system used in workstation is IRIX.

Figure 4. Modeled rock

45

R


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Figure 5. Rock movements respect to the double-bottom

Rock displacement

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 0.80 1.60 2.40 3.20 4.00 4.80 5.60 6.40 7.20 8.00 8.80 9.60

Horizontal displacement (m)

Verticaldisplacement(m)

Figure 6. Rock displacement

Maximum penetration

t=0.24 [s]

Termination of the

rock displacement

Rock starts to penetrate to

the double-bottom t=0.026


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4. Data processing

Resulting data is given in time domain after every 1.29E-3 seconds (1.93E-2 [m]). Single

simulation takes about 20-35 hours depending on a particular case and rock penetration. The

amount of the resulting data in single simulation is about 100 KB in text files and 30 MB in

video files. Videos of outer and inner bottom plating damages are taken for every simulation.

For more convenient and comprehensible processing, the simulation data is converted from

time domain into displacement domain. To evaluate the effect of different design, force

histories are analysed after each simulation. Forces needed for tearing both in outer and inner

bottom plating and also average grounding force were calculated and presented in every

simulation. Average force is calculated during the time when rock has attained its final

penetration value and moves horizontally in longitudinal direction. To evaluate the extent of

the damage average breath of the tearing is measured as well as temporal initiation of the

tearing. In some simulations also deformation energy is measured.

5. Results and discussion

According to recorded time histories and above-mentioned calculated values some general

conclusions can be drawn and behaviour of the different designs can be presented. On

analysis cases are divided into two halves- cases with same rock radius (cases A, B, C and D)

and cases with different rock radius (cases A, A2 and A3). Both halves are investigated

separately. On comparison main interests are on following points:

Average vertical and horizontal grounding forces

Tearing width

Penetration depth and force values at the moment of tear initiation

Cases A, B, C, D

First the results for the cases A, B, C and D are presented and analysed. Results are both

presented on graphical and numerical mode.


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Average vertical and horizontal impact forces

Values for the average vertical grounding force are presented on graphs 1 and 2, and

numerically on table 1. Graphs 3, 4 and table 2 present the values for horizontal forces. On the

graphs 1 and 3 vertical and horizontal impact forces are presented as a function of final

penetration depth as it gives good overview how are the relations between the different

designs on different final penetration values. Graphs 2 and 4 basically present the same

values, but on mode where it is easier to see how much the values on different penetration

values differ from the average value. Average values on graphs 1 and 3 are presented with

dots in corresponding colour and on graphs 2 and 4 with blue rectangles.

-3,0E+07

-2,5E+07

-2,0E+07

-1,5E+07

-1,0E+07

-5,0E+06

0,0E+00

0 0,5 1 1,5 2 2,5 3 3,5 4

Penetration [m]

Force[N]

CASE A

CASE B

CASE C

CASE D

CASE E

Graph 1. Average vertical forces for cases A, B, C, D


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-3,0E+07

-2,5E+07

-2,0E+07

-1,5E+07

-1,0E+07

-5,0E+06

0,0E+00

CASE A CASE B CASE C CASE D CASE E

Force[N]

3,5

3

2,5

2

1,5

1

0.5

Average

Graph 2. Average vertical forces for cases A, B, C, D (sorted by cases)

Average force values shown in the graphs are calculated by using force values from the

middle range.

In the middle range only three penetration values are considered- 1.5, 2.0 and 2.5 metres.

Therefore average force value on the graphs is simply average of the three force values on

mentioned penetration depths. The middle range reflects the situation where outer plating of

the double-bottom is widely damaged and inner plating is slightly damaged or still intact.

From the graphs it can be seen that case B gives lowest average force value in the middle

range. Reason is that compared to other cases case B gives much lower force values on

penetration depths from 1.5 to 3.0 metres. It can be explained by the fact that on mrntioned

range (1.5-3.0) other cases (except B) are already deforming (lower penetration values) or

tearing (higher values) the inner plating, but in case B rock contacts with the inner plating no

before the penetration value 2.5.

If the beginning of the graph is considered it can be seen that on penetration value 0.5 case B

gives quite average value. Only cases D (stiffeners) and C give higher value, which can be

explained by their higher stiffness. It can be seen that on penetration value 1.0 case B gives

almost highest value (equal to case C).


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Case C gives highest average force values and has also highest values in most of the

penetration values. On penetration value 0.5 case C is the only double-bottom version, which

stays intact. It reflects also on its high force value on that point.

Case E (girders) has second highest average force value. As its construction is quite stiff,

tearing on penetration value 0.5 occurs very early and because of that also force value on that

penetration depth is the lowest.

Table 1. Vertical force values

Penetration/ case A B C D E

0,5 -5,448E+06 -5,824E+06 -8,592E+06 -7,444E+06 -4,538E+06

1 -6,349E+06 -7,261E+06 -7,413E+06 -6,757E+06 -6,794E+06

1,5 -9,320E+06 -8,631E+06 -1,053E+07 -9,657E+06 -1,120E+07

2 -1,424E+07 -1,090E+07 -1,658E+07 -1,482E+07 -1,547E+07

2,5 -1,868E+07 -1,437E+07 -2,212E+07 -2,022E+07 -2,007E+07

3 -2,065E+07 -1,992E+07 -2,277E+07 -2,155E+07 -2,387E+07

3,5 -2,232E+07 -2,316E+07 -2,641E+07 -2,335E+07 -2,391E+07

Average (1.5-2.5 [m]) -1,408E+07 -1,130E+07 -1,641E+07 -1,490E+07 -1,558E+07

-2,0E+07

-1,8E+07

-1,6E+07

-1,4E+07

-1,2E+07

-1,0E+07

-8,0E+06

-6,0E+06

-4,0E+06

-2,0E+06

0,0E+000 0,5 1 1,5 2 2,5 3 3,5 4

Penetration [m]

Force[N]

CASE A

CASE B

CASE C

CASE D

CASE E

Average

Graph 3. Average horizontal forces for cases A, B, C, D


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-2,0E+07

-1,6E+07

-1,2E+07

-8,0E+06

-4,0E+06

0,0E+00


Force[N]

3,5

3

2,5

2

1,5

1

0.5

Average

Graph 4. Average horizontal forces for cases A, B, C, D (sorted by the cases)

As it can be seen, graphs for horizontal force values (graphs 3 and 4) are quite similar to those

in case of vertical forces. On penetration values 0.5 to 1.5 all cases give quite similar results.

On higher penetrations it can be seen that case B gives clearly lower values (average 13%) on

all penetration depths. Reason for that is quite same as it was on case of the vertical forces.

From the table 3 comes out that in case B tearing in inner plating occurs not before the

penetration depth 3.5, which indicates that contact between the inner plating, and rock occurs

later compared to other cases.

Cases C and D give average force values equal to each other and slightly higher than cases D

and A.

Table 2. Horizontal force valuesPenetration/ case A B C D E

0,5 -2,977E+06 -3,245E+06 -3,657E+06 -3,303E+06 -2,773E+06

1 -4,606E+06 -5,206E+06 -5,237E+06 -4,854E+06 -4,796E+06

1,5 -6,496E+06 -6,152E+06 -7,163E+06 -6,775E+06 -7,394E+06

2 -9,157E+06 -7,562E+06 -1,040E+07 -9,348E+06 -1,062E+07

2,5 -1,275E+07 -9,928E+06 -1,456E+07 -1,356E+07 -1,407E+07

3 -1,500E+07 -1,291E+07 -1,577E+07 -1,498E+07 -1,713E+07

3,5 -1,734E+07 -1,550E+07 -1,903E+07 -1,679E+07 -1,806E+07

Average (1.5-2.5 [m]) -9,466E+06 -7,881E+06 -1,071E+07 -9,894E+06 -1,069E+07


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Tearing width

Flowingly tear widths are analysed. For every simulation tearing width was measured using

measures only from that part of the model where rock was moving only horizontally and

width of the rupture changing only slightly or was almost constant. It is necessary to do it so

as in some cases at the very beginning of the rupture tearing width is several times higher than

it is at the constant part. So conclusively it can be said that tear widths given in graphs x to x

and on tables x and x describes only that part of the rupture where rock was moving only

horizontally and not the very beginning of the rock. On appendices 1 to 6 measures are given

both for constant width of the tearing as well as for the widest breath. Figure 7 helps to

understand the above-described phenomena.

Figure 7.Tearing width

Values for the tearing widths are given in graphs 5 (outer plating) and 6 (inner plating).

Numerically results are presented in table 3.

CONSTANT PART

WIDEST BREATH

DIRECTION OF

THE ROCK


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1,490 1,4661,349

1,506

1,654

0

0,5

1

1,5

2

2,5

3


Rockpenetration[m]

3.5

3

2.5

2

1.5

1

0.5

Average

Graph 5. Average breaths of the outer plating tears

1,647

0,490

1,377

0,824

1,070

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5


Rockpenetration[m]

2.5

3

3.5

Average

Graph 6. Average breaths of the inner plating tears


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Outer plating tearing

As it can be seen from the graph 5 differences in average tearing width values are quite small.

Cases A, B and D give nearly similar values. Case C (plating) gives little smaller (9 %) and

case E (girders) higher values (11 %) than other 3 cases. In case E higher tearing width can be

explained by the higher stiffness of the double-bottom. In case of double-bottom version E

greater number of longitudinal girders increases stiffness of the double-bottom and also rock

causes greater damage to the double-bottom, as bottom does not follow rock movements as

well as in other cases. In case C greater plating thickness (18 [mm]) does not ruptures as

easily as in case of thinner (12 [mm]) plates and stronger plating also deforms inner

constructions more easily.

Inner plating tearing

In case of inner bottom tearing, differences between the tearing widths are bigger. Values forthe case B (higher double-bottom) are not straight comparable to the other cases as double-

bottom heights are different and so it gives clearly the slowest tear width value. If other four

cases are compared it can be seen that case D (stiffeners) gives smallest and case A highest

value. Average tear width for the case A is twice as big as it is in case of the D version. Also

the case E (girders) gives good values compared to the cases A (35 % narrower tear) and C

(22 % narrower). In case of the bottom version D stronger stiffeners are dividing contact force

into a larger area and plating is deformed more widely and smoothly.

Table 3. Values for tearing widths

FINAL PENETRATION [m] CASE

Outer plating A B C D E

0,5 0,36 0,23 0,00 0,30 0,40

1,0 0,95 0,95 0,93 0,94 0,98

1,5 1,13 1,17 1,09 1,19 1,48

2,0 1,47 1,46 1,27 1,46 1,70

2,5 1,90 1,90 1,75 1,69 2,09

3,0 1,87 2,10 2,17 2,16 2,20

3,5 2,75 2,45 2,23 2,80 2,73

Average 1,49 1,47 1,35 1,51 1,65Inner plating A B C D E

0,5 0 0 0 0 0

1 0 0 0 0 0

1,5 0 0 0 0 0

2 0 0 0 0 0

2,5 0,32 0 0,28 0,141 0,31

3 1,87 0 1,05 0,78 1,25

3,5 2,75 0,49 2,8 1,55 1,65

Average 1,647 0,490 1,377 0,824 1,070


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In every simulation rock achieves its final penetration value during the same period of time,

but as the final penetration value is different for every simulation, rock meets structural

members like floors, girders and stiffeners in every simulations at different positions. That is

the reason why there is a quite big scatter in penetration values necessary to cause tearing to

the plating. To smooth the effect the above described problem average penetration values are

calculated and compared. Same applies also to force values at the moment of tear initiation. It

should be noted that average values are calculated using only those values where tearing has

already occurred.

0,5270,493

0,619

0,556

0,460

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8


Roc

kpenetration[m]

0.5

1

1.5

2

2.5

3

3.5

Average

Graph 7. Penetration needed to cause tearing to the outer plating


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-1,25E+07-1,17E+07

-1,96E+07

-1,38E+07

-1,10E+07

-2,5E+07

-2,0E+07

-1,5E+07

-1,0E+07

-5,0E+06

0,0E+00CASE A CASE B CASE C CASE D CASE E

Force[N]

3.5

3

2

2.5

1.5

10.5

Average

Graph 8. Force values at the moment of outer plating tear initiation

Table 4. Penetrations at the moment of outer plating tear initiation

Finalpenetration A B C D E

0,5 0,47 0,479 - 0,472 0,306

1 0,534 0,482 0,561 0,533 0,435

1,5 0,529 0,504 0,722 0,636 0,424

2 0,524 0,473 0,555 0,524 0,483

2,5 0,509 0,529 0,59 0,604 0,451

3 0,541 0,534 0,654 0,541 0,608

3,5 0,582 0,448 0,6313 0,581 0,510

Average 0,527 0,493 0,619 0,556 0,460

Outer plating

It can be seen from the graphs 7 and 8 that case E has lowest value for the penetration

necessary to cause tearing to the outer plating. Case E is very weak especially at low final

penetration values- 0.5 to 1.5 [m], where it ruptures in much lower penetration values

compared to other cases. Scatter between the case E and the other cases is large-

approximately 39 % on lower final penetration values. Scatter is decreasing when higher final

penetration values are considered and at the end it is roughly 10 %. Cases C and D are having

highest values for penetration before cracking occurs.


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Table 5. Force values at the moment of outer plating tear initiation

Final

penetration A B C D E

0,5 -6,91E+06 -7,80E+06 - -7,26E+06 -6,385E+06

1 -1,13E+07 -1,00E+07 -1,52E+07 -1,26E+07 -1,030E+07

1,5 -1,24E+07 -1,29E+07 -1,88E+07 -1,49E+07 -1,034E+07

2 -1,25E+07 -1,22E+07 -1,67E+07 -1,38E+07 -1,028E+072,5 -1,35E+07 -1,43E+07 -1,93E+07 -1,61E+07 -1,273E+07

3 -1,50E+07 -1,34E+07 -2,34E+07 -1,54E+07 -1,225E+07

3,5 -1,58E+07 -1,15E+07 -2,40E+07 -1,65E+07 -1,447E+07

Average -1,25E+07 -1,17E+07 -1,96E+07 -1,38E+07 -1,10E+07

If forces at the moment of outer plating tear initiation are under the consideration it can be

seen that case C (plating) gives 1.4 to 1.8 times higher force level than the other cases. Result

is quite obvious as it indicates that to cause tearing to the 18 [mm] plating needs much higher

force level than to cause tearing to the same type of material, but 12 [mm] in thickness. Case

E has lowest force values and scatter between the case E and other cases is approximately

25%. Reason for that is in small penetration values structure in case E does not bend so

widely as it does in other cases and tearing occurs easily.

Inner plating

Results for the necessary penetration values and forces at the moment of tear initiation are

given at graphs 9 and 10. Numerical results are in table 6.

Penetration needed to cause tearing to the inner plating is quite same for all the cases except

case B, which is obvious as case B has 50% higher double-bottom. Scatter between the cases

A, C, D, E is approximately 5% and again case E has the lowest value.


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2,363

3,100

2,351 2,3432,221

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5


Rockpenetration[m]

0.5

1

1.5

2

2.5

33.5

Average

Graph 9. Penetration needed to cause tearing to the inner plating

-2,89E+07

-3,13E+07

-3,85E+07

-3,35E+07

-3,85E+07

-5,0E+07

-4,5E+07

-4,0E+07

-3,5E+07

-3,0E+07

-2,5E+07

-2,0E+07

-1,5E+07

-1,0E+07

-5,0E+06

0,0E+00CASE A CASE B CASE C CASE D CASE E

Force[N]

0.5

1

1.5

2

2.5

3

3.5

Average

Graph 10.Forces at the moment of inner plating tear initiation


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In case of the force values at the moment of tear initiation differences are much bigger. Also

relations between the cases are different as they were in case of the penetrations. Case A gives

the lowest value and cases C and E are having equal force value, which is also the highest

value. In both cases (C and E) it can be explained by the fact that amount of the deformation

work to be done in order to cause tearing to the inner plating is higher and the double-bottom

still has high resistance against further rock movements.

Table 6. Penetration needed to cause tearing to the inner plating


0,5 - - - - -

1 - - - - -

1,5 - - - - -

2 - - - - -

2,5 2,36 - 2,35 2,43 2,36

3 2,3 - 2,4 2,3 2,42

3,5 2,43 3,1 2,302 2,3 1,88

Average 2,363 3,100 2,351 2,343 2,221

Table 7. Force values at the moment of inner plating tear initiation


0,5 - - - - -

1 - - - - -1,5 - - - - -

2 - - - - -

2,5 -2,33E+07 - -2,86E+07 -2,56E+07 -3,379E+07

3 -3,63E+07 - -4,33E+07 -3,55E+07 -4,556E+07

3,5 -2,72E+07 -3,13E+07 -4,37E+07 -3,93E+07 -3,625E+07

Average -2,89E+07 -3,13E+07 -3,85E+07 -3,35E+07 -3,85E+07


24/122

24

CASES A, A2, A3

In cases A, A2 and A3 double-bottom design remains the same, but rock radius is changed

and has values 1.1, 2 and 3 [m]. By comparing those 3 cases it is possible to evaluate what

kind of effect rock radius has to tearing properties and force values.

Average vertical and horizontal forces

Average vertical and horizontal forces are presented on graphs 11, 12 and in table 8.

-3,5E+07

-3,0E+07

-2,5E+07

-2,0E+07

-1,5E+07

-1,0E+07

-5,0E+06

0,0E+00

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0

Penetration (m)

Force(N)

CASE A (r=1.1)

CASE A2 (r=2)

CASE A3 (r=3)

Graph 11.Average vertical forces

If vertical force values are considered (graph 11) it can be seen that increasing rock radius

from 1.1 [m] to 2 [m] increases force level approximately 1.25 times and increasing radius

from 1.1 to 3 [m] increases force level 1.6 times.


25/122


26/122

26

Tear width

If tear width values are considered it can be seen that in case of outer plating it is hard to find

some trend how rock radius affects the tear width. Average tear width values are 1.49, 1.38,

1.54 [m] for rock radiuses respectively 1.1, 2.0 and 3.0 [m]. As it can be seen from the results

that increasing the rock radius decreases the tear width or vice versa. It can be explained by

the fact that rocks with different radiuses meet the structural members (especially girders) on

different positions and girders and plates are deformed by different mechanisms.

0

0,5

1

1,5

2

2,5

3

CASE A CASE A2 CASE A3

Penetration[m]

3,5

3

2,5

2

1,5

1

0,5

Average

Graph 13. Average breaths of the outer plating tears

In case of inner plating tearing it is easy to see that higher rock radiuses decrease the tear

width. In case of larger rock double-bottom is bended more heavily and rock also does not

start to cut the inner plating so early.

1.49

1.38

1.54


27/122

27

0

0,5

1

1,5

2

2,5

3


Penetration[m]

3,5

3

2,5

Average

Graph 14.Average breaths of the inner plating tears

Numerical results for the outer and inner plating tear breaths are given in table 9.

Table 9. Tear breaths

OUTER PLATING INNER PLATINGPenetration A A2 A3 A A2 A3

0,5 0,36 - - - - -

1,0 0,95 0,61 - - - -

1,5 1,13 1,09 0,84 - - -

2,0 1,47 1,356 1,25 - - -

2,5 1,9 1,56 1,48 0,32 - -

3,0 1,87 1,256 1,935 0,6687 0,69 0,49

3,5 2,75 2,4 2,21 2,73 1,66 1,27

Average 1,49 1,38 1,543 1,24 1,18 0,88

1.241.18

0.88


28/122

28


Penetration and force values at the moment of outer plating tear initiation are given on graphs

15, 16 and in table 10.

0,527

0,881

1,341

0,0

0,5

1,0

1,5

2,0

2,5


Pe

netration[m]

3,5

3

2,5

2

1,5

1

0,5

Average

Graph 15.Necessary penetration values to cause tearing to the outer plating

From the graphs for the outer plating penetration and forces comes out that increasing rock

radius clearly increases force level and also rock goes deeper to the double-bottom before its

plating starts tearing. Reason for that is obviously larger deformable volume and wider

bending of the whole double-bottom.

In case of penetration values there is almost linear correlation between the rock radius and the

necessary penetration. When rock radius is increased 1.8 times (2/1.1) average necessary

penetration value increases 1.67 times (0.881/0.527) and when rock radius is increased 2.7times (3/1.1) average necessary penetration value increases 2.55 times (1.341/0.527).


29/122

29

-1,25E+07

-2,20E+07-2,32E+07

-3,5E+07

-3,0E+07

-2,5E+07

-2,0E+07

-1,5E+07

-1,0E+07

-5,0E+06

0,0E+00


Force[m]

3,5

3

2,5

2

1,5

1

0,5

Average

Graph 16.Forces at the moment of outer plating tear initiation

In case of the force values linear correlation does not apply anymore and changing radius

from 1.1 to 2 [m] increases average force level 1.76 times, but increase from 1.1 to 3 [m]

increases it only 1.86 times.

Table 10. Penetration depths and force values at the moment of outer plating tear

initiation

Penetration Force

Finalpenetration A A2 A3 A A2 A3

0,5 0,470 - - -6,91E+06 - -

1,0 0,534 0,776 - -1,13E+07 -1,84E+07 -

1,5 0,529 0,836 0,905 -1,24E+07 -2,16E+07 -3,13E+07

2,0 0,524 0,852 1,298 -1,25E+07 -2,64E+07 -2,49E+07

2,5 0,509 0,815 1,042 -1,35E+07 -2,56E+07 -1,76E+07

3,0 0,541 0,926 1,250 -1,50E+07 -2,01E+07 -1,85E+07

3,5 0,580 1,080 2,210 -1,58E+07 -1,97E+07 -2,37E+07

Average 0,527 0,881 1,341 -1,25E+07 -2,20E+07 -2,32E+07


30/122

30

Inner plating

Penetration depths and force values at the moment of inner plating tear initiation are given on

graphs 17, 18 and in table 11.

2,365

2,564

2,754

0,0

0,5

1,0

1,5

2,0

2,5

3,0


Penetration[m]

3,5

3

2,5

Average

Graph 17.Necessary penetration values to cause tearing to the inner plating

As it can be seen from the graph 17 rock radius clearly increases the necessary penetration

values, but not as strongly as it was in case of the outer plating tear. Increasing radius from

1.1 to 2 or to 3[m] necessary penetration values increase respectively 1.08 or 1.16 times.

In case of the force values (graph 18) appear that effect of the rock radius is different from the

effect in case of the outer plating. Changing rock radius from 1.1 to 2 [m] increases the force

level 1.5 times and when radius is changed to 3 [m] force level rises 2.0 times.


31/122

31

-2,90E+07

-4,40E+07

-5,90E+07

-7,0E+07

-6,0E+07

-5,0E+07

-4,0E+07

-3,0E+07

-2,0E+07

-1,0E+07

0,0E+00


Force[m]

3,5

3

2,5

Average

Graph 18.Forces at the moment of inner plating tear initiation

Table 11. Penetration depths and force values at the moment of inner plating tear

initiation

Necessary penetration Forces at the moment of tear initiationFinal

penetration A A2 A3 A A2 A3

0,5 - - - - - -

1,0 - - - - - -

1,5 - - - - - -

2,0 - - - - - -

2,5 2,362 - - -2,33E+07 - -

3,0 2,304 2,643 2,712 -3,63E+07 -4,55E+07 -5,47E+07

3,5 2,430 2,486 2,796 -2,72E+07 -4,24E+07 -6,32E+07

Average 2,365 2,564 2,754 -2,90E+07 -4,40E+07 -5,90E+07


32/122

32

Literature

1. LS-Dyna theoretical manual

2. LS-Dyna user manual

Appendices

Appendix 1 Case A

Appendix 2 Case B

Appendix 3 Case C

Appendix 4 Case D

Appendix 5 Case A2

Appendix 6 Case A3


33/122

A1.1 APPENDIX 1. Case A (Basic)

DB I CASE A (Basic)

Measures

Cone top radius 1.1 [m]Double-bottom

Lenght 12 [m]

Breath 17 [m]Height 1.6 [m]

Girders

Thickness 0.011 [m]

Spacing 4.26

Girder stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing0.8

[m]

Floors

Thickness 0.011 [m]

Spacing 2.4 [m]

Floor stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing 0.71 [m]

External platingThickness 0.012 [m]

Internal plating

Thickness 0.017 [m]

Plating stiffeners

bottom

Height 0.26 [m]

Thickness 0.00361/0.26 [m]

Spacing 0.71 [m]

tank-top

Height 0.26 [m]

Thickness 0.00361/0.26 [m]

Spacing 0.71 [m]


34/122


DB I CASE A (Basic)

Velocity of the ship 15 m/s

Approach of the rock to db 0.5 m

Tear to outer plating (values in the moment ofinitiation)

time 2.18E-01 sec

x-disp 3.25E+00 m

z-disp 4.70E-01 m

x-force -2.56E+06 N

z-force -6.91E+06 N

Average breath of the tear 3.60E-01 m

Average X- force -2.98E+06 N

Average Z-force -5.45E+06 N


35/122


X-force (H=0.5 m)

-6.E+06

-5.E+06

-4.E+06

-3.E+06

-2.E+06

-1.E+06

0.E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

Initiation of op tear

x-force

Average

Z- force (H=0.5 m)-1.E+07

-9.E+06

-8.E+06

-7.E+06

-6.E+06

-5.E+06

-4.E+06

-3.E+06

-2.E+06

-1.E+06

0.E+00

0 1 2 3 4 5 6 7 8 9 10

x- displacement (m)

z-force(N)

Z-force


Average


36/122


DB I CASE A



Tear to outer plating (values in themoment of initiation)

time 1.40E-01 sec

x-disp 2.08E+00 m

z-disp 5.34E-01 m

x-force -3.37E+06 N

z-force -1.13E+07 N





37/122


X-force (H=1.0 m)

-8.E+06

-7.E+06

-6.E+06

-5.E+06

-4.E+06

-3.E+06

-2.E+06

-1.E+06

0.E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

x-force

Initation of op tear

Average

Z- force (H=1.0 m)

-1.25E+07

-1.05E+07

-8.50E+06

-6.50E+06

-4.50E+06

-2.50E+06

-5.00E+05

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force(n)

z-force


Average


38/122


DB I CASE A




time 1.13E-01 sec

x-disp 1.69E+00 m

z-disp 5.29E-01 m

x-force -3.74E+06 N

z-force -1.24E+07 N

Average breath of the tear 1.13E+00 m




39/122


X-force (H=1.5 m)

-9.E+06

-8.E+06

-7.E+06

-6.E+06

-5.E+06

-4.E+06

-3.E+06

-2.E+06

-1.E+06

0.E+000 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force(N)

X-force


Average

Z- force (H=1.5 m)

-1.3E+07

-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displaceme nt (m )

z-force

(N)

Z-force

Initation o f op tear

Average


40/122


DB I CASE A



Tear to outer plating (values in the moment of initiation)

time 9.98E-02 sec

x-disp 1.49E+00 m

z-disp 5.24E-01 m

x-force -3.23E+06 N

z-force -1.25E+07 N





41/122


X-force (H=2.0 m)

-1.35E+07

-1.15E+07

-9.50E+06

-7.50E+06

-5.50E+06

-3.50E+06

-1.50E+06

0 1 2 3 4 5 6 7 8 9 10

x-displaceme nt (m)

x-force

(N)

x-force


Average

Z- force (H=2.0 m )

-2.5E+07

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force(N)

Z-force


Average


42/122


DB I CASE A




time 9.09E-02 sec

x-disp 1.35E+00 m

z-disp 5.09E-01 m

x-force -2.33E+06 N

z-force -1.35E+07 N

Average breath of the op tear 1.90E+00 m

Tear to inner bottom (values in the moment ofinitiation)

time 2.11E-01 sec

x-disp 3.15E+00 m

z-disp 2.36E+00 m

x-force -1.03E+07 N

z-force -2.33E+07 N

Average breath of the ib tear 3.20E-01 m




43/122


x-force (H=2.5 m)

-1.8E+07

-1.6E+07

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

x-force(N)

X-force

Initation of op tearInitation of ib tear

Average

Z- force (H=2.5 m)-2.6E+07

-2.1E+07

-1.6E+07

-1.1E+07

-6.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)


Initation of ib tear

Average

z-force


44/122


DB I CASE AVelocity of the ship 15 m/s



time 8.58E-02 sec

x-disp 1.29E+00 m

z-disp 5.41E-01 m

x-force - N

z-force -1.50E+07 N

Average breath of the op tear 5,178x1,87 m


time 1.72E-01 sec

x-disp 2.57E+00 m

z-disp 2.30E+00 m

x-force - N

z-force -3.63E+07 N


Average X- force 0.00E+00 N



45/122


Z- force (H=3.0 m)

-3.9E+07

-3.4E+07

-2.9E+07

-2.4E+07

-1.9E+07

-1.4E+07

-9.0E+06

-4.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-displacement(N)



Average

z-force


46/122


DB I CASE A

29-Nov-01

Velocity of the ship 15 m/sApproach of the rock to db 3.5 m


time 8.32E-02 sec

x-disp 1.25E+00 m

z-disp 5.82E-01 m

x-force -1.17E+06 N

z-force -1.58E+07 NAverage breath of the op tear 6.91x2.75 m


time 1.60E-01 sec

x-disp 2.40E+00 m

z-disp 2.43E+00 m

x-force -9.64E+06 N

z-force -2.72E+07 NAverage breath of the ib tear 2.73 m




47/122


x-force (H=3.5 m)

-2.2E+07

-2.0E+07

-1.7E+07

-1.5E+07

-1.2E+07

-9.5E+06

-7.0E+06

-4.5E+06

-2.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force(N)

X-force



Average

Z- force (H=3.5 m)

-4.0E+07

-3.5E+07

-3.0E+07

-2.5E+07

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)


Average

z-force


48/122

A2.1 APPENDIX 2. Case B (DB height)

DB I CASE B

Measures

Double-bottom

Lenght 12 [m]

Breath 17 [m]

Height 2.4 [m]

Girders

Thickness 0.011 [m]

Spacing 4.26

Girder stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing 0.8 [m]

FloorsThickness 0.011 [m]

Spacing 2.4 [m]

Floor stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing 0.71 [m]

External plating

Thickness 0.012 [m]

Internal plating

Thickness 0.017 [m]

Plating stiffeners

bottom

Height 0.3 [m]

Thickness 0.00361/0.26 [m]

Spacing 0.71 [m]

tank-top

Height 0.26 [m]

Thickness 0.00361/0.26 [m]

Spacing 0.71 [m]


49/122


DB I CASE B




time 2.47E-01 sec

x-disp 3.69E+00 m

z-disp 4.79E-01 m

x-force -3.18E+06 N

z-force -7.80E+06 N





50/122


X-force (H=0.5 m)-6.E+06

-5.E+06

-4.E+06

-3.E+06

-2.E+06

-1.E+06

0.E+00

0 1 2 3 4 5 6 7 8 9 10x-displacement (m)

x-force

(N)

Initiation o f op tear

x-forceAverage

Z- force (H=0.5 m )-1.E+07

-9.E+06

-8.E+06

-7.E+06

-6.E+06

-5.E+06

-4.E+06

-3.E+06

-2.E+06

-1.E+06

0.E+00

0 1 2 3 4 5 6 7 8 9 10

x- displacement (m)

z-force

(N)

Z-force


Average


51/122


DB I CASE B




time 1.32E-01 sec

x-disp 1.97E+00 m

z-disp 4.82E-01 m

x-force -3.41E+06 N

z-force -1.00E+07 N





52/122


X-force (H=1.0 m)

-8.E+06

-7.E+06

-6.E+06

-5.E+06

-4.E+06

-3.E+06

-2.E+06

-1.E+06

0.E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

x-force

(N)

x-force

Initation of op tearAverage

Z- force (H=1.0 m)

-1.25E+07

-1.05E+07

-8.50E+06

-6.50E+06

-4.50E+06

-2.50E+06

-5.00E+05

0 1 2 3 4 5 6 7 8 9 10

x-displacement(m)

z-force

(n)

z-force


Average


53/122


DB I CASE B




time 1.11E-01 sec

x-disp 1.66E+00 m

z-disp 5.04E-01 m

x-force -3.91E+06 N

z-force -1.29E+07 N





54/122


X-force (H=1.5 m)

-9.E+06

-8.E+06

-7.E+06

-6.E+06

-5.E+06

-4.E+06

-3.E+06

-2.E+06

-1.E+06

0.E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X- force


Average

Z- force (H=1.5 m)

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)

Z-force


Average


55/122


DB I CASE B




time 9.60E-02 sec

x-disp 1.43E+00 m

z-disp 4.73E-01 m

x-force -2.88E+06 N

z-force -1.22E+07 N





56/122


X-force (H=2.0 m)-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

x-force

Initiation o f op tear

Average

Z- force (H=2.0 m)

-1.6E+07

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

z-force(N)

Z-force


Average


57/122


DB I CASE B




time 9.22E-02 sec

x-disp 1.37E+00 m

z-disp 5.29E-01 m

x-force -2.41E+06 N

z-force -1.43E+07 N





58/122


X-force (H=2.5 m)

-1.30E+07

-1.10E+07

-9.00E+06

-7.00E+06

-5.00E+06

-3.00E+06

-1.00E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

x-forceInitiation of op tear

Average

Z- force (H=2.5 m)

-2.0E+07

-1.8E+07

-1.6E+07

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)

Z-force


Average


59/122


DB I CASE B




time 8.58E-02 sec

x-disp 1.28E+00 m

z-disp 5.34E-01 m

x-force -1.88E+06 N

z-force -1.34E+07 N





60/122


X-force (H=3.0 m)

-1.7E+07

-1.5E+07

-1.3E+07

-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

x-force

(N)

X- force


Average

Z- force (H=3.0 m)

-2.5E+07

-2.3E+07

-2.0E+07

-1.8E+07

-1.5E+07

-1.3E+07

-1.0E+07

-7.5E+06

-5.0E+06

-2.5E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)

Z- force


Average


61/122


DB I CASE B

23-Oct-01

Velocity of the ship 15 m/sApproach of the rock to db 3.5 m


time 7.68E-02 sec

x-disp 1.14E+00 m

z-disp 4.48E-01 m

x-force -1.73E+06 N

z-force -1.15E+07 NAverage breath of the op tear 2.45E+00 m


time 1.95E-01 sec

x-disp 2.89E+00 m

z-disp 3.10E+00 m

x-force -1.17E+07 N

z-force -3.13E+07 NAverage breath of the ib tear 4.90E-01 m




62/122


X-force (H=3.5 m)

-1.9E+07

-1.7E+07

-1.5E+07

-1.3E+07

-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

x-force

(N)

X- force


Average

Initiation of IB tear

Z- force (H=3.5 m)

-3.6E+07

-3.1E+07

-2.6E+07

-2.1E+07

-1.6E+07

-1.1E+07

-6.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

z-force

(N)

Z- force

Average


Initiation of IB tear


63/122

A3.1 APPENDIX 3. Case C (Plating thickness)

DB I CASE C

Measures

Double-bottom

Lenght 12 [m]

Breath 17 [m]

Height 1.6 [m]

Girders

Thickness 0.011 [m]

Spacing 4.26

Girder stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing 0.8 [m]


Spacing 2.4 [m]

Floor stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing 0.71 [m]

External plating

Thickness 0.018 [m]

Internal plating

Thickness 0.017 [m]

Plating stiffeners

bottom

Height 0.26 [m]

Thickness 0.00361/0.26 [m]

Spacing 0.71 [m]

inner bottom

Height 0.26 [m]

Thickness 0.00361/0.26 [m]

Spacing 0.71 [m]


64/122


DB I CASE C




time no tear to op. sec

x-disp no tear to op. m

z-disp no tear to op. m

x-force no tear to op. N

z-force no tear to op. N

Average breath of the tear no tear to op. m




65/122


X-force (H=0.5 m)

-6.0E+06

-5.0E+06

-4.0E+06

-3.0E+06

-2.0E+06

-1.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

x-force

(N)

x-force

Average

Z- force (H=0.5 m)

-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x- displacement (m)

z-force

(N)

Z-force

Average


66/122


DB I CASE C




time 1.43E-01 sec

x-disp 2.14E+00 m

z-disp 5.61E-01 m

x-force -3.77E+06 N

z-force -1.52E+07 N





67/122


X-force (H=1.0 m)

-8.E+06

-7.E+06

-6.E+06

-5.E+06

-4.E+06

-3.E+06

-2.E+06

-1.E+06

0.E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

x-force


Average

Z- force (H=1.0 m )

-1.6E+07

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 2 4 6 8 10

x-displacem ent (m)

z-force

(n)

z-force

Average

Initation of op. tear


68/122


DB I CASE C




time 1.32E-01 sec

x-disp 1.96E+00 m

z-disp 7.22E-01 m

x-force -3.86E+06 N

z-force -1.88E+07 N





69/122


X-force (H=1.5 m)

-1.0E+07

-9.0E+06

-8.0E+06

-7.0E+06

-6.0E+06

-5.0E+06

-4.0E+06

-3.0E+06

-2.0E+06

-1.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-force


Average

Z- force (H=1.5 m)

-2.0E+07

-1.8E+07

-1.6E+07

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)

Z-force


Average


70/122


DB I CASE C




time 1.02E-01 sec

x-disp 1.52E+00 m

z-disp 5.55E-01 m

x-force -3.96E+06 N

z-force -1.67E+07 N





71/122


X-force (H=2.0 m)

-1.5E+07

-1.3E+07

-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

x-force

Initiation of op tearAverage

Z- force (H=2.0 m)

-2.5E+07

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)

Z-force


Average


72/122


DB I CASE C




time 9.60E-02 sec

x-disp 1.43E+00 m

z-disp 5.90E-01 m

x-force -4.05E+06 N

z-force -1.93E+07 N



time 2.11E-01 sec

x-disp 3.14E+00 m

z-disp 2.35E+00 m

x-force -1.16E+07 N

z-force -2.86E+07 N





73/122


x-force (H=2.5 m)

-2.1E+07

-1.9E+07

-1.6E+07

-1.4E+07

-1.1E+07

-8.5E+06

-6.0E+06

-3.5E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-force


Average

Z- force (H=2.5 m)-3.1E+07

-2.6E+07

-2.1E+07

-1.6E+07

-1.1E+07

-6.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)



Average

z-force


74/122


DB I CASE C




time 9.216E-02 sec

x-disp 1.382E+00 m

z-disp 6.54E-01 m

x-force -1.822E+06 N

z-force -2.34E+07 N

Average breath of the op tear 6.01x2,1725 m

Tear to inner bottom (values in the moment of initiation)

time 1.766E-01 sec

x-disp 2.650E+00 m

z-disp 2.40E+00 m


z-force -4.33E+07 N

Average breath of the ib tear 1.05E+00 m




75/122


x-force (H=3.0 m)

-2.3E+07

-2.1E+07

-1.8E+07

-1.6E+07

-1.3E+07

-1.1E+07

-8.0E+06

-5.5E+06

-3.0E+06

-5.0E+05

0 1 2 3 4 5 6 7 8 9 10

x-displaceme nt (m)

x-force

(N)

X-force


Initation o f ib tear

Average

Z- force (H=3.0 m)

-4.5E+07

-4.0E+07

-3.5E+07

-3.0E+07

-2.5E+07

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)



Average

z-force


76/122


77/122


x-force (H=3.5 m)

-2.5E+07

-2.3E+07

-2.0E+07

-1.8E+07

-1.5E+07

-1.3E+07

-1.0E+07

-7.5E+06

-5.0E+06

-2.5E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displaceme nt (m)

x-force(N)

X-force



Average

Z- force (H=3.5 m)

-5.0E+07

-4.5E+07

-4.0E+07

-3.5E+07

-3.0E+07

-2.5E+07

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displaceme nt (m)

z-force

(N)



Average

z-force


78/122

A4.1 APPENDIX 4. Case D (Stiffeners)

DB I CASE D

Measures

Double-bottom

Lenght 12 [m]

Breath 17 [m]

Height 1.6 [m]

Girders

Thickness 0.011 [m]

Spacing 4.26

Girder stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing 0.8 [m]


Spacing 2.4 [m]

Floor stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing 0.71 [m]

External plating

Thickness 0.012 [m]

Inner bottom plating

Thickness 0.017 [m]

Plating stiffeners

bottom

Height 0.3 [m]

Thickness 0.00528/0.30 [m]

Spacing 0.71 [m]

inner bottom

Height 0.26 [m]

Thickness 0.00361/0.26 [m]

Spacing 0.71 [m]


79/122


DB I CASE D




INITATION

time 3.07E-01 sec

x-disp 4.59E+00 m

z-disp 4.72E-01 m

x-force -3.67E+06 N

z-force -7.26E+06N

TERMINATION

time 3.14E-01 sec

x-disp 4.68E+00 m

z-disp 4.72E-01 m

x-force -2.86E+06 N

z-force -6.81E+06 N


Length of the tear 3.04E-01 m




80/122


81/122


DB I CASE D




time 1.40E-01 sec

x-disp 2.08E+00 m

z-disp 5.33E-01 m

x-force -3.72E+06 N

z-force -1.26E+07 N





82/122


X-force (H=1.0 m )

-8.0E+06

-7.0E+06

-6.0E+06

-5.0E+06

-4.0E+06

-3.0E+06

-2.0E+06

-1.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacemen t (m)

x-force

(N)

x-force


Average

Z- force (H=1.0 m)

-1.3E+07

-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement(m)

z-force

(n)

z-force


Average


83/122


DB I CASE D


Approach of the rock todb

1.5 m


time 1.24E-01 sec

x-disp 1.85E+00 m

z-disp 6.36E-01 m

x-force -4.43E+06 N

z-force -1.49E+07 N

Average breath of the

tear

1.19E+00 m




84/122


85/122


DB I CASE D




time 9.98E-02 sec

x-disp 1.49E+00 m

z-disp 5.24E-01 m

x-force -3.56E+06 N

z-force -1.38E+07 N





86/122


X-force (H=2.0 m)

-1.3E+07

-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

x-force


Average

Z- force (H=2.0 m)

-2.0E+07

-1.8E+07

-1.6E+07

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displaceme nt (m)

z-force

(N)

Z-force


Average


87/122


DB I CASE D




time 9.60E-02 sec

x-disp 1.44E+00 m

z-disp 6.04E-01 m

x-force -2.63E+06 N

z-force -1.61E+07 N


1 st tear to inner bottom (values in the moment ofinitiation)

time 2.18E-01 sec

x-disp 3.26E+00 m

z-disp 2.43E+00 m

x-force -1.04E+07 N

z-force -2.56E+07 N

length of the tear 2.20 m

Average breath of the ib tear 0.50m

2nd tear to inner bottom (values in the moment ofinitiation)

time 5.03E-01 sec

x-disp 7.55E+00 m

z-disp 2.50E+00 m

x-force -1.24E+07 N

z-force -1.93E+07 N

length of the tear 2.25 mAverage breath of the ib tear 0.14 m




88/122


x-force (H=2.5 m)

-1.7E+07

-1.5E+07

-1.3E+07

-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-forceInitation of op tear

Initation of1st ib tear

Average

Z- force (H=2.5 m)-3.0E+07

-2.5E+07

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

Z-force

(N)



Average

z-force


89/122


DB I CASE D


Approach of the rock todb

3.0 m


time 8.58E-02 sec

x-disp 1.29E+00 m

z-disp 5.41E-01 m

x-force -1.53E+06 N

z-force -1.54E+07 N

Average breath of the op

tear

5.05x2,16 m


time 1.72E-01 sec

x-disp 2.57E+00 m

z-disp 2.30E+00 m

x-force -1.02E+07 N

z-force -3.55E+07 N

Average breath of the ibtear

7.80E-01 m




90/122


x-force (H=3.0 m)

-2.0E+07

-1.8E+07

-1.6E+07

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-force



Average

Z- force (H=3.0 m)-3.9E+07

-3.4E+07

-2.9E+07

-2.4E+07

-1.9E+07

-1.4E+07

-9.0E+06

-4.0E+06

0 1 2 3 4 5 6 7 8 9 10x-displacem ent (m)

z-force

(N)



Average

z-force


91/122


DB I CASE D




time 8.32E-02 sec

x-disp 1.25E+00 m

z-disp 5.81E-01 m

x-force -1.39E+06 N

z-force -1.65E+07 N

Average breath of the op tear 6.7x2.8 m


time 1.55E-01 sec

x-disp 2.32E+00 m

z-disp 2.30E+00 m

x-force -1.01E+07 N

z-force -3.93E+07 N

Average breath of the ib tear 1.55 m




92/122


x-force (H=3.5 m)

-2.2E+07

-2.0E+07

-1.7E+07

-1.5E+07

-1.2E+07

-9.5E+06

-7.0E+06

-4.5E+06

-2.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-force



Average

Z- force (H=3.5 m)

-4.0E+07

-3.5E+07

-3.0E+07

-2.5E+07

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)



Average

z-force


93/122

A5.1 APPENDIX 5. Case A2 (rock radius=2 [m])

DB I CASE A2 (rock radius= 2[m])

Measures

Cone top radius 2 [m]Double-bottom

Lenght 12 [m]

Breath 17 [m]

Height 1.6 [m]

Girders

Thickness 0.011 [m]

Spacing 4.26

Girder stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing 0.8 [m]

Floors

Thickness 0.011 [m]

Spacing 2.4 [m]

Floor stiffeners

Thickness 0.012 [m]

Breath 0.15 [m]

Spacing 0.71 [m]

External plating

Thickness 0.012 [m]

Internal plating

Thickness 0.017 [m]

Plating stiffeners

bottom

Height 0.26 [m]

Thickness 0.00361/0.26 [m]

Spacing 0.71 [m]

tank-top

Height 0.26 [m]

Thickness 0.00361/0.26 [m]

Spacing 0.71 [m]


94/122


DB I CASE A2



Tear to outer plating (values in the momentof initiation)

time #N/A sec NO TEAR

x-disp #N/A m

z-disp #N/A m

x-force #N/A N

z-force #N/A N

Average breath of the op tear m

Tear to inner bottom (values in themoment of initiation)


x-disp #N/A m

z-disp #N/A m

x-force #N/A N

z-force #N/A N

Average breath of the ib tear m




95/122


x-force (H=0.5 m)

-5.0E+06

-4.5E+06

-4.0E+06

-3.5E+06

-3.0E+06

-2.5E+06

-2.0E+06

-1.5E+06

-1.0E+06

-5.0E+05

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-force



Average

Z- force (H=0.5 m)

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)

Initation of op tearInitation o f ib tear

Average

z-force


96/122


DB I CASE A2


Approach of the rock to db 1 m


time 1.728E-01 sec

x-disp 2.592E+00 m

z-disp 7.757E-01 m


z-force -1.840E+07 N

Average breath of the op tear 6.10E-01 m



x-disp #N/A m

z-disp #N/A m

x-force #N/A N

z-force #N/A N





97/122


x-force (H=1.0 m)

-8.0E+06

-7.0E+06

-6.0E+06

-5.0E+06

-4.0E+06

-3.0E+06

-2.0E+06

-1.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force(N)

X-force

Initation of op tea rInitation o f ib tear

Average

Z- force (H=1.0 m)-1.9E+07

-1.7E+07

-1.5E+07

-1.3E+07

-1.1E+07

-9.0E+06

-7.0E+06

-5.0E+06

-3.0E+06

-1.0E+06

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)



Average

z-force


98/122


DB I CASE A2




time 1.408E-01 sec

x-disp 2.112E+00 m

z-disp 8.356E-01 m






x-disp #N/A m

z-disp #N/A m

x-force #N/A N

z-force #N/A N





99/122


x-force (H=1.5 m)

-1.0E+07

-9.0E+06

-8.0E+06

-7.0E+06

-6.0E+06

-5.0E+06

-4.0E+06

-3.0E+06

-2.0E+06

-1.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-force



Average

Z- force (H=1.5 m )

-2.3E+07

-2.1E+07

-1.8E+07

-1.6E+07

-1.3E+07

-1.1E+07

-8.0E+06

-5.5E+06

-3.0E+06

-5.0E+05

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

z-force

(N)



Average

z-force


100/122


DB I CASE A2



Tear to outer plating (values in the momentof initiation)

time 1.229E-01 sec

x-disp 1.843E+00 m

z-disp 8.519E-01 m




Tear to inner bottom (values in the momentof initiation)


x-disp #N/A m

z-disp #N/A m

x-force #N/A N

z-force #N/A N





101/122


102/122


DB I CASE A2




time 1.088E-01 sec

x-disp 1.632E+00 m

z-disp 8.150E-01 m






x-disp #N/A m

z-disp #N/A m

x-force #N/A N

z-force #N/A N





103/122


x-force (H=2.5 m)

-1.8E+07

-1.6E+07

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-force



Average

Z- force (H=2.5 m )

-3.5E+07

-3.0E+07

-2.5E+07

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

z-force

(N)



Average

z-force


104/122


DB I CASE A2




time 1.062E-01 sec

x-disp 1.594E+00 m

z-disp 9.258E-01 m





time 1.920E-01 sec

x-disp 2.880E+00 m

z-disp 2.643E+00 m

x-force 0.000E+00 N


Average breath of the ib tear 0.69 m




105/122


x-force (H=3.0 m)

-2.0E+07

-1.8E+07

-1.6E+07

-1.4E+07

-1.2E+07

-1.0E+07

-8.0E+06

-6.0E+06

-4.0E+06

-2.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-force



Average

Z- force (H=3.0 m )

-5.0E+07

-4.5E+07

-4.0E+07

-3.5E+07

-3.0E+07

-2.5E+07

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacem ent (m)

z-force(N)



Average

z-force


106/122


DB I CASE A2




time 1.062E-01 sec

x-disp 1.594E+00 m

z-disp 1.080E+00 m





time 1.626E-01 sec

x-disp 2.438E+00 m

z-disp 2.486E+00 m

x-force 0.000E+00 N


Average breath of the ib tear 3.84x1.66 m




107/122


x-force (H=3.5 m)-2.5E+07

-2.3E+07

-2.0E+07

-1.8E+07

-1.5E+07

-1.3E+07

-1.0E+07

-7.5E+06

-5.0E+06

-2.5E+06

0.0E+00

0 1 2 3 4 5 6 7 8 9 10

x-displacement (m)

x-force

(N)

X-force

Initation o f op tear


Average

Z- force (H=3.5 m)-4.8E+07

-4.3E+07

-3.8E+07

-3.3E+07

-2.8E+07

-2.3E+07

-1.8E+07

-1.3E+07

-8.0E+06

Date post:	02-Jun-2018
Category:	Documents
Upload:	kristjan-tabri
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FE Simulation of a Double-bottom Grounding on a Conical Rock

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