Iceberg Model Description

In the impact simulation, the iceberg model influences the interaction largely. But, there is no common rules of the iceberg model. The research reports related to the structural safety in the high north made for the Petroleum Safety Authority Norway (PTIL NORD), the PTIL NORD ST5 (Ekeberg et al., 2018), the PTIL NORD ST19 (Lu et al., 2018) and the PTIL NORD ST20 (Ommani et al., 2018), are referred in the modelling of the iceberg in the thesis.

Geometry

As illustrated in the Figure2.6(b), the sharp part of the ice feature may be crushed during the contact. Thus, a spheroid ice model is built through a ellipse spinning around its short axis. The long axis and the short axis of the ellipse section is15m and10.4m, respectively. To reduce the computation cost, only a quarter of the iceberg marked in grey is modelled as shown in the Figure6.5.

Chapter 6. Slide Impact Simulation

Figure 6.5: Illustration of the iceberg model used in the impact simulation. The local model is marked with grey in the global model. The final model is shown on the right below.

The shape of the iceberg should be critical in the impact simulation. With the given geometry, the radius of curvature of the iceberg model is3.61m. The spacing between the web frames of the side structure is3.36m. The ratio between the curvature and the spacing is1.07, which means the curvature is close to the spacing. Thus, the used glacial ice feature is critical in this case and the impact simulation is unfavourable to the structure according to the summary of the PTIL NORD series research (Lu et al., 2020).

Mesh

Same as the previous simulations, the element type C3D8R in the ABAQUS is used to mesh the iceberg. Same mesh size of50mm is used at the beginning, but the input file could not be converted due to the hard limit in the memory buffer of the used ABAQUS V6.11. It is suggested to reduce DOFs in the model. With the finest mesh as shown in the Figure6.6, there are2564928elements in the iceberg model. The amount is even ten times of the ship model. Thus, it is necessary to increase the mesh size.

6.1 Simulation Setup in Abaqus

Figure 6.6:Illustration of the mesh of the iceberg model used in the impact simulation. The mesh size of50mm at the beginning is shown on the left. Increasing the mesh size to100mm, the iceberg model is shown on the right.

As discussed with the supervisors, the mesh size of the iceberg is increased to100mm as Vebjørn’s thesis (Kjerstad, 2019). There are326720elements in the iceberg model after the adjustment. Compared to the meshed model at the beginning, the new meshed model also assigns the good quality, meanwhile the computation cost is reduced largely.

Material

Because the mesh size is changed due to the computation capacity, the existed cali-brated material parameter set is not referred to theP C1anymore. If the original set is used in the present case, the contact force could be classified between theP C3andP C4 as shown in the Figure6.7. Thus, the material parameters are re-calibrated based on the set No.2in the Table5.6.

Figure 6.7:The contact force curves of a rough re-calibration after the mesh size changing. The case with the material as the set No.2in the Table5.6 is plotted in blue. The case with the re-calibrated material is plotted in red. Force[N]; Time[s]

Due to the time limit, a rough re-calibration is applied. It could be summarized that the parameters are calibrated to theP C2as shown in the figure. The new parameters of

Chapter 6. Slide Impact Simulation

the subroutine is listed in the Table6.2 and rest material properties applied are same as the Table5.5.

0 M N α Gf

0.001 1 0.5 5.5 5.5

Table 6.2:The parameters setup after the re-calibration

It is noticed that the contact force oscillates larger compared to the results in the cali-bration simulation of the Chapter5.4.3. The reason may be the small value of theo, which makes the damage stage starts too early in this case. Though the damage stage is extended longer by theαfor the larger element, the contact surface is still not complete due to the erosion. Thus, a detailed calibration for the mesh size of100mm should be done if time is enough.

Physical Properties

With the spheroid iceberg model and the used material parameters, the physical prop-erties of the iceberg could be summarized. Some of them need to be specified in the setup of the impact simulations.

The volume of the iceberg is given as:

V = πA·B·C

6 = 1224.6[m³] (6.2)

, where theA,BandCare lengths of the principal axes.

The total mass of the iceberg is given as:

m=ρ·V = 1102.14[t] (6.3)

, where theρis density of the iceberg.

In the impact simulation, the added mass of the iceberg needs to considered. The impact load is sensitive to its value. It is suggested to use the larger value between the infinite-frequency added mass and the zero-frequency added mass (Ommani et al., 2019).

To get such values, the hydrodynamic analysis is needed and beyond the personal capacity.

Thus, a simple but common assumption is made that the a constant added mass of half the total ice mass should be used.

A= 0.5m= 551.07[t] (6.4)

The global motion of the iceberg during the impact is related to the moment of inertia, which is determined as:

6.1 Simulation Setup in Abaqus , where thea,bandcare the half lengths of the principal axes

To provide a sufficient buoyancy, the merged volume of the iceberg should be1071.1m³. The estimated draft is8.1m. Thus, the height above the waterline is2.3m. The waterline length is9.58m. Through the calculated physical properties of the iceberg model, it could be classified as a bergy bit according to the classification of icebergs by size (Haykin et al., 1994).

Though it is not such a large one according to the size, the modelling of the iceberg is reasonable taken into account the slide impact case in the thesis. To result in the slide impact scenario that is introduced in the next part, the iceberg should be small enough to avoid the remote detection. Not until the iceberg approaches the ship to a certain distance, will it be noticed by the crew. Namely, the small iceberg as introduced is more possible to be involved in the slide impact case.

Mass-Beam Model

To investigate the rigid body motion of the iceberg, the global physical properties need to be applied to the iceberg model. But, the modelled quarter iceberg is not enough. A rigid solid and a rigid beam structure is added as shown in the Figure6.8. The quarter iceberg model is connected to the rigid solid. The rigid beam connects the rigid solid and the center of gravity (COG) of the ellipsoid iceberg.

Figure 6.8:Illustration of the mass-beam iceberg model used in the global impact simulation. The rigid ice solid is shown in a). The rigid ice beam is shown in b). The assembled mass-beam model is shown in c). The blue part is the deformed iceberg. The green part is the rigid ice solid. The red part is the rigid beam.

The rigid solid is extruded from an ellipse with the same shape as the quarter iceberg section. Same mesh size of100mmis applied. The thickness is set to100mmso that exact one layer of element is generated in the thickness direction. The element type C3D8R in the ABAQUS is used. The existence of the rigid solid guarantees the stability of the connection between the deformed part and the rigid part.

The rigid beam structure is assembled with one longer beam and two shorter beams.

The intersection of beams is the COG of the iceberg. Only one element is meshed along the longer beam. The shorter beams are divided into two elements. A rectangular beam section witha=b= 100mmis assigned. The element type B31, a two-node linear beam element in space, is applied in the ABAQUS. The total mass and the moments of inertia are applied at the COG. The added mass is applied through the Nonstructural Mass in the ABAQUS to the whole mass-beam model.

Chapter 6. Slide Impact Simulation Global Size Adjustment

With the introduced properties above, a small iceberg with the mass of nearly thousand tons is modelled. It is suggested by the supervisors to use larger iceberg model because little damage is anticipated in this case, which is proved by the simulation later.

To generate a critical case with more damage, the global iceberg model is scaled to be larger. With the same local model, a global mass of five and ten times of the original value is applied. The added mass, moment of inertia and distance to the COG (determining the length of the rigid beam) is also adjusted. The added mass is multiplied by five or ten. The moment of inertia is calculated based on the new mass value. The length of the rigid beam is multiplied by√³

5or √³

10. The large iceberg mass-beam model scaled by ten is shown in the Figure6.9. The rigid beam is extended to increase the distance to the COG.

Figure 6.9:Illustration of the large global iceberg model with longer rigid beam. The extended rigid beam is shown in red. The blue part is the deformed quarter iceberg. The white part is the rigid ice solid layer.

The detailed parameters of different global iceberg models are listed in the Table6.3 as a summary.

Table 6.3:Summary of the global iceberg model in the ABAQUS simulation Properties Small Iceberg Middle Iceberg Large Iceberg

Volume [m³] 1224.6 6123 12246

Mass [t] 1102.14 5510.7 11021.4

Added Mass [t] 551.07 2755.35 5510.7

Ixx[t·m²] 2.75·10⁴ 4.02·10⁵ 1.27·10⁶ Iyy[t·m²] 3.72·10⁴ 5.43·10⁵ 1.72·10⁶ Izz[t·m²] 2.75·10⁴ 4.02·10⁵ 1.27·10⁶

Distance to COG [m] 7.5 12.82 16.15