The main structure design principles and methods in limit states are described. The impor-tance of relative strength design is discussed. External mechanics and internal mechanics of the iceberg-structure interaction are described.
2.1.1 Limit State Criteria
The ships and offshore structures are designed to meet certain functions safely and eco-nomically. The term, limit state, is often referenced in the structure design check. When a certain limit state is used, it means a condition of the structure, beyond which it no longer fulfills the relevant design criterion and is considered as unsafe (Gulvanessian, 2002). Usu-ally, the limit states includes the Ultimate Limit State (ULS), the Serviceable Limit State (SLS), the Fatigue Limit State (FLS) and the Accidental Limit State (ALS):
• The ULS reflects the ultimate resistance for extreme loads, normally with a 100 year event.
• The SLS takes into account restrictions like deformations and motions during nor-mal use and occupancy.
• The FLS corresponds to the deduction of ultimate strength of the structure due to repetitive loads.
Chapter 2. Theory Review
• The ALS reflects a accidental collapse of the structure, normally with a 10000 year event.
For the ships and offshore structures operated in the ice-infested water, they are usually designed according to the ULS and checked according to the ALS.
In the ULS, mostly the linear elastic behaviour is assumed. Sometimes, for the struc-tures subjected to predominately permanent load, the plastic analysis as simplified rigid-plastic or elastic-rigid-plastic is also used. As mentioned above, the structure is designed to withstand loads with an annual exceedence probability of10−2 (with a return period of 100 years).
In the ALS, non-linear response of structure as buckling, yielding, etc, should be fo-cused. There are two conditions are considered. One is the ALS condition, in which the structure capacity to resist the accidental action effects is investigated and the structure may be damaged. These actions refers to an annual exceedance probability of10−4(with a return period of 10000 years). Another is the Post-ALS (or damaged) condition, in which the structure shall have resist progressive collapse with local damage under environmental actions. This environmental actions should correspond to the ULS criterion.
The interaction between iceberg and the structure could result in rather large pressure to penetrate or damage the structure so that the ALS criterion shall be used in this case.
Also, loads from rare iceberg impacts can be characterized as an Abnormal Level Ice Event according to ISO 19906 (ISO, 2019), which references to the ALS design criterion.
2.1.2 Relative Strength Design
Three design principles can be applied during the analysis of interaction between ice and structures. Depending on the relative strength of the structure and ice, strength design, ductile design and shared-energy design are included, which is also related to different design criteria as shown in the Figure2.1.
Figure 2.1:Characterisation of design principles depending on the distribution of energy dissipation in the ice mass and the structure. The ratio reflects the amount of the energy dissipated in the structure (Kim and Amdahl, 2013)
Strength design implies that the ice feature can be crushed and the structure is assumed
2.1 Marine Structure Design Principles to be rigid. The structure exhibits a resistance exceeding the failure strength of ice. Thus, most of the energy is absorbed by the ice and little plastic deformation is caused to the structure. This principle is identical to the conventional ULS design (NORSOK N-004), but will be conservative.
Ductile design implies that the ice feature is considered to be rigid and the structure shall have deformation. All the energy will be dissipated by the impacted structure as label ALS 1 shown in Figure2.1. In this principle, the shape of ice feature influences significantly because it is possible to choose a shape that doesn’t comply with the ALS criterion, but there is no widely accepted calculation model existing.
Shared-energy design implies that both the ice feature and the structure has consid-erable deformation. The energy dissipation relies on the detailed deformation process as label ALS 2 shown in Figure2.1. The challenge of this principle is that the mechanical properties of structure material and ice should be both modelled. The crushing or failure of the ice due to interaction with the structure will reshape the ice features locally or glob-ally. There are two kinds of analysis existing. One is the coupled analysis in which the deformation of the ice and structure at every moment shall influence each other. It is chal-lenging because of the dependence of the ice feature and structure on each other. Another is uncoupled analysis in which the pressure-deformation curve for the ice or structure is gotten assuming another one is rigid, respectively. An typical example using this method is the decoupling shared-energy analysis of an ice feature collision with a floating structure performed in NORD ST19 (Lu et al., 2018).
2.1.3 External and Internal Mechanics
In this thesis, the interaction between the iceberg and structure is mainly focused. Same as the analysis of the collision between ships in the ALS, the interaction could be split into two uncoupled processes, external mechanics and internal mechanics (Liu and Amdahl, 2010). The external mechanics solves the rigid body motions and determines the energy dissipated as strain energy. The internal mechanics deals with how the strain energy is dissipated in two collided objects.
The external mechanics for the iceberg-structure interaction has been developed for decades. A wildly used model is made by Popov with three-dimension to solve six de-grees of freedom (DOF) problem (Popov et al., 1969). With his model, the International Association of Classification Societies (IACS) proposed the IACS Unified Requirements for Polar Ships (IACS UR). Besides the specified model for ship-ice contact, external me-chanics adapted form ship-ship collision is also used. Liu proposed the impact meme-chanics that can be applied to both two-dimensional and three-dimensional problems (Liu and Amdahl, 2010). In his model, the equation of motion is solved in a local coordinate sys-tem determined by the hull shape at the collision point. Then a transformation matrix is proposed to derive the motion in global coordinate system. The dissipated energyEi is calculated as Equation2.1.
Ei= 1
2|( ¯mi4vi2)| (2.1)
,wherem¯iis an equivalent mass variable and4v2i is the change of the squared relative velocities.
Chapter 2. Theory Review
Two different external mechanics are also illustrated in Figure2.2 below. The model by Liu and Amdahl in Figure2.2(b) could better simulate the iceberg-structure interaction because the model by Popov in Figure2.2(b) limits the ice motion as level ice and neglects heave, pitch and roll motions.
(a) Impact of a ship against an ice floe (a: ship’s side; b:
ice floe; c:along A-A) (Popov et al., 1969)
(b) Collision scenarios and the main dimen-sions of the impact model (Liu and Amdahl, 2010)
Figure 2.2:Illustration of different external mechanics
As for the internal mechanics for the iceberg-structure interaction, it could be solved using the plasticity theory or nonlinear finite element analysis (NLFEA). It is also related to the relative strength design mentioned above. Thus, the structure deformation and the ice deformation could be solved separately with the rigid assumption of another one as a simplification. The coupling analysis can also be applied but good modelling of shape and material is needed.
Figure 2.3: Estimation of the force and deformation for ice-structure impacts adopted from ship collision (Ice curve to the left; Resistance curve to the right;Es,ice, Es,str: strain energy dissipation in ice and structure;ws,ice, ws,str: deformation of ice and structure;Fice: ice force;Rstr: structure resisdence;) (Amdahl, 2019)
2.2 General Ice Physics