report - vegvesen.no impact (glancing and head-on impact), while the purple graph shows the...

REPORT BJØRNAFJORDEN SUBMERGED FLOATING TUBE BRIDGE SHIP IMPACT

2

Revision Date Reason for Issue Prep. by Contr. by Appr. by

01 31.05.2016 Issued for Client Approval MEN,KWA THS SAH

REPORT

Project name:

BJØRNAFJORDEN SUBMERGED FLOATING TUBE BRIDGE

Document name:

SHIP IMPACT Project number : 12149-03

Document number : 12149-OO-R-302

Date : 31.05.2016

Revision : 01

Number of pages : 47

Prepared by : Magnus Engseth, Kasper Wåsjø

Controlled by : Tore Helge Søreide

Approved by : Stein Atle Haugerud

SHIP IMPACT / 12149-OO-R-302, rev. 01

3 Table of Content 1 INTRODUCTION .............................................................. 4

1.1 Design Philosophy ........................................................................................ 4

2 PROBABILITY OF IMPACT ................................................. 5

2.1 Ship Impact ................................................................................................ 5

2.2 Submarine Impact on tubes .......................................................................... 8

3 SFTB DESIGN LOADS .................................................... 11

3.1 Ship impact on pontoons ............................................................................. 11

3.2 Submarine impact on SFTB wall .................................................................... 14

4 SFTB DESIGN CALCULATIONS ........................................ 16

4.1 Ship Impact ............................................................................................... 16

4.2 Submarine Impact ...................................................................................... 16

5 WEAK LINK .................................................................. 17

5.1 Design Requirements .................................................................................. 20

5.2 Weak Link Brace ......................................................................................... 24

5.3 Weak Link Shaft ......................................................................................... 29

6 CAPACITY CONTROL FOR SUBMARINE IMPACT ON TUNNEL

WALL ........................................................................... 34

6.1 General ..................................................................................................... 34

6.2 Submarine Data ......................................................................................... 34

6.3 ULA class force indentation curve ................................................................. 34

6.4 Structural analyses of SFTB hull ................................................................... 37

6.5 Results ...................................................................................................... 40

6.6 Capacity evaluation of SFTB ......................................................................... 45

7 REFERENCES ................................................................ 46


4 1 INTRODUCTION This report deals with the case of a ship and submarine impact. The probability analysis carried out by SSPA [1], which define the design load, forms the basis for the design loads. The report seeks to clarify how the SFTB design mitigate the risk of an impact from a surface or submarine vessel. The memo also incorporates the comments on the matter made by NPRA and the expert group during the expert review in September 2015. This report replaces memo 12149-OO-R-015.

1.1 Design Philosophy Ship and submarine impacts are accidental load conditions related to a recurrence period of 10 000 years. The Norwegian Public Roads Administration (NPRA) has in handbook N400 set this as the limit where less likely events are disregarded.

In the Accidental Limit State (ALS) loads are applied without load factors, and it is allowed to utilize lower material safety factors than in Ultimate Limit State (ULS) and Serviceability Limit State (SLS). Local collapse is allowed, but the global stability must be maintained so that total collapse is avoided. For the SFTB this means that the cross section of the main tube is allowed to crack, as long as the water penetration rate is low enough to allow ample time to escape the SFTB.

A ship impact to one of the pontoons will most likely cause severe deformation to the pontoon shaft and some deformation to the pontoon itself. It is therefore a chance that the pontoon will lose its ability to support the SFTB after such an event. For that reason, the SFTB is designed to withstand loss of one pontoon in ALS. The pontoon is designed with watertight compartments to prevent it from sinking after it is separated from the rest of the bridge.

The deformation of the pontoon and its shaft will dissipate energy from the impact, but as a conservative assumption the bridge is designed to take the full blow of the impact. In other words, the pontoon and its shaft is assumed to remain elastic. By following this design philosophy we are actually designing the SFTB for two extremes that cannot occur at the same time. With this approach, we achieve a very robust design that is able to accommodate future changes in the design conditions.

The reduction of the impact caused by the deformation of the pontoons can allow for significantly higher impact energies than the design impact for the Bjørnafjord crossing. The concept of designing sacrificial elements to dissipate energy while preserving the integrity of the primary structure is not new in structural engineering. Chapter 5 presents calculations that show how a shaft designed to break at a certain load can reduce the load transferred to the SFTB significantly.


5 2 PROBABILITY OF IMPACT In the development of a Submerged Floating Tube Bridge (SFTB) for a fixed crossing over the Bjørnafjord, both tether- and pontoon-stabilized SFTB solutions are considered. Whereas a pontoon supported SFTB has the advantage of being independent of water depth, it has to cope with the interaction with ships. Both concepts however, are prone to impact from submarines. The tether-stabilized SFTB must also sustain impacts to the tether groups without collapsing.

2.1 Ship Impact The marine traffic in the Bjørnafjord comprise cargo ships, tankers, passenger vessels, high speed crafts and fishing boats. Annually the crossing site is passed by some 1 700 vessels, while 5 500 vessels are transiting the fairway outside the Bjørnafjord entrance (Figure 2.1-1). In a deterministic risk analysis [1] based on a forecasted sea traffic (2035) the overall probability for accidental ship collisions is predicted to 9.5 ⋅ 10-4 per year with associated impact energies above 1 MJ without any risk mitigating measures. Table 2.1-1 summarizes the design ships used in the probability study.

> Table 2.1-1: Summary of design ships used in risk calculation model [1]

Ship type

Length overall Beam Max draught Displacement Max speed

1 Service/General cargo 47 m 7 m 2.9 m 722 m3 13 knots

2 Tanker 73 m 13 m 4.8 m 3 200 m3 16 knots

3 Tanker 89 m 13 m 5.4 m 4 850 m3 16 knots

4 General cargo 110 m 18 m 7.0 m 10 500 m3 16 knots

5 Other 135 m 20 m 8.0 m 15 000 m3 18 knots

6 Container 160 m 23 m 7.0 m 16 905 m3 22 knots

7 RoRo vessel 170 m 26 m 6.5 m 17 500 m3 22 knots

8 Cruise ship 188 m 29 m 5.4 m 17 400 m3 24 knots

9 Cruise Ship 240 m 29 m 6.0 m 28 300 m3 24 knots


6

> Figure 2.1-1: Density plot of yearly AIS movements [1]

The SFTB has no air draught restriction and neither of the design ships have a draught exceeding the available 30 meters (Table 2.1-1). Furthermore, two large ship passages in the south and north end of the fjord leads to a small probability of ship impact.

By placing the ship passages where the traffic is most dense today (Figure 2.1-1) the SFTB is able to provide a fjord crossing with very few restrictions on the ship traffic.

> Table 2.1-2: Design impact energies Eimp for head-on collision without restrictions on ship traffic

Return period Impact energy

100 years -

1 000 years 0.3 MJ

10 000 years 339 MJ

100 000 years 725 MJ

A return period of 50 years corresponds to the characteristic value for variable loads. The SFTB must satisfy SLS-conditions at this impact energy. If we look at Table 2.1-2 we see that the impact energy for return periods lower than 1000 years is negligible. Figure 2.1-2 plots the impact energy against the return period.


7

> Figure 2.1-2: Impact energy plotted against the recurrence period [1]

> Figure 2.1-3: Elevation and plan view of the pontoon layout used for the risk analysis. The fairways are placed south of axis 6 and north of axis 29.

2.1.1 Impacts with more than one pontoon

It is conceivable that a ship crashes into more than one pontoon. If the ship strikes the first pontoon with enough energy and have a course leading to impact with the next pontoon we might get a situation where two pontoons are lost or damaged.

SSPA have carried out simulations to investigate the likeliness of such an event. The analysis give a probability of 3.8∙10-5 for a second impact. This is within the omission criteria set forth by NPRA in handbook N400, which states that accident scenarios associated with a probability of less than 10-4 can be disregarded.

0

100

200

300

400

0 2 000 4 000 6 000 8 000 10 000 12 000

Impa

ct e

nerg

y [

MJ]

Recurrence period [years]


8 2.2 Submarine Impact on tubes Bjørnafjorden is currently used by the Royal Norwegian Navy as naval training area for submarines. An evaluation of the overall probability for submarine impact has been investigated by SSPA, Ref. [2], based on information from the Navy. The analysis from SSPA assumes that the training area will still be located in Bjørnafjorden in the future, and the critical item for impact probability is the distance from the training area to the SFTB. Figure 2.2-1 depicts a sketch of the SSPA approach.

> Figure 2.2-1: SSPA approach for submarine impact probability analyses

Several important parameters for the probability analyses have been assessed in close collaboration with the Royal Norwegian Navy:

• Exercise days per year • Number of submarines engaged in each exercise • Operational time per day • Failure frequency (loss of control, failure) • Operational velocity profile • Fraction of operating time at different water depth intervals • Self repair and failure detection as function of time

The actual numbers and distributions used are not presented in this report due to restrictions from the Navy. The probability of impact with velocity above 15 knots are based on the above assumptions, and further presented, see Figure 2.2-3. Velocities above 15 knots is considered as critical for SFTB tube capacity evaluation based on preliminary calculations.


9

> Figure 2.2-2: Probability for submarine impact above 15 knots as function of distance to training area

Figure 2.2-3 shows the probability of impact above 15 knots on the tube as function of distance to the submarine training area. The green line shows the overall probability for impact (glancing and head-on impact), while the purple graph shows the probability for head on impact. The head on collision is the critical case for the SFTB integrity. As seen in Figure 2.2-2, the probability is below 1.0 ∙ 10−4 for head on impact when the training area is situated 1.5 km or more away from the SFTB. If glancing is included, the distance must be above 4 km.

Figure 2.2-3 gives the force-indentation curve and energy absorption of the submarine. The curve is a result of an explicit FE analysis of the submarine hull, performed by DNV-GL for SVV, Ref. [3].

> Figure 2.2-3: Impact force and energy absorption in submarine hull


10 The curve shows a maximum force of 64 MN on the SFTB wall from a full speed impact of 20 knots. For a 15 knots impact, the energy is halved, and the force is reduced to 22 MN. Based on preliminary calculations, the probabilities for impact with speeds above 15 knots are considered to be most critical.

As there still remain uncertainties regarding the location for training area, impact from a submarine with a displacement of 1 150 ton displacement and maximum speed of 20 knots speed is considered for tethers and the main tubes. This corresponds to an energy level of 57.5 MJ.


11 3 SFTB DESIGN LOADS 3.1 Ship impact on pontoons The action effects from ship impact are simulated by means of a global transient dynamic analysis accounting for inertia properties and added mass of both ship and structure. The time-history for the impulse loading will be calculated from design impact energy Eimp as determined in section 2.1. In the risk assessment performed for the Bjørnafjord crossing [1] a design ship has been selected as basis for collision energy predictions. A 240 m LOA cruise vessel with a displacement of 40 000 ton has been selected as preliminary design ship for pontoon collisions from passing ships (tentatively estimated representative also for transiting ships).

The risk assessment analysis [1] does not contain any information about the force-deformation characteristics for the design ship. However, force-indentation curves adequate for early stage design can be obtained from explicit load-indentation formula found in [4] which are derived from the ship impact provisions in Eurocode 1 [5]. For head-on bow collision, the bi-linear load-indentation relationship reads:

Previous benchmarking of the force-indentation curves obtained from the above formula with detailed three-dimensional non-linear FE-simulations has shown fairly good agreement for midsize to large vessels. Hence, since it is not evident that the selected design ship will produce the highest impact response, this allows us to consider impact from different hull types and sizes (Figure 3.1-1) relevant for Bjørnafjorden, refer [1]. This is further motivated by the fact that the impact energies resulting from risk analyses includes contributions from different vessel classes and is therefore not related to a specific type of hull.

> Figure 3.1-1: Force-indentation curve for head-on bow collision derived from EN

1991-1-7 for relevant ship classes.

The pontoon is a concrete cylinder, which is much stiffer than the ship hull. As small deformations are expected, the pontoon is idealized as a linear elastic spring. The spring

High speed craft

Cargo ship

Cruise ship

Container ship

Passing

Passing

0

100

200

300

400

500

0 5 10

Fship [MN]

Intendation u [m]


12 stiffness representing the pontoon is set equal to 2000 MN/m. This value is based on previous analyses carried out on similar concrete cylinders.

3.1.1 Elastic analysis

The stiffness of the ship and the pontoon, together with the impact energy and mass of the ship defines the impulse force on the SFTB. Because of the large inertia of the SFTB, it will behave like a rigid body during a ship impact. The stiffness of the ship hull is linear for deformations less than 4.7 meters according to Figure 3.1-1. A first estimate for the impulse is therefore defined by two linear-elastic springs in series (the ship and the pontoon), connected to ground and subject to a mass, M, with an initial velocity, v0, where:

𝐸𝐸 = 0.5 ∙ 𝑀𝑀 ∙ 𝑣𝑣02 = 350 𝑀𝑀𝑀𝑀

The following calculations define an undamped linear-elastic impact:

> Figure 3.1-2: Undamped linear elastic impact, hull indentation as function of time

The peak deformation is less than 4.7 meters, i.e. the linearization of Kship is OK.


13

> Figure 3.1-3: Undamped linear elastic impact, impact force as function of time

3.1.2 Plastic Analysis

The above calculations assume an elastic impact. In reality, the ship hull will undergo large plastic deformations that will draw energy out of the system. An elastic impact will therefore be a high estimate of the actual impact force. Abaqus 6.14 is used to evaluate an impulse based on a bi-linear plastic spring for the ship, and a linear elastic spring for the pontoon. In other words, the plastic deformation of the concrete pontoon is assumed negligible compared to the deformations of the ship hull.

Figure 3.1-4 show the results from the plastic analysis. The plastic deformation of the ship hull absorbs about half the impact energy (~175 MJ). This reduces the peak force from 196 MN to 150 MN, and increases the impact duration from 2.7 s to 3.0 s. The plastic analysis is run with both a 40 kt and 25 kt ship to see the effect of the parameter change. Figure 3.1-5 compares the result from the elastic analysis and the plastic analyses. Less mass, but same energy, gives a smaller peak force and a shorter impulse period.

> Figure 3.1-4: Force, indentation and energy plotted versus time. Output from Abaqus. Mass of ship is 40 kt.

3.1.3 Design Impulse for ship impact on pontoon

The plastic deformation of the ship hull gives a peak force that is approximately 23% lower than the elastic force. The impulse period is also increased by 10%. The impulse from the plastic analysis will be used in the design calculations.


14 The input from the risk analysis is purely an impact energy. It does not say anything about the combination of mass and impact velocity that give this energy level. Two different ship sizes are therefore investigated, and the impact velocity is adjusted to match the given energy level.

The base-case is the type of ship most likely to cause the impact, which is a cruise or container ship according to Figure 3.1-1. These ships have a mass of approximately 25 000 tonne. The other case is a larger ship with a mass of 40 000 tonne, which will probably only pass the bridge. The stiffness from the second stiffest graph in Figure 3.1-1 is used to approximate the hull of this ship.

Figure 3.1-5 compares the results from the two design ships. Higher mass gives a larger peak force and a longer period. The increased peak force comes from the higher stiffness in the larger ship, while the increased period is a result of the increased mass.

> Figure 3.1-5: Force impulse from 40 000 t and 25 000 t ship, with impact energy 350 MJ. Comparison of results from elastic and plastic analysis.

3.2 Submarine impact on SFTB wall Similar analyses as presented in sec. 3.1.2 are performed for the submarine impact on SFTB wall by transient analyses in ANSYS 16.1. The analysis is based on the submarine force-indentation curve presented in Figure 2.2-3, and the local stiffness of the tunnel wall is included in the analyses by modelling a section of the tunnel wall. Further details are presented in Sec. 6.

The resulting impulse on the SFTB is depicted in Figure 3.1-4.

0

50

100

150

200

250

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

Forc

e [M

N]

Time [s]

E350_M25 [MN]

E350_M40 [MN]

Linear-elastic, M25

Linear-elastic, M40


15

> Figure 3.2-1 Impulse force on SFTB from head on collision at maximum speed

Compared to the ship impact energies, the submarine impact only represents a fraction of the impulse for the design of the SFTB.


16 4 SFTB DESIGN CALCULATIONS 4.1 Ship Impact The design impulse found in section 3.1.3 is applied to the SFTB in a transient dynamic (time-history) analysis. The analysis is carried out in SOFiSTiK 2016. The equations of motion are solved using the Newmark Average Acceleration Method.

A force-envelope is saved from the time-history, and combined with the other load cases according to the Design Basis [6]. The analyses and results are presented in Ref. [7].

4.2 Submarine Impact As the design impulse from submarine impact is significantly lower than the ship impact, the submarine impact is not governing for the global design of the SFTB.

The local SFTB wall design due to loads from submarine impact is presented in Sec. 6.


17 5 WEAK LINK Probability simulations like those that define the impact energies for the Bjørnafjord are heavily dependent on the input. The expected traffic might change in the future, and at this stage of the project, proving robustness for future changes is valuable. The contents of this chapter is based on [8], [9] and [10].

The concept of designing sacrificial elements to dissipate energy while preserving the integrity of the primary structure is not new in structural engineering. The structural fuse concept has frequently been used in building structures and bridges in seismic regions since the 1970s. The idea to utilize the structural fuse concept for ship impact protection in a SFTB was first proposed in a concept developed for the Høgsfjord crossing project in the mid 90’s (Figure 4.2-1), in which a bolted shaft connection was foreseen sheared off in the event of a ship impact.

Later, the idea of such a mitigating technique became again relevant for the development of SFTB concepts for the Sognefjord crossing where significant impact energies had to be handled. As a result of parallel studies various weak link concepts were proposed.

> Figure 4.2-1: SFTB concept developed by Selmer AS for the Høgsfjord (1994).

In the process of qualifying a weak link concept for the current Bjørnafjord crossing, three alternative weak link concepts were in consultation with NPRA nominated for further assessment. The selected weak link concepts, categorized according to type of pontoon-tube connection, are briefly described below.

(1) Truss integrated WL

A tubular truss tower originally proposed for use with Vierendeel tube connections (Aas-Jakobsen, Johs. Holt, Cowi, 2012). The tower is activated as structural fuse for marked higher impact loads than the upper bound resistance defined by the environmental loads on the pontoon. The tower is envisaged to possess enough lateral drift capacity for the columns to fail in tension at the column ends prior to forming any plastic hinge action (see Figure 4.2-2). For the tower to drift primarily by column tilting the columns are designed with strength and stiffness reserves.

The truss configuration shown in Figure 4.2-2 was originally laid out for deeper tunnel draft and a smaller tube spacing. The concept is adopted to the Bjørnafjord SFTB by increasing the column spacing so that only one bay will be needed. The maximum load transferred to the bridge is limited by a bolted connection at the base of the columns designed to break at a certain load. The columns are placed on the inside of the tubes to exclude potential damage to the tunnel for a climbing ship scenario.


18 (2) Shaft integrated WL

A shear type weak link was developed in the Sognefjord feasibility study (Dr.techn. Olav Olsen, Reinertsen 2012, [11]) for use in large diameter cylindrical steel columns (see Figure 4.2-3). A clearly defined load path is obtained by separating the horizontal shear from the other load effects in the shaft. The weak link is trigged by shearing off a centric dowel pin. The relative displacement in the shaft separation joint provokes subsequent clipping of the vertical tension connectors. The weak link is designed to break at a target impact energy level, while remaining elastic under normal operational conditions.

(3) Bracing integrated WL

The sacrificial connection to the pontoon shown in Figure 4.2-4 (Dr.techn. Olav Olsen, Reinertsen, Norconsult, 2015) is based on the same philosophy as the previous WL concept 1, except that the columns are placed outside the tubes. This will give a more stable platform for a long pontoon, but in return the diagonal struts will be much longer which makes them more exposed to Vortex Induced Vibrations (VIV). To overcome this problem the bending stiffness of the diagonals must be increased.

Figure 4.2-2: WL concept 1: Truss integrated weak link.


19

> Figure 4.2-3: WL concept 2 – Shaft integrated weak link.

Figure 4.2-4: WL concept 3 – Bracing integrated weak link


20 5.1 Design Requirements

5.1.1 General Requirements

A ship impact protection based on separation of the pontoon from the rest of the overall structure is based on the assumption that the SFTB has sufficient redundancy to withstand the loss of one pontoon. In addition to maintaining structural integrity, this also requires that the design requirements for ULS and SLS can be met for the concrete tunnel for all relevant load conditions until a new pontoon is re-installed. This may require compensatory ballasting.

A further prerequisite for the weak link concept is also that the struck pontoon must be able to maintain floating stability and do not damage the tunnel or other pontoons after it is detached and drifts freely. Adequate freeboard and floating stability in damaged condition shall be obtained by compartmentation of the pontoons in watertight cells. Beyond two-compartments damage stability, filling of buoyancy material in the outer chambers may also be considered.

As part of the ship impact protection, measures are taken to mitigate damage to the vessel’s hull. This applies particulary to small and mid-size vessels.

5.1.2 Design Criterion

It is important to note that a conservative design of the weak link will lead to a non-conservative design of the overall structural system. Therefore, the design criteria shall reflect lower bound and upper bound considerations when determining the target capacity of the weak link.

The determination of the failure resistance of the weak link mechanism is influenced by uncertainties related to several factors as variation in material strength, geometric deviations, inaccuracies in the design model and quality of execution and workmanship. Consequently, a possible variation in the design resistance must be accounted for. In a deterministic design approach the variation can be reflected by the introduction of an upper and lower characteristic value for the ultimate weak link resistance, in the following designated Rk,sup and Rk,inf, respectively. The design criteria for the weak link system is formulated by the conditions:

(a) Rk,sup < Design resistance of overall structure (at ultimate)

(b) Rk,inf > Action effects induced by environmental loads on the pontoon

The structural resistance R will have a statistically normal distribution due to random uncertainties in the material strength (M), execution (U) and calculations (B). Each of the aforementioned uncertainties has a coefficient of variation (vm), (vu) og (vb). One can express the total statistical variation as 𝑅𝑅 = 𝑀𝑀 ∙ 𝑈𝑈 ∙ 𝐵𝐵, where M, U, and B are distribution functions for the uncertainties. The coefficient of variation for the total variation thus becomes:

𝑣𝑣𝑟𝑟 = �𝑣𝑣𝑚𝑚2 + 𝑣𝑣𝑢𝑢2 + 𝑣𝑣𝑏𝑏2

In addition to the random variation, there will normally be a systematic deviation or bias between real expectation values and nominal characteristic values. Values for coefficients of variation and bias for yield strength can be found in the literature ref. [12], [13], [14], [15] and [16] and for ultimate strength [12], [14] and [16]. The variation of strength will be evaluated for the steel quality in question.

Characteristic design strength will normally be based on a 5 % fractile, i.e. a reduction in design strength of 1.65 vm.


21

> Figure 5.1-1: Determination of upper (Rk,sup) og lower (Rk,inf) resistance for the weak link connection based on the cumulative distribution function for normal distribution.

For the design strength, one can assume that random deviations in execution and calculation models are accounted for in the material factor γM2. For steel structures the design standard dictates the material factor to 1.25. In addition, it will also be random and systematic errors in the material strength.

This implies a reduction in design strength in relation to the expected value Rm:

— Bias : 1.05 — Variation in strength vm : 0.08 — Material coefficient γM2 : 1.25

The reduced design resistance for the weak link becomes:

𝑅𝑅𝑘𝑘,𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑚𝑚𝐵𝐵

(1 − 1.65 ∙ 0.08) 1𝛾𝛾𝑀𝑀2

= 𝑅𝑅𝑚𝑚1.05

(1 − 1.65 ∙ 0.08) 11.25

= 0.66 𝑅𝑅𝑚𝑚

For the maximum ultimate resistance there is no material coefficient and one must take into account random defects in workmanship and calculations. This gives;

— Bias : 1.1 — Variation in strength vm : 0.05 - 0.10 — Variation in execution vu : 0.05 — Variation in calculations vb : 0.07

This yields the total coefficient of variation to:

Expected value Rm

5 %

Rk,5

95 %

Rk,95Rk,sup

∆sup

Rk,inf

∆inf

0.0

0.5

1.0

250 300 350 400 450 500

Resistance R


22 𝑣𝑣𝑟𝑟 = √0.12 + 0.052 + 0.072 = 0.13

The maximum ultimate resistance for the weak link connection thus becomes:

𝑅𝑅𝑘𝑘,𝑠𝑠𝑢𝑢𝑠𝑠 = 𝑅𝑅𝑚𝑚(1 + 1.65 ∙ 0.13) ∙ 𝐵𝐵 = 𝑅𝑅𝑚𝑚(1 + 1.65 ∙ 0.13) = 1.34 𝑅𝑅𝑚𝑚

The ratio between the maximum and minimum failure resistance then becomes:

𝑅𝑅𝑘𝑘,𝑠𝑠𝑠𝑠𝑠𝑠

𝑅𝑅𝑘𝑘,𝑖𝑖𝑖𝑖𝑖𝑖= 1.34

0.66= 2.03

This relationship between the maximum and minimum resistance applies if they correspond to the same failure mode. If the failure modes are different, one can get another ratio. This applies, for example if a friction fender is implemented which gives lower maximum resistance when sliding without affecting the minimum resistance.

It is pointed out that any capacity reduction caused by corrosion or mechanical deterioration in the weak link mechanism is not reflected here, but should be considered in conjunction with the choice of corrosion protection measures and inspection and maintenance regime.


23 5.1.3 Design Loads on Pontoons

The design loads from static and dynamic analyses are summed up in the tables below. The static loads are calculated with Sofistik while the dynamic loads are calculated with a time domain analysis in 3DFloat. Current is the only source of horizontal (shear) forces in the shafts from static load cases. Static loads acting directly on the SFTB will essentially cause displacements of the pontoons rather than shear forces in the shafts.

The dynamic shear forces are largely from inertia effects. The SFTB is displaced by waves and the pontoons are forced to follow the bridge. In concept 4080 the pontoon was changed to a circular shape and the reduction in added mass has reduced the horizontal forces significantly from previous concepts.

> Table 5.1-1: Forces in pontoon shaft in the Ultimate Limit State (ULS).

Static Dynamic Total

Axial (comp./tension) 41.3 MN/26.4MN 19.2 MN/19.2 MN 60.5 MN/45.6 MN

Shear, transverse to bridge 0.4 MN 11.2 MN 11.6 MN

Shear, bridge direction - 11.2 MN 11.2 MN

Moment, bridge direction - 144 MNm 144 MNm

Moment, transverse to bridge - 104 MNm 104 MNm

Torsion - 2.7 MNm 2.7 MNm

> Table 5.1-2: Forces in pontoon shaft in the Serviceability Limit State (Non-frequent) and Fatigue Limit State (SLS, FLS).


Axial (comp./tension) 26.0 MN/17.9 MN 9.6 MN/9.6 MN 35.6 MN/27.5 MN

Shear, transverse 0.2 MN 5.6 MN 5.8 MN

Shear, bridge direction - 5.6 MN 5.6 MN


Moment, transverse - 52 MNm 52 MNm


> Table 5.1-3: Forces in pontoon shaft in the Accidental Limit State (ALS).


Axial (comp./tension) 27.7 MN/18.4 MN 12 MN/12 MN 39.7 MN/30.4 MN

Shear, transverse 0.25 MN 7 MN 7.25 MN

Shear, bridge direction - 7 MN 7 MN


Moment, transverse - 65 MNm 65 MNm



24 5.2 Weak Link Brace

The first weak link concept is a system with braced columns. The introduction to this chapter describes three different concepts that limit the forces transferred to the SFTB. This section describe concept 1, while concept 3 is not examined in detail. Concept 2 is presented in section 5.3.

5.2.1 Weak Link Mechanism

The weak link comprises four columns and eight bracing struts. The columns and braces are connected to the bridge through a cast steel joint (Figure 5.2-2). All connections are bolted for easy installation and to make replacing components after a ship impact as easy as possible. Bolts are also more reliable with respect to fatigue as monitoring crack initiation and growth in welds would be hard with so many critical connections under water. The steel joints are designed to remain elastic during a ship impact. After such an event the damaged shaft and pontoon can be disconnected and a new pontoon can be bolted to the existing joint. The joint is replaceable in case it should incur damage in event of a crash.

The compression members in the braces are designed to avoid buckling at SLS loads. At ULS loads the compression members are allowed to buckle and therefore the tension members have to carry the entire force. The bolted connection between the braces and the joints are designed with overstrength to make sure that the fracture develops in the struts. The struts contribute with most of the shear capacity of the pontoon shaft. The maximum tensile strength of the struts will therefore effectively limit the maximum force that can be transferred to the SFTB.

The bolted connection between the columns and the steel joints are designed to break, and release the pontoon, after the braces have fractured. Table 5.2-1 summarize the dimensions of the components in the weak link. Figure 5.2-3 show the full weak link with dimensions. The dimensions presented here are a result of the ULS design, which is described in detail in memo 12149-OO-N-016.

> Table 5.2-1: Summary of cross section parameters

Component Diameter Wall thickness Cross section classification

Steel grade Connection

Columns 1 500 mm 35 mm Class 2 S355 20 pcs. M90-10.9

> Figure 5.2-1: Isometric view of pontoon and weak link

> Figure 5.2-2: Detail of cast steel joint between SFTB, columns and braces


25 Braces 610 mm 16 mm Class 2 S460 12 pcs. M90-10.9

> Figure 5.2-3: Plan, elevation and isometric view of the shaft for the pontoons - with dimensions.


26 5.2.2 Reaction of Weak Link to Ship Impact

The weak link is analysed with a dynamic time-history analysis in Abaqus 6.14. The analysis model uses non-linear material definitions with a Johnson-Cook fracture criterion [17]. Non-linear geometric effects are considered, including general contact between all members.

A parameter study focusing on variations in geometry and loading revealed that the weak link behaves as intended in the design. The weak link capacity peaks at 38 MN. The pre-peak response is relatively independent of the kinetic energy of the colliding ship, and the peak is reached after about 0.4-0.5 seconds. Post-peak results however are more dependent on the energy level of the impact.

Higher energy expectedly causes a quicker course of events. A 1000 MJ impact causes fracture of the braces about 1.2 seconds into the impact, while a 350 MJ impact fractures the braces at about 1.8-2.0 seconds. The composition of ship displacement and impact velocity making up the impact energy is shown to have little effect on the results, as expected.

Figure 5.2-5 shows the response of a 350 MJ impact from two different ship sizes. The impact velocity is tuned to achieve the desired energy level. The progressive failure of the weak link is highlighted. Figure 5.2-4 show the deformed shape of the weak link just after the braces have fractured.

> Figure 5.2-5: Reaction Force at base of pontoon after a 350 MJ ship impact. The green line shows the response from a 40 000-ton ship, while the blue line show the response from a 25 000-ton ship.

0,0

5,0

10,0

15,0

20,0

25,0

30,0

35,0

40,0

45,0

0,00 1,00 2,00 3,00 4,00 5,00 6,00

Rea

ctio

n fo

rce

[MN

]

Time [s]

> Figure 5.2-4: Isometric view of deformed weak link just after the braces have fractured.

Buckling of compressive members

Fracture of braces

Fracture of bolted

connection


27 5.2.3 Capacity Envelope of Weak Link

Based on the results from the parameter study upper and lower capacity envelopes of the weak link are developed (Figure 5.2-6). This is a significant reduction in force compared to the theoretical impulse without a weak link (Figure 5.2-7). The weak link reduces the peak load by a factor of four and increase the impulse period by a factor of two.

> Figure 5.2-6: Capacity envelope for the weak link.

0,0

5,0

10,0

15,0

20,0

25,0

30,0

35,0

40,0

0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0

Rea

ctio

n fo

rce

[MN

]

Time [s]


28

> Figure 5.2-7: Comparison of impulse without weak link and envelope from Figure 5.2-6.

All graphs represent 350 MJ impact (>10 000 years return period). The red dotted line indicates the factored ULS loads.

The three impulses from Figure 5.2-7 are applied to the global model in a transient dynamic analysis. The load is applied as a horizontal and vertical force couple representing the horizontal shear and moment caused by the eccentric placement of the impact with respect to the SFTB. The resulting reaction of the SFTB is combined with the environmental loads and the static loads according to the ALS combination rules in Eurocode.

Design checks of the resulting load combinations reveal that the highest utilization of the SFTB from the impulse that will occur without a weak link is 80%. The SFTB will crack at some points, which may cause some leakage but collapse of the structure is avoided. It is important to note that this is a very conservative design approach as a completely rigid transfer of forces from the pontoon to the SFTB is practically impossible to achieve. Minor leakage is also acceptable in the case of an accidental load with return period higher than 10 000 years.

Furthermore, if we apply the maximum and minimum impulse transferred by the weak link to the SFTB a much better result is achieved. The maximum utilization of the SFTB’s capacity is about 10% while no cracks are developed.

0

20

40

60

80

100

120

140

160

0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0

Forc

e [M

N]

Time [s]

E350_M40 [MN]

Max envelope [MN]

Min envelope [MN]

Factored ULS load


29 5.3 Weak Link Shaft

5.3.1 Weak Link Mechanism

When hit, the collision force acting on the pontoon is transferred via the steel cylindrical shafts to the tube structure by frame action. As shown in Figure 5.3-1 the weak link section is subjected to both bending, shear and axial force. Depending on the direction of the impact, the shaft can be loaded in both axial (membrane) compression and tension. Thus, in order to limit the range of the ultimate failure load, the weak link should be based on a simple and clearly defined mechanism as to avoid any interaction between different failure modes. Consequently, it is chosen to relate the failure mechanism to the shear force, which is separated from the moment and axial force by means of a shear pin located in the center of the shaft. The axial membrane forces are transferred by contact pressure and pre-tensioned steel rods along the shaft periphery (Figure 5.3-2).

> Figure 5.3-1: Impact-induced response in the weak link [11].

The impact mechanism is engaged by shearing off the sacrificial shear pin. Shearing failure is characterized as brittle failure mode and the ultimate resistance is little influenced by the strain hardening. In order to provoke a horizontal rupture surface in the middle of the separation joint, the solid steel shear pin will be prepared with a girdled groove acting as stress raiser.

Shearing off the dowel pin will trigger a relative sliding displacement between the mating shaft diaphragms. If there is enough energy left from the impact this movement will shear off the tension rods successively until all energy is dissipated or the pontoon is separated from the SFTB.

The tension rods and variations in loading in the SFTB will set up an axial force through the weak link. This axial force will provide a frictional resistance that will increase the shear capacity of the shaft. To mitigate this problem special self-lubricating slider plates are placed between the top and bottom shaft. These bearings are maintenance free during their service life and have a friction coefficient between 0.05 and 0.1 [18].


30

> Figure 5.3-2: Vertical section of shaft and the weak link connection [11]

5.3.2 Tension Rods

The tension rods carry axial loads through the weak link and are prestressed to a level that ensures pressure through the connection in the ultimate limit state (ULS). It is also checked that the minimum pressure in serviceability limit state (SLS) is large enough to provide higher frictional resistance than the wave load. This reduces the fatigue load on the shear-pin considerably.

The tension rods are massive and have steel grade S460. The diameter is 72 mm. To reduce the degrees of freedom (DOF) in the global model the tension rods are modeled with beam elements. With beam elements it is hard to capture shear fracture. A local analysis of the shearing mechanism is therefore used to calculate the force-displacement of the tension rod. This data is then used as input for a fracture criterion in the global model. The results from this analysis is presented in Figure 5.3-3 and Figure 5.3-4.

Shear plinth

Prestressing strands

Stiff frames

Cutter


31

(a)

(b)

(c)

> Figure 5.3-3: Figure (a) show a local assembly of the tension rod while figure (b) show the tension rod after shear fracture with a 100 mm gap in the clipping mechanism. Figure (c) show the rod after fracture with a 20 mm clipping mechanism

If we look at the fracture plotted in Figure 5.3-3b, we see that this actually is a tension fracture. Such fractures are ductile and strain hardening makes the ultimate capacity considerably larger than the yield capacity. By reducing the gap in the clipping mechanism a more brittle shear fracture is achieved (Figure 5.3-3c). The results of this analysis are presented in Figure 5.3-4.

> Figure 5.3-4: Force displacement graph for tension rod with 0%, 50% and 85% pre-tensioning. Gap in clipping mechanism is 20 mm.

0

200

400

600

800

1 000

1 200

1 400

1 600

0 20 40 60 80 100

She

ar F

orce

[kN

]

Transverse displacement [mm]

No pre-tension, mesh450% pre-tension, mesh485% pre-tension, mesh4


32 5.3.3 Reaction of Weak Link to Ship Impact

The weak link is analyzed for different levels of impact energy (Table 5.3-1). The resulting reaction force is presented in Figure 5.3-5. Both the 1250 MJ and the 250 MJ impact leads to a fracture in the weak link. The 25 MJ impact however leads to no plastic deformation at all.

> Table 5.3-1: Impact scenarios with return period

Mass Impact velocity Energy Return period

25 000 ton 10.0 m/s 1250 MJ > 1 000 000 yr

25 000 ton 4.5 m/s 250 MJ 10 000 yr

25 000 ton 1.4 m/s 25 MJ 4 000 yr

> Figure 5.3-5: A comparison of the reaction force in the bridge from ship impacts with different energy levels

The tension rods have to be strong enough to carry the axial load but weak enough to be sheared off during a ship impact. This contradiction leads to a greater variation in the weak links performance. If all the tension rods were engaged at the same time they would provide a very high capacity. To mitigate this the rods are engaged sequentially in two groups by differentiating the size of the clipping holes.

Figure 5.3-6 shows a break-down of the reaction force for the weak link. The sequence of fracture develops as intended. It is worth noting that the friction force is constant until the first set of tension rods fracture. This means that the force couple set up by the global moment in the system causing increased pressure through one of the shafts does not increase the friction resistance. This is actually logical as the same force couple also reduces the pressure through the other shaft.

The SFTB has not undergone any design checks for the impulse transferred through this weak link. However, the forces are of such magnitude that the conclusions drawn in section 5.2.3 are valid also for this concept.

0

10

20

30

40

50

60

70

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

Forc

e [M

N]

Time [s]

Reaction force, 1250 MJ




33

> Figure 5.3-6: A break-down of the contributions to the reaction force from a 1250 MJ

ship impact

5.4 Summary Two alternative weak link concepts are presented, the brace and the shaft system, respectively. The braced solution is the mechanically simplest, as based on well documented failure modes for conventional structure elements. Above the two solutions rules the fact that the SFTB in ALS condition is able to withstand the ship impact energy without any weak link.

0

10

20

30

40

50

60

70

0,00 0,25 0,50 0,75 1,00 1,25 1,50

Forc

e [M

N]

Time [s]


Shear Pin

Tension Rods

Friction

Fracture of first set of tension rods Fracture of second set of tension rods

Fracture of shear pin


34 6 CAPACITY CONTROL SFTB WALL FOR SUBMARINE IMPACT

6.1 General Bjørnafjorden is used by the Royal Norwegian Navy as naval training area for submarines. The assessment by SSPA on probability for submarine impact, Ref. [2], gives a probability as function of distance to the training area. As this distance is not yet decided, it is assumed that the training area is close to the SFTB site.

The criticality of an impact from a submarine on the SFTB, based on head on collision from a ULA class submarine with maximum speed, is further investigated.

6.2 Submarine Data An impact from the ULA class submarine from the Norwegian Navy is chosen as the case study for SFTB integrity. Data used for the ULA class is listed below:

• Length: 59 m • Width: 5.4 m • Submerged displacement: 1150 tonne • Maximum speed: approx. 20 knots

> Figure 6.2-1 ULA class submarine (source: snl.no)

The force deformation characteristic of the ULA class submarine has been investigated during the project by DNV-GL, Ref. [3]. A summary of the findings are presented in Sec. 6.3.

6.3 ULA class force indentation curve This section presents a short summary of the results obtained by DNV-GL.

The front end of the ULA-class submarine is modelled in the FEA-program Abaqus. The geometry model of the fore end is shown in Figure 6.3-1.


35

> Figure 6.3-1 geometry of ULA class fore end, [3]

First order plate elements are utilized with size 30 x 30 mm. This is considered sufficient to capture all relevant failure modes of the submarine hull. The material for the submarine hull is based on expected values (not lower bound values) from a new DNV_GL recommended practice which is not yet published. The true stress – true strain relation for NV-NS steel is reproduced in Figure 6.3-2.


36

> Figure 6.3-2 True Stress - True Strain relation for material in submarine hull, [3]

The SFTB hull is modelled as rigid, i.e. no significant deformation is assumed to occur in the SFTB. The impact is a plastic centric head on impact. All energy is hence dissipated in the submarine hull in these analyses. The impact is considered as quasi-static, which means that the rigid SFTB is pressed into the submarine hull in the analyses at a slow speed. Consequently, inertia effects are ignored. The boundary conditions and constraints are depicted in Figure 6.3-3.

> Figure 6.3-3 Boundary conditions and constraints, [3]


37 The resulting force-indentation curve from the analyses is reproduced in Figure 6.3-4. This curve serves as basis for the capacity evaluation of the SFTB hull.

> Figure 6.3-4 Force – indentation curve for the ULA-class submarine, [3]

The following can be observed from the figure:

• Indentation shown as the horizontal axis and force/energy at the vertical axis. • Blue graph shows the force. As seen, the force is relatively small for the first 1.5 m

of indentation, maximum approximately 25 MN. Total dissipated energy for an indentation of 1.5 m is 25 MJ.

• Abrupt increase in force between 1.5 and 2 m indentation. Deformation of stiffer structures inside the hull is likely for these energy levels. Force increases to 65 MN.

• All kinetic energy of the submarine (50 MJ) is dissipated after 2.1 m indentation.

The force – indentation curve is further used in the structural analyses of the SFTB hull.

6.4 Structural analyses of SFTB hull The local response in the SFTB concrete wall is based on the analyses by DNV-GL.

6.4.1 FEA-model

A model of a SFTB section is created in the FEA-software ANSYS (R16.1). A total length of the modelled SFTB section is 60 m. This is chosen to avoid disturbance from end constraints in the obtained results. The SFTB model consists of cubic 20 node solid elements, with mesh size equal to 20x20x20 cm in the impact zone. A model with solid elements is chosen to correctly capture the distribution of shear forces, and to accurately capture the bending of the walls. The FE model is depicted in Figure 6.4-1. A linear elastic model is used, with density and elasticity according to Ref. [6].

The submarine is modelled as a solid object with correct mass. The shape of the submarine is included to show the dimensions of the SFTB compared to the ULA-class submarine. The load transfer between the submarine and SFTB is made by a non-linear spring, connecting the nodes of the SFTB to the submarine.


38

> Figure 6.4-1 Solid element model in ANSYS

The submarine is modelled as a rigid body with mass of 1150 tonnes.

6.4.2 Boundary condition

The SFTB is fixed in both ends. Only the local modes are hence captured by this model.

6.4.3 Load application

Two scenarios are considered for the capacity evaluation of the SFTB; central impact and submarine shifted 2 m upwards related to SFTB, see Figure 6.4-2.

Central impact

Eccentric impact

Submarine shifted 2 m

upwards

> Figure 6.4-2 Submarine orientation for SFTB capacity assessment

The contact area between the SFTB and the submarine will depend on the actual indentation of the submarine. In the analyses, the loaded area will be applied as the contour of the intersection between a sphere with equal diameter as the submarine width and the SFTB. The contours and areas for a central impact are depicted in Figure 6.4-3.


39

> Figure 6.4-3 Loaded areas for different submarine indentation.

DNV indicates an indentation of 2.1 m for the maximum energy impact. The load area for 2.1 m is hence further used.

Dynamic analyses are utilized for the response analyses. The submarine is modelled with an initial velocity of 10 m/s (approximately 20 knots), and is connected to the SFTB by a nonlinear spring based on the DNV-GL report. The spring is connected to the nodes inside the 2.0 m contour in Figure 6.4-3. The spring characteristics are linearized as depicted with the red dotted line in Figure 6.4-4.

> Figure 6.4-4 Nonlinear spring behavior (idealized as red dotted line)

Note that the curve presented in Figure 6.4-4 is used for both the central impact and when the submarine is shifted compared to the SFTB. For the latter, this is considered as a conservative approach.


40 6.5 Results The results from the analyses are presented in the following sub-sections.

6.5.1 General

The analysis shows that the submarine will be decelerated from a velocity of 10 m/s to 0 m/s in 0.33 s. The maximum indentation is then 2.2 m. The load from the submarine onto the SFTB wall at the different time steps is depicted in Figure 6.5-1 and Table 6.5-1.

> Figure 6.5-1 Contact force vs impact duration

As seen, the total duration of the impact is close to 0.5 s. Further description of the indentation, velocity and contact force is shown in Table 6.5-1.

Added mass for the submarine is not included in the model. For the submarine this represents in the order of 5 % increase for surge mass and would give a bit longer duration of impact without any effect on contact force magnitude.


41 > Table 6.5-1 Results for selected time steps, eccentric impact

Time Deformation plot Indentation Velocity Spring force

initial

0 m 10 m/s 0

0.1s

0.95 m 8.8 m/s 18.5 MN

0.2 s

1.7 m 6.5 m/s 40 MN

0.33 s

2.2 m 0 m/s 61 MN

The sectional forces for use in the local capacity control are obtained from the analyses by integrating the stresses across the thickness of the considered wall. The selection of critical section is based upon review of the analyses result both in time and space. The SFTB results are shown in Table 6.5-2.


42 > Table 6.5-2 SFTB results from analyses

Result

Deformation

vonMises stress

Bottom and top shear stresses


43 Side shear stresses

Based on the above results in Table 6.5-2, the sections presented in Figure 6.5-2 are considered for the local control for the eccentric impact.

> Figure 6.5-2 Critical sections for capacity assessment


44 The maximum integrated sectional forces for the sections presented in Figure 6.5-2 are presented in Table 6.5-3

> Table 6.5-3 Integrated sectional forces for eccentric impact

Location Axial force (MN/m)*

Bending moment (MNm/m)

Shear force (MN/m)

Lower end (shear) -5.55 0.33 3.89

Upper end (shear) -8.00 1.54 2.84

Sides (shear) -6.81 0.71 1.79

Mid-point bending about horizontal axis

-6.60 3.77 0.50

Mid-point bending about vertical axis

-8.83 2.11 0.00

The results from the critical locations for the centric impact are depicted in Table 6.5-4.

> Table 6.5-4 Integrated sectional forces for central impact

Location Axial force (MN/m)*

Bending moment (MNm/m)

Shear force (MN/m)

Lower end (shear) -5.36 1.31 2.80

Upper end (shear) -5.84 1.96 2.24

Sides (shear) -5.68 0.46 1.6

Mid-point bending about horizontal axis

-5.20 3.02 0

Mid-point bending about vertical axis

-6.00 1.70 0

*Axial force from submarine impact alone. Note that prestressing and hoop forces from water pressure come in addition in the capacity control.

As seen, the sectional forces are in general of smaller magnitude for the central impact. The forces are further basis for the capacity assessment.


45 6.6 Capacity evaluation of SFTB The capacity control is based on point checks, using the maximum value obtained for the different sections. This is considered as a conservative approach, as no redistribution of forces is assumed.

The following assumptions are made for the capacity evaluation:

• Concrete quality B55 • ALS condition,

o Load factor 1.0 o Material factor concrete : 1.2 o Material factor normal reinforcement: 1.0 o Material factor prestressing reinforcement: 1.0

• Reinforcement: 2Ø32 c200 in both directions and on both sides • Shear reinforcement:

o Ø12c400c200 in general o Ø16c200c200 in a distance of 1.6 m to each side of the traffic plate

• Prestressing o 7.5 MPa in longitudinal direction o 2.5 MPa in hoop direction

• Hoop stress from external water pressure: 2.9 MPa • Shear control according to NS3473

6.6.1 Shear force utilization

The shear force utilization for eccentric impact for the point control is shown in Table 6.6-1.

> Table 6.6-1 Utilizations for submarine impact

Location Utilization

Eccentric/centric

Failure mode

Lower end (shear) 0.86 / 0.62 Tensile shear failure

Upper end (shear) 0.79 / 0.94 Tensile shear failure

Sides (shear) 0.49 / 0.45 Tensile shear failure

Mid-point bending about horizontal axis 0.78 / 0.62 Combined axial force and bending moment

Mid-point bending about vertical axis 0.52 / 0.48 Combined axial force and bending moment

Based on the utilizations for the point controls presented in Table 6.6-1, capacity is proven for an event where a ULA class submarine hits the SFTB with maximum speed of 20 knots.


46 7 REFERENCES

[1] SSPA Sweden AB, "Risk Assessment for the Planned Crossing of Bjørnafjorden," 2015.

[2] SSPA, "Appendix 11 – Submarine collision with SFT crossing Bjørnafjorden," 2016.

[3] DNV-GL, "Kollisjonsanalyser av Undervannsfartøy mot Rørbro - E39," DNV-GL, 2016.

[4] L. C. Hoang, "Ship Collisions with Pile-Supported Structures - Estimates of Strength and Ductility Requirements," Structural Engineering International, vol. 22, no. 3, pp. 359-364, 2012.

[5] Standard Norge, "Eurokode 1 - Laster på konstruksjoner - Del 1-7: Almenne laster - Ulykkeslaster," Standard Norge, 2006.

[6] Dr.techn.Olav Olsen, Reinertsen, Norconsult, "Bjørnafjord submerged floating tunnel - Design Basis," 2015.

[7] Dr.techn.Olav Olsen, Reinertsen, Norconsult, "12149-OO-R-310 - Bjørnafjorden SFTB - Technical report," 2016.

[8] Dr.techn.Olav Olsen, "12149-OO-N-010 Weak-link parameter study," 2015.

[9] Dr.techn.Olav Olsen, "12149-OO-N-011 Weak-link shaft," 2015.

[10] Dr.techn.Olav Olsen, "12149-OO-N-016 Final Design Proposal for Weak Link".

[11] Dr.techn.Olav Olsen, Reinertsen, "Feasibility study for crossing of the Sognefjord - Submerged Floating Tunnel," 2012.

[12] T. Moan, "Safety Levels Across Different Types of Structural Forms and Materials- Implicite in Codes for Offshore Structures," SINTEF, 1995.

[13] T. Moan, "The Inherent Safety of Structures Designed According to the NPD Regulations," SINTEF, 1988.

[14] P. E. Hess, D. Bruchman, I. A. Assakkaf and B. M. Ayyub, "Uncertainties in Material and Geometric Strength and Load Variables," Naval Engineers Journal, vol. 114, no. 2, pp. 139-166, 2002.

[15] S. Fjeld, "Reliability of Offshore Structures," Journal of Petroleum Technology, vol. 30, no. 10, 1978.

[16] J. Hou, S. Fu, X. An and Y. He, "Study on Statistical Characteristic of Strength of Steel Plate Used for Penstocks of Hydropower Stations," in 15th World Conference on Nondestructive Testing, Rome, 2000.


47 [17] G. R. Johnson and W. H. Cook, "Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures," Engineering Fracture Mechanics, pp. 31-48, 1985.

[18] Lubron, "Lubron Bearing systems - Self-lubricating bearings," [Online]. Available: http://www.lubron.com/images/tx%20offshore.pdf. [Accessed 27 April 2015].

[19] O. Hechler, G. Axmann and B. Donnay, The right choice of steel according to the Eurocode, ArcelorMittal, 2009.


report - vegvesen.no impact (glancing and head-on impact), while the purple graph shows the...

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