OE4680 2013 - Exam - 24062013

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Exam: OE4680 Arctic Engineering Date/Time: Monday, 24 June 2013, 14:00 ‐ 17:00 h

Name: ……………………………………………………………………

Student Number: ……………………………………………………………………

All questions are to be answered in English.

In case of obvious mistakes or omissions in the problems, make your own assumptions. No books, notes or other written material permitted, except for a dictionary and a calculator.

Please switch off your telephone(s)!

Please write your name, student number, date and course code on every page!

The exam questionnaire is to be handed in together with your answers.

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Exam OE4680 Arctic Engineering Monday, 24 June 2013, 14:00‐17:00 h

Problem 1: Arctic Regions and Ice Features (35%)

The locations given in Figure 1 showing the northern hemisphere, have seen recent offshore developments or

are considered viable for future offshore developments.

a. Name the 3 locations depicted in Figure 1 and give an estimation of the water depth at these locations.

(exact depths are not asked here, choose from “very shallow” to “very deep”)

b. Describe the typical ice features that you expect to encounter at these locations.

c. Discuss the advantages (pros) and limitations (cons) of the following hydrocarbon production concepts for

use in Arctic conditions:

Gravity Based Structure

Ship‐shaped

Floating

Production,

Storage

and

Offloading

unit

(FPSO)

Retained Artificial Island

d. Which of the concepts from question 1c. would you choose for each of the locations in Figure 1? Explain

why this concept is the best option and explain why the other concepts do not perform optimally at the

considered location. In other words: per area give comments on all 3 structures.

e. What are the 4 physical ice properties that influence the strength of ice?

f. Use each of the 4 physical ice properties to explain why sea ice is generally stronger at its surface than at its

bottom.

g.

When sea

ice

forms

and

grows

it

obtains

different

forms

and

shapes

while

going

through

the

different

stages of its life. With respect to this, explain the following terms:

Shuga

Pancake Ice

Congelation Ice

For the determination of ice actions, both the size effect ánd the scale effect are of importance.

h. Explain both the size effect (on structural strength of ice) as well as the scale effect.

1

2

3

Figure 1: The Northern Hemisphere

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Problem 2: Ice Actions due to Ice Ridges (40%)

Note here that excerpts of ISO19906 and a list of parameters is given in the appendix!

Figure 2a shows a large oil platform that was recently constructed in the Swedish sector of the Baltic Sea. This

somewhat unconventional gravity based structure has a square shape with a width of 32 m. The most severe

ice actions

this

structure

has

to

endure

are

caused

by

first

‐year

ice

ridges.

Figure

2b

shows

such

an

ice

ridge

in

first‐year level ice in the Baltic Sea.

a. Draw a cross‐section of a first‐year ice ridge and name its characteristic features.

b. How does the consolidated layer form in a first‐year ice ridge and why is it thicker than the level ice in

which the ridge formed?

The consolidated layer of a 100 year Baltic Sea ice ridge has a thickness of 2.4 m, while the distance between

the bottom of the consolidated layer and the base of the keel is 13.2 m.

c. Calculate the ice action due to the crushing of the consolidated layer against the structure.

d. Using ISO19906, determine the maximum ice action due to the remainder of the ridge keel.

Upon impact with the structure the ice ridge has a velocity of 1.4 m/s and it is estimated that the ice ridge

weighs approximately 36·106 kg.

e. Determine the maximum penetration of the ice ridge, due to its impact on the structure.

Assume here that area of interaction between ridge and structure is constant and at its maximum.

f. What is the limiting mechanism that occurs during ice ridge impact and what is the limiting mechanism

that occurs after maximum penetration has been reached? Briefly explain your answers.

While the

ice

ridge

lies

still

against

the

structure,

the

ice

action

on

the

structure

follows

either

from

the

ridge

building action behind the ice ridge or from the driving forces on the level ice floe behind the ice ridge. Here,

the level ice floe behind the ice ridge has an area of 4 km2 and an average thickness of 1.2 m.

g. Determine whether or not the ice ridge will remain still against the structure and calculate the

corresponding ice action on the structure.

In the Baltic Sea, the average salinity of the sea ice has a range of 5 to 8 ppt and the typical ice floe surface

temperature is about ‐16°C. Assume here that the seawater freezing point is ‐1.93°C.

h. Determine the flexural strength for design purposes according to ISO19906.

Suppose that you would redesign the gravity based structure to have a sloped shape at the waterline allowing

the ice ridge to fail in bending rather than crushing. Consider a slope angle 50 (to the horizontal), an ice‐

structure friction

coefficient

0.04 and the same width of the structure at the waterline as before.

i. Calculate the horizontal breaking component of the ice action for bending failure of the consolidated layer

of the ice ridge.

Figure 2: a) Gravity Based Structure; b) Interaction with an ice ridge .

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Problem 3: Dynamic Ice‐Structure Interaction (25%)

To determine the dynamic interaction between the structure and the ice ridge from problem 2,

we model their interaction according to Figure 3. The ice ridge has a mass moment of inertia J and the

resistance of the level ice against the rotation of the ice ridge is modelled by a rotational spring r k . Note here

that the mass of the ice ridge was previously given by the mass mridge.

Initially, based on observations, it was proposed that the dynamic behaviour of the crushing interaction

between the ice ridge and the gravity based structure is well resembled by a single spring k cr . Furthermore,

it was proposed that the rotation of the ice ridge may be neglected.

a. What is the type of modelling applied here? Explain why and give a short explanation of this modelling

approach. b.

Determine the natural frequency of the oil platform (i.e. without the ridge) and determine the natural

frequency of the interaction between the structure and the ridge.

c.

What mode or regime, describing the dynamic crushing interaction, do you expect to occur here? Explain

why and give a short description of the typical dynamic behaviour for this regime.

From measurements recently done at the Baltic Sea, it was found that

the behaviour of the crushing interaction between ridge and structure

can be improved by describing the crushing load using the force‐

indentation diagram depicted to the right. From these measurements,

it was also found that the rotation of ridges plays an important role in

the interaction between structures and ice ridges.

The equation

of

motion

for

the

rotation

of

the

ice

ridge

is

found

as:

r J k M t

Here, M(t) is the time‐dependent moment applied on the ice ridge due to its interaction with the structure.

d.

What is the type of modelling applied now? Explain why and give a short explanation of this modelling

approach.

e.

Determine the natural frequency corresponding to the rotation of the ice ridge.

f. What mode or regime, describing the dynamic crushing interaction, do you expect to occur now? Explain

why and give a short description of the typical dynamic behaviour for this regime.

As a first indication of the dynamic interaction between ridge and structure during impact of the ice ridge, we

may assume the crushing load to be constant, i.e. time‐and indentation‐independent, and equal to F cr = 90 MN.

g.

Assuming the

initial

conditions

0t t , derive the expression for the rotation t . h. Determine the maximum rotation of the ice ridge in degrees, during its impact on the structure. Assume

here that a typical impact event takes approximately 8 seconds.

Figure 3: Dynamic interaction between the oil platform and an ice ridge and associated parameters.

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Appendix: Excerpts from ISO19906 and additional parameters

Global ice actions due to crushing:

Based on various field studies, the global ice pressure can be determined as:

1

mn

cons

G R

cons

h w p C

h h

(A.8‐21)

With:

Global ice actions due to bending

Although the total load to fail ice in bending also includes lifting (or submerging), clearing and other components, the main

part of the bending load is given by the horizontal breaking load. The horizontal breaking load BH is found as:

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Global ice actions due to ridges

Ridge building action

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Brine Volume:

Compressive Strength

Flexural Strength

Based on a large number of small‐scale tests, the flexural strength f of sea ice decreases with increasing brine

volume, which includes the effect of ice temperature, and is given (in MPa) as:

5,881,76 b

v

f e (A.8‐80)

Where b

v is the brine volume fraction.

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Drag equation

In fluid dynamics, the drag equation is commonly known as:

212d d

F C V A

Where

F d is the drag force

ρ density of the considered medium

V velocity of the considered medium

A reference area

C d drag coefficient

Overview of Parameters:

Parameters

Symbol

Value

Unit

Metocean data for the Baltic Sea

Wind velocity V a 19 m/s

Current velocity V w 3,7 m/s

Air temperature T a ‐16 °C

Physical and Mechanical properties

Density sea water ρw 1024 kg/m3

Salinity sea water Sw 35 ppt

Sea water freezing point T fr ‐1,93 °C

Drag coefficient sea water C d,w 0,002 ‐

Density sea ice ρi 911 kg/m3

Young’s modulus sea ice E 5 GPa

Poisson's ratio sea ice ν 0,3 ‐

Air density (at ‐16°C) ρa 1,37 kg/m3

Drag coefficient air C d,a 0,025 ‐

Standard gravity G 9,81 m/s2

Ice ridge parameters

Ridge velocity v ridge 1,4 m/s

Ridge mass mridge 36·106

kg

Keel porosity e 30 %

Keel cohesion c 7 kPa

Angle of internal friction angle ϕ 30 °

Ridge building coefficient R 6 ‐

Sloped structure parameters

Cone angle α 50 °

Ice‐structure friction coefficient μ 0,04 ‐

OE4680 2013 - Exam - 24062013

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