Problem 1 A job interview
Imagine you are invited to a job interview at an engineering company. You are in the process of finishing off
your MSc with the title “Prediction of extreme response of a jack-up platform in harsh environment”. In the
meeting you were interviewed by two guys from the management side of the company and a young woman
representing the technical staff. In fact she is heading the group you will be working in if you start working
there. After an introductory half an hour where the management guys told about how marvelous this company
was and what a bright future that lay ahead of you if joined the company, your possible future group leader
took over:
“I see you have made B in “Design of offshore structures”. This was my favorite course at ntnu, in particular, I
really enjoyed the statistics that was lectured. We also note with interest that your thesis is dealing with
prediction of extreme response in jack-ups. You background is very interesting for us! I will with therefore
throw in some few question related to subject we are concerned with and like to hear your response to these.”
The questions that she raised are given below. Please answer all these questions briefly.
a) Design of jackets in intermediate water depths
* Which standards do you suggest that we should use when design jackets at the Norwegian
Continental Shelf?
* If you are going to design a jacket in 80m water depth of the Polar Bear Oil Field, what design
method would you recommend?
* From the information included after the exam text, can you set up the ULS environmental input in
agreement with your suggested method. Regarding wind it is sufficient to give the wind speed to be
used 10m above sea level and regarding current it is sufficient to give surface current.
b) Time domain solution of equation of motion
* What are the necessary input and the assumptions you have to make in order to solve the equation
of motion in time domain for a jacket structure? Discuss what you need on an in principle level.
* Duration of simulation is to be 3 hours. How can you ensure this by your input if your computer
program is based equidistant frequency components (e.g. standard FFT)?
(NB! Do not enter into a very detail discussion of time domain simulation.)
c) Probability paper
* What is property of a probability paper for a given distribution?
* Construct a probability paper for the following distribution:
𝑥
𝐹𝑋 (𝑥) = 1 − 𝑒𝑥𝑝 {− ( )}
𝛾
(1.1)
ì æ xöü
FX (x) = 1- exp í- ç ÷ ý
î èn øþ
Problem 2 Prediction of extreme response of a jack-up
The management of student oil is considering using a jack-up structure as the drilling platform at a water
depth of 80m at Polar Bear Oil Field. The environmental conditions for the Polar Bear Oil Field are given in
the last part of the exam text. The deck mass of the structure is 25*106 kg and the mass of the legs shall be
neglected in the following. The deck rests of 3 identical legs. The resulting stiffness regarding deck
displacement in first mode (longest natural period) free vibration is kleg = c/d3. c = 68.22*106 Nm2 is a
coefficient representing the resulting effect of leg flexibility and degree of sea bed fixity of legs. d is the
distance from sea bed to center of gravity of deck. In the following c is to be considered as constant and the
center of gravity shall be assumed to be 10m above deck bottom.
a) Determine the minimum airgap that can be used for the jack-up as a self-standing unit (not close to
the jacket) using the Metocean Design Basis for the Polar Bear Oil Field.
Calculated the largest undamped natural period for this condition.
It is also considered to apply the jack-up for drilling through the jacket deck. In this case the distance
from bottom of deck of jack-up to mean surface level is 50m. What is the undamped natural period for
such an operation?
b) For the ULS design sea state (worst sea state along the contour) an analysis (twelve 3-hour time
domain simulations) has shown that the 3-hour maximum deck displacement accounting for dynamics
can be described by the following Gumbel model:
𝐹𝑋 (𝑥) =
exp {− 𝑒𝑥𝑝 {−
𝑥 −1.4
}}
0.14
ì
ì x -1.4 ü ü
FX (x) = exp í- exp íýý
î 0.14 þ þ
î
(2.1)
Estimate the characteristic extreme value for ULS (10-2 – annual probability value) you will
recommend for the design consideration. Give the background for the choices you make in this
connection.
Can you estimate a lower bound for the ALS characteristic value using the distribution function above
(Eq. (2.1)?
c) Student Oil has a sister platform presently operating in rather similar conditions both with respect to
depth and sea bed conditions. At design of that platform, the 3-hour extreme value distribution for the
deck displacement was estimated to be:
𝐹𝑋 (𝑥) =
exp {− 𝑒𝑥𝑝 {−
𝑥 −1.45
}}
0.11
ì
ì x -1.45 ü ü
FX (x) = exp í- exp íýý
î 0.11 þ þ
î
(2.2)
Explain how you could indicate whether or not there is a significant difference between distribution
functions found for the 2 platforms. Describe the steps you will do and why you will do it, but beyond
demonstrating the technique you shall not do any calculation.
After reading your uncertainty discussion a manager from Student Oil comes to you and asks how the
company can determine the ULS - and ALS extreme values with as good accuracy as possible.
What would be your advices?
d) For the platform operating over a jacket and installed only some few meters from the jacket, it has
been proposed by the consulting company working for Student Oil that a full long term analysis using
a peak-over-threshold (POT) analysis should be adopted. The selected environmental data has 280
storm events (above selected threshold) during 58 years.
The consulting company has calculated the most probable storm maximum deck displacement 𝑦̃ for
all the storms. They have fitted a truncated Weibull model to these observations:
𝐹𝑌̃ (𝑦̃) = 1 − 𝑒𝑥𝑝 {− (
𝑦̃ − 𝛿 𝜃
𝜀
) }
ìï æ y - d ö q üï
Ff (y) = 1- exp í- ç
÷ ý
ïî è e ø ïþ
(2.3)
They have told management of Student Oil that the company can find ULS and ALS values from this
expression. Can you estimate the value of 𝑌̃ corresponding to an annual exceedance probability of q?
Do you have any comments to this result as an estimate for the q-probability deck displacement? Is
the estimate conservative or non-conservative? Explain background for your answer.