Title:

A Monte Carlo approach for probabilistic analysis of offshore structures and its design implications

Offshore structures are exposed to random wave loading in the ocean environment
and hence the (longterm) probability distribution of their extreme responses to wave
loading is of great value in the design of these structures. Due to nonlinearity of the
drag component of Morison wave loading and also due to intermittency of wave
loading on members in the splash zone, the response is often nonGaussian; therefore,
I
simple techniques for derivation of the probability distributions of the extreme
responses are not available. Conventional time simulation (CTS) method is a
convenient technique to achieve this objective as it is capable of accounting for
various nonlinearities. The main shortcoming of the CTS method is that it is
computationally very demanding as reliable estimates of an extreme event with a very
low probability of exceedence require extensive simulations to reduce the sampling
variability to acceptable values. The purpose of this project is to replace the complex
offshore structural system with a much simpler system to make simulations much less
costly; consequently, reliable estimates of extreme events can be made for design
purposes.
Finitememory nonlinear systems (FMNS) are extensively used in establishing a
simple relationship between the output and input of complicated nonlinear systems.
This thesis is devoted to the development of an equivalent finitememory nonlinear
system for efficient prediction of the response of an offshore structure to (random)
Morison wave loading. For validation, responses from the equivalent FMNS model
have been compared with corresponding responses from the CTS procedure in the
time, frequency and probability domains. In particular, the 100year responses from
the FMNS and CTS methods have been compared. Overall, 216 different cases have
been investigated consisting of six responses (draginduced, inertiainduced and total
base shear together with draginduced, inertiainduced and total overturning moment),
four different structures (quasistatic, JCP2, JCP5 and JCP8), three different sea states
(H, = I5m, 10m and 5rn), and finally, three different current situations (zero, positive
and negative currents = ±0.9m/sec). This was necessary to ensure that the conclusions
of this study are comprehensive and have wide application. JCP2, JCPS and JCP8
refer to three test structures with first mode natural frequencies of0.40Hz, 0.1 9Hz and
O.l2Hz, respectively. The dynamic effect on the responses of the JCP2 structure is
relatively small. On the other hand, the dynamic effects for JCPS and JCP8 responses
are moderate and large, respectively. It should, however, be considered that the sea
surface is not stationary and that it can best be represented by a large number of sea
states, each having its own specific probability of occurrence. It is, therefore, the 100
year responses derived from the longterm (accounting for the effect of all the sea
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states at the site of the structure) distribution of the extreme responses which is
required for probabilistic analysis of offshore structures. It was observed that the 100
year responses from the FMNS method (and a more accurate variation of it) are
accurate within a few percent of its value from the less efficient CTS method.
Linear random wave theory (LRWT) is a generally acceptable method for
determining water particle kinematics below mean water level (MWL) as it is found
to predict sensible kinematics. However, water particle kinematics at points above
MWL, calculated from LRWT, suffer from unrealistically large highfrequency
components. A number of empirical techniques have been suggested to provide a
more realistic representation of near surface wave kinematics. Each of these methods
is intended to calculate sensible kinematics above the MWL, yet they have been found
to differ from one another in the results yielded. Although it is well known that
different methods of simulating water particle kinematics lead to different values of
extreme responses, no systematic study has been conducted to investigate their effect
on the magnitude of the l00year responses, which are required for design.
Using conventional time simulation method, it has been shown that the Wheeler and
the vertical stretching methods, both popular in the industry, lead to significantly
different estimates of the l00year responses. The ratio between l00year responses
from the Wheeler and the vertical stretching methods has been found to be as low as
0.66 in some cases. It is, therefore, desirable to come up with a method that resolves
this problem. To this end, two new techniques, i.e. the effective node elevation and
the effective water depth methods, have been introduced in this study. Water particle
kinematics in the near surface zone from the effective node elevation and the effective
water depth methods, lie between those from the Wheeler and the vertical stretching
methods. This is promising as there is some evidence that the water particle
kinematics under crests from the Wheeler method are underestimated and that those
from the vertical stretching method are somewhat exaggerated. Furthermore, it has
been shown that the effective node and the effective water depth procedures lead to
lOOyear responses which lie between those predicted from the Wheeler and the
vertical stretching methods, and hence may be more suitable for design. However,
further researchis required to determine which method is more appropriate.
The foregoing ratios between l00year responses were also calculated by the FMNS
method to demonstrate that both CTS and MFMNS methods lead to similar results
and conclusions. The FMNS is, however, much more efficient than the CTS method,
and therefore, can pave the way for comprehensive parametric studies such as
investigating the effect of leg spacing and natural frequency on the magnitude of the
l00year responses. This will pave the way for the optimal design of offshore
structures.
