title: A Monte Carlo approach for probabilistic analysis of offshore structures and its design implications
Creators: name: Irza  Mohd Zaki, Noor
Publisher: name: University of Liverpool Repository
Year: 2023

description: Offshore structures are exposed to random wave loading in the ocean environment and hence the (long-term) 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 non-Gaussian; 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. Finite-memory 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 finite-memory 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 100-year responses from the FMNS and CTS methods have been compared. Overall, 216 different cases have been investigated consisting of six responses (drag-induced, inertia-induced and total base shear together with drag-induced, inertia-induced and total overturning moment), four different structures (quasi-static, 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 long-term (accounting for the effect of all the sea ; 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 high-frequency 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 l00-year 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 l00-year responses. The ratio between l00-year 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 lOO-year responses which lie between those predicted from the Wheeler and the vertical stretching methods, and hence may be more suitable for design. However, further research-is required to determine which method is more appropriate. The foregoing ratios between l00-year 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 l00-year responses. This will pave the way for the optimal design of offshore structures.