Uncertainty Assessment of Wave Loads and Ultimate Strength of Tankers and Bulk Carriers in a Reliability Framework
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- Institutt for marin teknikk 
The main aim of the research work in this thesis is to investigate the uncertainty of wave-induced loads and ultimate strength of tankers and bulk carriers in a reliability framework. The ship structure is generally designed in accordance with a classification society's rules to be able to withstand the extreme external environmental loads and internal cargo and ballast loads and fulfill its function in the expected service life span without serious negative consequences such as oil leakage, structural failure, and loss of cargoes and human lives. Aiming at building more robust and safer ships, the International Association of Classification Societies (IACS) has developed harmonized Common Structural Rules for double hull oil tankers (CSR-DT) and bulk carriers (CSR-BC) based on a sound technical background. The reliability-based ultimate strength design criteria have been first implemented in CSR based on the calibrated ultimate strength requirements in connection with tankers. Compared to the previous design criteria based on allowable working stress and first yielding, the design requirement based on ultimate strength is more appropriate and accurate in representing the real structural load-carrying capacity. Structural reliability analysis (SRA) can be used to directly calculate the probability of failure or work as a tool to calibrate design requirements prescribed by rules to be consistent with the specified target failure level. While the reliability methodologies are very well established for the structural reliability analysis of ship structures, the main challenge remaining is to have proper and accurate estimates of the characteristic values and associated inherent physical and pertinent systematic uncertainties of both acting loads and structural resistance included in the limit state functions. The research work in this thesis has covered three topics related to ships, i.e., wave-induced loads (global and local loads), ultimate hull girder strength and structural reliability analysis with respect to ultimate limit state. The wave loads asserted on the ship hull by the surrounding water can be classed into two groups, namely, global wave loads (e.g., wave-induced bending moments) and local loads (e.g., wave pressure). Among the global wave loads, the vertical wave-induced bending moment (VWBM) is the most important from the design point of view. The design value of VWBM can be obtained either from prescriptive ship rules or direct calculations. The ship rules express the loads by simplified formulations obtained based on experience with various kinds of vessels. However, these formulations are only functions of the ship's length, breadth and block coefficient without explicit consideration of the routes, scatters diagrams, loading conditions, operational profiles and other features of ships. The results given by these formulations are also subject to uncertainty for a given vessel, especially for a novel ship which is outside the ship rules. In this thesis, the waveinduced loads have been investigated for three representative vessels including a very large crude oil carrier (VLCC), a new generation product tanker with dimensions outside the range of the validity for the conventional rule formulations, and a Capesize bulk carrier. Direct calculations of VWBM and wave pressure have been carried out by linear hydrodynamics. The uncertainties related to the direct calculations with various hydrodynamic programs (VERES based on 2D strip theory and WASIM based on 3D Rankine panel method), wave scatter diagrams and operational restrictions have been investigated. It is found that the method applied in the linear hydrodynamic analysis has a significant influence on the long-term prediction of the VWBM. The long-term prediction of VWBM at an exceedance probability level of 10-8 by the 3D theory code (WASIM) is generally found to be about 80-85% of that obtained by using the 2D strip theory code (VERES) while the long-term predictions of VWBM for the VLCC and bulk carrier based on 3D code WASIM and IACS wave data are in very good agreement with the design values derived from the simplified formulations given by IACS CSR. The effect of heavy weather avoidance on the longterm predictions of VWBM is another focus in the study. The effect of heavy weather avoidance is studied by modifying the wave scatter diagram based on operational envelopes determined by operational criteria. It is found that if sea states with significant wave height Hs above 10m are effectively avoided, the VWBM predicted by direct calculations based on 3D WASIM and IACS wave scatter diagram can be reduced by 15%. In principle, the global wave-induced loads are the integrated results of wave pressure and inertial loads over the ship hull. The wave pressure is also very important for the safety design of ship structures. The external wave pressure along the midship transverse section of tankers and bulk carriers has been investigated with WASIM software. Different mesh resolutions are used to discretize the hull surface. It is found that the difference between coarse and fine mesh discretization of the hull surface is negligible. However, the roll damping, as expected has a significant impact on the amplitude of wave pressure, especially in beam sea and oblique sea. The effect of heavy weather avoidance on the long-term prediction of wave pressure along the midship transverse sections of tankers and bulk carriers has been evaluated based on the proposed practical model used for VWBM. Two different wave data, namely, IACS data and OCEANOR data, are considered. The results show that the influence of heavy weather avoidance on the extreme value of wave pressure along the midship transverse section is dependent on the location along the transverse section and how the heavy weather avoidance is accounted for. The accurate assessment of the ultimate strength behavior is also a very important part of safety checks of ship structures based on ultimate limit states. The ultimate strength under longitudinal bending loads in sagging condition is denoted as the most critical failure mode for tankers. However, due to the specific loading pattern of bulk carriers, the alternate hold loading (AHL) with high density cargo loaded in odd-numbered cargo holds introduces significant double bottom hogging bending in the empty centre cargo hold. Therefore, the alternate hold loading condition in hogging is also very crucial for the bulk carrier's safety. The ultimate hull girder strength of a Capesize bulk carrier has been systematically assessed using nonlinear finite element analysis with ABAQUS software under pure longitudinal bending loads and combined global and local loads in the hogging and alternate hold loading condition, respectively. A three-cargo-hold finite element model with fine mesh in the empty centre cargo hold is developed for the nonlinear finite element analysis. The initial geometrical imperfections are introduced in the double bottom of the centre cargo hold. Both material and geometrical nonlinearities are taken into account in the finite element analysis. The local loads, i.e., the external sea pressure and internal cargo pressure, are adopted according to CSR-BC. The ultimate hull girder strength with various local pressure load levels has been extensively investigated in the hogging and AHL condition. It is found that the ultimate strength of the hull girder of the subject bulk carrier in the hogging and AHL condition can be significantly reduced due to the action of the local pressure loads compared with that obtained under pure hogging bending loads. In particular, the studies of bulk carriers are based on the ISSC 2000 benchmarked bulk carrier and alternative designs established by varying the plate thickness with design modification factor in the bottom panels. Structural reliability analysis can be used to directly calculate the probability of failure or work as a powerful and practical tool for the calibration of design criteria used in rules. The structural reliability analysis of ultimate strength of a Capesize bulk carrier in the hogging and AHL condition has been conducted in this thesis. For large bulk carriers, the ultimate strength in the hogging and AHL condition is very important for the safety of ships since the local loads due to internal cargo loads and external sea pressure can significantly decrease the ultimate hogging bending capacity. In this thesis, the ultimate bending capacity of the subject bulk carrier has been obtained based on the nonlinear finite element analysis and a practical interaction equation has been established to consider the effect of combined global and local loads. The global and local loads are determined in accordance with CSR-BC. The effect of heavy weather avoidance on the global and local loads has been evaluated in the structural reliability analysis. The First Order Reliability Method (FORM) is employed to calculate the annual probability of failure of this bulk carrier in the hogging and AHL condition. The results show that the local loads have a significant influence on the failure probability of such vessels in the hogging and AHL condition, and considering heavy weather avoidance can also greatly decrease the probability of failure.