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Time-domain models were developed to predict the response of a tethered buoy subject to hydrodynamic loadings. A coupled analysis of the interaction of a buoy and its mooring is included and three-dimensional response is assumed. External loadings include hydrodynamic forces, tethers tensions, wind loadings and the weight of both cable and buoy. System nonlinearities include, large rotational and translational motions, and non-conservative fluid loadings. The mooring problem is formulated as a nonlinear two-point-boundary-value-problem. The problem is then converted to a combine initial-value and boundary-value problem to a discrete boundary-value problem at particular time, using a Newmark-like difference formula. At each instant in time the nonlinear boundary-value problem is solved by direct integration and using a successive iterative algorithm, such that boundary conditions are always satisfied. Buoy equations of motion are derived by both a small angle assumption and a large angle assumption. The small angle formulation uses the Eulerian angle for rotational coordinates. Coupling between the buoy and cable is performed by adopting the buoy equations of motion as boundary conditions at one end for the mooring problem. The rotational coordinates for the large angle formulation are represented by Euler parameters. The large angle formulation is solved by a predictor-corrector type of time integration of buoy motions constrained by tether forces. Coupling between the buoy and moorings is then enforced through matching of the velocity of the tether attachment points on the buoy with velocity of the tether ends; the velocities of tether attachment points serve as boundary conditions for the various mooring cables attached. Multiple time steps are used to account for different sizes of integration time step required for stability of solution in the buoy and tether. Numerical examples are provided to contrast the validity and capability of the formulations and solution techniques. Responses of three types of buoy (sphere, spar and disc) are predicted by the present models and compared to results obtained by experiments. Application of the present model to solve a multi-leg/multi-point mooring system is also provided. / Graduation date: 1996

The reliability of the main cable of a suspension bridge is crucial to the reliability of the entire bridge. Throughout the life of a suspension bridge, its main cables are subject to corrosion due to various factors, and the deterioration of strength is a slowly evolving and dynamic process. The goal of this research is to find the pattern of how the strength of steel wires inside a suspension bridge cable changes with time. Two methodologies are proposed based on the analysis of five data sets which were collected by testing pristine wires, artificially corroded wires, and wires taken from three suspension bridges: Severn Bridge, Forth Road Bridge and Williamsburg Bridge. The first methodology is to model wire strength as a random process in space whose marginal probability distribution and power spectral density evolve with time. Both the marginal distribution and the power spectral density are parameterized with time-dependent parameters. This enables the use of Monte Carlo methods to estimate the failure probability of wires at any given time. An often encountered problem -- the incompatibility between the non-Gaussian marginal probability distribution and prescribed power spectral density -- which arises when simulating non-Gaussian random processes using translational field theory, is also studied. It is shown by copula theory that the selected marginal distribution imposes restrictions on the selection of power spectral density function. The second methodology is to model the deterioration rate of wire strength as a stochastic process in time, under Ito's stochastic calculus framework. The deterioration rate process is identified as a mean-reversion stochastic process taking non-negative values. It is proposed that the actual deterioration of wire strength depends on the deterioration rate, and may also depend on the state of the wire strength itself. The probability distribution of wire strength at any given time can be obtained by integrating the deterioration rate process. The model parameters are calibrated from the available data sets by matching moments or minimizing differences between probability distributions.