Accurately determining the current state of a suspension bridge’s main cables is a critical component to reliably assessing the safety of the bridge. The primary cause for the deterioration of cable strength with time is universally recognized to be the corrosion of high strength steel wires, which together comprise the main cable. Hidden from view by the cable wrapping, this corrosion often goes undetected for years and is typically only discovered during costly and intrusive inspections. Furthermore, current inspection methods provide an incomplete picture of the variation in wire condition across the cable cross section. As a result, cable strength estimation techniques that rely solely on inspection data introduce a considerable degree of uncertainty. Finally, a method has not been developed for estimating the continuing decline in cable strength due to ongoing corrosion. A recent direction in research attempts to address the shortcomings of current inspection methodologies and the intent of this thesis is to further build upon these findings. In these recent studies, environmental conditions inside main cables are monitored to obtain information regarding the corrosive nature of the cable’s internal environment. The first goal of this thesis is to further this research direction by introducing a corrosion rate model for bridge wires that relates the monitored environmental parameters within a cable to the corrosion rate of bridge wires. Initially, temperature, relative humidity, pH, and Cl- concentration have been identified as the most relevant variables for predicting the corrosion rate of a bridge wire. By applying machine learning methods to a corrosion dataset in conjunction with these monitored environmental inputs, a long term corrosion rate model for bridge wires has been developed that is capable of capturing variability associated with these environmental parameters. This long term corrosion rate model is then applied to establish a methodology that will allow bridge owners and engineers to estimate the remaining strength of a main cable at any point in time. This is accomplished through the use of continually monitored environmental parameters which are input into the corrosion rate model. Incorporating the long term corrosion rate model developed in this thesis with current strength estimation techniques, the methodology presented in this thesis for the estimation of the remaining strength of suspension bridge cables may be readily adapted to other bridges and can be used to complement the current best practices for bridge inspection.

Uncertainty is ubiquitous in civil infrastructure systems and has a major impact on decision-making for structural safety and reliability, and for assessing and managing risk. This dissertation explores the field both from the theoretical-mathematical modeling point of view, as well as from the practical applications perspective. Two problems addressed in the dissertation: 1) how to quantify the randomness in material properties and 2) what’s the impact for the uncertainties in material properties on the response/safety of the civil structures. There are two distinct parts in the dissertation. Part I focuses on the strength evaluation of main cables for long span suspension bridges. A novel methodology is proposed to evaluate the ultimate strength of the main cables of suspension bridges using information obtained from site inspections and from tensile strength tests on selected wire samples extracted from the bridge’s main cables. A new model is proposed accounting for the spatial variation of individual wires’ strength along their length, an important physical attribute of corroded wires considered here for the first time. This model includes: (1) mapping the corrosion stage variation along one-panel-long wires that are visible during an inspection, (2) establishing probability distribution functions for the ultimate tensile strength of 18″ long wire segments in each corrosion stage group, (3) generating random realizations of the ultimate strength of all the wires in the cable’s cross section, accounting for their strength variation along the entire panel length, and (4) accounting for the effect of broken wires in the evaluation panel as well as in adjacent panels. A Monte Carlo simulation approach is finally proposed to generate random realizations of the ultimate overall strength of the cable, using an incremental loading procedure. The final outcome is the probability distribution of the ultimate strength of the entire cable. The methodology is demonstrated through the cable strength evaluation of the FDR Mid-Hudson Bridge and Bear Mountain Bridge in New York state, and compared with corresponding results obtained using the current guidelines of NCHRP Report 534. Part II is more theoretical in nature and focuses on estimating the stochastic response variability of structures with uncertain material properties modeled by stochastic fields. The concept of Variability Response Function (VRF) is applied in the dissertation to quantify the response variability (e.g., mean and variance) of statically indeterminate structures. Two types of response for statically indeterminate beams at a specific location x are studied: bending moment M(x) and displacement/deflection w(x). By solving the governing equations of the statically indeterminate structure, the responses along the length of the beam, M(x) and w(x), are expressed as a function of its (random) zero-moment location denoted by h. For bending moment M(x), combined with a second-order Taylor series expansion of the random zero-moment location h, novel Variability Response Function-based integral expressions for the variance of the response bending moment, Var[M(x)], are established. Extensive numerical examples are provided where the accuracy of the results obtained using the proposed formulation is validated using Monte Carlo simulations involving stochastic fields that follow truncated Gaussian and shifted lognormal probability distribution functions. These Monte Carlo simulation results indicate that the proposed Variability Response Functions are probability-distribution-independent. For deflection w(x), by introducing hinges at zero-moment location h, a statically indeterminate structure can be transformed into its equivalent statically determinate structure. An approximate close-form analytical expression of VRF is therefore built based on the transformed statically determinate structure with all (probabilistically) possible hinge locations. An ensemble average is taken to get the overall variability response function of the system, which can be replaced by the VRF with the hinge located at the same zero-moment point with the deterministic system without any randomness. This Variability Response Function can provide approximate estimates of the stochastic response variability with reasonable accuracy. Moreover, to get more accurate estimates of the statically indeterminate system, the results from the approximate variability response function can be further refined by introducing a correction term Dw. Finally, the corrected response variability of the original statically indeterminate structure can be obtained with almost perfect accuracy (compared to brute force Monte Carlo simulations). To sum up, the proposed VRFs of statically indeterminate beams, for both bending moment and deflection, have numerous desirable attributes including the capability to perform a full sensitivity analysis of the response variability with respect to the spectral characteristics of the random field modeling the uncertain material/system properties and establishing realizable upper bounds of the response variability.