Probabilistic modelling of wind induced load effects for suspension bridges with emphasis on long-term extreme value analysis

Abstract

Economic development has gradually promoted an increase in the demand for and size of long-span bridges worldwide. A tangible example of such development is the Coastal Highway Route E39 led by the Norwegian Public Roads Administration (NPRA). The project proposes the construction of a 1000 km ferry-free highway from the cities of Kristiansand to Trondheim, including 8 major fjord crossings spanning from 1300 to 5000 m at water depths from 500 to 1250 m. The longest, single-span suspension bridge planned within the project is the 3000 m bridge across Sulafjord in the county of Møre og Romsdal in western Norway. The project has encouraged several research studies from which this thesis takes off. Structures such as the Sulafjord Bridge pose a major challenge to the existing technologies of bridge construction. As bridges become longer, they become more flexible and susceptible to wind loading. However, wind loading and its effects are often oversimplified in most of the current design guidelines. Some of these simplifications may be acceptable for designing regular structures but are unaccurate for long-span bridges. Recent experience based on full-scale measurements has shown discrepancies between the observations and available analytical formulations. Therefore, the need to revaluate the design guidelines is exposed. Existing research has pointed out the omission of the stochastic behaviour of the structural response and wind turbulence as the main reason for these discrepancies. Alternatively, full long-term analysis is recognized as the most accurate way to evaluate the stochastic behaviour of the structural response given the fluctuations of the environmental conditions during the lifetime of a structure. Nevertheless, the traditional full long-term analysis is based on numerical integration and requires the evaluation of the short-term response statistics from several environmental states. This requirement renders the approach unfeasible for practical engineering applications such as the Sulafjord Bridge. The objective of this thesis is to propose a reliable and computationally efficient, full long-term framework for the wind-resistant design of long-span bridges. The Sulafjord Bridge was selected as a case study. Although the results are site-specific, the framework can be easily extended to similar projects given that site-specific data are available, which is the case for most projects of this magnitude. The thesis is composed of a collection of papers, each of which accomplishes a portion of the general objective. The first paper shows surrogate modelling strategies to reduce the computational effort in the estimation of the short-term statistics of the wind responses given a wind state. Conversely, the paper applied the data of the Hardanger Bridge as the accuracy of the surrogate modelling was compared with full-scale, measured bridge responses (not available at Sulafjord). The second paper presents the wind characterization of the Sulafjord site with the environmental contour method and a probabilistic model of wind turbulence. The third paper presents a full long-term analysis of the extreme response and compares the results with the existing methods utilized in the design guidelines. In this paper, we also proposed a framework to reduce the computational effort of the full long-term analysis by replacing the traditional analysis based on numerical integration with importance sampling Monte Carlo (ISMC) simulations. The fourth and final paper combines the strategies of surrogate modelling and importance sampling Monte Carlo simulations to enhance the efficiency of full long-term analysis. The results of this thesis showed that environmental contours were the most efficient strategy for representing the characterization of the wind conditions at the Sulafjord Bridge site. The contours captured the variability measured wind turbulence and provided a more complete and yet intuitive description of the wind field compared with the current design methodology. Extreme responses from the environmental contours were on average 14% higher than the common practice based on the short-term method. The surrogate modelling strategy was a very accurate alternative for estimating the short-term statistics. The models evaluated in this thesis showed a complementary mean absolute percent error (1-MAPE) of 98% compared with analytical predictions of the buffeting response, and the full long-term framework based on the surrogate model required less than 1% of the computational effort of the traditional full long-term analysis. The most important finding of this thesis is that the extreme response from the full long-term analysis was on average more than 25% larger than the traditional short-term methodology.