Rocking of offshore lighthouses under extreme wave impacts: Limit analysis, analytic formulations and distinct element method

Abstract

This study describes the structural response of historic lighthouses to extreme wave impacts. Located offshore on exposed rocks, 19th Century lighthouses were built with large interlocked granite blocks and have survived weathering for nearly two centuries. Under extreme wave impacts, lighthouses of this structural typology may uplift and rock, whereas sliding is prevented by the vertical interlocking. The uplift and sliding thresholds calculated with the limit analysis method reveal why this structural system is capable of bearing extreme wave impacts without failure. The ingenious vertical keying is proven to be a major characteristic that contributes to the resilience of these lighthouses. The structural response is explained with the use of analytic formulations of the rocking motion. Detailed analysis of the response to wave impact is conducted with reference to Wolf Rock lighthouse. The impact wave corresponding to a 250-year effective return period is identified using non-stationary Bayesian extreme analysis. Moreover, wave flume tests on a scaled cylindrical structure were performed to identify the wave impact force time-history shapes. Based on two waves: a theoretical time-history based on existing models in the literature and the measured time-histories from small-scale experiments, a series of synthetic force time-history sequences are generated for the purposes of a parametric analysis. This parametric analysis, with the Distinct Element Method, using the commercial software 3DEC, reveals the influence of the duration and shape of the force time-history function. For impacts with the same impulse values, shorter time impacts produce the most intense opening of joints, despite causing smaller horizontal displacements. Furthermore, variability in the structural response is revealed even for impacts of the same impulse, duration and maximum force but different shape of the force time-history.