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.

The measurement of wave forces acting on marine structures is a complicated task, both during physical experiments and, even more so, in the field. Force transducers adopted in laboratory experiments require a minimum level of structural movement, thus violating the main assumption of fully rigid structure and introducing a dynamic response of the system. Sometimes the induced vibrations are so intense that they completely nullify the reliability of the experiments. On-site, it is even more complex, since there are no force transducers of the size and capacity able to measure such massive force intensity acting over the very large domain of a marine structure. To this end, this investigation proposes a Bayesian methodology aimed to remove the undesired effects from the directly (laboratory applications) or indirectly (field applications) measured wave forces. The paper presents three applications of the method: i) a theoretical application on a synthetic signal for which MATLAB® procedures are provided, ii) an experimental application on laboratory data collected during experiments aimed to model broken wave loading on a cylinder upon a shoal and iii) a field application designed to reconstruct the wave force that generated recorded vibrations on the Wolf Rock lighthouse during Hurricane Ophelia. The proposed methodology allows the inclusion of existing information on breaking and broken wave forces through the process-based informative prior distributions, while it also provides the formal framework for uncertainty quantification of the results through the posterior distribution. Notable findings are that the broken wave loading shows similar features for both laboratory and field data. The load time series is characterised by an initial impulsive component constituted by two peaks and followed by a delayed smoother one. The first two peaks are due to the initial impact of the aerated front and to the sudden deceleration of the falling water mass previously upward accelerated by the initial impact. The third, less intense peak, is due to the interaction between the cylinder and remaining water mass carried by the individual wave. Finally, the method allows to properly identify the length of the impulsive loading component. The implications of this length on the use of the impulse theory for the assessment or design of marine structures are discussed.

Historic rock lighthouses are unusual structures that are situated in hostile marine environments to provide warning to mariners. Even in an era of satellite navigation their role continues to be an important one, but their survivability into the future is not assured. Out of concern for their ongoing service, the multidisciplinary STORMLAMP project is assessing their survivability under wave loading. This paper presents the various stages of investigations into the structural integrity and stability assessment of the Fastnet lighthouse, situated just off the coast of Ireland. The paper describes: Extreme Bayesian analysis to quantify waves of particular return periods resulting in a 1 in 250 year return period wave with H _0.1% of 17.6 m and an associated maximum force of 20,765 kN; logistically challenging field modal tests revealing the key modal parameters, like the modal masses of 1822 t and 1 675 t for 4.8 Hz and 5.0 Hz modes respectively, the cantilevered nature of the overall lighthouse and the directional effects due to the asymmetric contact with the granite rock; and details of a discontinuous finite element model that is used to determine the stability of the tower under the 1 in 250 year return period breaking wave condition, which is well within stability and material strength limits, causing maximum horizontal displacements in the order of 1 mm at the top of the tower. The overall assessment is that the sheer mass of the lighthouse and its interconnected joints are able to withstand the worst of the Atlantic storms.

Despite use of GPS, lighthouses remain critical infrastructure for preserving safety of mariners and maritime trade, and the most dramatic examples are probably the Victorian era masonry towers located on remote offshore reefs around the British Isles and exposed to extreme weather conditions. Due to their age and likely increasing future loading, dynamic field investigations were undertaken for condition assessment. The field investigations of a sample of seven lighthouses had focused on experimental modal analysis (EMA) of shaker force and acceleration response data in order to identify sets of modal parameters (MPs) specifically including modal mass, which is useful for linking loading and response. However, the EMA missed significant useful information, which could be recovered from operational modal analysis (OMA) of additional ambient vibration data recorded during the field measurements, as well as from subsequent long-term monitoring of Wolf Rock lighthouse. Horizontal vibration modes of the towers appear as pairs of modes of similar shape and with close natural frequency due to the quasi-axisymmetric structural form(s), and the lowest frequency pairs are most important to identify since they contribute most to response to breaking wave impact loads. Reliably identifying both the close natural frequencies and the corresponding mode shape orientations was impossible with EMA. Bayesian OMA (BAYOMA) provided the most insight into the modal behaviour, while at the same time providing insight into the fundamental limitations for identifying close modes. Specific conclusions from the OMA described in this paper are: • Due to varying degree of asymmetry in the ‘concave elliptic frustum’ lighthouse shapes, mode frequencies in a pair were found to differ by between 0.75% and 3.8%. • Unlike EMA, OMA was able to identify (or estimate) the horizontal directions of the mode pairs corresponding to the very close natural frequencies. • Visually apparent structural symmetry may not be strongly linked to mode shape orientations. • Mode frequency variation over time may exceed -but is not accounted for in- the calculated identification uncertainty of MPs. • There is a trade-off between mode shape orientation uncertainty and closeness of frequencies in a close-mode pair.