Waterborne debris impacts during extreme hydrodynamic events can significantly damage masonry structures. In the current design practice, these forces are commonly characterised by equivalent force-time (F-t) diagrams calculated with analytical models. The US standard ASCE/SEI 7–22 contains a specific model. However, recent studies suggest that the ASCE model may significantly overestimate the load demand and propose an alternative, more accurate analytical model, i.e. the Mass and Stiffness Ratio Model (MSRM). This paper assesses the ASCE design procedure in relation to a potential alternative MSRM application. In doing this, the structural behaviour of a running-bond masonry wall is analysed when subjected to impact loads calculated with the ASCE and MSRM models. The minimum debris design properties by ASCE are used. Various impact scenarios are considered by changing impact locations across the wall. High-fidelity simulations employing micro modelling strategies, nonlinear material models, and strain rate dependent constitutive laws are used. Results show that the ASCE design formulae overestimate maximum structural displacements by over four times, causing disproportionate damage compared to MSRM results. These results highlight the need to revise the ASCE design provision for debris impacts, and the MSRM are recommended as a more efficient alternative to calculate debris impacts F-t diagrams.

Coastal systems evolve through a wide variety of physical, ecological and human processes, operating over multiple timescales. One coastal type of interest is an unmanaged, soft-cliffed coast, where hydrodynamic, erosive and avalanching processes interact to create a dynamic and often rapidly receding coast. Anthropogenic sea level rise is expected to accelerate recession and cause cliff submergence, a transition in coastal typology, impacting local communities, habitats and infrastructure. In this presentation, we explore the long-term (centuries and longer) geomorphological behaviour of a soft-cliffed coast forced by relative sea level rise. We describe continuous erosive processes by a generalised set of time-averaged hydrodynamic and erosion governing equations, driving smooth deformation of coastal morphology. This description is general enough to encompass many existing hydrodynamic and erosion models, meaning that results derived in this work hold for a large family of model parameters and parametrisations. A key physical process on soft-cliffed coasts is collapsing of the cliff face. The timescale of collapsing is shorter than the time-averaged hydrodynamic and erosion timescales and can be treated as an instantaneous process. This jump in state means that the mathematical framework of non-smooth (or hybrid) dynamical systems must be used to explore the evolution of these coasts. We identify two geomorphological states toward which the system converges: a repeatedly collapsing receding cliff system, approached when sea level is static, and a transgressing rocky platform without a cliff, approached for high rates of sea level rise. Our analysis focuses on the transitions between these attracting states over anthropogenic sea level rise scenarios. We find that cliff submergence can be characterised as a “tipping point” behaviour, reframing changes in coastal type as potentially irreversible impacts of anthropogenic climate change. This is an underexplored geomorphological phenomenon and may help us interpret the history of the Earth’s coastal systems, as well as explore future scenarios. The description of time-averaged hydrodynamic and erosion processes is general, strengthening the statement that the tipping point behaviour discussed is a realistic phenomenon, rather than a mechanism only seen for specific model parametrisations. This work also impacts the modelling of human-coastal coupled systems, since some management decisions, e.g. beach nourishments and the erection of coastal defences may be treated as instantaneous processes, and the framework of non-smooth dynamical systems is one avenue towards understanding long-term system behaviour.

A new methodology to link datasets of regional Probabilistic Tsunami Hazard Assessment (PTHA) with inputs for numerical simulation site-specific tsunami inundation was developed. The present study focused on the NEAMTHM18, which is a PTHA database developed for earthquake-generated tsunamis mapping the North Eastern Atlantic, the Mediterranean, and connected seas coasts. This approach was motivated by the need to use PTHA frameworks as a foundation to provide boundary conditions to detailed tsunami inundation simulations. The proposed methodology was organised into three subsequent steps, starting from the definition of the hazard indicator. This step is followed by the definition of a finite set of incident free water surface time series after defining some additional hypotheses. Finally, inundation simulations were carried out and used as the basis of successive aggregated hazard maps. The methodology was demonstrated by applying it to the Messina Strait, focusing on three different interest areas, for which aggregated hazard maps were obtained and compared to simplified inundation maps already available from government agencies. These latter were shown to overestimate the inundation maps obtained with the high-resolution simulations, while at the same time being consistent. This highlighted the necessity of carrying out these additional studies when designing critical infrastructures. The prediction of more limited inundation areas in this study is then associated, in contrast to previously developed simplified inundation maps, to the ability of this new method to consider the effect of the coast with high resolution, which is essential for reliable hazard assessment. Additionally, this study also suggested that the use of the N-WAVE theory might be appropriate for these types of studies. The results were also qualitatively compared with historical data from the 1908 Messina Strait tsunami. Finally, the present study helps to highlight the needs of end users when conducting detailed tsunami modelling and infrastructure design, applying PTHA databases that have been already developed. These needs might then be used as foundational requirements for future developments of PTHA tools.

Flood evacuation outcomes are critically shaped by human behaviour, yet empirical data on individual decision-making remain scarce due to the dangers and logistical challenges of collecting data during real natural hazards. To address this gap, this study used Virtual Reality (VR) to examine how social cues, specifically crowd behaviour, interact with factors such as crowd size, clarity of the safe destination, and floodwater level to influence evacuation choices and delays. Four within-subjects VR experiments were conducted with 84 participants, systematically testing these variables in an immersive flood scenario. Results showed that crowd behaviour strongly determined both route choice and evacuation latency, often outweighing other factors. Participants tended to follow crowds into floodwater, demonstrating the influence of social information. However, this influence weakened when water levels were very high, indicating a threshold that overrides social cues. Larger crowds and unclear destination information further increased reliance on social information and pre-movement times. These findings highlight the powerful role of social dynamics in emergency decision-making and underscore the need to integrate realistic human behaviour, particularly social influence, into flood risk models, public warnings, and evacuation planning to improve community resilience and safety.

Solitary waves are commonly used to model long waves, such as tsunamis. Limited research is available for such waves propagating in converging water bodies, such as fjords, bays, and estuaries, where reflection and large amplified waves can be observed. Therefore, an extended analytical solution is presented to calculate the non-dimensional asymptotic amplified wave amplitude Aw and its trajectory for the oblique interaction of two distinct weakly non-linear solitary waves based on line-soliton solutions of the Kadomtsev–Petviashvili equation. Furthermore, an analytical model is developed for wave propagation in a converging geometry featuring Mach reflection. An oblique angle ψ̂ of Mach stem and a general stem angle φ are defined, along with their explicit calculation formulas. The Simulating WAves till SHore model based on the non-hydrostatic, non-linear shallow water equations, is used to validate the solutions and the analytical model numerically. The simulation results for Aw and ψ̂ show asymptotic behavior and converge toward the prediction of the extended solutions. At an average oblique angle of 17° between two solitary waves, the discrepancy between the numerical and analytical results for Aw is up to −9.0% for the first-order and +8.3% for the second-order solutions, respectively. For the most asymmetrical converging geometry examined, the simulated result of φ=14.2° remains 92.0% of the theoretical value. These findings indicate that the proposed solutions can readily and accurately predict the angles and amplitudes of amplified waves resulting from the interaction of weakly non-linear solitary waves in extensive converging water bodies.

Tsunamis and other extreme hydrodynamic events have the potential to transport large debris that, along with the flow, are capable of causing severe damage to coastal structures and infrastructures. Therefore, modelling such processes is essential when assessing the multiple hazards associated to this type of events. In harbour areas, transport inland of shipping containers and subsequent impacts are relevant examples of waterborne debris hazards. The present work addresses two gaps in the scientific research of this problem using numerical methods; the understanding of the effect of containers initial layouts and that of the flow impact angle on the transport and diffusion. To fill these gaps a numerical study was carried out using idealised flow conditions. To this end a Smoothed Particles Hydrodynamics solver (DualSPHysics), coupled with a Discrete Element Method model (Project CHRONO), was used and initially validated with experiments published in the literature. Subsequently, four layouts commonly used in shipping containers yards were simulated, including incident flow depth and impact angle variability, resulting in 76 total simulations. The results were analysed in terms of normalised standard deviation and normalised range differences with respect to the initial values of both parameters. These parameters were related to the flow impact angle, water depth to containers height ratio DhR, and normalised displacement of the container clusters centroids. Standard deviation and range are shown to reach, for almost all results, a quasi-steady state by the end of the simulations. It is shown that the standard deviation and range are more sensitive to the impact angle for DhR <= 1.7. In this case, the configurations with flow impacting orthogonally to one of the containers axes show larger values of the two parameters than for intermediate angles. For larger values, DhR drives the standard deviation and range, independently from the impact angle. DhR is shown to be a physical parameter that well describes the relative importance of dispersion and advection of containers transported in extreme hydrodynamic events. Finally, existing relationships, that assume an infinite growth of the range, are shown to overestimate numerical results at the stage in which dispersion does not grow further. Two new regression formulae are numerically derived to predict the dispersion parameters at this stage. They include the effects of the cluster layout, impact angle a and DhR making them a valid alternative to existing relationships.

Around 60% of global rivers do not form deltas, but relatively little attention has been given to the conditions at river mouths at which delta formation is prevented. Here we present an equation for predicting the spread of river-delivered sediments at coastlines subject to combined high energy waves and tidal ranges, for which delta formation is inhibited. This equation is validated against previous numerical modelling work on an idealised coast with a discharging river using Delft3D. The equation is derived from a mass-conserving bottom-evolution equation, reformulated to a partial differential equation, from which the analytical solution is determined using the method of Eigenfunction expansion. The analytical approach is calibrated against the results of the Delft3D simulations, in order to determine values of two independent variables (downslope diffusion coefficient κ and input width B) controlling the shape of alongshore sediment distribution after a given time. This approach leads to only very small errors in determining alongshore sediment distribution when compared to the computationally expensive Delft3D simulations, and may be calculated in a fraction of the time.

Application of conditional generative adversarial network (cGAN) offers a promising approach for predicting the nonlinear behaviour of masonry. However, the large variability in masonry's mechanical properties makes developing comprehensive models highly time- and resource-intensive. This paper presents a continual learning (CL) approach to expand the predictive capabilities of a pre-trained cGAN model, designed to predict full mechanical response fields of masonry panels, to new domains of unseen material property combinations. Elastic weight consolidation (EWC) regularisation is adopted to mitigate catastrophic forgetting in the initial training domain. The effects of fine-tuning hyperparameters, trainable blocks, and fine-tuning subset configurations, are investigated to optimise fine-tuning performance. The fine-tuned model demonstrates excellent capability in predicting the strain maps and reaction forces and capturing extreme strain values within the expanded domain, while avoiding catastrophic forgetting. This approach outperforms costly full re-training from scratch, demonstrating a viable and computationally efficient solution for extending the generalisation capabilities of datadriven models.

To evaluate the structural safety against waterborne debris impacts, the impact loads are usually computed with analytical models such as those proposed by ASCE/SEI 7-22. These models often assume a massless structure to simplify the analytical formulations, which can be an oversimplifying and inaccurate assumption in cases where the structure is heavier and more flexible than the debris. To address this problem, we aim to define the domain in which the existing models are inaccurate and to propose a new analytical model to accurately compute the debris impact forces through comprehensive finite element simulations and analytical modelling. We defined such a domain in the design space of structure-to-debris mass and stiffness ratios and assessed which are the most accurate analytical models to compute debris impact forces across this space. Our proposed model significantly improves upon the overestimating results of the ASCE/SEI 7-22 model when both stiffness and mass are important in determining the impact forces.

Masonry walls are highly vulnerable to waterborne debris impact loads occurring during extreme hydrodynamic events. These loads are usually represented with a force-time (F-t) diagram calculated using analytical models. Such models are currently derived from elastic structures, neglecting the effects of potential failure mechanisms activated by the impact. At the same time, current design standards lack design prescriptions that consider structural failure in debris impact design. To address this gap, the present paper investigates the effects of structural failure on F-t diagrams and proposes a new model, the Energy and Impulse-Momentum Model (EIMM), to compute analytical nonlinear F-t diagrams that account for such structural nonlinearities. The focus is on masonry structures due to their popularity in the built environment, but the findings can be extended to any impact scenario. It is shown that structural failure significantly reduces the impact force due to the decrease in structural stiffness. A Performance Index, PI, is used to quantify this reduction and is proposed as a potential design parameter. It is also shown that the proposed EIMM can effectively compute nonlinear analytical F-t diagrams. The results of this research deliver new knowledge and methods for debris impact design of nonlinear structures needed to guarantee public technical safety of structures in extreme hydrodynamic events.

Soft rock cliffs are common coastal features made of erodible material, such as clay and glacial deposits. The erosion of soft-cliffed coasts threatens communities around the world, destroying homes and habitats. Here we present a numerical model suited for estimating the evolution of these coastal systems over centuries in response to sea level rise (SLR) alone. To achieve computational efficiency, we propose a simple conceptual model, based on a mass- conservation approach. In this model we have relaxed the conditions used by Wolinsky and Murray (2009) when solving the Exner equation for cliffed coastlines. In particular, the assumptions of constant SLR and simplified inland topography. In this work we remove these restrictions, and obtain a simple behavioural equation for soft-cliffed coasts for which an analytical solution exists. This allows study of the conditions for existence of an equilibrium rate and the dynamics of equilibrium approach.

Studies based on probabilistic frameworks defined a methodology known as Probabilistic Tsunami Hazard Assessment, or PTHA (Grezio et al., 2017), are increasingly common and becoming essential for planning risk reduction, which significantly helps in saving lives and reducing economic losses. PTHAs usually provide to the final user a single or a set of tsunami parameters, e.g., wave amplitude a, wave height H, Maximum Inundation Height MIH, defined at a prescribed distance from the coast, to assess the hazard to a certain coastal stretch. The propagation inshore of these parameters is usually simplified and does not consider specific local bathymetry features. Due to this, directly using simplified propagation tools might not be cautelative when developing projects for high relevance areas or critical infrastructure, where high resolution results are needed (Tonini et al., 2021). A specific methodology to consider the variability of the coast with high resolution numerical simulations starting from a PTHA database is therefore needed for reliable hazard assessment. Here, this new methodology is developed starting from the hazard curves provided by the NEAMTHM18 to obtain tsunami input time series for propagation and inundation numerical modelling, which is then used for high resolution hazard assessment of an area of interest.

Extreme hydrodynamic events, such as those driven by tsunamis, most notably in Tohoku, Japan 2011 (Mori et al., 2011) and in Indonesia 2004 and 2018 (Sassa et al., 2019), have shown the need to consider debris for an accurate hazard assessment. Three main processes are relevant in this context: (I) debris transport and dispersion (Naito et al. 2014), (II) debris impact on coastal structures and infrastructures (Stolle et al., 2018, De Iasio et al., 2023) and (III) debris damming (Mauti et al., 2020). For (II) and (III), multiple design guidelines for structures, such as the FEMA P646 (FEMA, 2012) and American Society for Civil Engineers design codes (ASCE, 2016), were developed. (I) is mainly addressed either by simple empirical laws or by laboratory experiments. Numerical simulations of debris transport are still challenging in realistic conditions (Koh et al. 2023). Simple empirical rules describe debris lateral dispersion defined by a spreading area ±22.5° from the initial position (Naito et al. 2014), and by a dispersion law depending on the number of debris transported (Nistor et al., 2017). Harbours and nearby areas are exposed to container transport hazard (Naito et al. 2014., Koh et al. 2023). This makes understanding the role of tsunamis impact angle and storage yard layout on the movement of shipping containers particularly important. While dispersion at city scale can be simulated with depth integrated models (Koh et al. (2023), the analysis of the pick-up stage and near field transport requires modelling of the six degrees of freedom of the waterborne debris. Due to their nature, Lagrangian numerical models have been used to simulate these problems. More specifically Smoothed Particles Hydrodynamics (SPH) models coupled with the Multiphysics model CHRONO have recently demonstrated their capability in accurately simulating these type of phenomena (Ruffini et al., 2021, 2023). Using this numerical approach, this study aims to provide insight into the role of the initial debris layout in the hazard generated by their mobilisation, focusing on shipping containers in harbours.

Tsunamis are long gravity waves caused by the displacement of a large volume of water, such as through tectonic movements or landslides. They threaten passing ships, dams and buildings, leading to devastating disasters. The characteristics of tsunamis, such as the wave height, wavelength and direction, are significantly influenced by the geometry of the water body (Ruffini et al., 2019; Chen et al., 2023). Tsunamis propagating in converging water bodies impact the sidewalls or shores at an oblique angle. To gain a deeper understanding of how tsunamis propagate in converging water bodies, Chen et al. (2023) conducted a study on the propagation of solitary waves along the symmetry axis of idealised, symmetrical, converging water bodies. They discovered that Mach reflection has a substantial impact on the distribution of wave amplitudes in relatively wide channels and suggested a new predictive approach.

The interest for the impact of climate change on ocean waves within the Mediterranean Sea has motivated a number of studies aimed at identifying trends in sea states parameters from historical multi-decadal wave records. In the last two decades progress in computing and the availability of suitable time series from observations further supported research on this topic. With the aim of identifying consensus among previous research on the Mediterranean Sea and its sub-basins, this review analysed the results presented in peer reviewed articles researching historical ocean waves trends published after the year 2000. Most studies focused on the significant wave height trends, while direction and wave period appear to be under-studied in this context. We analysed trends in mean wave climate and extreme sea states. We divided the Mediterranean basin in 12 sub-basins and analysed the results available in the literature from a wide range of data sources, such as satellite altimetry and numerical models, among others. The consensus on the significant wave height mean climate trends is limited, while statistically significant trends in extreme values are detected in the western Mediterranean Sea, in particular in the Gulf of Lion and in the Tyrrhenian Sea, with complex spatial distributions. Negative extreme sea state trends in the sub-basins, although frequently identified, are mostly not significant. We discuss the sources of uncertainty in results introduced by the data used, statistics employed to characterise mean or extreme conditions, length of the time period used for the analysis, and thresholds used to prove trends statistical significance. The reduction of such uncertainties, and the relationship between trends in sea states and weather processes are identified as priority for future research.

The primary challenge in designing and analysing masonry structures is predicting their mechanical response. In particular, fast and direct prediction of masonry mechanical response field is desirable. This motivates the present study to introduce an innovative model using a conditional generative adversarial neural network (cGAN) for this purpose within linear or nonlinear ranges. This model establishes a direct connection between masonry microstructural features and both local and global mechanical responses full-fields, overpassing the path dependency of nonlinear mechanical problems. The model predicts strain maps and reaction forces of masonry panels under different loading scenarios and at any level of loading, solely from masonry panels images that encode material properties and loading scenarios into different shades of colours, without the need for information about material constitutive laws. This revolutionary approach holds the potential to serve as metamodel alternative to computationally expensive finite element (FE) simulations for masonry structures.

In flood- and tsunamis-prone areas, waterborne debris impacts on structures cannot be neglected in structural design and assessment. For these purposes, the current practice is to represent these loads with their force-time (F-t) diagram and use them in structural analyses. Many existing models to compute such diagrams, among which the design formulas by ASCE/SEI 7–22, assume the structure to be massless. However, the accuracy of this assumption lacks extensive investigation. This is studied here for the first time using Finite Element (FE) simulations conducted on a plate structure under debris impact loads. Different cases of structure-to-debris mass and stiffness ratios are investigated. It is found that if the mass ratio is higher than a critical value, the structural mass significantly affects the F-t diagrams by causing an abrupt rise of the impact force and force values proportional to the mass ratio. These loads substantially differ from those computed under the massless structure assumption. It is also found that the existing analytical models become significantly inaccurate in predicting the F-t diagrams under the effects of the structural mass. It is finally pointed out that the scenarios where the structural mass is crucial include many realistic cases of impacts on masonry, concrete and solid cross-layered wooden panels (XLAM) walls. These results, together with post-disaster evidence of significant structural damage due to debris impacts and the growing risk of extreme floods due to climate change, highlight the significant practical interest of this study.

The dynamic interaction between cliff, beach and shore-platform is key to assessing the sediment balance for coastal erosion risk assessments, but this is poorly understood. We present a dataset containing daily, 3D,colour LiDAR scans of a 450 m coastal section at Happisburgh, Norfolk, UK. This previously para-glaciated region comprises mixed sand-gravel sediments, which are less well-understood and well-studied than sandy beaches. From Apr-Dec 2019, 236 daily surveys were carried out. The dataset presented includes: survey areas, transects LiDAR scans, georeferenced orthophotos, meteorological- and oceanographical conditions during the Apr-Dec observation period. Full LiDAR point-clouds are available for 67 scans (Oct-Dec). Hourly time-series of offshore sea-state parameters (significant wave height, mean propagation direction, selected spectral periods) were obtained by downscaling the ERA5 global reanalysis data (global atmosphere, land surface and ocean waves) using the numerical model Simulating Waves Nearshore (SWAN). We indicate how to obtain hourly precipitation time-series by interpolating ERA5 data. This dataset is important for researchers understanding the interaction between cliff, beach and shore-platform in open-coast mixed-sand-gravel environments.

Only around 40% of rivers globally have deltas, but the conditions which inhibit or facilitate river delta formation are not well understood. Many studies have investigated the response of delta development to marine and river conditions. However, few have investigated the limits of such processes beyond which delta formation may be prevented, and none have done so using numerical modeling. This is in part due to ambiguity in the definition of the term "delta," which can make identification difficult in ambiguous cases. Here we propose a systematic method for identifying deltas, based on: accumulation of sediment above the low tide water level; proximity of such deposits to the initial coastline; and the presence of active channels. We run 42 simulations with identical river (1280m3s-1) $(1280\ {\text{m}}<^>{3}{\text{s}}<^>{-1})$ and sediment (0.048m3s-1) $(0.048\ {\text{m}}<^>{3}{\text{s}}<^>{-1})$ discharges, under combinations of significant wave height and tidal range typical for coasts globally, and determine if/when a delta is formed by this definition. Where deltas do form, we classify four formational regimes-river-controlled, river/tide-controlled, wave-controlled, and wave/tide-controlled-and discuss the mechanisms of delta development for each regime. Furthermore, we find that, under the discharge conditions considered, delta formation is prevented for combinations of, approximately, significant wave heights of 2.0m $2.0\ \mathrm{m}$ and tidal ranges >= 3.0m ${\ge} 3.0\ \mathrm{m}$. We hypothesize that inhibition of delta formation can be explained as a consequence of sufficient marine-driven alongshore sediment transport. This is tested by deriving a 1D alongshore sediment diffusion equation, and comparing predictions made using this formula to the cross-shore integrated sediment volumes of the simulations. River deltas are accumulations of sand and/or silt that form where rivers discharge to the ocean. Not all rivers form deltas, however, and the conditions that allow or prevent delta formation are not well understood. Here, we run a series of computer simulations modeling a river with unchanging discharge of water and sand, discharging into a marine basin featuring varying combinations of waves and tides. We propose an approach to defining precisely when a delta is or is not present, and apply this in order to determine when/if deltas form in our simulations. The results of these simulations are used to identify the limits of wave height and tidal range beyond which delta formation may be prevented under the discharge conditions modeled. These limits are found to exist at, approximately, combinations of wave heights of around 2.0 m and tidal ranges of 3.0 m or more. We also discuss the ways in which the growth of deltas varies under different combinations of waves and tides. Finally, we use a mathematical formula to test the idea that delta formation may be prevented when sediment is driven alongshore away from the river mouth by waves and tides faster than it can accumulate. Idealized numerical modeling of river discharge under varied waves and tides suggests limits beyond which delta formation is prevented Distinct mechanisms of delta formation under larger waves and tides than those modeled in previous studies are elucidated Alongshore diffusion by combined waves and tides is proposed as an explanatory mechanism by which delta formation is inhibited or prevented

As confirmed by recent post-disaster surveys, masonry buildings may experience substantial damage under waterborne debris impacts in extreme hydrodynamic event scenarios, e.g., floods or tsunamis. The common approach to model such load scenarios is to carry out structural analyses where the debris action is implemented through a representative force-time diagram. Recent studies demonstrated that the strain rate-dependent structural behaviour is activated in masonry structures when subjected to the impact force of waterborne debris, making the implementation of the strain rate-dependent materials necessary to carry out reliable structural simulations. However, these data have been collected using a specific model to compute the impact force-time diagrams developed from numerical and experimental data, which is different from the model prescribed by the US standard ASCE/SEI 7–22 to compute such loads. These two models lead to different force-time diagrams. Therefore, the design strategy imposed by the ASCE standard might affect the high strain rate effects with unknown implications. This study aims to investigate this research gap using nonlinear Finite Element (FE) simulations. A masonry wall is modelled with a micro-modelling approach. The water flow pressures and the debris impact force are applied. It is found that the F-t diagram given by the ASCE model causes significantly different strain rate-time histories in terms of increment rate and peak values across the structure.