On the uncertainties in stone armor stability

Coastal rubble mound armor stability has historically been based on empirical equations correlating armor stone movement resistance to wave-induced forces. These equations are primarily derived from small-scale laboratory studies and exhibit considerable uncertainty. While new relationships have been introduced to broaden their applicability, little progress has made in recent decades to reduce equation uncertainty. Uncertainty in stability is primarily due to intrinsic aleatory uncertainty related to the stochastic nature of waves, stone geometry, and inter-stone contacts/interlocking, as well as epistemic uncertainty associated with knowledge limitations, modeling errors, and measurements. Here, we refer to aleatory uncertainty as inherit and epistemic uncertainty as reducible. Effects of aleatory uncertainty in hydraulic stability have often assumed dominant over epistemic uncertainty. However, the magnitude of both contributions has not yet been explicitly quantified to validate this assumption. Modern probabilistic design and simulation methodologies demand deeper understanding of uncertainties. A clear understanding of the relative magnitudes of epistemic and aleatory uncertainty will guide studies toward improving physics research. Efforts to describe complex wave-structure interaction phenomena have prompted new experimental campaigns, generating comprehensive datasets from diverse laboratories worldwide. The present research synthesizes data across a wide range of international studies to quantify and improve uncertainty understanding in stone armor stability. Existing experimental data in the literature have been examined and synthesized, leading to the formation of a new database encompassing varied water depth regimes from deep to very shallow. Data synthesis was accomplished by collecting and describing data from 7 different studies and homogenizing parametric characteristics to the extent possible considering the disparate nature of the native data. Benefiting from this extensive database, the most widely-used armor stability formulae were compared within the framework of quantifying uncertainty. This comparison revealed that no stability formula significantly outperforms others due to the high uncertainty in the available data. However, the raw data cannot be fully synthesized and homogenized without further modeling because of the disparate modeling approaches, non-homogeneous nature of the parametric data and the limited understanding possible of the detailed laboratory measurement techniques and data analysis. The 7 studies were simulated with a numerical high-fidelity phase-resolving wave transformation model to better homogenize the data. To achieve this, a one-dimensional fully nonlinear Boussinesq numerical model (Coulwave) was implemented to replicate incident and reflected wave conditions for all tests in the 7 studies. Wave parameters were matched near the wave generator and the structure toe to facilitate a consistent comparison of laboratory and numerical studies. This approach enhances the understanding of hydrodynamic uncertainty, shedding light on the primary sources and magnitudes of intrinsic and epistemic uncertainty. It also enables separation of errors caused by stability formulae and wave transformation model/stability formula (combined), allowing the assessment of the effect of wave prediction errors on stability prediction errors. The stability relations associated with the experimental studies were again evaluated using the synthesized homogenized data. The numerical model proved effective in clarifying uncertainty. A marginal reduction in hydrodynamic uncertainty was achieved compared to the total uncertainty illustrating that a majority of the uncertainty is not associated with the wave and water level conditions. Analysis of the datasets revealed a significant similarity among them, with aleatory uncertainty being predominant and closely associated with damage. Existing equations performed well in deep water conditions, but notable weaknesses were identified in shallow waters. Results suggest that incorporating depth, bathymetric slope, structure slope, and wave steepness/breaking characteristics based on bathymetry, in addition to structure slope, is crucial for improved equations. Additionally, the integration of offshore (spectral) wave period and inshore (spectral) wave height into the equations enhances predictive accuracy. In very shallow water, the influence of wave period appears to be of minor importance compared to deep water. Results conclusively indicate that the wave momentum flux parameter maintains a direct proportionality to the drag force exerted along the structure slope, displaying a discernible correlation with incident wave and depth parameters. Therefore, adopting such an approach enhances the understanding of physics and forces acting on stone armor units, and so appears to be a promising path forward for the optimal armor stability relationship that spans all wave and water depth regimes. In pursuit of this objective, initial attempts have been made to propose new stability equations, offering valuable insights and, in combination with uncertainty quantification, represents a significant advancement in probabilistic stone armor layer design and assessment.

La presente ricerca si propone di raccogliere e sintetizzare i dati provenienti da una vasta gamma di studi internazionali al fine di quantificare e migliorare la comprensione dell’incertezza nella stabilità delle opere a gettata in massi naturali. La sintesi dei dati è stata effettuata tramite la raccolta e la descrizione dei dati provenienti da 7 diversi studi, omogeneizzando le caratteristiche parametriche per quanto possibile, tenendo conto della natura eterogenea dei dati originali. Successivamente, gli studi sono stati simulati utilizzando un modello numerico ad alta precisione per la propagazione del moto ondoso (Coulwave), al fine di migliorare l’omogeneizzazione dei dati dal punto di vista idrodinamico. I risultati ottenuti sono stati impiegati per quantificare l’incertezza idrodinamica e per determinare i contributi relativi dell’incertezza aleatoria ed epistemica e del bias nelle misurazioni del danno, consentendo così la separazione e la valutazione degli effetti degli errori di previsione sull’errore indotto dalle equazioni di stabilità. Cinque dei 7 studi analizzati hanno prodotto equazioni di stabilità ben note, le quali sono state riadattate ai nuovi dati omogeneizzati al fine di evidenziarne i punti di forza e di debolezza dei vari modelli predittivi empirici. Sebbene tutte le formulazioni funzionino bene in acque profonde, sono stati rilevati dei limiti in acque basse e molto basse. Infine, sono proposte nuove equazioni di stabilità che coprono diversi regimi di profondità, e in combinazione con l’incertezza quantificata, offrono un significativo progresso nella progettazione probabilistica delle mantellate delle opere a gettata.