On the risk of fatigue failure of structural elements exposed to bottom wave slamming -- Impulse response regime

TL;DR

This work evaluates whether fatigue damage from bottom-wave slamming can govern the design of marine structural elements when the impact duration is short relative to the structure's vibratory response time, i.e., in the impulse regime with $t_{ m imp}\ll t_{ m vib}$. It develops a general framework coupling a single-dominant-mode impulse response, extended SN-curves with both low- and high-/very-high-cycle branches, and stochastic sea-state/impact modeling to compare fatigue risk against ultimate-strength exceedance. Using Monte Carlo simulations over long-term exposures, it shows fatigue-driven failure can necessitate sizing constraints 3–5× more conservative than those based solely on $S_{u}$ for typical lifetimes and elevations, with fatigue damage predominantly arising from high-/very-high-cycle regimes and from moderately nonlinear waves. The study also analyzes how body elevation and wave-nonlinearity effects influence the relative importance of fatigue, discusses parameter-inference steps for real structures, and outlines extensions to forward/seakeeping motions and non-impulse regimes. The findings highlight fatigue as a potentially critical but design-sensitive factor for slamming-prone elements, suggesting careful consideration of impulse dynamics, SN-curve randomness, and long-term exposure in reliability-based sizing.

Abstract

This study aims to investigate whether fatigue damage induced by bottom wave slamming can be a failure mode important to consider when sizing a marine structural element. The body exposed to wave impacts is assumed to have a shape and structural arrangement such that the duration of wave-impact loads is short relative to the structure's vibratory response time. In this dynamical regime, fatigue is found to be a potentially important failure mechanism: accounting for the risk of failure due to fatigue damage may result in design constraints that are significantly more conservative than those based on the risk of ultimate strength exceedance. The role of fatigue damage depends on the elevation of the body. It is predominant for low elevations, for which slamming events are frequent. Since this study aims to provide general insight, the specific details of the body, such as its shape and structural arrangement, are not specified. Instead, a general framework is used for the analysis. The way forward to address a specific case study, possibly including the effects of forward and seakeeping motions, is briefly explained.

Figures (8)

• Figure 1: Flow diagram of the approach. The input data of the problem are indicated by blue boxes with square corners.
• Figure 1: Cross section of the wedge-shaped structure considered in Faltinsen (1999). The maximum strain reported in Fig. \ref{['fig_faltinsen']} is measured in the middle of the second longitudinal stiffener (the one pointed to by an arrow on the diagram). See faltinsen_1999 for more details.
• Figure 2: Illustration of the impulse stress-response regime considered in the present study. The stress response is assumed to be dominated by a single structural mode. In this dynamical regime, the stress amplitude of the first cycle, $s^{(1)}$, is approximately proportional to the load impulse (i.e., the time-integral of the load).
• Figure 2: Nondimensional maximum strain, $Q$, as a function of a parameter $P$ that is proportional to $t_{\rm imp} / t_{\rm vib}$ (see main text). Numerical data points are shown as circles. The data points with $P < 0.25$ are highlighted in red: they belong to the impulse regime, $t_{\rm imp} \ll t_{\rm vib}$. The red solid line is a least-squares fit of these data points with a linear function $Q = \Theta P$. [Data points were extracted from Fig. 17 in faltinsen_1999]
• Figure 3: Left:$SN$ curve pattern used in this study. The different constraints which define this $SN$ curve are annotated: (i) the stress amplitude at $N=1$, $S_0 \equiv S(N=1)$, is used as a normalization factor of the proposed $$SN${}$ curve pattern. $S_0$ is expected to be close to the ultimate strength of the material; (ii) the stress level at the end of the low cycle branch is set to $S=S_{\rm 0}/2$ at $N=10^4$. The transition stress level, $S_{\rm 0}/2$, can be considered as a proxy for the yield strength; (iii) the power law index of the high cycle branch is equal to $-1/3$; (iv) the very high cycle branch starts at $N= 10^7$ and has a power law index equal to $-1/5$. Right:$SN$ curve randomness. In the illustration, the median $SN$ curve is shown as a dashed line. The noisy gray curve illustrates the case where the randomness is modeled through option 2 (see §\ref{['subsubsec_snRnd']}) The solid gray curve illustrates the case where the randomness is modeled through a random shift factor, $\alpha_{\rm shift}$ (option 1). The dotted lines show the $\pm 2\delta$ band. The "$- 2\delta$" curve (i.e., the dotted line on the left of the median $SN$ curve) matches the curve pattern shown on the left panel.