Sloping Seabed Research Articles

Probabilistic analysis of wave-induced dynamic response in a poroelastic sloping seabed using random finite element method

Wave loading can lead to transient liquefaction and instability in a porous seabed and can therefore cause marine structures to fail. The failure mechanism of seabed involving many complex factors and uncertainties has not been fully revealed. The properties of marine sediments, usually assessed as constant parameters in traditional deterministic analyses, actually vary spatially because of geomorphic processes and loading history. This study therefore presents a probabilistic analysis of wave-induced dynamic responses in a poroelastic sloping seabed by applying a random finite element method. Spatial variabilities of the cross-correlated permeability and shear modulus of marine soils are taken into account using random field theory. The response of poroelastic sloping seabed is analyzed based on Biot's theory and linear wave theory considering changes in wave height and length when propagated from relatively deep to shallower water. A LiveLink code is written to integrate the random field simulation and the finite element model for the probabilistic analysis of a spatially heterogeneous seabed. Monte Carlo simulations are carried out to obtain the statistics and associated uncertainties of the seabed response. Effects of cross-correlation of random fields and the slope angle on the response of a poroelastic sloping seabed were also investigated.

Long wave reflection by an array of submerged trapezoidal breakwaters on a sloping seabed

For linear long waves propagating over an array of submerged trapezoidal breakwaters on a sloping seabed, a closed-form solution for the reflection coefficient is derived. The validity of this solution is verified by comparing with published numerical and analytical results in several cases. Then the effects of the slope of seabed, breakwater height, breakwater width, the slope of breakwaters, and the number of breakwaters on Bragg resonant reflection are successively investigated. It is found that the sloping seabed only enhances the strength of Bragg reflection, but also shifts the resonance frequency to a lower value. Besides, the higher-order Bragg resonance is not always weaker than primary Bragg resonance and is more likely to be influenced by breakwater width. By adjusting topographic parameters, the present solution could also be applied to the Bragg scattering by an array of trenches on a sloping seabed.

Response and Instability of Sloping Seabed Supporting Small Marine Structures: Wave–Structure–Soil Interaction Analysis

Abstract Wave-induced liquefaction in seabed may adversely impact the stability and bearing capacity of the foundation elements of coastal structures. The interaction of wave, seabed, and structure has been studied mostly for only mildly sloping seabed (<5deg) using a decoupled approach. However, some of the marine hydrokinetic devices (MHKs) may be built on or anchored to the seabed with significant steepness. The wave-induced response and instantaneous liquefaction within sloping seabed supporting a small structure (representing a small MHK device) are evaluated herein by developing an almost fully coupled finite element model. The effects of coupling approach on the stress response and liquefaction of the seabed soils are investigated. Subsequently, post-liquefaction deformation of seabed soils around the structure is assessed. The poroelasticity equations governing the seabed response coupled with those for other domains are solved simultaneously. For post-liquefaction analysis, the soil is modeled as elastic-perfectly plastic material. The development of instantaneously liquefied zones near the foundation is studied in terms of seabed steepness and wave parameters. The changes in the effective stress paths due to the development of liquefied zones are evaluated in view of the soil's critical state. The results indicate that the decoupled solution yields significantly larger stresses and liquefaction zones around the structure. The seabed response and the liquefaction zones become smaller for steeper slopes. The presence of liquefied zones brings the stress state closer to the failure envelope, reduces the confining stresses, and induces larger plastic strains around the foundation element.

Vector form intrinsic finite element analysis of deepwater J-laying pipelines on sloping seabed

The dynamic responses of offshore pipelines induced by J-laying effects are remarkable and dominate the pipeline design and installation feasibility in practice. Most previous studies have focused on the analysis of pipeline installation on the horizontal seabed. In this paper, an extended J-lay model based on the vector mechanics principle is developed to investigate dynamic behaviors of laying pipelines on the sloping seabed. Two representative seabed slope types are taken into account involving the positive and negative slopes. The laying pipeline is divided into a sequence of mass particles linked by massless elements, and the deformations of the elements and the rotations of the particles are calculated to obtain the internal forces. The explicit central difference technique is applied to solve the movement governing equations of pipeline particles by program coding. Two illustrative cases of a 12-inch pipeline being laid separately from the horizontal seabed to the positive and negative sloping seabed are simulated under a random sea state. The influences of seabed slope type and angle on pipeline responses are estimated quantitatively. Significant differences of pipeline behaviors between the positive and negative sloping seabed are observed, which offer very intuitive evidences of seabed slope effects concerning deepwater J-laying pipelines.

A new buckle initiation concept based on the energy barrier of subsea pipelines laid on the sloping seabed

Lateral buckling may occur for subsea pipelines operating under high-temperature conditions and buckle initiation techniques are usually employed to trigger man-made buckles at pre-designed locations to avoid rogue buckles. Based on the energy barrier, a new buckle initiation concept is proposed to trigger lateral buckling for subsea pipelines laying on a sloping seabed. The corresponding mathematical model is formulated, which can also be applied to the case of a horizontal seabed by setting the sloping angle to be zero. The energy difference between pre- and post-buckling states is evaluated to determine the Maxwell temperature and the energy barrier. The influence of the sloping angle on the lateral and axial deformations and typical post-buckling behaviour is analysed. The results show that the downward buckling mode prefers to occur since the minimum critical temperature, the Maxwell temperature and the energy barrier are all lower than that for upward buckling mode. In the downward buckling mode, both the maximum displacement and the maximum stress locate at the central lobe. However, they may locate at the side lobes in the upward buckling mode when the sloping angle is large enough.

Surface Chlorophyll-A Fronts in the Yellow and Bohai Seas Based on Satellite Data

Chlorophyll fronts are important to monitor and map the oceanic front, especially in the season when sea surface temperature (SST) fronts weaken. In this study, surface chlorophyll-a (chl-a) fronts in the Yellow and Bohai seas were characterized for the first time using satellite data. Five distinct chl-a fronts (i.e., the Bohai Strait, Shandong Peninsula, Jiangsu, Liaodong Peninsula, and Korean Peninsula fronts) were observed in summer along the 40 m isobaths and faded in other seasons. Notably, these fronts coincided with SST fronts. Strong chl-a fronts emerged during summer due to chl-a blooms in eutrophic coastal waters paired with surface chl-a fading in strongly stratified offshore waters and coastal physical fronts. Although SST fronts were strong during winter, light limitation and strong vertical mixing in offshore waters led to low chl-a in both coastal and offshore waters, suppressing chl-a front formation. Both chl-a and SST fronts coincided with steep seabed slopes (slope ratio > 1), suggesting that seabed slope may be an indicator of oceanic front location.

Maximum wave run-up over beaches of convex/concave bottom profiles

In this communication, we provide exact solution for the wave run-up event owing to impulsively started solitary waves towards beaches of various sloping bottom profiles. A rigorous asymptotic formula is obtained corresponding to the solitary wave maximum wave height depending on concavity feature of the coast bottom. It unifies many well-studied beaches and their run-up predictions in the literature. It also explains how the sloping profiles will contribute to the wave run-up process by the response of the approaching long waves. The main outcome of the work is that for the smaller offshore amplitude to offshore depth ratios, oceans with high sloping seabeds result in the least maximum wave run-ups no matter whether the concave or convex coastline bottom profiles (for profile shapes refer to figure 1) are accounted. Unlike this, higher maximum wave run-ups take place with enhanced amplitude ratios. Shores with a concave bottom shape are shown to delay the run-up process by significantly opposing the moving waves acting like a tsunami barrier. However, convex bottom cross-sectional beaches are assisted by the faster wave climbing feature and with increased maximum wave run-ups. More convex bottom profiles show up peculiar singular structures with larger run ups The presented wave run-up formula with the convex/concave beach profiles may be beneficial in many future coastal applications in terms of coastline processes, despite the fact that the proposed solution is linearized with limited range of validity.

Analysis of wave-induced submarine landslides in nearly saturated sediments at intermediate water depths

Evaluation of wave impacts on submarine landslides is an essential element in geohazard studies. The slight desaturation of sediments (due to dissociation of gas hydrates) has been found to adversely impact the slide of the sloping seabed in the Fraser River Delta in Canada. In this study, to investigate the role of wave action on the slide of partially saturated seabed slopes, an integrated FEM model is developed. Despite most earlier studies that used a simplified decoupled undrained analysis, in this article, a more realistic model for coupled flow-and-deformation processes (within the sediments) and fluid-seabed interaction is utilized. Linear wave theory and Biot’s poroelasticity for the fluid and seabed domains are considered, respectively, and continuity of flux and traction is enforced along the interface of the media. The instability of the sloping seabed is investigated using strength reduction finite element method (SRFEM) with Mohr-Coulomb failure criterion. The limitation of limit equilibrium methods in the evaluation of submarine landslides is shown through comparison with SRFEM analyses where partly-dynamic and quasi-static idealizations of seabed response are considered. Finally, the adverse impacts of slight desaturation on seabed instability are assessed, and the reduction of the stability number with seabed steepness is presented.

Hydrodynamic Analysis of Twin-Hull Structures Supporting Floating PV Systems in Offshore and Coastal Regions

In this paper, a novel model based on the boundary element method (BEM) is presented for the hydrodynamic analysis of floating twin-hull structures carrying photovoltaic panels, supporting the study of wave responses and their effects on power performance in variable bathymetry regions. The analysis is restricted to two spatial dimensions for simplicity. The method is free of any mild-slope assumptions. A boundary integral representation is applied for the near field in the vicinity of the floating body, which involved simple (Rankine) sources, while the far field is modeled using complete (normal-mode) series expansions that are derived using separation of variables in the constant depth half-strips on either side of the middle, non-uniform domain, where the depth exhibited a general variation, overcoming a mild bottom-slope assumption. The numerical solution is obtained by means of a low-order panel method. Numerical results are presented concerning twin-hull floating bodies of simple geometry lying over uniform and sloping seabeds. With the aid of systematic comparisons, the effects of the bottom slope and curvature on the hydrodynamic characteristics (hydrodynamic coefficients and responses) of the floating bodies are illustrated and discussed. Finally, the effects of waves on the floating PV performance are presented, indicating significant variations of the performance index ranging from 0 to 15% depending on the sea state.

Experimental investigations on the stability of clayey sloping seabed under wave actions

A series of wave flume tests have been performed in this paper to investigate the responses of clayey sloping seabed under wave actions, including the characteristics of wave shoaling, seabed topography and excess pore pressure. Different wave heights H, water depths D and two slope angles β (4° and 10°) were adopted and their effects were analyzed. It is found that obvious wave shoaling appears during the process of wave propagation along the sloping seabed. There are primarily two failure modes of the clayey sloping seabed under wave actions: for the bank sloping seabed, waves propagate and break on the slope and the seabed soil is scoured as pieces; for the submerged sloping seabed, a large area of shallow landslide occurs along the slope from top to bottom. It is also found that under plunging wave actions, the pore pressure response in clayey sloping seabed can be divided into three modes. The changes of three-dimensional seabed topography in the tests were captured and the quantity of clay scoured by waves was evaluated. Based on the experimental data, an advanced formula has been proposed to assess the critical failure condition and the quantity of the sloping clayey seabed scoured under wave actions.

The Role of 2D Seepage on Sediment Incipient Motion around a Pipeline

Pipelines have been used as one of the main transportation methods for the offshore industry, with increasing activities in marine resources recently. Prediction of seabed instability is one of key factors that must be taken into consideration for an offshore pipeline project. As the first step of the scour process, sediment incipient motion has been intensively studied in the past. Most previous investigations didn’t consider the wave-induced seepage in the elevation of sediment motion. In this paper, two-dimensional seepage was considered to modify the conventional Shields number and its associated impact on sediment incipient motion around the trenched pipeline was investigated. Both flat and sloping seabeds are considered. The numerical results indicated that a peak or valley of the modified Shields number was formed below the pipeline and horizontal seepage flow tremendously impact the sediment motion in the vicinity of the pipeline. Parametric analysis concludes: the influence of the seepage around the pipeline becomes more significant in a large wave, shallow water in a seabed with large shear modulus and permeability, and larger pipeline diameter and smaller flow gap ratio. This will make soil particles be more easily dragged away from the seabed.

Three dimensional numerical modelling for wave radiation problem under arbitrary seabed condition

Three dimensional Rankine source model is utilized to investigate the hydrodynamic responses for wave radiation problems under arbitrary seabed condition in time domain. The free surface, seabed surface and body surface are presented by layer of continuous panels rather than a discretization by isolated points. These panels are positioned exactly on the fluid boundary surfaces and no desingularization technique required. To accommodate the sloping seabed profile, a straightforward source panel distribution on seabed surface is newly developed with two parameters determined by numerical tests. The accuracy and efficiency of the numerical solutions are validated by comparison with published data. The influences of flat seabed, uneven seabed and sloping seabeds are examined. Numerical simulations demonstrate that various seabed profiles have significant and complicated effects on the body hydrodynamic response characteristics.

Anomalous wave statistics following sudden depth transitions: application of an alternative Boussinesq-type formulation

Recent studies of water waves propagating over sloping seabeds have shown that sudden transitions from deeper to shallower depths can produce significant increases in the skewness and kurtosis of the free surface elevation and hence in the probability of rogue wave occurrence. Gramstad et al. (Phys. Fluids 25 (12): 122103, 2013) have shown that the key physics underlying these increases can be captured by a weakly dispersive and weakly nonlinear Boussinesq-type model. In the present paper, a numerical model based on an alternative Boussinesq-type formulation is used to repeat these earlier simulations. Although qualitative agreement is achieved, the present model is found to be unable to reproduce accurately the findings of the earlier study. Model parameter tests are then used to demonstrate that the present Boussinesq-type formulation is not well-suited to modelling the propagation of waves over sudden depth transitions. The present study nonetheless provides useful insight into the complexity encountered when modelling this type of problem and outlines a number of promising avenues for further research.

Stability of the Gunneklev Fjord sediments

The seabed of the Gunneklev Fjord, with exceptionally soft contaminated sediment, is to be capped. The sediment, containing, among others, mercury and dioxins mixed with natural mud, has an undrained shear strength less than 1 kPa and thickness up to 2.5 m. To reduce the potential for leaching of mercury and dioxin from these sediments, Hydro Energy AS developed a remediation plan for Gunneklev Fjord which includes capping of the contaminated sediment with either sand or a mixture of sand and active charcoal. This paper presents an assessment of the risk associated with the cap placement over the contaminated sediment. The potential for the cap causing sliding of the sediment, which could re-expose even more severely contaminated layers and spread the contaminated material, was analysed deterministically and probabilistically. The sediment’s undrained shear strength and thickness and the cap thickness were modelled as random variables. The deterministic analyses gave a safety factor over 3. The probabilistic analyses indicated, however, that the probability of sliding can be high for areas where the seabed inclination is steeper than 1:50, and if the average undrained shear strength is less than 0.4 kPa. The analyses highlight the importance of careful cap placement on the sloping seabed of the fjord, and the need to control the cap thickness. The analyses were used to support decision-making on the design of the cap and the placement method.

Breaking Location of Internal Solitary Waves Over a Sloping Seabed

AbstractWe present a semi‐analytical model for predicting the breaking location of internal solitary waves (ISWs) over a sloping seabed. Our conceptual model is based on laboratory experiments, performed in a wave tank, that reproduce the ISW breaking mechanisms and show how the steepening of the trailing edge leads to verticalization of the wave profile during the shoaling phase. We derive the location of ISWs breaking, that is, the wave verticalization point, through two‐layer, interfacial theoretical models and conservation of wave mass. We apply our model to the case of tidally forced ISWs that are generated in the Strait of Messina (Central Mediterranean Sea), where northward traveling ISWs are expected to refract and break over the frontal slope of Capo Vaticano. Our application is then assessed through numerical investigations, which allow to consider realistic field conditions in terms of water column stratification and geometrical setting. Our results, and the expected ISW‐induced bed shear stress, suggest a link between the predicted breaking locations and the occurrence of sediment resuspension over that specific portion of the slope.

Low-dimensional offshore wave input for extreme event quantification

In offshore engineering design, nonlinear wave models are often used to propagate stochastic waves from an input boundary to the location of an offshore structure. Each wave realization is typically characterized by a high-dimensional input time-series, and a reliable determination of the extreme events is associated with substantial computational effort. As the sea depth decreases, extreme events become more difficult to evaluate. We here construct a low-dimensional characterization of the candidate input time series to circumvent the search for extreme wave events in a high-dimensional input probability space. Each wave input is represented by a unique low-dimensional set of parameters for which standard surrogate approximations, such as Gaussian processes, can estimate the short-term exceedance probability efficiently and accurately. We demonstrate the advantages of the new approach with a simple shallow-water wave model based on the Korteweg–de Vries equation for which we can provide an accurate reference solution based on the simple Monte Carlo method. We furthermore apply the method to a fully nonlinear wave model for wave propagation over a sloping seabed. The results demonstrate that the Gaussian process can learn accurately the tail of the heavy-tailed distribution of the maximum wave crest elevation based on only $$1.7\%$$ of the required Monte Carlo evaluations.

Geometric modeling of Holocene large-river delta growth patterns, as constrained by environmental settings

Topographic/bathymetric conditions of the continental shelf can significantly influence the long-term growth of river deltas. In particular, these conditions constrain the accommodation space for sedimentation in the deltaic areas. In this study, we use a conceptual geometric model to evaluate the role played by this factor, on the basis of the principle of mass conservation. The Ganges-Brahmaputra, Mekong and Nile deltas are examined as three typical examples, in terms of their different original seabed morphologies. The control variate method is applied to eliminate the effect of the difference in model input variables. The results show that, assuming a constant sediment load, the delta growth rate will decrease with time; a higher value of the original seabed slope leads to a lower shoreline progradation rate for the subaerial delta and a higher growth rate for the subaqueous delta. Thus, the original seabed morphology represented by slope is a critical factor affecting the evolution of Holocene large-river deltas. These results explain the interrelationships between sediment load, deltaic plain area, and the original seabed slopes for the 27 large-river deltas worldwide, located in the middle/low latitudes, with different tectonic backgrounds. In the future, the conceptual geometric model may be combined with sediment dynamic modeling to identify more details of the evolution of these deltas.

Influence of trench geometry on fatigue response of steel catenary risers by using a boundary layer solution on a sloped seabed

Previous studies have shown that the geometry of the trench affects the fatigue response of steel catenary risers (SCR). Fatigue performance of SCR in the touchdown zone (TDZ) has been investigated in several studies, sometimes leading to contradictory results, with no coherent agreement regarding if the effect of the trench on fatigue performance of SCR would be beneficial or detrimental. This paper aims at developing a model based on the well-known boundary layer method (BLM) to capture the trench effect on the fatigue performance of SCR. Using analytical and numerical approaches, a meaningful relationship was observed between the slope of trench shoulders, the magnitude of the peak fatigue damage, and its location in the trench. It was also observed that the effect of trench formation on the fatigue performance of SCR could be predicted by using TDP oscillations on a sloped seabed. The study contributes to achieving a coherent agreement about the trench effect on fatigue.

Two-Dimensional Numerical Modelling of a Moored Floating Body under Sloping Seabed Conditions

A coupled floating body-mooring line model is developed by combining a boundary element model for a two-dimensional floating body and a catenary mooring line model. The boundary element model is formulated in the time domain by a continuous Rankine source, and a reflection potential is introduced to account for the wave reflection due to sloping seabed. This newly developed model is validated by comparisons against available data. Then, dynamic response analyses are performed for the moored body in various seabed conditions. Compared with a flat seabed, a sloping seabed causes unsymmetrical mooring line configuration and generates noticeable effects in the motion responses of the floating body.

A DMM-EMM-RSM hybrid technique on two-dimensional frequency-domain hydroelasticity of floating structures over variable bathymetry

This paper proposes a hybrid technique combining the discrete modules method (DMM) (Lu et al., 2016), the eigenfunction matching method (EMM) (Tsai et al., 2011) and a further extended Rankine source method (RSM) to treat the two-dimensional hydroelastic problem of floating structures over variable bathymetry. In the hybrid technique, DMM is employed to discrete a floating structure into a set of rigid modules connected by elastic beams with equivalent deformation conditions of the structure; the incident wave potential over variable bathymetry without the presence of floating structures is obtained by EMM; a Rankine source method developed by Feng et al. (2017) is further extended to gain the diffracted and radiated wave potentials with the discreted multi-rigid-modules over variable bathymetry. A coupled model for the hydroelasticity of floating structures over variable bathymetry can be established by substituting the external wave loads exerted by the obtained incident, diffracted and radiated potentials into the multi-rigid-body dynamic equation by DMM in the frequency-domain. The convergence of the hybrid technique is validated through a good agreement against published data (Riyansyah et al., 2010) for hydroelastic responses of a two-dimensional floating structure over a flat seabed. Effects of sloping seabeds on hydroelastic responses of the floating structure are preliminarily investigated by the present hybrid technique.