Assessment of global wave forces and moments on porous vertical barriers in random wave fields

Experimental investigations on wave induced dynamic pressures over slotted vertical barriers in random wave fields

Chevron's Platform Hermosa, located offshore California in 602 ft of water has been instrumented in order to extract global wave forces for correlation with measured waves and currents. Finite element studies showed that global forces on the platform could be calculated from measurements of axial leg strains near the platform base. Field calibrations to determine the relationship between applied force and measured strain were performed using an ocean-going tug. The wave load measurement approach, the field calibration procedure, the analysis of the calibration data, and comparisons of the calibration results with finite element predictions are prcscntcd. Discrepancies between prediction and measurement in these comparisons emphasize the importance of field calibrations when relying on strain measurements for extraction of wave forces. INTRODUCTION Wave tank model test results and available fullscale wave force data are not entirely satisfactory for evaluating wave force calculation procedures for drilling and production platforms. Data from wave tank tests suffer from scale effects. Field data either lack field calibration or are from structures with simple geometries. For example, data from Wave Projects I and II 1 are difficult to apply to full structures because only local forces on individual vertical cylinders were measured. The Conoco Test Structure wave forces2 and Platform Magnus3 were inferred from measured strains in structural members for a full platform, but lacked a field calibration. Conclusions regarding the adequacy of wave force calculation procedures drawn from uncalibrated field data are questionable. The Exxon 0TS5 was notable in that the structure was calibrated in the field; however it was a l/3-scale model of a structure with a relatively simple geometry. The Hermosa wave force project was designed to address shortcomings of existing data by obtaining full-scale wave and current force data from a field-calibrated platform. Platform Hermosa in the Point Arguello field, offshore California (see Fig. 1), was designed to allow convenient deployment of instruments to underwater locations. A square access tube, running from mudline to the well deck, is welded to each of its corner legs. The availability of these tubes provided motivation to find a way to use the platform response to measure applied overturning moment due to wave and current forces. Theoretical studies and computer simulation showed that such measurements were possible by measuring the leg strains near the base. An important ingredient of the method is a calibration accomplished by applying known loads to the instrumented structure while recording the strain and motion response. Some instrumentation was already in place on the platform. This was augmented with strain sensors and additional accelerometers. The calibration was performed using a 5000 hp tugboat to apply the known loads. PLATFORM INSTRUMENTATION A sketch of Platform Hermosa showing the location of many of the installed sensors is shown in Figure 1. Diagonally opposite pairs of triaxial accelerometers are situated at four elevations, including one not shown at the well deck (cl. +51 ft).

For a constructed offshore structure, wave force evaluation on its foundation in an intricate wave field will benefit the load data collection and structural safety monitoring. Then, the collected data can provide valuable references for similar structures constructed in the same ocean region in the future. A real-time wave force prediction can further contribute to the active control of the structural dynamic responses. According to the incident waves known or unknown, the wave force reconstruction issue can be divided into two categories. When the incident waves are known, the wave forces on the cylinder can be achieved by the theoretical methods or numerical methods. When the incident waves are unknown, researchers try to reconstruct the wave force indirectly. For a small-scale cylinder, researchers predicted the wave forces by using the Morison equation in random wave fields with measured data of wave elevation. These studies indicated a shortcut for determining the wave force on the cylinder by using the data of water surface elevation. However, the wave fields are assumed to be undisturbed by the structure in the mentioned studies. For a vertical larger-scale cylinder, Liu et al. (2018) established a prediction method to reconstruct wave force by using the recorded data of wave elevation around the cylinder. A linear method for the circular cylinder is provided that shows an excellent reconstruction of wave force for its dominant frequent components. However, reconstruction results showed that high frequency wave forces are underestimated and low frequency wave forces are overestimated, which means the linear method is incapable to predict the nonlinear wave forces on the structure. An improved method is built for reconstructing wave forces on a circular cylinder in the real-time. Two different algorithms, Fast Fourier Translation (FFT) and Recursive Least Squares (RLS), for real-time reconstruction are conducted. The present method can be applied for the data collection of wave loads on a constructed offshore structure.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/PYOuCNP8pgQ

Wave forces and dynamic pressures on slotted vertical wave barriers with an impermeable wall in random wave fields

This paper presents new laboratory data on long-wave (surf-beat) forcing by the random breaking of shorter gravity water waves on a plane beach. The data include incident and outgoing wave amplitudes, together with shoreline oscillation amplitudes at long-wave frequencies, from which the correlation between forced long waves and short-wave groups is examined. A detailed analysis of the cross-shore structure of the long-wave motion is presented, and the observations are critically compared with existing theories for two-dimensional surf-beat generation. The surf beat shows a strong dependency on normalized surf-zone width, consistent with long-wave forcing by a time-varying breakpoint, with little evidence of the release and reflection of incident bound long waves for the random-wave simulations considered. The seaward-propagating long waves show a positive correlation with incident short-wave groups and are linearly dependent on short-wave amplitude. The phase relationship between the incident bound long waves and radiated free long waves is also consistent with breakpoint forcing. In combination with previous work, the present data suggest that the breakpoint variability may be the dominant forcing mechanism during conditions with steep incident short waves.

The wave transformation due to pile-rock porous structure in combination with vertical porous barrier is studied under oblique wave action. The pile-rock breakwaters consists of two rows of closely spaced piles and a rock core between them is effective in dissipating wave energy when compared with traditional rigid breakwaters due to its reduced deadweight of construction materials and additional stability. Three different cases of the vertical barrier configurations such as fully-extended barrier, bottom-standing barrier and surface-piercing barrier placed in front of the pile-rock porous structure are considered for the investigation. The numerical study is performed using the eigenfunction expansion and the associated orthogonal mode-coupling relations considering the continuity of pressure and velocity for the vertical barrier, seaward and leeward structural interfaces. The Darcy’s law is incorporated for the flow through porous media and the porosity factor of the structure is introduced using the complex porous effect parameter. The numerical results for the wave reflection, transmission and dissipation coefficient, wave force on front and rear side of porous structure along with the wave force on the barrier interface are evaluated for different hydraulic characteristics. The analysis is presented for varying structural porosity, angle of incidence, structural thickness, friction factor, length between vertical barrier and porous structure for the three different cconfigurations of vertical barrier. The numerical investigation performed in the present study will be useful for the design and analysis of the composite breakwater system to protect the offshore facility from high waves.

Small-scale field experiment on wave forces on a U-OWC breakwater

This paper deals with the random forces produced by high ocean waves on submerged horizontal circular cylinders. Arena [1] obtained the analytical solution of the random wave field for two dimensional waves by extending the classical Ogilvie solution [2,3] to the case of random waves. In this paper, the wave force acting on the cylinder is investigated and the Froude Krylov force [4], on the ideal water cylinder, is calculated from the random incident wave field. Both forces represent a Gaussian random process of time. The diffraction coefficient of the wave force is obtained as quotient between the standard deviations of the force on the solid cylinder and of the Froude Krylov force. It is found that the diffraction coefficient of the horizontal force Cdo is equal to the Cdv of the vertical force. Finally, it is shown that, given that a very large wave force occurs on the cylinder, it may be calculated, in time domain, starting from the Froude Krylov force. It is then shown that this result is due to the fact that the frequency spectrum of the force acting on the cylinder is nearly identical to that of the Froude-Krylov force.

An analytical approach for the calculation of random wave forces on submerged tunnels

Experimental investigations on wave impact pressures under the deck and global wave forces and moments on offshore jacket platform for partial and full green water conditions

Wave pressures and forces on slotted vertical wave barriers

An analytical study is presented here to investigate the scattering of oblique flexural gravity waves by a pair of totally submerged vertically placed porous barriers, located at some distance from each other, for a homogenous fluid flowing over a porous sea-bed. A thin ice-sheet, replacing the usual free surface, is considered as the upper surface where it is treated as a thin elastic plate by following Euler–Bernoulli beam equation. The complete analytical solution, under the assumption of small-amplitude theory and structural response, is acquired by employing eigenfunction expansion and least square method for the problem of flexural gravity waves interacting with the submerged porous barriers. Subsequently, computation for the reflection and transmission coefficients, energy loss and wave forces are carried out and discussed for different parameter values corresponding to the ice-sheet, porous sea-bed, and porous barriers. This study establishes that the oscillatory behavior exhibited by the reflection of the waves. It further shows that when the inertial effect of the porous-effect parameter of the barriers is increased, the minima in wave reflection occur. The vertical porous barriers are found to dissipate a significant portion of the wave energy when an increase in the inertial effect of the porous barriers is affected. The hydrodynamic force on the barriers also follows an oscillatory pattern, and it increases when the length of the barrier is increased. Furthermore, wave transmission decreases significantly due to the energy dissipation by the porous sea-bed. It is demonstrated that corresponding to various structural parameters, almost no reflection and full transmission take place for an impermeable sea-bed and also when only real porosity parameter of the porous sea-bed is considered. The effect of the ice-sheet on the propagation of the flexural waves is also examined by obtaining a number of results for variation of various parameters. Variation in the elastic parameter of the floating ice-sheet is observed to command a considerable influence when the wave impinges upon the submerged vertical porous barriers.

Wave action on a vertical wall with a submerged horizontal plate: Analysis of phase variation of forces and probability of exceedance

We study the long-term evolution of weakly nonlinear random gravity water wave fields developing with and without wind forcing. The focus of the work is on deriving, from first principles, the evolution of the departure of the field statistics from Gaussianity. Higher-order statistical moments of elevation (skewness and kurtosis) are used as a measure of this departure. Non-Gaussianity of a weakly nonlinear random wave field has two components. The first is due to nonlinear wave–wave interactions. We refer to this component as ‘dynamic’, since it is linked to wave field evolution. The other component is due to bound harmonics. It is non-zero for every wave field with finite amplitude, contributes both to skewness and kurtosis of gravity water waves and can be determined entirely from the instantaneous spectrum of surface elevation. The key result of the work, supported both by direct numerical simulation (DNS) and by the analysis of simulated and experimental (JONSWAP) spectra, is that in generic situations of a broadband random wave field the dynamic contribution to kurtosis is small in absolute value, and negligibly small compared with the bound harmonics component. Therefore, the latter dominates, and both skewness and kurtosis can be obtained directly from the instantaneous wave spectra. Thus, the departure of evolving wave fields from Gaussianity can be obtained from evolving wave spectra, complementing the capability of forecasting spectra and capitalizing on the existing methodology. We find that both skewness and kurtosis are significant for typical oceanic waves; the non-zero positive kurtosis implies a tangible increase of freak wave probability. For random wave fields generated by steady or slowly varying wind and for swell the derived large-time asymptotics of skewness and kurtosis predict power law decay of the moments. The exponents of these laws are determined by the degree of homogeneity of the interaction coefficients. For all self-similar regimes the kurtosis decays twice as fast as the skewness. These formulae complement the known large-time asymptotics for spectral evolution prescribed by the Hasselmann equation. The results are verified by the DNS of random wave fields based on the Zakharov equation. The predicted asymptotic behaviour is shown to be very robust: it holds both for steady and gusty winds.

Wave interaction with ‘⊥’-type breakwaters