Dynamic Mooring Field Experiment and Design of a Wave Energy Converter Platform Test System

Wave energy converters (WECs), which harvest energy from the ocean via various mechanisms, have been developing progressively toward commercialization over the last decades. At this time, there are increasing needs to test wave energy technologies in the ocean after their scaled models have been tested in the laboratories. Compared to wave tank tests where the environmental input is usually waves alone, ocean field tests give environmental inputs of waves, wind, and current. Under such conditions, the survivability design of WEC mooring systems becomes especially important under harsh ocean environments. For example, the main mooring of a 1:4.5 prototype Wave Dragon broke during a severe storm in 2005 [1], causing the platform to be stranded at the beach.

There are three important aspects of WEC mooring survivability design: anchor movability, fatigue damage, and extreme mooring tension. They are usually studied through numerical analysis. The numerical model commonly used for such analysis is the fully-coupled method, i.e., the method couples the dynamic motions and forces of the mooring lines and the floating structure. This method calculates the dynamic responses of the floating structure and its mooring system simultaneously [2]. Comparing to the loosely coupled method which calculates the dynamic response of the floating structure in one step and the dynamic response of its mooring system in another step, the fully-coupled method is more accurate when the dynamic interaction between the floating structure and mooring system is significant.

The finite-element based fully-coupled method has been implemented for many types of conventional floating structures in the oil industry, including turret moored tanks [2,3], spars [4–7], floating production and storage offloading vessels [8–11], and tension-leg platforms [12,13]. The numerical codes applied in the above studies included a toolbox comprised of simo (vessel) and riflex (mooring), deepcat (comprised of counat (vessel) + cable3d (mooring)), winpost, couple, rams, dynasim-a, prosim, and orcaflex.

Compared to conventional floating structures, floating WECs have their own characteristics. For example, floating WECs generally have relatively small dimensions compared to the typical ocean wind-generated wavelengths (60–150 m) and are deployed in shallow to intermediate water depths (less than 150 m [14]) [15]. To validate the accuracy of the fully-coupled method for floating WECs, wave tank tests have been conducted for a catenary mooring line of a cylindrical drum buoy in Johanning et al. [16] and a three-leg catenary mooring system of an instrumented buoy in Harnois et al. [17]. However, there are some limitations in these two wave tank tests. Specifically, in Johanning et al. [16], the displacement of the drum buoy was prescribed, which means that the mooring system does not affect the motion of the drum buoy; and in Harnois et al. [17], only waves were generated (no wind and current).

Other than wave tank tests, there were only a few field tests that validated the fully-coupled method for WEC mooring systems. In Harnois et al. [17], field measured mooring tensions were compared to numerical predictions. However, large differences were found because of unknown anchor position.

This paper studied the accuracy of the fully-coupled numerical method in predicting mooring tensions of a typical WEC mooring system and conducted detailed analysis of the survivability of the mooring system including anchor movability, fatigue damage, and extreme mooring tension based on both numerical data and field data. In Sec. 2, the field test conducted on offshore of the OR coast for a mobile ocean test berth for WECs [18–21] is introduced. In Sec. 3, algorithms of the fully-coupled method are presented. In Sec. 4, numerical modeling details of the hydrodynamic parameters, selecting typical scenarios, and determining anchor positions are provided and accuracy of the method is studied in the application of WECs. In Sec. 5, anchor movement is investigated using predicted anchor pulling force. In Sec. 6, fatigue damage of the mooring system is evaluated based on both measured and predicted mooring tensions. In Sec. 7, extreme tensions on the mooring lines are estimated under specified extreme environmental conditions. In Sec. 8, concluding remarks are provided.

As shown in Fig. 1, a mobile ocean test berth, named the Ocean Sentinel (OS), was deployed at the Pacific Marine Energy Center's (PMEC, formerly the Northwest National Marine Renewable Energy Center (NNMREC)) North Energy Test Site (NETS) (also called PMEC-North), 3–5 km offshore of the city of Newport, OR, in the summer of 2013 to better understand the OS mooring system and validate the numerical model [21]. The measured data obtained from the field test included the mooring tensions, the OS positions, and the environmental conditions (wind, current, and waves).

Figures 2(a) and 2(b) show the plan and side views of the OS and its multi-body catenary mooring system, respectively, with details of mooring components including mooring chains, surface buoys, polyester lines, spectra lines, and anchors. Note that spectra lines are fiber lines made of special material developed and manufactured by Honeywell International Inc., Charlotte, NC, with a registered trade name Spectra.

In this study, we use the orcaflex numerical model, which is based on the fully-coupled mooring and structural dynamic method. There are three types of structures included in the model: the large volume structure (e.g., ships), the slender structure (e.g., mooring lines and risers), and the small volume structure (e.g., floating buoys). The large volume structure is modeled as a nodal component with six degrees-of-freedom (DOF); the small volume structure is modeled as a nodal component with 3DOF or 6DOF; and the slender structure is discretized into a series of line segments [22]. Note that each line segment of the slender structure is a composition of a massless segment and two nodes lump the segment mass. The massless segment models the axial, torsional, and bending properties of the line segment; the two nodes (located at the two ends of each line segment) model the other properties of the line segment (mass, gravity weight, and buoyance).

For the three types of structures, the external force F_e is calculated differently

1. For large volume structures, the external force F_e is calculated as

   $Fe=Fg+Fh+Ff+Fd+Fr+Fdrag_w+Fdrag_a+Fm$

   (2)

The OS experienced various harsh environmental conditions (strong wind, current, and waves) including two storms during its 2013 field test. The positions of the OS over the duration of the field test (July 30–Sept. 22) are plotted in Fig. 3. Before Sept. 22, the OS was located inside a position domain marked by thin dashed lines. On Sept. 22, the OS drifted significantly out of the position domain during a storm. The trajectory of OS positions on Sept. 22 is shown by solid lines in Fig. 3. Note that the combination of longitude and latitude specifies the position of the OS on the surface of the Earth with respect to the Prime Meridian and Equator. The area that the OS moves within is measured in meters for an easier understanding of its dimensions as indicated by the double-headed arrows in the figure.

To study the dynamic response of the OS and its mooring system under the above harsh environmental conditions, we select four typical scenarios before the significant OS drift, namely A, B, C, and D, which correspond to the OS GPS positions “a,” “b,” “c,” and “d” respectively in Fig. 3 

• At scenario A (from 02:40 p.m. to 03:00 p.m. on Aug. 04), the OS was located near the south edge of its position domain. The OS was at position “a” at both 02:40 p.m. and 03:00 p.m. on Aug. 04. Environmental conditions are assumed to be unchanged during this period, and the anchors are assumed to be stationary.

• At scenario B (from 07:40 p.m. to 08:00 p.m. on Aug. 29), the OS was located near the northeast edge of its position domain. The OS was at position “b” at both 07:40 p.m. and 08:00 p.m. on Aug. 29. As in scenario A, the environmental conditions are assumed to be unchanged during this period, and the anchors are assumed to be stationary.

• At scenario C (from 04:40 p.m. to 05:00 p.m. on Sept. 22), the OS was located near the northeast edge of its position domain. The OS was at position “c” at both 04:40 p.m. and 05:00 p.m. on Sept. 22. As in scenarios A and B, the environmental conditions are assumed to be unchanged during this period, and the anchors are assumed to be unmoved.

At scenario D (from 05:00 p.m. to 05:20 p.m. on Sept. 22), the OS was at position “c” at 05:00 p.m. and drifted a large distance of 6.7 m to position “d” (outside its position domain) at 05:20 p.m. (see Fig. 4). In addition, the OS continued drifting another 7.2 m in the following 20 min. Therefore, one or more anchors are assumed to have moved significantly during this period.

Scenarios A–D with the severe environmental conditions (wind, current, and waves) are selected for studies of numerical prediction accuracy and anchor movability. The environmental conditions for these four scenarios are listed in Table 1. At scenario A, the strong environmental conditions were mainly pointing south; at scenarios B, C, and D, the strong environmental conditions were mainly pointing north. Note that waves and ocean current conditions were measured continuously by a TRIAXYS buoy (see Fig. 1) deployed approximately 140 m away from the OS and recorded every 20 min [23]. Wind condition was measured continuously by a Vector Instruments A100R/WP200 anemometer installed on the OS (4 m above the mean water level (MWL)) and recorded every 10 min. In the numerical model, the measured wind speed is converted to wind speed at 10 m above the mean water level using the power law and Hellman exponent [24]. The wind, current, and wave directions in this paper are defined as the directions in which they are moving. The direction angle is 0 deg when the direction was pointing north, and increases as the direction rotates clockwise, e.g., the direction angle is 90 deg when the direction is pointing east.

The random ocean waves are modeled by a series of wave components with different directions, periods, and phases. The series of wave components produce the same wave frequency spectrum and directional spread spectrum as the measured waves. The modeled wave frequency spectrum at scenario C is demonstrated in Fig. 5. The time series of surface elevation was not recorded due to data storage limitation for long-period observation (3 months). Instead, wave data including significant wave height, peak wave period, mean wave direction, and wave spectral density were recorded every 20 min. Again, wind speed and direction were measured at 4 m above the mean water level. Wind profile (wind speeds at different heights) was not measured.

The ocean current is modeled according to the measured current directions and speeds at different water depths. Note that the current profile was only measured at water depths from 2.15 m to 26.65 m. The current speed profile above the water depth of 2.15 m is based on the interpolation of second-order polynomials, and the current profile below the water depth of 26.65 m is assumed to vary linearly to zero speed at the seafloor. The modeled current speed profile at scenario C is demonstrated in Fig. 6.

Modeling of the OS and its mooring components can be summarized as follows: first, the OS is modeled as a large volume structure; second, the mooring lines (chains, polyester lines, and spectra lines) are modeled as slender structures; third, the surface buoys are modeled as 6DOF lumped structures; and fourth (and last), the anchors are modeled as points fixed on the sea floor. The properties of the OS [21] are listed in Table 2. For the modeling of OS, some hydrodynamic coefficients (Froude–Krylov force, diffraction force, radiation damping, and added mass) are calculated by an external 3D radiation and diffraction program, ansys aqwa, and imported to orcaflex (Fig. 7). The water drag coefficients of the OS are based on DNV [25], which considers the effect of both cross section shape and Keulegan Carpenter number, as shown in Fig. 8. The wind drag coefficient of the OS is calculated based on Blendermann [26], as shown in Fig. 9.

The modeling details of the mooring components are listed in Table 3. The drag coefficients and added mass coefficients for the mooring components are calculated internally in orcaflex based on the mooring type (chain or rope).

During the deployment of the OS mooring system, the anchor positions were recorded when anchors were dropped from the utility vessel. Because of the initial horizontal speed of the anchors (close to the vessel speed), the current drift effect and the delay between the time of anchor dropping and the time of GPS recording, the recorded anchor positions can be different from the actual anchor positions on the seafloor (the differences were estimated to be within 11 m [23]).

The differences between the recorded and actual anchor positions are investigated by comparing the numerical and experimental excursion-tension curves. The numerical excursion-tension curve, which is the quasi-static relationship between the horizontal distance (excursion) from the OS to the mooring anchor and the mooring tension on the OS, is calculated through static analysis of the numerical model. The experimental excursion-tension curve is calculated based on the recorded anchor positions.

Figure 10 shows a comparison between the numerical excursion-tension curve and the experimental excursion-tension curve (based on the recorded anchor position) for individual bow, port, and starboard mooring lines. (Note: compared to wind driven surface current the tidal current was relatively weak at the site, which is 5 km off the OR coast.) Each light gray dot in Fig. 10 shows the excursion of the OS and the mean mooring tension for every 20 min before the OS anchor drifted. The shapes of the numerical and experimental curves are generally similar to each other. However, there are offsets in excursion between the numerical and experimental curves for the port and starboard mooring lines, and the experimental curve for the bow mooring line bifurcates at larger excursions. The reason for the offset and bifurcation is that the measured anchor positions differ from the actual positions as explained at the beginning of this section. The anchor positions can be adjusted using a proposed method described next to better match experimental and numerical results.

Based on the quasi-static relationship between the OS excursion and mooring tension calculated by the numerical model, the horizontal distance between the OS and an anchor in the field can be estimated using the mean mooring tensions. As illustrated in Fig. 11, the horizontal distances between the OS and mooring anchors are estimated at scenarios A and B. For example, at scenario A, the average tension of bow mooring line is 3.0 kN (the curve of quasi-static bow mooring tension with respect to OS excursion) corresponding to 147.2 m of horizontal distance between the OS and the bow anchor. Similarly, we can also calculate the horizontal distance between the OS and the starboard anchor at scenario A (127.5 m) and the distances between the OS and the bow anchor (147.2 m) and the port anchor (127.7 m) at scenario B.

Based on the calculated horizontal distances for the bow, port, and starboard anchors, the adjusted anchor positions can be obtained as illustrated in Fig. 12. The adjusted positions of the bow, port, and starboard anchors are 9.1 m, 4.6 m, and 23.2 m away from their recorded positions, respectively. Compared to the anticipated maximum difference between the measured and actual anchor positions (11 m), the difference between the adjusted and recorded positions for the starboard anchor exceeds the anticipated difference significantly. This phenomenon is possibly caused by errors in measuring or recording the GPS position of the starboard anchor. Note that the finding of this excessive difference for the starboard anchor demonstrates the importance of the anchor position adjustment method, which was also used by Harnois et al. [27] to estimate anchor positions.

After adjusting the anchor positions, the new experimental excursion-tension curve compares quite well with the numerical excursion-tension curve for individual bow, port, and starboard mooring lines (demonstrated in Fig. 13). The new experimental curves for the port and starboard mooring lines move toward the left of the original experimental curves, making them closer to the numerical curves. In addition, the bifurcation of the original experimental curve for the bow mooring line (see Fig. 10) vanishes after the bow anchor position is adjusted. Note that the method of using the quasi-static excursion-tension curve to determine the anchor position was also used successfully by Johanning and Smith [28].

The responses of the OS and its mooring system are simulated at the adjusted anchor positions at field test scenarios of A, B, and C. According to Chen et al. [4], nonlinear surface water waves may result in low-frequency (LF) wave excitation force. The LF force may cause large structure motion at resonance. To capture the LF response of the OS, the simulation time is increased to 3 h, instead of 20 min of time interval in field data recording.

To examine the accuracy of the fully-coupled method in orcaflex, the predicted means, standard deviations, and maximums of mooring tensions under the three typical scenarios (A, B, C) are compared to those of the field measurements, respectively (see Table 4). Note that only the mooring forces of upwave lines are listed as the downwave mooring lines are in slack condition. For example, as shown in Fig. 12, the starboard mooring line was in slack condition at scenario C with wave direction toward the northeast.

The relative differences between the predicted and measured mean mooring tensions on the OS are in the range of 0–22%. These differences are thought to be mainly caused by the discrepancies in estimating the wind and water drag forces and the second-order wave drift force. These differences can also be caused by the uncertainty of environmental conditions, but the effect should be relatively small because environmental conditions are measured every 20 min. The relative differences between the predicted and measured standard deviations and maximums of dynamic mooring tensions are in the range of −34% to 37% and −16% to 30%, respectively. These differences could be caused by the following factors: linear assumption of first-order wave forces (hydrostatic force, Froude–Krylov force, diffraction force, and radiation force) calculated in aqwa and exported to orcaflex, the simplified modeling of the surface buoys (modeled as 6DOF lumped structures), water and wind drag coefficients, nonlinear stiffness of mooring line, surface buoy behavior, snap loads, marine growth, line aging, and loadcell aging (note that only numerical results of three scenarios A, B, C are compared with field measurements. At scenario D, the mooring anchor had moved, thus, scenario D is not included in Table 4).

Though there are some ocean tests of WECs, only a few of them studied the accuracy of the fully-coupled numerical model, due to lack of field measured mooring force and measured environmental conditions. In Ringsberg et al. [29], the predicted mean mooring forces were up to 11% higher than the measured mean forces at moderate/calm sea states and up to 40% higher at higher sea states. As a comparison, in this study, the predicted mean mooring forces are up to 22% higher than the measured mean forces at moderate and higher sea states. In Johanning and Smith [28], the predicted dynamic mooring forces were −11% to 38% different than the measured dynamic forces. As a comparison, in this study, the predicted dynamic mooring forces were −34% to 37% different than the measured dynamic forces.

By comparing the numerical prediction accuracy of this study and other literature [3,13,17,30], the influencing factors (mooring line type, water depth, experiment location, environmental loads, environmental conditions, L/H ratio) are listed in Table 5. The accuracy of the fully-coupled method in predicting mooring tensions for structures of this study and other literature is compared in Table 5. Note that S1, S2, and S3 are the abbreviations of scenario 1, scenario 2, and scenario 3, respectively. SA, SB, and SC of the OS mooring system correspond to the scenarios of A, B, and C, respectively. Scenario D is not included in the comparison because anchor movement might occur. Line 1, Line 2, and Line 3 of the OS mooring system correspond to bow, port, and starboard lines, respectively. L is the length of the mooring chain and H is the water depth (as pointed out above, only the mooring forces of upwave lines are listed as the downwave mooring lines are in slack condition. For example, as shown earlier in Fig. 12, the starboard mooring line was in slack condition at scenario C with wave direction toward the northeast).

The relative differences of the studies above are affected significantly by the types of mooring systems (taut and catenary moorings). While the relative differences of mean mooring line tensions for the taut mooring lines (−2% to 16%) are close to those for the catenary mooring lines (−1% to 2%), the relative differences of standard deviations for the taut mooring lines (166–535%) are much larger than those for the catenary mooring lines (−34% to 37%). This may be because mooring stiffness of the taut moorings was much larger than those of the catenary mooring lines.

The relative differences for the catenary moorings are affected moderately by the L/H ratio and water depths. For the Turret Moored Tank results in Ormberg et al. [3], the relative differences of mooring tension standard deviations (7–18%) are smaller than those for the Buoy in Harnois et al. [17] and the OS (−34% to 37%). This could be because the L/H ratio (mooring length/water depth) of the Turret Moored Tank mooring line, which is 4.4 is larger than the L/H ratios of the Buoy and the OS, which range from 1.2 to 1.7. This could also be because the water depth of the Turret Moored Tank, which is 330 m, is larger than the water depths of the Buoy and the OS, which are 30 m and 47 m, respectively.

In Table 5, the mooring systems of the OS and the Buoy are considered to be typical WEC mooring systems. The reasons are as follows: first, the dimensions of both the OS and the Buoy are close to the dimensions of typical WECs, which are relatively small compared to typical ocean wind-generated wavelengths (60–150 m); and the water depths of both the OS and the Buoy mooring systems were relatively small.

The relative differences for the above WEC moorings are affected by the experimental test conditions (field test (under waves, wind, and current) and tank test (under waves)). While the relative differences in standard deviations for the OS mooring (−34% to 37%) are close to those for the Buoy mooring (−29% to 26%), the relative differences of mean tensions for the OS mooring (0–22%) are much larger than those for the Buoy mooring (−1% to 1%). This could be because there are no current and wind loads in the tank test of the Buoy, i.e., the mean mooring tension on the OS is caused by the current drag force, wind drag force, pretension, and second-order wave drift force while the mean mooring tension on the Buoy is only caused by pretension and second-order wave drift force. Other reasons can be (1) the OS mooring configuration (for each mooring leg, there is one catenary line and one horizontal line connected by a surface buoy) is more complex than the Buoy mooring configuration (single catenary line) and (2) the field measured environmental conditions have larger uncertainty than laboratory measured environmental conditions.

This numerical model, along with the guidelines of anchor movability, fatigue damage, and extreme mooring tension presented in the following sections, can be used to evaluate the mooring design feasibility of new WECs (e.g., Liu et al. [31]). The numerical model can also be used to evaluate the WEC mooring systems that were ocean tested [32–34]. Harnois et al. [17] indicated that inaccurate anchor position of the field test caused large differences between numerical predictions and field test results: the predicted mean mooring forces were up to 70% higher than the measured mean forces; the predicted standard deviations of mooring forces were up to 82% higher than the measured standard deviations. The method of this study, which uses the quasi-static excursion-tension curve to determine the anchor position, could be used in Harnois et al. [17] and significantly increase the numerical prediction accuracy.

As mentioned earlier, the OS drifted significantly in scenario D. To study the anchor movement during this period, the instantaneous values of r_a for the bow, port, and starboard anchors are calculated by the numerical model.

Since the anchor movement is related to both the magnitude and duration of the effective force on the anchor, the mean and maximum values of r_a for the individual bow, port, and starboard anchors are listed in Table 6. In addition, the instantaneous r_a of each mooring anchor is plotted in Fig. 14 for a 40 s period including the time of maximum r_a. The dash line indicates the instantaneous r_a, and the solid line indicates the mean value of r_a.

As demonstrated in both Table 6 and Fig. 14, dynamic analysis is important for studying anchor movement, because the instantaneous values of r_a for the bow, port, and starboard mooring anchors oscillate in a relatively large amplitude compared to the mean values of r_a. The anchor movability is related to the time that r_a is above the threshold of one, indicated by both the mean r_a and peak r_a. Movability for each anchor is discussed as follows:

• The port anchor was likely dragged at scenario D, i.e., the significant OS drift. This is because the mean value of r_a for port anchor (0.66) is relatively large compared to 1; the maximum value of r_a (1.66) is significantly larger than 1; and r_a frequently reaches to values larger than 1 within the duration of 40 s in the figure.

• The bow anchor was likely not dragged at scenario D. This is because the mean value of r_a (0.25) for the bow anchor is relatively small compared to 1; and r_a increases rapidly from almost zero to its maximum value (0.95) and drops rapidly after that (this phenomenon is typically caused by a short-duration snap load of the mooring chain). Note that the mooring chain or cable becoming slack, and retightening is the most common reason for snap load, as discussed in Palm [36].

• The starboard anchor was likely not dragged at scenario D. This is because the mean value of r_a (0.09) for the starboard anchor is very small compared to 1; and r_a increases rapidly from almost zero to its maximum value (1.14) due to snap load and drops rapidly after that.

In the original design, the specified extreme conditions are 7.0 m significant wave height, 10.0 m/s wind speed, and 0.51 m/s current speed. Compared to the measured environmental conditions at scenario D, which are 3.5 m significant wave height, 17.1 m/s wind speed, and 0.53 m/s current speed, the current and wind speed in the original design were underestimated. Other reasons for inadequate anchor design could be: (1) in the original design the extreme condition of waves, current, and wind toward the north was not numerically simulated, and (2) the vertical pulling force on the anchor, which reduces the anchor holding capacity, was not included in the anchor movability calculation in the original design.

As defined in Eq. (12), the value of r_a is also affected by the friction coefficient c, which ranges from 0.20 to 0.74 depending on sand type, anchor material, and surface smoothness [37]. Figure 15 plots the maximum values of r_a corresponding to typical friction coefficients, for the bow, port, and starboard anchors of scenario D. It is shown that the maximum value of r_a correlates closely to the friction coefficient. This means that the friction coefficient needs to be judicially selected for each numerical study. Note that the friction coefficient of the anchors in this study (rough concrete anchors deployed on Oolitic sand) is 0.74. This value is generally larger than the anchor friction coefficients of other sea floor types and anchor materials.

After the numerical model of fully-coupled method is validated, the dynamic mooring tensions of the OS can be predicted for a series of statistical environmental conditions at the PMEC-North. Then the corresponding fatigue damage of the OS mooring system can be estimated based on the predictions as follows.

The simulated whole year statistical environmental conditions at the NETS including wind, waves, and current conditions are listed in Table 7. The statistical wind and wave conditions, based on the historical wind and wave data from the National Data Buoy Center (NDBC) buoy 46050 located 30 km west of the PMEC-North, were provided by ABS [39]. Based on the measured current speed along water depth during the field test (see Fig. 6), the current profile is specified as follows: the current speed changes linearly with water depth from 0.6 m/s at the sea surface to 0 m/s at the water depth of 30 m; the current speed below the water depth of 30 m is 0 m/s. The directions of the wind, waves, and current are collinear.

In each bin of the environmental conditions listed in Table 7, the magnitudes of the wind, waves, and current speeds are constant, while the direction changes from $0deg$ to $315deg$ with a $45deg$ spacing. Each direction corresponds to one environmental condition of the bin and is simulated for 30 min. The probabilities of occurrence for the directions in each bin were provided by ABS [39] and are listed in Table 8. Note that the direction definition in ABS [39] is different from (i.e., opposite of) the direction definition in this study.

The rainflow cycles of both the simulated and measured mooring tensions on the OS are extracted with a threshold of 4.45 N (1 lbf) using the matlab toolbox WAFO [40]. The fatigue damage per hour is estimated for the individual mooring lines at both the statistical whole year environmental conditions and the measured environmental conditions during the field test (shown in Fig. 16). Generally, the fatigue damage increases with increased wave height, given the same wave period; the fatigue damage increases with decreased wave period, given the same wave height. The fatigue damages are different for different mooring lines. The fatigue damage of the port line is larger than that of the bow line; the fatigue damage of the bow line is larger than that of the starboard line. The above findings are consistent with what were found in Thies et al. [41], where fatigue damage of WEC mooring lines was studied based on extensive field test data.

The ways to calculate the fatigue damage for the two sets of environmental conditions are summarized as follows: first, the fatigue damage for each bin of statistical environmental conditions (listed in Table 7) is calculated as a summation of the fatigue damage of all directions in the bin multiplied by their corresponding probability of occurrences. For the convenience of comparing the fatigue damage between different bins, the total probability of occurrence for each bin is scaled up to 100%. The fatigue damage for each bin of measured environmental conditions (grouped by both wave height and peak wave period) is calculated as the average of the fatigue damage within the bin (the probability of occurrence for each bin is scaled up to 100%). Note that the predicted fatigue damage is calculated for only one wave period per wave height, while the measured fatigue damage is calculated for multiple wave periods per wave height.

As shown in Fig. 16, the predicted fatigue damage with significant wave heights of 2.10 m, 2.76 m, and 3.96 m is close to the measured fatigue damage. The numerical model also predicts fatigue damage for extreme wave heights not measured during the ocean test, at significant wave heights of 5.68 m and 7.93 m.

The predicted fatigue damage for individual mooring lines generally increases as the significant wave height increases. However, for the starboard mooring line, the predicted fatigue damage of the significant wave height Hs = 5.68 m and Hs = 7.93 m are smaller than that of the significant wave height Hs = 3.96 m. This is because the environmental directions associated with Hs = 5.68 m and Hs = 7.93 m are generally toward the north; under such conditions the starboard mooring line was in slack condition.

In mooring design guidelines, the return period of extreme environmental conditions is at least 10 years for mobile floating units in the vicinity of other structures [42,43]. If the return period is 100 years, combining all independent extremes (waves, wind, and current) at the same return period is usually too conservative. In this case, three methods are suggested for adjustment: (1) reduction factors are applied to individual independent extremes of 100-year return period [14]; (2) a 100-year return period is applied to each candidate (waves, wind, or current) in turn and fairly realistic, unfavorable levels are applied to other effects [38]; and (3) both the reduction factor and multiple levels of return period methods can be used together [43].

Based on the historical data of waves and wind recorded hourly by the NDBC buoy 46050 from 1991 to 2015, the monthly extreme values of significant wave height and wind speed with 10 and 100 years of return level are estimated for the NETS and plotted in Figs. 17 and 18, respectively. Both the significant wave height and the wind speed vary significantly among different months of a year. For example, the 10-year return levels for the significant wave height and the wind speed are 3.5 m and 13.3 m/s, respectively, in July; while they are 10.7 m and 22.5 m/s, respectively, in December.

The maximum of the monthly 100-year significant wave heights estimated in this study is 17.9 m (corresponding to the month of November). It is in good agreement with the 100-year significant wave height of 17.5 m given by Dallman and Neary [45]. The latter value is the largest significant wave height on the 100-year contour of significant wave height with respect to wave period, where the contour is estimated based on the inverse first-order reliability method using the same wave data of this study (measured by the NDBC buoy 46050).

Note that the 95% confidence interval for the wave height or wind speed with return period of 100 years is large compared to those with return period of 10 years, as shown in Figs. 17 and 18. This is because only 25 years of historical data are available from the NDBC buoy 46050. Note also that some waves and wind conditions were not observed over certain time periods during the whole deployment of the NDBC buoy 46050, which may be caused by the harsh environmental conditions of storms. In Serafin and Ruggiero [46], larger values of extreme significant wave height were estimated after taking into account those missing observations.

Based on the historical data of current speed recorded by NH10 buoy from 1997 to 2004 [47], the monthly extreme values of current speed with 10 years of return level are estimated and plotted in Fig. 19. Note that the 95% confidence interval for the current speed with return period of 10 years is relatively large. This is because only 7 years of historical data are available from NH10 buoy. Note also that the 100-year current speeds are not presented, because the duration of measured current data (7 years) is relatively small.

The specified extreme environmental conditions of this study are as follows (listed in Table 10): the extreme significant wave height, wind, and current speeds are specified to be their corresponding 10-year return levels for the period from July to September; the directions of the wind, waves, and current are collinear and range from $0deg$ to $180deg$ with a spacing of $30deg$⁠. Note that the OS was deployed 3–5 km west of the OR coast, thus the wave directions from $210deg$ to $330deg$ (propagating to the west) are not included.

In predicting extreme mooring tensions of the OS, simulations are conducted in two steps. First, dynamic responses of the OS mooring system under the specified extreme environmental conditions (shown in Table 10) are simulated for 3 h in each environmental direction (⁠$0deg$⁠, $30deg$⁠,…, $180deg$⁠). Second, in the direction of the maximum predicted mooring tensions, the simulations are conducted for a total of ten times (each time the simulation is specified with a different random seed in wave generation). Based on the maximum tensions predicted by the simulations in step 2, the design tensions T_D of the polyester line and mooring chain are calculated using Eq. (15). The results are listed in Table 11. Multiplying the design tensions with a safety factor of 1.67 [43], the design strengths of the polyester line and mooring chain are calculated to be 69.54 kN and 74.27 kN, respectively. Therefore, the strengths of the polyester line and mooring chain used in the OS field test are adequate (according to the numbers given by the manufacturer, the strengths of the deployed polyester line and mooring chain are 266.9 kN and 258.0 kN, respectively).

Field testing is a natural next step for many WECs after model-scale laboratory tests. However, designing a mooring system that is functional and can survive ocean site environmental conditions during the ocean deployment is challenging given the uncertainties in both the ocean environment and numerical predictions.

This paper provides detailed mooring survivability studies of anchor movability, fatigue damage, and extreme mooring tension based on field data measured from the ocean mooring test of a mobile ocean test berth (the OS) and numerical data predicted by a fully-coupled method. Guidelines for these survivability studies are summarized as follows:

• Anchor movability: (1) select scenarios where the moored structure is near the edge of its position domain and when severe environmental conditions occur; (2) conduct numerical simulations for these scenarios; (3) calculate r_a which is the ratio of the effective force on the anchor to the static anchor resistance for each scenario; and (4) investigate the anchor movability based on mean r_a and peak r_a.

• Fatigue damage: (1) specify the fatigue design conditions based on historical ocean data; (2) conduct numerical simulation of 30 min for each fatigue design condition; and (3) estimate fatigue damage based on numerical results and probabilities of occurrence for all the fatigue design conditions

• Extreme mooring tension: (1) specify extreme design conditions based on historical ocean data; (2) conduct numerical simulation of 3 h for each extreme design condition; (3) select the extreme design condition with the maximum mooring tension and conduct ten numerical simulations under this design condition with different random seeds in wave generation; (4) based on mean and standard deviation of the maximum mooring tensions predicted in step 3, calculate the design extreme tension; and (5) calculate the design strength by multiplying the extreme tension with a safety factor.

This paper also provides numerical modeling details of the hydrodynamic parameters, selecting typical scenarios, and determining anchor positions and compares the numerical prediction accuracy of the commonly used fully-coupled method of this study with reference prediction accuracy in the literature. It is found that the prediction accuracy is affected by multiple factors including mooring line type, water depth, experiment location, environmental loads, environmental conditions, and L/H ratio.

The main findings from the OS mooring analysis are listed as follows:

• Compared to field test measurements, the numerical model was shown to provide accurate predictions in typical scenarios A–C with harsh waves, current, and wind conditions. The relative differences between the predicted and measured mooring tensions are 0–22%, −34% to 37%, and −16% to 30% for the mean, standard deviation, and maximum of mooring tensions, respectively.

• Under scenario D, corresponding to the significant OS drift during the field test under severe storm conditions, the port anchor was found to be dragged significantly. The anchor movability was investigated using the mean and peak values of the ratio of instantaneous effective force to static anchor resistance.

• The predicted fatigue damage of the mooring lines was shown to be in good agreement with the measured fatigue damage of the field test. Under extreme wave conditions (beyond what occurred during the field test), the fatigue damage was also predicted.

Under extreme waves, wind, and current conditions, the extreme mooring tensions of the polyester line and mooring chain were predicted through dynamic simulations and the required strengths of the polyester line and mooring chain were calculated using the design equation. The results showed that the polyester line and mooring chain used in the field test had adequate strengths. This conclusion should be qualified with the fact that the anchors were not designed adequately to prevent drifting during the storm.

The following three topics are suggested for future study:

1. A comprehensive study of numerical prediction accuracy with respect to environmental conditions should be conducted using the extensive field data from the OS ocean testing, where more cases would be simulated and compared to field measurements.

2. Validation of the parameters in the mooring design equations in their applications for WECs through studying the reliability index of the mooring system based on the measured mooring tensions during the OS field test should be conducted. The parameters used in this study were developed mainly for conventional floating structures in the oil industry and may not be optimal for WEC device design.

3. Influence of the power take off (PTO) on the behavior of a WEC mooring system should be conducted. This is important as energy extraction by the PTO may affect the hydrodynamic responses of the WEC device significantly under a variety of environmental conditions. This can be examined using the numerical code employed in this study or open-source codes such as wec-sim which has advanced PTO modeling capacity.

Financial support from the U.S. Department of Energy Grant No. DE-FG36-08GO18179-M001 is gratefully acknowledged.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.