OMAE HIGH FREQUENCY LOADING AND RESPONSE OF OFFSHORE STRUCTURES IN STEEP WAVES

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1 Proceedings of the ASME 11 3th International Conference on Ocean, Offshore and Arctic Engineering OMAE11 June 19-24, 11, Rotterdam, The Netherlands OMAE11-51 HIGH FREQUENCY LOADING AND RESPONSE OF OFFSHORE STRUCTURES IN STEEP WAVES Thomas B. Johannessen * Aker Solutions NO-1326 Fornebu, Norway ABSTRACT Offshore structures such as the TLP or the GBS have natural frequencies which are much higher than the frequencies of the incident waves in the survival conditions. Nevertheless, many offshore structures experience significant resonant response of modes with periods in the range of 2s to 5s, particularly in steep waves. In particular the ringing response of offshore structures characterised by sudden, large and isolated resonant response packets, has been a concern for many years. The loads which give rise to these events are difficult to describe both because they are small in magnitude relative to the load level close to the wave spectral peak and also because they are nonlinear in nature. In the present paper, available theoretical methods for high frequency loading is employed for irregular waves and compared with model tests. The methods which are used in the present are first and second order diffraction methods as well as a third order loading model for slender cylinders applied to irregular waves with continuous wave spectra. The results are compared with measurements of tether response and overturning moments on a TLP and a GBS respectively. Provided that the incident waves are treated carefully and care is taken in treating the high frequency tail of the incident wave, it is found that methods which are presently available give a good representation of the resonant response for the GBS structure. The GBS structure has a relatively low natural frequency and a mode shape which is excited easily by horizontal loading in the surface zone. In contrast, weakly nonlinear theory does not capture the high frequency loading on a TLP which has resonant frequencies at more than five times the spectral peak in the survival seastates. For this case it is found that wave impact with both the columns and the deck gives significant contributions to the resonant tether response. This is the case even if no significant horizontal deck impact is observed and highlights the need for a reliable deck impact load model. INTRODUCTION An important characteristics of offshore structures in harsh wave environments is the placement of the natural frequencies of the structure relative to the typical survival condition wave frequencies. Ship type structures typically have three of the natural frequencies placed in the range of wave frequencies and survive since the damping in heave and pitch is very large and by avoiding beam seas in the survival conditions. A semisubmersible is build with all six rigid body natural frequencies below the wave range and has very gentle motion characteristics. TLP structures have three natural frequencies above and three below the wave range whereas bottom fixed structures like the GBS or the Jacket are made stiff so that all the natural frequencies are above the survival wave frequencies. By moving the natural frequencies away from the wave frequencies, the structures receive little or no direct excitation from the waves at the natural frequencies in the survival conditions. Nevertheless some structures experience significant response at the natural frequencies and it is notoriously hard to calculate the load which gives rise to responses of this type. Not only is it necessary to pick out an excitation component which is small (but with the right frequency) compared with the direct wave induced loading, the load mechanism itself is nonlinear and difficult to calculate. It is the object of the present paper to study the high frequency response of TLP and GBS structures and the ability to calculate these. Comparisons between model tests and calculations are presented for two structures, namely the Draugen GBS and the Snorre A TLP shown in Figure 1 and Figure 2. The Draugen E thomas-b.johannessen@akersolutions.com 1 Copyright 11 by ASME

2 GBS is a slender monocolumn structure placed at 255 m water depth in the Northern North Sea. The model test shows significant resonant response of the first structural mode which has a shape resembling cantilever bending about the top of the caisson. The model test model has a period of this mode of 5 s although this is not the period of the offshore prototype. Main particulars and analysis details of the Draugen GBS are shown in Table 1. place in nonlinear interaction, makes the FNV model applicable to broad banded, continuous wave spectra. The latter point is discussed in detail in [3]. The paper starts by describing the methods used in calculating the excitation loading and response. It is a point that the methods which have been applied to the two structures are identical and that they represent weakly nonlinear wave loading and not impact type loading. The results are then compared with model tests of the Draugen GBS and the Snorre TLP. The results are discussed and plans for further work are outlined. Figure 1 Artist s impression of the Draugen GBS The Snorre A TLP is a classic TLP placed at 38 m water depth in the same area of the North Sea. Model testing indicated significant resonant response in the tether system indicating resonant heave, pitch and roll motion. The natural periods of the resonant modes are approximately 2.4 s. Main particulars and analysis details of the Snorre A are shown in Table 2. The starting point for the method which is employed is the nonslender ringing load model proposed by Krokstad et al. (1998) [1] which uses first and second order diffraction results and a third order model for loads on vertical slender cylinders first proposed by Faltinsen, Newman & Vinje (1995) [2]. The latter is found to be robust for relatively large cylinder diameters [1]. The essential difference in the present work relative to the original analysis method proposed in [1] is that the third order load is expressed as interaction between individual wave components rather than products of first and second order incident wave properties. This, together with a maximum frequency difference between waves which are allowed to take Figure 2 Artist s impression of the Snorre A TLP Water Depth Height of Caisson Diameter in water line Diameter of Caisson Diameter above Caisson Airgap Natural period of first mode 255 m 45. m 16.4 m Approx. 1 m Approx. 44 m 26.2 m 5. s Number of panels in ½ hull 32 Number of surface panels in 1 st 68 within 24 m radius quadrant First Order Analysis 4 periods 3. s to 3. s Second Order Analysis Grid of 43 frequencies between.52 Hz and.197 Hz Drag Coefficient.7 for circular members 2. for rectangular members Time window in time domain 29 s with 36 s taper analysis Number of load nodes in response 27 model Seastates in analysis JONSWAP wave spectra Hs=.9 m, Tp=16.1 s Table 1 GBS analysis parameters and main particulars 2 Copyright 11 by ASME

3 Displacement Mass Tether Tension Riser Tension Column c-c spacing Column Diameter Pontoon Height x Width Pontoon Bilge Radius Underside of Double Bottom of Deck Water Depth Draft Natural period in Surge & Sway Natural Period in Yaw Natural Period in Heave Natural Period in Roll & Pitch Mt Mt 2434 Mt 3397 Mt 76 m 25 m 11.5 m x 11.5 m 2. m 64.5 m above keel 38 m 38.3 m 84 s 69 s 2.3 s 2.4 s Number of panels in ¼ hull 1993 Number of surface panels in 1 st quadrant 2696 within 24 m radius First Order Analysis 54 periods 1.5 s to 6 s Second Order Analysis Grid of 33 frequencies between.12 Hz and.25 Hz Drag Coefficient.7 for circular members 2. for rectangular members Time window in time domain analysis 259 s with 32 s taper Seastates in analysis -2-4 Torsethaugen wave spectra [4] Hs=13.2 m, Tp=13. s Hs=18.2 m, Tp=17.4 s Table 2 TLP analysis parameters and main particulars at MSL METHOD General The general principle of the analysis is that wave induced loading is calculated in the time domain on a fixed model and applied to a response model of the structure. The following steps are applied and (2) is the second order surface elevation calculated from the measured rather than the linear free surface elevation. This method has been used previously in [6] and is capable of yielding near Gaussian surface elevation distributions with strongly nonlinear seastates as input. The properties of the six three hour simulations of the seastates considered for the Draugen GBS are shown in Figure 3. Variance [m 2 ] Skewness [-] Kurtosis [-] Max & Min Surface Elevations[m] Measured data Run # Run # Run # Run # Linearised with dw=.32 Rad/s Figure 3 Properties of linearised seastates Linear Diffraction 1. A linear surface elevation time history is established based on the measured time history. 2. This time history is used to calculate time histories of hydrodynamic loads. 3. These loads are applied to a response model and the structural response is evaluated Incident Waves A simple and efficient method is employed to make an estimate of the underlying regime of free waves in a measured time series: ' O (1) Where is the free surface elevation, (1) and (2) are, respectively, the linear and second order [5] surface elevation Figure 4 ½ Draugen GBS hydrodynamic panel model Linear diffraction loading on the structures have been calculated based on the WAMIT software for a large number of 3 Copyright 11 by ASME

4 frequencies. The hydrodynamic panel models which have been employed are shown in Figure 4 and Figure 5 for the Draugen GBS and the Snorre TLP respectively. Whereas the Snorre TLP is calculated as a rigid body with six global force components transferred to the load model, the linear and second order pressures on the Draugen GBS are lumped into nodes and distributed over the structural response model. Figure 5 ¼ Snorre A TLP analysis model Second Order Diffraction The same panel models and WAMIT software have been used to calculate the second order wavenumber sum forces on the fixed structures. Second order loads for the interaction between two unidirectional wave components and the structure have been calculated in a very fine grid around the diagonal ( 1 = 2 ) ensuring that the resulting frequency sum ( ) covers the range around the relevant natural periods. 2(Rad/s) (Rad/s) T=5s T=8s T=3s diagonal dw<.32 Figure 6 Draugen GBS sum frequency pairs This is illustrated in Figure 6 showing the interaction terms which are being considered. Also shown are lines of equal excitation period. It is seen that the GBS analysis covers excitation periods between approximately 3 s and 7.5 s for the interaction of wave components which are not spread more than.32 Rad/s apart. Note also that the spacing between the frequencies is even and corresponds to the length of the time window which is being employed in the analysis. For Snorre TLP, the same method is used calculating the second order in a grid covering excitation between 2. and 3.2 s for wave components which are not spread by more than.34 Rad/s. In particular for the Snorre TLP, the accurate calculation of the second order forces is difficult since it is necessary to calculate interaction between quite high frequency wave components in order to get the excitation terms at the natural frequency. Using the model shown in Figure 5 together with a careful modelling of the surface mesh, however, the results appear to be reasonable. The amplitudes of the second order heave and pitch quadratic transfer function (QTF) at an excitation frequency of 2.4 s are shown in Figure 7. Results for both the indirect method and the direct pressure integration estimates are shown and are in close agreement indicating that the values are reliable [7]. Heave QTF [knm -2 ] Frequency Difference [Rad/s] Pitch QTF [knm m -2 ] Frequency Difference [Rad/s] Figure 7 QTF amplitudes for excitation at constant frequency sum 2.6 Rad/s at 45 deg wave incidence. Solid line is the force calculated by the indirect method whereas dots indicate forces calculated by the direct method. a) Heave excitation b) Pitch excitation Third Order FNV Nonlinear loads on a slender vertical column was calculated for regular waves by Faltinsen, Newman & Vinje [2] and extended to irregular waves by Newman [8]. This method is referred to in the following as the FNV load type. In particular the third order sum frequency load term is robust and useful. This is given as the frequency sum terms in the product of the first and second order surface elevation and the first order velocity potential at the free surface: F a) b) FNV x r 2 xt xtz z xz g x xt z where subscript denotes partial differentiation, r is the cylinder radius, and and g are the density of water and the acceleration (2) 4 Copyright 11 by ASME

5 of gravity respectively. F x FNV(3) is a horizontal load which acts at the still water level. Morison Drag Loading Drag loading is included in a simple way by including Morison elements in the shaft of the GBS and the columns and pontoons of the TLP. The undisturbed wave particle velocities are calculated based on the measured surface elevation using the method proposed in [9]. For the Draugen GBS, the drag excitation is calculated for a fixed structure whereas the relative velocities are used for the TLP. Using a constant damping term for the structural response of the GBS may therefore lead to an underprediction of the damping in the former since the relative motion is not included. Handling continuous spectra Both the underlying equation for the second order surface elevation and the expression for the third order FNV load contain products involving high derivatives of the velocity potential at z=. A realistic wave spectrum will typically decay according to -4 which implies that the value of some of the terms required in the calculation of second order surface elevation or FNV load will be highly dependent on the cut-off frequency of the spectrum. The spectral densities of some of the linear terms which appear in equation (2) are shown in Figure 8 in logarithmic scale and it is seen that it is difficult to set a reliable cut-off frequency. Logplot of Spectral Power Density (1) xz (1) z= xzt (1) z= xt (1) z= x (1) and z (1) z= Frequency [f/f p] Figure 8 Properties of linear waves in continuous spectra Calculation of nonlinear time series The calculation of second order wave properties and diffraction loads require double series of all the wave components which make up the time history of the surface elevation. The calculation of third order FNV loads requires triple sums of all wave components at each time step. In order to reduce the number of wave components and thus the computation time, a moving window formulation is applied as shown in Figure 9. At each time step, a window is defined and a wave time series is established from the original series which is periodic with this window length and tapered with the taper function shown. The set of Fourier components which defines this time history is then used in subsequent analysis of wave induced loads. This is a purely practical consideration introduced in order to reduce computation time which converges very rapidly with respect to window length and taper length. A window length and taper length of respectively ten and one typical wave period is sufficient. Surface Elevation [m] Surface Elevation Trace for Fourier Analysis Analysed Data Point Window Figure 9 Moving window formulation for irregular wave analysis Response Models Having calculated hydrodynamic load time series, it is necessary to apply this to a response model in order to investigate the resonant high frequency response of the structure. 1 Scale[-] The divergence of nonlinear terms with respect to high frequency cut-off was studied in detail in [3] and was found to be due to nonlinear interaction between wave components with very different frequencies. By expressing the products in equation 2 as frequency sum interaction terms and setting a maximum bandwidth between wave components which are allowed to interact, the FNV load may be used also for irregular waves with realistic spectra. The maximum bandwidth approach is the key to make reliable calculations of FNV loads and nonlinear wave properties in irregular waves. For the Draugen GBS, an in-house 2D beam model is used with 33 structural elements and 35 nodes distributed over the GBS. 27 of the nodes receive time series of hydrodynamic loads. The beam model is carefully tuned to represent the model test model by distributing the stiffness and mass (including added mass) of the elements carefully and by tuning the damping against decay tests in still water. The TLP is modelled as a rigid body using the analysis program SIMO developed by Marintek. Tethers and Risers are modelled as rigid slender elements connected to the TLP by 5 Copyright 11 by ASME

6 massless springs resembling the model test set-up closely. The accuracy of the response model has been verified against the model test by comparing with decay tests in all six degrees of freedom. The SIMO model and model test has been described earlier in []. RESULTS Draugen GBS The model testing of the Draugen GBS is a classic ringing reference which has been described previously [11]. The first structural mode has a natural period of approximately 5 s and consists primarily of cantilever type bending about the top of the caisson together with a small rotation at mudline (soil stiffness). The first mode is dominant with no significant response of the higher modes. At present the measured moments immediately above the caisson and approximately 25 m below the Still Water Level (SWL) are considered. The former consists of both wave frequency and resonant response whereas the latter contains almost no wave frequency response. Wave2_Cal [m] mom1 [MNm] ( ) g a) E+4 2E+4 1E+4 E+ -1E+4-2E+4-3E E+3 2.E+3 2.E+3 1.E+3 5.E+2.E+ -5.E+2-1.E+3-2.E+3-2.E+3-3.E+3-3.E Figure 11 Typical 3hr Maximum Event (3) a/ Incident wave, b/ bending moment directly above caisson (el 45.2), c/ bending moment 24.9 m below SWL (el. 23.1). Red and black lines indicate measured and calculated moments respectively. 5. b) c) mom4 [MNm] Wave2_Cal [m] mom1 [MNm] 25 a) E+4 3E+4 2E+4 1E+4 E+ -1E+4-2E+4-3E+4-4E+4-5E b) 4.E+3 c) 3.E+3 mom4 [MNm] 2.E+3 1.E+3.E+ -1.E+3-2.E+3-3.E+3-4.E+3-5.E Figure King Ring Event (17) a/ Incident wave, b/ bending moment directly above caisson (el 45.2), c/ bending moment 24.9 m below SWL (el. 23.1). Red and black lines indicate measured and calculated moments respectively. The measured surface elevation and the calculated and measured moments of the largest event encountered in the model testing campaign are shown in Figure. It is seen that both the level and the phasing between the wave frequency and the resonant response is captured well by the analysis model. The same is observed in Figure 11 which considers a more typical three hour max event. The response model does perhaps show a tendency for the resonant response to decay more slowly than the model test measurements. This may be due to the fact that the relative motion between the structure and the waves is not taken into account but this is in any case not important for the largest response. Cumulative Probability -ln(-ln(f)) Overturning Moment [MNm] Figure 12 Distribution of min largest bending moments in 6 3 hr simulations directly above the caisson (45.2 m). Filled in circles indicate total moments whereas open circles and crosses indicate moments which are respectively lowand high- pass filtered at.16 Hz. Measured data are shown in red and calculations in black. The results from the six three hour simulations which are available have been broken into min segments and the maximum and minimum bending moment in each segment have been extracted. The cumulative distributions are shown in Figure 12 both for the total results, for the resonant response only (high pass filtered at.16 Hz) and for the wave frequency response only (low pass filtered at.16 Hz). The agreement between calculations and measurements is very good indeed. It appears that although the natural frequency of the first mode is more than three times the spectral peak frequency, the 6 Copyright 11 by ASME

7 physics of the resonant loading is well described by the present load model. Furthermore, neither the linear nor the second order diffraction loading is contributing significantly to the excitation of the resonant frequency, the bulk of the excitation is due to the third order FNV loading. Figure 13 shows the spectral density of the overturning moment (about mudline) due to the different load contributions. The overturning moment about mudline is a useful simple parameter for evaluating the ability to excite the first mode. Since the loads are nonlinear, the spectral density gives only qualitative information about the frequency range where the different load effects are significant, but it seems clear the FNV load is becoming dominant around 5s. Wave Direction NW SW NE SE For a structure like the Draugen GBS where the resonant mode is excited by horizontal loading in the surface zone, where the natural period is not more than four times the spectral peak, weakly nonlinear theory up to third order seems to give an excellent representation of governing extreme loads. If in addition the structure is reasonably slender and the incident wave field is not significantly modified by a complex array of shafts, the third order FNV load gives a good representation of weakly nonlinear load levels. Spectral Density of Overturning Moment [(knm) 2 s] 1E+16 1E+ 1E+14 1E+13 1E+12 1E+11 1E Frequency [Hz] Linear diffraction load Second order diffraction load Third order FNV load Figure 13 Spectral density of overturning moment excitation Snorre A TLP Tether tension in the Snorre A has been studied previously in []. Based on extensive model testing of the TLP it was found that governing year loads occurred in diagonal seas with the governing minimum load level occurring in the downwave tether and the governing maximum tether load occurring in the upwave tether (Figure 14). The maximum load level occurred in the steep -2 seastate and contained significant resonant tether response. Figure 14 Outline of Snorre A column, pontoons and deck. Diamonds indicate airgap measurement positions. Using a model based on linear theory and a simple von Karman [12] type model for impulse loading on the columns it was concluded in [] that the governing year tether tension could be predicted reasonably accurately. Unlike the present method which is truncated consistently at the third frequency sum harmonic, an impulse formulation contains excitation at all frequencies and is typically used for water impact problems. The transverse force, F T, on the column and moment, M SWL, about the still water level are described as: FT M SWL d dt Av a tv vt 1 a v v t 2 t where A is the added mass (relative to the still water level) of a circular column, v is the relative horizontal particle velocity, is the surface elevation, is the density of seawater and a is the cross sectional area of the column. When the method described above and in [] is employed, all calculations are carried out using SIMO alone based on a linear time series of surface elevation. SIMO uses linear wave particle kinematics up to the still water level and constant velocities in the crest region above this. In the example considered in Figure below, SIMO calculates a horizontal crest velocity associated with the large crest of 7.8 m/s. A large year event is shown in Figure a) for the -2 seastate which was found to be governing for maximum year tether tension. The incident wave has a crest height of less than 14 m. The smallest airgap which was measured at the positions indicated in Figure 14 was more than 8 m, so the only deck loading was a very slight vertical loading due to runup on the columns. The associated measured tether tension is shown in Figure b). Note that the resonant tether tension is significant and caused primarily by roll and pitch since there is (3) 7 Copyright 11 by ASME

8 little resonant response across the diagonal (in tether NE and SW). 9 8 C) Figure c) show the tether tension calculated using the present weakly nonlinear method. It is clear that the present method does not capture the excitation of the resonant modes. There are two reasons for this. Firstly, the natural frequencies lie more than five spectral peak periods above the spectral peak frequencies. In the present plot also the (incomplete) fourth order FNV moment is included, but it appears that consistently truncated weakly nonlinear methods cannot excite such high frequencies. Secondly, the centroid of mass and horizontal added mass of the TLP lies almost exactly at the SWL so that a horizontal force acting at the SWL does not excite roll and pitch. This is of course a good thing since there is little real excitation for the resonant modes, but it makes analysis difficult. Figure d) shows the same analysis with the impulse model in equation 3 used as the nonlinear load model in stead of second and third order theory. For TLPs of this type, it appears that an impulse model gives a better estimate of the resonant tether response than a weakly nonlinear model. Tether Tension [kn] Tether Tension [kn] NW SE NE / SW 9 d) Incident Wave Elevation at Origin [m] Tether Tension [kn] a) b) NW SE NE / SW NW SE NE / SW Figure Model Test Event in seastate -2 in Phase 2 (974). a) incident wave time history, b) measured tether tension, c) tether tension by present weakly nonlinear method, d) tether tension according to [] with impulse loading on columns. The model test of the Snorre TLP was carried out without synchronising the waves and wind so the direct comparison in Figure becomes somewhat qualitative. Only the waves are reproduced in the analysis, a representative wind spectrum is used in the analysis but it has not been attempted to backcalculate the time series of wind velocity. A more systematic comparison with model test results based on a statistical analysis of random seeds is given in []. Figure nevertheless illustrates the two important points that the impulse model appears to be superior to the weakly nonlinear model and that roll and pitch is responsible for the bulk of the resonant response in the year condition. Figure 16 is concerned with a larger wave event in a year condition. The incident (undisturbed) crest elevation shown in Figure 16 a) is 21.2 m at the origin with an available airgap to the underside of the deck box of 24.4 m (draft is 4.1 m in this condition). The wave generally goes clear of the deck and no horizontal impact forces are recorded, but two of the airgap probes upwave of the SE column indicate that the wave has hit the deck. This implies that there is an area 8 Copyright 11 by ASME

9 around the columns which has a negative airgap which is a normal situation in a year condition generally assumed not to give global response effects. Figure 16 b) shows the tether tension in the same event. There is significant resonant response and a large portion is caused by heave (seen in isolation in the NE and SW tethers) rather than roll and pitch. Since no modulation between heave, roll and pitch was observed in the decay tests this is surprising since it implies that vertical loads are giving significant high frequency tether response. The columns are vertical and very high frequency excitation at the pontoons or underneath the columns is believed to be unlikely, so the remaining candidate for heave excitation is vertical deck impact. Figure 16 c) shows the vertical loading on each of the four individual segments which make up the deck box and it appears that the vertical load on the SE deck box is responsible for significant resonant heave response. In order to calculate the resonant response of a TLP of the present type it appears that it is necessary to include strongly nonlinear wave impact loading both on the columns and on the deck box even if the TLP is not subject to significant wave impact with the topside. Incident Wave Elevation at Origin [m] a) b) vertical Load on Deck Quadrant [kn] NW NE SE SW Figure 16 Model test event in seastate -4 in Phase 1 (5541). a) incident wave time history, b) measured tether tension, c) vertical load on deck box quadrant DISCUSSION For a simple GBS structure with a resonant mode which is excited by horizontal loads in the surface zone and where the resonant frequency is not significantly larger than four times the peak period, the present weakly nonlinear model appears to capture the ringing loading remarkably well. It has been verified that the deck elevation is sufficiently large to avoid significant horizontal wave impact with the topside. Local strongly nonlinear effects like vertical loads due to wave runup close to the shaft and horizontal loads due to breaking waves on the shaft seem to give no significant effect compared with the third order FNV loads. The FNV load is developed for undisturbed waves incident on a single, vertical cylinder with constant radius. At present the conical shape of the Draugen shaft is implemented in a naïve fashion by using the local diameter at the intersection between the undisturbed wave and the shaft centre. This seems to work well for the Draugen GBS but may not be general. For more complex geometries with an array of shafts, the weakly nonlinear assumption may still be valid if the natural period is comparable with the present natural period, but it will be a challenge to develop a third order load model which is valid for a wave field deformed by other shafts and with a non-circular and non-uniform cross section. c) Tether Tension [kn] NW SE NE / SW The Snorre TLP has the stiff natural frequencies at more than five times the spectral peak of the survival waves. Weakly nonlinear methods of the type considered here seem to be incapable of exciting the structure at such high frequencies. In addition, the centroid of mass and horizontal added mass lies close to the free surface, so the FNV load gives little or no third order excitation of the structure. At these high frequencies, it appears that the much simpler impulse formulation employed in [] gives a better estimate of horizontal excitation at these high frequencies. This is a formulation of the von Karman [12] type which provides a simple estimate of the horizontal impulse 9 Copyright 11 by ASME

10 loading on the columns due to steep waves and is capable of giving loads at high frequencies. Due to the high natural frequencies and its centroid of mass, the Snorre TLP is not very vulnerable to high frequency excitation in the survival conditions. A surprising result in the year condition, however, has been that it appears that a significant portion of the resonant response seem to stem from TLP heave. It appears that vertical deck loads are capable of setting up significant resonant heave response even if no major exceedence of the available airgap is observed. If it is indeed the case that relatively local vertical deck loads around the columns can set up significant high frequency response in the tethers, it highlights the importance of developing reliable deck loading models for TLP structures. ACKNOWLEDGEMENTS The author is grateful to A/S Norske Shell and Statoil ASA and their partners for allowing the use of the Draugen and Snorre A model test results. REFERENCES [1] Krokstad, J.R., Stansberg, C.T., Nestegård, A. & Marthinsen, T., (1998), A New Nonslender Ringing Load Approach Verified Against Experiments, J. Offsh. Mech. and Arctic Eng., 1, pp - 29 [2] Faltinsen, O.M., Newman, J.N. & Vinje, T.,(1995), Nonlinear Wave Loads on a Slender, Vertical Cylinder, J. Fluid Mech., 289, pp [3] Johannessen, T.B., (11), Nonlinear superposition methods applied to continuous ocean wave spectra ', In Press: J. Offs. Mech. and Arctic Eng. [4] Torsethaugen, K., (1996), Model for a Doublypeaked Spectrum, SINTEF, STF22A964, SINTEF, Trondheim [5] Longuet-Higgins, M.S. & Stewart, R.W., (196), Changes in the form of short gravity waves on long waves and tidal currents, J. Fluid Mech., 8, pp [6] Johannessen, T. B. (8) : On the Use of Linear and Weakly Nonlinear Wave Theory in Continuous Ocean Wave Spectra: Convergence with Respect to Frequency, Paper # , Proc. 27 th OMAE Conf., Estoril, Portugal [7] Lee, C.H., Newman, J.N., Kim, M.H. & Yue, D.K.P, (1991), The computation fo second-order wave loads, Proc. th Int. OMAE Conf., New York, USA, pp [8] Newman, J.N., (1996), Nonlinear Scattering of Long Waves by a Vertical Cylinder, in Waves and Nonlinear Processes in Hydrodynamics, Grue et al. (eds.), Kluwer, pp 91-2 [9] Johannessen, T.B., (), Calculations of kinematics underneath measured time histories of steep water waves', Applied Ocean Research, 32, pp [] Johannessen, T.B. & Sandvik, A.K., (5), 'Analysis of extreme TLP tension amplitudes with comparison to model test', Paper # OMAE5 6743, Proc. 24th OMAE Conference, Halkidiki, Greece [11] Grue, J. & Huseby, M., (2), Higher-harmonic wave forces and ringing of vertical cylinders, Appl. Oc.Res., 24, pp [12] von Karman, T., (1929), The Impact of Seaplane Floats During Landing, Technical Note #321, National Advisory Committee for Aeronautics, Washington Copyright 11 by ASME