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Fig. 33. Water level sensitivity for double-sided cones. Comparisons between round and sharp cones are shown. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47

Figure 33 Water level sensitivity for double-sided cones. Comparisons between round and sharp cones are shown. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47

Related Figures (36)

Fig. 1. Tested configurations, NRC tests. According to the Froude model scaling, the prototype time (¢) and force (F) from a model
Fig. 1. Tested configurations, NRC tests. According to the Froude model scaling, the prototype time (¢) and force (F) from a model
Corrections of measured ice force due to deviations in ice thickness and strengths
Corrections of measured ice force due to deviations in ice thickness and strengths
Fig. 3. Maximum force when crushing occurs. The first two components are illustrated in Fig. 6, by applying a 0.27 Hz FFT filter to the force signal. There appears to be a certain correlation between the buckling component amplitude and the amplitude of
Fig. 3. Maximum force when crushing occurs. The first two components are illustrated in Fig. 6, by applying a 0.27 Hz FFT filter to the force signal. There appears to be a certain correlation between the buckling component amplitude and the amplitude of
Fig. 2. Example of time series and spectra of 60 s of data when crushing occurs. Same test setup as in Fig. 5 is used. The ice velocity is 1 m/s. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 2. Example of time series and spectra of 60 s of data when crushing occurs. Same test setup as in Fig. 5 is used. The ice velocity is 1 m/s. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 4. Ramp results when crushing occurs. The figure shows two separate tests. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47 the crushing component in the sense that, close to the peak of the buckling component, the crushing component has a reasonable large value. But they are not correlated in the sense that the peaks are occurring at the exact same time. The phase of the crushing component seems to be rather random. The maximum high pass component is typically, say, 50% of the low pass component. No significant velocity dependence is experienced when the above-describe« mixed mode occurs (cf. Figs. 7 and 8).
Fig. 4. Ramp results when crushing occurs. The figure shows two separate tests. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47 the crushing component in the sense that, close to the peak of the buckling component, the crushing component has a reasonable large value. But they are not correlated in the sense that the peaks are occurring at the exact same time. The phase of the crushing component seems to be rather random. The maximum high pass component is typically, say, 50% of the low pass component. No significant velocity dependence is experienced when the above-describe« mixed mode occurs (cf. Figs. 7 and 8).
Fig. 5. Example of time series and spectra of 60 s of data when mixed-mode failure occurs. Same test setup as in Fig. 2 is used. The ice velocity is 1 m/s. A simple method of extending the information obtained during the model test to a time series of 10- min duration will be presented. The method is crushing component seems to be rather random. The
Fig. 5. Example of time series and spectra of 60 s of data when mixed-mode failure occurs. Same test setup as in Fig. 2 is used. The ice velocity is 1 m/s. A simple method of extending the information obtained during the model test to a time series of 10- min duration will be presented. The method is crushing component seems to be rather random. The
Fig. 7. Maximum force when mixed mode occurs. defined as illustrated in Fig. 9. The distribution ty and parameters of the maximum forces of the mixe mode events is determined event, the time series is n maximum force. Connecting random-selected events, scaled randomly to fit the ormalised relative to t peak distribution, enabl the generation of time series of 10-min duration. T time scale is not changed, length scale of the combined thus, the variation in t (cf. Fig. 10). For each pe d- ne es ne ne time series may be larger than in the original results. Note that this should not influence the lock-in component of the force. The data are separated in two velocity ranges: 0.2<Viee<0.5 and 0.5<V;,-<1.0 m/s. For each of the two velocity ranges, the mixed-mode events are
Fig. 7. Maximum force when mixed mode occurs. defined as illustrated in Fig. 9. The distribution ty and parameters of the maximum forces of the mixe mode events is determined event, the time series is n maximum force. Connecting random-selected events, scaled randomly to fit the ormalised relative to t peak distribution, enabl the generation of time series of 10-min duration. T time scale is not changed, length scale of the combined thus, the variation in t (cf. Fig. 10). For each pe d- ne es ne ne time series may be larger than in the original results. Note that this should not influence the lock-in component of the force. The data are separated in two velocity ranges: 0.2<Viee<0.5 and 0.5<V;,-<1.0 m/s. For each of the two velocity ranges, the mixed-mode events are
Fig. 6. Force components of time series from Fig. 5.
Fig. 6. Force components of time series from Fig. 5.
Fig. 8. Ramp results when mixed mode occurs. 1.3<f,<2.6. It is important to scale the time to keep the ratio of structure eigenfrequency to lock-in frequency. The time should be scaled by a factor of 1.8/f,. 2.3.1. Modifying results for other stiffness/eigenfre- quency
Fig. 8. Ramp results when mixed mode occurs. 1.3<f,<2.6. It is important to scale the time to keep the ratio of structure eigenfrequency to lock-in frequency. The time should be scaled by a factor of 1.8/f,. 2.3.1. Modifying results for other stiffness/eigenfre- quency
Fig. 9. Example of definition of parts in time series. Only mixed-mode events are used. In mixed mode, the eigenfrequency is very important for the ice load, as discussed above. If the model tests should be interpreted to apply for another eigenfrequency, care should be taken. It would be reasonable though to expect that the amplitudes of the ice force would not change considerably for eigen- frequencies (determined in water) in the range of If the model tests should be interpreted to apply for another stiffness and mass, but the same eigenfre- quency, the structure displacement is expected to be larger, but because more failure types are involved, one can only guess about the effect that this would have.
Fig. 9. Example of definition of parts in time series. Only mixed-mode events are used. In mixed mode, the eigenfrequency is very important for the ice load, as discussed above. If the model tests should be interpreted to apply for another eigenfrequency, care should be taken. It would be reasonable though to expect that the amplitudes of the ice force would not change considerably for eigen- frequencies (determined in water) in the range of If the model tests should be interpreted to apply for another stiffness and mass, but the same eigenfre- quency, the structure displacement is expected to be larger, but because more failure types are involved, one can only guess about the effect that this would have.
Fig. 11. Example of perturbation of mixed-mode events. All time series of the mixed-mode events are zero padded to a fixed length before the FFT analysis is Perturbation of the mixed-mode events in the extension method described above might be a method to test the sensitivity of the shape of these events. A method will be suggested and preliminary results presented. The basis of the method is the perturbation of the complex Fast Fourier Transform (FFT) spec-
Fig. 11. Example of perturbation of mixed-mode events. All time series of the mixed-mode events are zero padded to a fixed length before the FFT analysis is Perturbation of the mixed-mode events in the extension method described above might be a method to test the sensitivity of the shape of these events. A method will be suggested and preliminary results presented. The basis of the method is the perturbation of the complex Fast Fourier Transform (FFT) spec-
Fig. 10. Statistics of time-series parts. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 10. Statistics of time-series parts. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 12. Definition of mode shapes in GTSTRUDL calculations. performed, to ensure that the spectra of all time-series parts are comparative.
Fig. 12. Definition of mode shapes in GTSTRUDL calculations. performed, to ensure that the spectra of all time-series parts are comparative.
Fig. 13. Ice load contra shear force at bottom level. The maximum shear force is 1.2 times the maximum ice force. where kmeasi 18 a predefined constant defined from the statistics of all buckling event time series in the An example of a time-series peak before and after perturbation is shown in Fig. 11. The perturbed time series are not independent of the original time series due to the induced restrictions to the amount of perturbation. On the other hand, it is necessary to maintain the basic physics in the results. The perturbation procedure, including a determination of the required limitation of perturbation (mainly to phase spectrum), has not yet been finalized and compared with the more simple composition proce- dure. One disadvantage is that the perturbed ice force
Fig. 13. Ice load contra shear force at bottom level. The maximum shear force is 1.2 times the maximum ice force. where kmeasi 18 a predefined constant defined from the statistics of all buckling event time series in the An example of a time-series peak before and after perturbation is shown in Fig. 11. The perturbed time series are not independent of the original time series due to the induced restrictions to the amount of perturbation. On the other hand, it is necessary to maintain the basic physics in the results. The perturbation procedure, including a determination of the required limitation of perturbation (mainly to phase spectrum), has not yet been finalized and compared with the more simple composition proce- dure. One disadvantage is that the perturbed ice force
Fig. 14. Contributions to the shear force at bottom level using mode separation in GISTRUDL. The mode shapes are shown in Fig. 12 H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 14. Contributions to the shear force at bottom level using mode separation in GISTRUDL. The mode shapes are shown in Fig. 12 H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 15. Ice force multiplied by moment arm contra bending moment at bottom level. The maximum moments are the same
Fig. 15. Ice force multiplied by moment arm contra bending moment at bottom level. The maximum moments are the same
Fig. 16. Contributions to the bending moment at bottom level using mode separation in GTSTRUDL. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 16. Contributions to the bending moment at bottom level using mode separation in GTSTRUDL. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 18. Example of time-series and spectra of 60 seconds of data, inverted cones. During the physical model tests, the displacement, velocity, acceleration and force are measured as time series, and the mass, stiffness and the viscous damp- where F' is the ice force, m is the mass, c is the damping, k is the stiffness, and x is the displacement. The damping is assumed to be viscous damping, and the amount of damping is expressed in terms of the
Fig. 18. Example of time-series and spectra of 60 seconds of data, inverted cones. During the physical model tests, the displacement, velocity, acceleration and force are measured as time series, and the mass, stiffness and the viscous damp- where F' is the ice force, m is the mass, c is the damping, k is the stiffness, and x is the displacement. The damping is assumed to be viscous damping, and the amount of damping is expressed in terms of the
Fig. 17. Water level configurations for the down bending cone at the 55° and 65° slope angle. ing in water are also determined. Because the physical model tests represent a single degree of freedom oscillation, the equation of motion is: peak frequency is, accordingly, about 0.4 Hz. For other velocities, the breaking failure frequency may be estimated from:
Fig. 17. Water level configurations for the down bending cone at the 55° and 65° slope angle. ing in water are also determined. Because the physical model tests represent a single degree of freedom oscillation, the equation of motion is: peak frequency is, accordingly, about 0.4 Hz. For other velocities, the breaking failure frequency may be estimated from:
Fig. 19. Spectral peak frequency for the 55° cone.
Fig. 19. Spectral peak frequency for the 55° cone.
Fig. 20. Spectral peak frequency for the 65° cone. A major concern in the cone design 1s _ the required cone height. In the past, rather conservative requirements have been specified by various researchers, although this has not been reflected in he API (1995). The requirement of a large cone height could rapidly become a killing assumption to wind turbine foundations, as this would result in a arge cone with associated increased wave loads and construction costs. Basically, the cone geometry should make sure that no crushing of ice takes place on the vertical cylinder. With 0.6-m-thick ice, the failure mode is dominated by bending failure at water levels larger than WL2—0.75 m when the cone ends in elevation —1.75 m (c.f. Fig. 21). From this, it may be concluded that a distance of 0.5 m from the bottom of the ice to the intersection point with the vertical structure should be sufficient for the given ice thickness of 0.6 m. When the failure mode is dominated by bending, minor velocity dependency is present. The combined dependence upon water level and ice velocity is illustrated on Fig. 22 for water levels dominated by bending failure. For water levels below WL<0.75, the ice failure is dominated by crushing, and for the largest water levels, only bending takes place. In between hese ranges, a mixed breaking/crushing failure is observed, which can be detected by the angle of force resultant (see Fig. 23). Hence, in this range of water levels, the tendency is that the force decreases
Fig. 20. Spectral peak frequency for the 65° cone. A major concern in the cone design 1s _ the required cone height. In the past, rather conservative requirements have been specified by various researchers, although this has not been reflected in he API (1995). The requirement of a large cone height could rapidly become a killing assumption to wind turbine foundations, as this would result in a arge cone with associated increased wave loads and construction costs. Basically, the cone geometry should make sure that no crushing of ice takes place on the vertical cylinder. With 0.6-m-thick ice, the failure mode is dominated by bending failure at water levels larger than WL2—0.75 m when the cone ends in elevation —1.75 m (c.f. Fig. 21). From this, it may be concluded that a distance of 0.5 m from the bottom of the ice to the intersection point with the vertical structure should be sufficient for the given ice thickness of 0.6 m. When the failure mode is dominated by bending, minor velocity dependency is present. The combined dependence upon water level and ice velocity is illustrated on Fig. 22 for water levels dominated by bending failure. For water levels below WL<0.75, the ice failure is dominated by crushing, and for the largest water levels, only bending takes place. In between hese ranges, a mixed breaking/crushing failure is observed, which can be detected by the angle of force resultant (see Fig. 23). Hence, in this range of water levels, the tendency is that the force decreases
Fig. 21. Water level sensitivity. All water levels and all velocities. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47 for increased water level, although the effective diameter increases with the water level. The general conclusion is that, for an inadequate cone length, the design should be based on forces in the 2-MN range. The exact water level where conditions equal those of a pure vertical cylinder and associated forces in the range of 5 MN has not yet been determined. ing in values less than, but very close to, predictions by the Ralston (Ref) formula (0.075 for measurec results, compared with 0.1 for Ralston formula). Due to resonance, a certain increase in the oscillations ir the first mode (0.38 Hz) of the tower does occur fot the larger ice velocities (around V;,.=1 m/s).
Fig. 21. Water level sensitivity. All water levels and all velocities. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47 for increased water level, although the effective diameter increases with the water level. The general conclusion is that, for an inadequate cone length, the design should be based on forces in the 2-MN range. The exact water level where conditions equal those of a pure vertical cylinder and associated forces in the range of 5 MN has not yet been determined. ing in values less than, but very close to, predictions by the Ralston (Ref) formula (0.075 for measurec results, compared with 0.1 for Ralston formula). Due to resonance, a certain increase in the oscillations ir the first mode (0.38 Hz) of the tower does occur fot the larger ice velocities (around V;,.=1 m/s).
Fig. 22. Water level sensitivity separated in ice velocities for water levels above WL=> —0.75 m In general, the loads on the cones were increasing with increasing ice velocity, Vice. To produce a maximum number of independent time series, the time series and max events were corrected to ice velocity V;,.<=1 m/s by means of linear regression of The main results are presented in Table 3. The model tests show consistent results compared with previous model tests and field measurements, result-
Fig. 22. Water level sensitivity separated in ice velocities for water levels above WL=> —0.75 m In general, the loads on the cones were increasing with increasing ice velocity, Vice. To produce a maximum number of independent time series, the time series and max events were corrected to ice velocity V;,.<=1 m/s by means of linear regression of The main results are presented in Table 3. The model tests show consistent results compared with previous model tests and field measurements, result-
Comparison of results from model tests for inverted cone witk Ralston’s formula [Dw ,=9.5 m (at water level), D=4.3 m (at bottom of cone), t=0.57 m, r¢=0.5 MPa, [cone-ice=0-1/0.2] * Average for only tests at V=1 m/s.
Comparison of results from model tests for inverted cone witk Ralston’s formula [Dw ,=9.5 m (at water level), D=4.3 m (at bottom of cone), t=0.57 m, r¢=0.5 MPa, [cone-ice=0-1/0.2] * Average for only tests at V=1 m/s.
Fig. 23. Two examples of force resultants, with flexure and crushing/flexure type, respectively. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 23. Two examples of force resultants, with flexure and crushing/flexure type, respectively. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 24. Ice velocity dependency of statistical values of the ice force. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 24. Ice velocity dependency of statistical values of the ice force. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 25. Determination of general exponential functions after splitting up in | min time series. Results from relevant ice velocities, V, are shown.
Fig. 25. Determination of general exponential functions after splitting up in | min time series. Results from relevant ice velocities, V, are shown.
Ice velocity statistics
Ice velocity statistics
Fig. 26. Ice velocity statistics. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47 a design time series of 10-min prototype time used in connection with combined ice/wind load analysis. The time series from wind and ice are assumed uncorrelated. assumed representative for the same load case. Hence, all time series can be put after each other. The time series of each velocity are then split up in 1-min time series, and the maximum values are extracted. Exceedance curves are fitted to the maximum values from a general exponential distribution given by:
Fig. 26. Ice velocity statistics. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47 a design time series of 10-min prototype time used in connection with combined ice/wind load analysis. The time series from wind and ice are assumed uncorrelated. assumed representative for the same load case. Hence, all time series can be put after each other. The time series of each velocity are then split up in 1-min time series, and the maximum values are extracted. Exceedance curves are fitted to the maximum values from a general exponential distribution given by:
Fig. 27. Statistical summation of ice load over velocities (max force/relative probability). H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 27. Statistical summation of ice load over velocities (max force/relative probability). H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 28. Example of determination of time series parts for artificial generation of time series. The experiments with sharp corner (r=0.01 m) have a maximum at the water level 0.42 m, where the centre of the ice floe is slightly above the corner, which might be due to the fact that the friction force from a given volume of accumulated ice above the
Fig. 28. Example of determination of time series parts for artificial generation of time series. The experiments with sharp corner (r=0.01 m) have a maximum at the water level 0.42 m, where the centre of the ice floe is slightly above the corner, which might be due to the fact that the friction force from a given volume of accumulated ice above the
Fig. 29. Normal distribution plots of max force and periods for the time series parts as shown in Fig. 28. Only the results of one of the measured time series are shown. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 29. Normal distribution plots of max force and periods for the time series parts as shown in Fig. 28. Only the results of one of the measured time series are shown. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 30. Example of form database for time-series parts.
Fig. 30. Example of form database for time-series parts.
Fig. 32. Water level configurations for tests with double-sided cones. ~S The introduction of the round corner (r=0.15 m) causes quite dramatic changes to the maximum ice force. The maximum force of all measurements increases by 50% relative to the sharp corner results to a level of 2.0 MN, and the maximum force is no longer observed at the water level 0.42 m. Although Regarding the experiments with water levels 1.75, 2.0 and 2.25 m, the maximum force shows a tendency to increase with the water level despite that the area of attack decreases. This indicates that, if the distance from top of the ice to the upper intersection point of ice cone and cylinder is less than about 0.5 m, crushing (at least partial) against the cylinder could
Fig. 32. Water level configurations for tests with double-sided cones. ~S The introduction of the round corner (r=0.15 m) causes quite dramatic changes to the maximum ice force. The maximum force of all measurements increases by 50% relative to the sharp corner results to a level of 2.0 MN, and the maximum force is no longer observed at the water level 0.42 m. Although Regarding the experiments with water levels 1.75, 2.0 and 2.25 m, the maximum force shows a tendency to increase with the water level despite that the area of attack decreases. This indicates that, if the distance from top of the ice to the upper intersection point of ice cone and cylinder is less than about 0.5 m, crushing (at least partial) against the cylinder could
Fig. 31. Example of generated time series. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
Fig. 31. Example of generated time series. H. Gravesen et al. / Cold Regions Science and Technology 41 (2005) 25-47
example of maximum of combined extreme ice force with operational wind force for an inverted cone with a cone angle of 55° The number of events are n=100 each of 10 min. Table 5
example of maximum of combined extreme ice force with operational wind force for an inverted cone with a cone angle of 55° The number of events are n=100 each of 10 min. Table 5
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