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PREDICTION DOWNTIME OF DREDGES OPERATING IN THE OPEN SEA

J.E.W. Wichers1 and E. J. Claessens2

ABSTRACT Beach nourishment, maintaining excess channels to harbors, dredging trenches for pipe lines and covering pipelines with stone, trailing suction hopper dredges, cutter suction dredges and stone dumping vessels, are used. All vessels are operating in the open sea exposed to wind, waves and current and often hampered by the weather conditions. In the last decade the offshore industry has made a considerable progress to predict downtime. The mentioned offshore techniques to determine the downtime were applied to the existing MARIN computer programs for cutter suction dredges (DREDSIM), DT trailing suction hopper dredges (DPSIM) and DP stone dumping vessels (DPSIM). For the determination of downtime of a dredge at a certain location and during a certain season, wave scatter diagrams combined with current and wind data are often used. The determination of the operating limits in these sea states (downtime points) is of prime importance. If these downtime points or lines are known, the downtime can be calculated as an average downtime by using scatter diagrams. Although it may give valuable information, it does not give the real downtime during a project. A more realistic approach to predict the downtime during a project is the method of the long-term time-domain simulation. Key items in the long-term simulations are: • the long-term time-domain simulation of the weather conditions and • both pre- and post processing of downtime lines and • anticipated scenarios. In this paper the tools as developed at MARIN to predict the operational limits will be presented. The status on the developments at MARIN on the prediction methods to generate swell and sea waves based on available long-term wind data are discussed. These two highlighted key items together with applied scenarios make it possible to predict in a reliable statistical manner the realistic duration of a project to be carried out in the open sea. Keywords: dredges, scatter diagram, downtime, wind/wave models, long term simulations, scenarios

INTRODUCTION In the last decade the offshore industry has made a considerable progress to predict downtime. The mentioned offshore techniques to determine the downtime are applied to the existing MARIN computer programs for cutter suction dredges (DREDSIM), DP trailing suction hopper dredges (DPSIM) and DP stone dumping vessels (DPSIM). By means of these programs the operational limits of a dredge for a combination of waves, wind and current conditions (and water depth) can be determined (downtime lines). Using a scatter diagram for a certain location, water depth and season, the downtime, however, is given as an average downtime. Although it may give valuable information, it does not give the real downtime during a project. A more realistic approach to predict the downtime during a project is the method of the long-term time-domain simulation.

1 Johan Wichers, Vice-President, MARIN USA Inc., 2500 City West Blvd Suite 300, Houston, TX 77042, phone

713-267-2234, fax 713-267-2267, e-mail jewwichers@earthlink.net. 2 Ellen Claessens, Meteorologist, MARIN, 2 Haagsteeg, Wageningen, The Netherlands, phone 31-317 493466,

fax 31-317-493245, e-mail e.claessens@marin.nl

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The time series must last for multi-times the net project duration (NPD) providing sufficient reliable statistical information with respect to number of interruptions, waiting time, loss of production etc. The NPD stands for the anticipated calm water duration of the project. By means of the earlier mentioned downtime lines and the scenarios applied to the long-term weather condition, the average real project duration (RPD) and the statistical distribution function (standard deviation) of the duration of the job can be determined. The percentage of the average downtime can be determined according to ((RPD-NPD)/RPD)*100%, while the standard deviation of the distribution function is a measure for the spread of the job duration. Key items in the long-term simulations are: • the long-term time-domain simulation of the weather conditions and • both pre- and post-processing of downtime lines and • anticipated scenarios. Starting point of the long-term time simulation of the weather condition is the knowledge of the long-term wind velocities and direction. The long-term wind wave time-domain simulations can be achieved by means of the wind data. This approach includes the correct persistence relation between the duration of the sea states. Further knowledge of the occurrence of swell and current speed and their directions must be available. Based on these data, in return scatter diagrams for different wave directions including current and swell (statistically for, for instance, a season or a year) can be derived. The tools as developed at MARIN to predict the operational limits (= downtime lines) for a cutter suction dredge and a DP trailing suction hopper dredge will be described. The developments at MARIN on the prediction methods to generate the long-term time series of waves based on available long-term wind data and available swell data are discussed. An example is shown. These two highlighted key items together with applied scenarios make it possible to predict in a statistical manner the realistic duration of a project to be carried out in the open sea.

TOOLS TO PREDICT THE OPERATIONAL LIMITS OF DREDGES Introduction In order to predict the downtime of dredges operating in the open sea, the operational limits have to be known. For a specified dredge the limiting sea states have to be known to determine the average downtime based on scatter diagrams or the average job duration and the distribution of the duration of the job based on long-term time-domain simulations. In the following more specific information on the tools to determine the workability of a suction cutter suction dredge and DT trailing suction hopper dredge is given. Criteria and Scenarios The operational limits are determined by criteria. Trespassing of criteria involves for instance stopping of production or pulling out the storm gear or abandoning dredge location. By means of the operational limits or downtime lines the average downtime using scatter diagrams can be determined. For the determination of the job duration, however, not only the criteria but also scenarios have to be known. Criteria and scenarios are closely related. Scenarios in fact describe the handling procedures after a criterion is reached. The scenarios may depend on possible weather forecast (waiting time), may describe time intervals for disconnecting and retrieval of equipment, for sailing time to dump areas, for sailing time to safe haven and may include the lower sea states to leave safe haven, start installation and production. Depending on location, equipment and other factors complex scenarios may be used. As an example criteria for a cutter suction dredge may be: - forces in the spud pole - either forces in swing wires or holding capacity of the deck winches or the holding capacity of anchors - forces/moments in ladder hinge - accelerations on the bridge.

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And for a DT trailing suction hopper dredge the criteria as an example may be: - under keel clearance - relative distance between bilge keels and pipes/stringers - stroke heave compensators - station keeping capacity - acceleration FPP-coupling floating hose. To determine the limits of the sea states, in which the mentioned criteria of forces and motions may occur, computations have to be carried out. The computational tools are briefly described below. Cutter Suction Dredges Due to the relative stiff mooring system of a spud pole moored cutter suction dredge, wave loading will dominate the behavior of the dredge and wind and current loads are mostly neglected. The system of a cutter suction dredge consists of two bodies, being the barge and the ladder, which are kinetically and dynamically coupled. The ladder is connected to the barge by means of the ladder hinge and the hoisting wires. The mooring system consists of the spud pole and swing wires, having the correct properties of elasticity (and pre-tension). At least two operational limits can be distinguished: - the limit for operational condition - the limit to stay on location with the ladder hoisted out of the breach. In operational conditions the properties of the soil cutting reaction forces between cutter head and breach are taken into account. The two conditions are shown in the Figures 1 and 2.

Fig. 1. Spud pole/swing wires moored cutter suction dredge with ladder hoisted. The difference in behavior of both conditions is significant. With the ladder in hoisted position the dredge is relatively free to move inducing considerable forces in the spud pole and swing wires. In the operational condition, however, the motions of the dredge are restrained due to the side pre-tension of the cutter head in the breach and the limiting motions of the cutter head in the breach in ladder direction. While the forces and motions of the dredge in hoisted condition may be considered to be linear with the wave loading, in operational condition, however, the forces and motions are strongly non-linear. The computations can be carried out with the program for cutter suction dredges DREDSIM. For a comprehensive treatment of the computational procedures reference is made to Wichers (1987).

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Fig. 2. Spud pole/swing wire moored cutter suction dredge in operational condition. DT Trailing Suction Hopper Dredges The system of a trailing-suction hopper dredge can be divided in a main body, the vessel, a body of an upper pipe both on starboard and port side, a body of a lower pipe including the drag head both on starboard and port side. The upper and lower pipes are connected by means of universal joints. The pipes are connected to the vessel by means of upper joints and stringers. The total system will consist of five bodies, which are kinetically and dynamically coupled. The coupled system is exposed to loads due to waves, wind and relative current, the drag head forces, the action of main screw(s) and rudder(s), lateral tunnel thrusters and possible azimuthing thrusters. It is assumed that swell compensators are placed on board of the ship, which will compensate the wave frequency motions of the suction pipes and drag heads. A typical layout of a hopper dredge is given in Figure 3. To study the performance of the vessel in terms of workability the following items should be considered: - The total system is assumed to be a superposition of low-speed and low frequency motions due to the wave drift

forces. Consequently, the loads on the vessel in the horizontal plane, the hydrodynamic loads on the pipes and the forces in the stringers cause the motions of the drag heads. The capability of the DT system to counteract the external forces and to keep the drag head on the desired track has to be known.

- The (combined) wave frequency motions caused by roll, heave and sway at locations along the bilge keel in close proximity of the pipes and stringers can hamper the operational process. The statistics of the relative motions between the bilge and the pipe and/or stringers should be known.

- The relative speed of the vessel and the wave frequency velocities at the location of the upper joint will determine the trailing speed of the drag head.

In dredge condition at least two operational conditions have to be considered: - sailing with suction pipes on starboard and port side (no drift angle) - sailing with one suction pipe either on starboard or port side (under drift angle).

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The DT capability (thrust on main propeller(s), effect rudder(s), stern and bow thruster(s)), the wind, current and wave drift loads on the hull, the drag/lift loads on the pipe and the soil reaction forces on the drag head and the resulting behavior of the complete system can be computed by computer program DPSIM. In the program the lead for the control system for DT is the deviation of the location of the drag head from the desired track. A comprehensive description of the DT trailing suction hopper dredge is given in Wichers (1987).

Fig. 3. Layout of a typical trailing suction hopper dredge. By means of the mentioned tools the downtime lines for different wave headings can be determined to predict the average downtime on basis of scatter diagrams. In this case the waves are described as 1-D spectra (=combined wave parameters Hs, T2 and mean direction μ). Here Hs is the significant wave height and T2 the zero-up crossing period. For the job duration long-term wave simulations are necessary. In the long-term wave simulations, however, not only the combined wave parameters Hs and T2 and mean direction μ. but also the separate wave parameters of the wind waves (Hsw and T2w) and swell (Hss and T2s) and their associated mean directions (μw and μs respectively) can be distinguished. The set of computations to be performed to determine the downtime lines may depend on the results of the long-term wave simulations (combinations of wind waves and swell and directions). Therefore the procedure to determine the downtime lines will be discussed after the description of the time-domain wave simulation as given in the next chapter.

GENERATION OF WAVE HISTORIES Introduction A more realistic approach to predict the downtime during a project is the method of the long-term wave simulation. The wave simulation has the advantage, that the average actual real production duration and the distribution of the duration of the job can be determined. Time series of the significant wave height, the associated mean wave period and the wave direction of long duration are necessary for the job simulation. A coherent set of information can be obtained from so-called hindcasts done with wind-wave models. Wind-wave models use the wind speed and direction as input to calculate for instance the significant wave height, the mean wave period and the mean wave direction. Some advantages of using wind-wave models are:

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• The mutual persistence is correct, if long-term time series of wind data are used. • The time series of the wave data are continuous and can be calculated at the exact location where the dredges

are operating. It is namely often difficult to find continuous time series of measured wave data. A drawback of using a wind-wave model is however the correct implementation of swell components. Later it will be discussed how to improve this implementation. Wind-Wave Models All wind-wave models are based on solving the so-called spectral action balance equation, see Figure 4. In this equation several wave processes are described to calculate the sea state. The following process is a source for the wave growth: • Wind driven wave generation. Processes acting as sinks are: • Dissipation of wave energy by white capping (deep and shallow water). • Dissipation of wave energy by depth-induced wave breaking (shallow water). • Dissipation of wave energy by bottom friction (shallow water). The redistribution of wave energy over the wave spectrum by non-linear wave-wave interactions is also taken into account. Wave propagation processes are: • Propagation through geographic and frequency space. • Refraction due to bottom and current (law of Snellius) variations. Refraction is the process, which occurs when

the wave direction changes due to phase speed variations along the wave crest. • Shoaling due to bottom and current variations. Shoaling is the effect of the bottom on waves propagating into

shallower water or in a current field without changing the wave direction. It results in higher waves. • Transmission through or blockage by obstacles (e.g. islands, breakwaters, reefs, headlands and rocks). Diffraction cannot be modeled in wind-wave models yet. It occurs for example when the geometry of the sea bottom is irregular. This results in large wave height variations within a local wave field. The diffraction is small in irregular wave fields (Holthuijsen et al. 1993, Komen et al. 1994, Ris et al. 1994, Ris, 1997, Ris et al. 1998, WMO 1998). MARIN is getting acquainted with the wind-wave model SWAN. This model is developed at the Delft University of Technology and can be found on the Internet-site http://swan.ct.tudelft.nl. Apart from the integral wave parameters (wave parameters as for instance the significant wave height, the mean wave period and the mean wave direction) the model also calculates the 1D- and 2D-wave spectra. In the 1D-spectra we have the energy densities as a function of wave frequency, while 2D-wave spectra give the energy densities as a function of wave frequency and direction. The spectral form of the wave spectra is free. The integral wave parameters are calculated from the 2-D wave spectrum. If this spectrum contains both swell and wind sea components, the integral wave parameters will be a weighted mean of these spectral components. The input for the SWAN model is: • The local geometry of the sea bottom. • The bottom friction. • The water level variations. The tides can hence be simulated. • The currents. • The wind speed and direction at 10 m height. • Swell incoming at the boundary of the area. There are however a few situations for which the model cannot be used, for instance in tropical cyclones (see also Claessens and Dallinga 1999).

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Time t Time t + tδ

Initial state

Wave data

HINDCASTnumerical/manual

Wind

AtmosphericANALYSIS

Modified state

FORECAST

AtmosphericFORECAST

Wave growth

Propagation

RefractionShoaling

Non-linearinteractions

Dissipation

Atmospheric forcing

Fig. 4. The sinks, source and wave propagation processes in wave models (WMO 1998).

In the next section an example will be given of a SWAN run for two wave buoy locations in the North Sea. The model results will be compared with buoy measurements of the DONAR database of the Directorate-General of Public Works and Water Management (Rijkswaterstaat). Example A validation run was carried out for the Southern North Sea (see Figure 5) for 21 September until 15 November 1996. The computational grid had a grid size of 504 x 320 km, with a resolution of 8 km. The bottom depth was taken from the Continental Shelf Model of Delft Hydraulics (see also Dingemans et al. 1998). This grid has also a grid size of 504 x 320 km; the resolution is however 4 km. The wind and wave data, which are used as input, are taken from an ECMWF re-analysis database for a period of five years (1994-1998) for the North Sea and the Gulf of Biscay. ECMWF stands for the European Center for Medium Range Weather Forecasts and is located in Reading, United Kingdom. This database contains the wind speed at 10 m height in the Eastern and Northern direction, the significant wave height, the peak period, the mean wave period and the wave direction of the total waves, the wind sea and the swell. The wind information is available on a 0.5° x 0.5º grid, while the wave information has a resolution of 1.5º x 1.5º. Both data are in time steps of six hours. The ECMWF uses its global atmospherical models intensively in routine weather forecasts. For scientific purposes these models are used in what is called a re-analysis over longer periods of time. Measured data is then used in a hindcast for these periods with the updated version of the atmospherical model. At the ECMWF a wind-wave model for deep water (WAM) is run coupled with the atmospherical model. The ECMWF distributes the re-analysis data through the national meteorological institutes (the KNMI in the Netherlands). The following locations where selected as input for the wind data: 51.5º N 2.5º E, 52.5º N 2.5º E, 54º N 0º E, 54º N 2.5º E and 54º N 6º E. Whereas the locations 54º N 1.5º E, 54º N 3º E, 54º N 4.5º E and 54º N 6º E where used for the incoming waves at the Northern boundary. Using the significant wave height, the mean wave period and the mean wave direction from ECMWF, the incoming waves at the northern boundary were parameterized by a JONSWAP spectrum with a peak-enhancement factor of 3.3. No incoming waves where simulated at the Southern boundary. The reason for this is that these waves are only 28 % of the time incoming and small wind waves (the average significant wave height is 0.68 m). No currents and tidal effects were taken into account.

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+*

*

Hull

Harwich

Dover

Den Helder

IJmuiden

Hoek van Holland

54.0N 1.5E 54.0N 3.0E 54.0N 4.5E 54.0N 6.0E54.0N 0.0E54.0N 2.5E

52.5N 2.5E

51.5N 2.5E

Fig. 5. The Southern North Sea with the bottom depth in m, the wave buoy locations (EUR and YM6), the locations

which are used for the wind data (51.5º N 2.5º E, 52.5º N 2.5º E, 54º N 0º E, 54º N 2.5º E and 54º N 6º E) and the locations which are used for the waves incoming at the boundary (54º N 1.5º E, 54º N 3º E, 54º N 4.5º E and 54º N 6º E).

The results of the validation run during the period of 56 days are compared with buoy measurements of the DONAR database of the Directorate-General of Public Works and Water Management (Rijkswaterstaat). These comparisons are given in the Figures 6 through 8. In Figure 6 the significant wave heights at Euro-0 and YM6 are presented, the associated zero-up-crossing periods at both locations are given in Figure 7, while the mean wave directions are shown in Figure 8. The mean wave direction is defined according to the nautical convention; waves coming from the North have a direction of 0º, while waves coming from the East have a direction of 90º. The wind speed and the associated computed significant wave height at Euro-0 and YM6 are given in Figure 9. It can be seen from Figure 6 and 9, that the validation period is a relative calm period, except for the last week of September and the first two weeks of November. The computed significant wave height compares over all quite well with the buoy measurements. However, SWAN underestimates the significant wave height sometimes. This can have the following two reasons: • The numerical diffusion of swell due to the implicit upwind difference scheme (see also Claessens and Dallinga

1999 and Dingemans et al. 1998). From simple tests it was concluded that approximately 54 % of the incoming waves were lost by the numerical diffusion. This results especially for swell conditions in underestimations in the computed significant wave height. Holthuijsen et al. (1999) recommends for this reason a maximum grid size of roughly 25 x 25 km with a spatial resolution between 50 and 1000 m. The errors due to numerical diffusion will be resolved in a next version of SWAN.

• The wind input is too coarse. The input of SWAN has to be defined on a rectangular regular grid. The ECMWF data is however defined on a geographical grid. For this reason only a few locations where selected for wind input. The wind data for grid points between these locations is interpolated by SWAN. MARIN is working on a grid translation, so finer wind input grids (0.5º x 0.5º) can be used in the future. Furthermore, the ECMWF wind data has a time step of 6 hours. Some peak values will probably be missing. Both effects result in underestimations and overestimations in the computed significant wave height, especially in storm situations.

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E u r o - 0S ig n i f i c a n t w a v e h e ig h t 2 1 S e p t e m b e r - 1 5 N o v e m b e r 1 9 9 6

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b u o yS W A N

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b u o yS W A N

Fig. 6. The measured (crosses) and computed (lines) significant wave height at Euro-0 and YM6 during a 56 days

period (21 September - 15 November 1996). Figure 7 shows that the zero-up crossing period usually is underestimated. The underestimations in the zero-up crossing period are larger than the underestimations in the significant wave height (respectively 0.8 s and 0.2 m averaged). The computed and measured mean wave direction compare quite well (see Figure 8), the difference is mostly not larger than 10º. The difference is large in situations of fast turning winds. This is a result of the coarse wind input.

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E u r o - 0Z e r o u p c r o s s in g p e r io d 2 1 S e p te m b e r - 1 5 N o v e m b e r 1 9 9 6

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S W A Nb u o y

Fig. 7. The measured (crosses) and computed (lines) zero-up crossing period at Euro-0 and YM6 during a 56 days

period (21 September - 15 November 1996).

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E u r o - 0M e a n w a v e d i r e c t io n 2 1 S e p te m b e r - 1 5 N o v e m b e r 1 9 9 6

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T im e [ d a y s ]

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Fig. 8. The measured (crosses) and computed (lines) mean wave direction at Euro-0 and YM6 during a 56 days

period (21 September - 15 November 1996).

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E u r o - 0S ig n i f ic a n t w a v e h e ig h t a n d w in d s p e e d 2 1 S e p te m b e r - 1 5 N o v e m b e r 1 9 9 6

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S ig n w a v e h e ig h t [m ]W in d s p e e d [B e a u fo r t ]

Fig. 9. The significant wave height (black continued line) and associated wind speed (grey dotted line) at Euro-0 and

YM6 during a 56 days period (21 September - 15 November 1996). From Figure 9 it can be concluded that the significant wave height follows the wind speed nicely. A correct wind input is thus important. Concluding Remarks It can be concluded, that the wind-wave model gives generally good results. The results can however be improved by more detailed wind input and a numerical scheme, which does not give such a large numerical diffusion (approximately 54 % of the incoming waves at the boundary are lost by the numerical diffusion). These problems are being resolved. The ECMWF re-analysis is done on a global grid for a 40-year period. Hence, the above example can also be done for a specified locations at the coast of e.g. Australia and for specified periods and multi times of that period. Wave scatter diagrams can be made from the above-presented integral wave parameters, if the wave climate is computed over a longer period (at least 5 years). This can also be done for a specified period or season (for example autumn) and for only swell or wind sea. The ECMWF delivers the integral wave parameters of swell and wind sea namely also separately. SWAN does not make a distinction between swell and wind sea yet, but these different spectral components can be distinguished quite easily.

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METHOD OF DOWNTIME PREDICTIONS

Determination of Downtime Lines If the criteria for a certain dredge are known, the operational limits (= downtime lines) as function of the water depth, the weather condition in terms of wave spectra with associated significant wave height, zero-up crossing period and wave direction, the current and wind speed and direction. For the determination of the operational limits of a DT trailing suction hopper dredge both the waves, current and wind and their associated directions have to be specified. For the cutter suction dredge in general only the waves and directions have to be defined. Concerning waves distinction can be made in the integral wave spectra (1-D) and combined wind wave and swell spectra from different directions (2-D). Considering the long-term wave simulation, the integral wave parameters being the Hs as function of T2 and average wave directions can be determined, achieving the associated wave scatter diagrams. Scatter diagrams with a relative large number of wave directions may be obtained. These 1-D data can be used for the computation of the down time points. In case the long-term wave simulation clearly expresses directional spreading of wind waves and swell both components have to be considered. From the long-term wave simulation the wind wave properties Hsw, T2w and direction μw and the swell properties Hss, T2s and direction μs can be classed. A large number of classed combinations can be obtained. These 2-D data can be used for the computations of the downtime points. As an example in the following the general procedure to determine the downtime lines for a suction cutter dredge is described. The 1-D wave data In Table 1 a scatter diagram (without distribution) is given for a large number of possible combinations of wave spectra. The T2 periods ranging from 6 to 19 seconds while the Hs are between 0.1 to 2.9 m. It is assumed that the spectrum forms correspond to a JONSWAP formulation with γ=3.3. The actual range of Hs and T2 and the spectral form may depend on the actual scatter diagram. The present diagram is e.g. valid for a water depth of 15 meter, while the suction cutter dredge is working in head waves (180°). To determine downtime lines for a suction cutter dredge two methods may be distinguished: - frequency-domain computations and - time-domain computations. Frequency-Domain. As mentioned before, in general the system of a cutter suction dredge with the ladder in hoisted condition can be considered as linear and the computations may be carried out in the frequency-domain. For this purpose it is assumed that the interface between spud pole and seabed acts as a universal joint. Further friction between the spud pole-spud keepers and slackness of the swing wires are neglected. In this case the dredge can be exposed to a spectrum with a significant wave height of 1 m, while the mean zero-up crossing period can be 6.5, 12.5 and 18.5 s, see Table 1. The result of the computations is for instance the standard deviation of the spud pole for each of the mentioned periods. The criterion of the spud pole may be defined as the most probable maximum (MPM) force. Based on the MPM force, by means of (linear) spectral analysis the limiting significant wave height for each of the periods can be directly determined (= downtime points). By fairing the downtime points the downtime line can be determined for this specific criterion. If the downtime line as function of period is strongly non-linear additional periods may be considered. The procedure can be repeated for other criteria. For another wave direction another sheet should be used. Time-Domain. In operational condition (cutter head is working in the breach) computations must be carried out in the time-domain (non-linear system). In this case for each wave spectrum a separate time-domain computation has to be carried out. To minimize the number of computations, a number of fixed points in the wave-period sheets can be chosen. The choice may depend on the spectra as known of the actual scatter diagram. In this case, see Table 1, 9 points were chosen. For each point the time-domain computations are carried out. The criterion is for instance the longitudinal hinge force of the ladder and defined as the MPM force. From each computation the MPM force of the hinge can be derived using for instance Weibull paper. In total 9 MPM forces can be obtained. By fairing the MPM-forces as function of Hs (constant T2) and by fairing the MPM-forces as

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Table 1. Wave-period sheet for a cutter suction dredge (water depth 15 meter, wave direction 180°). 2.7 < 2.9 m 2.5 < 2.7 m 2.3 < 2.5 m 2.1 < 2.3 m 1.9 < 2.1 m 1.7 < 1.9 m 1.5 < 1.7 m 1.3 < 1.5 m 1.1 < 1.3 m 0.9 < 1.1 m 0.7 < 0.9 m 0.5 < 0.7 m 0.3 < 0.5 m 0.1< 0.3 m Hs \ T2 6-7 s 8-9 s 10-11 s 12-13 s 14-15 s 16-17 s 18-19 s function of T2 (constant Hs) and comparing the values with the value of the criterion the downtime points can be approximately determined. By fairing the downtime points the downtime line can be determined for this specific criterion. If the downtime line seems to be strongly non-linear additional points may be considered. The procedure can be repeated for another criterion. For another wave direction a new set computations have to be carried at and implemented on another sheet. The 2-D wave data As said in case the long-term wave simulation clearly expresses directional spreading of wind waves and swell both components have to be considered. From the long-term wave simulation the wind wave and swell properties can be classed. A large number of classed combinations may be obtained. In Table 2 an example is given of a combination. Table 2. Combination of wind waves and swell for a cutter suction dredge (water depth 15 meter, wind wave direction 180°)

Wind waves Swell Hs in m 1.2 0.5 T2 in s 8 14 Dir. in degr. 180 225 Spectral form Jonswap γ=3.3 Gaussian In the combined cases time-domain computations have to be carried out for both the hoisted and working condition of the suction cutter dredge. Dependent on the number of classes and by interpolation the results using the MPM of the selected criterion the downtime points for the 2-D cases can be approximated. In contrary to the determination of the down time lines in the 1-D procedure, the determination of the down time lines in the 2-D cases somewhat more complex. In principle, however, the procedure is the same.

METHOD OF JOB DURATION PREDICTIONS It is assumed that the method of the determination of the average downtime of a project using scatter diagrams is known. A more realistic approach to predict the downtime during a project is the method of the long-term time-domain simulation. The basis for the method of the average job duration and statistical distribution of the job duration is the wind-wave model, the 1-D or/and 2-D downtime lines and the scenario’s. Based on the wind-wave models, time series can be generated which may last for multi-times the net project duration (NPD) providing sufficient reliable statistical information with respect to number of interruptions, waiting time, loss of production etc. The NPD stands for the anticipated calm water duration of the project. By means of the earlier

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mentioned downtime lines and the scenarios applied to the long-term weather condition, the average real project duration (RPD) and the statistical distribution function (standard deviation) of the duration of the job can be determined. The percentage of the average downtime can be determined according to ((RPD-NPD)/RPD)*100%, while the standard deviation of the distribution function is a measure for the spread of the job duration. Examples are given in van den Bos, 1998.

CONCLUSIONS In this paper the outline on the developments to predict the downtime of dredges operating in the open sea as is underway at MARIN is given. The determination of the operating limits in these sea states (downtime points) is of prime importance. If these downtime points or lines are known, the downtime can be calculated as an average downtime by using scatter diagrams. Although it may give valuable information, it does not give the real downtime during a project. A more realistic approach to predict the downtime during a project is the method of the long-term time-domain simulation. In respect to the last mentioned approach, the determination of the limiting seastates can be considered as reliable tools, while the generation of the necessary long-term wave simulation is progressing considerably well. Together with the criteria and with the applied scenario’s, it is expected that in the near future the present method will make it possible to predict in a reliable statistical manner the realistic duration of a project to be carried out in the open sea.

ACKNOWLEDGEMENTS

The authors wish to thank the following persons: • R.A. Grin who made the SWAN validation computations for his studies at the college of advanced technology

in Haarlem, the Netherlands. • R.P. Dallinga (MARIN) who is the motor behind the development of the wave climate computations. • A.P. Roskam of the National Institute for Coastal and Marine Management (RIKZ) for providing us the wave

buoy data from the DONAR database of the Directorate-General of Public Works and Water Management (Rijkswaterstaat).

• S. Kruizinga of the Royal Netherlands Meteorological Institute (KNMI) who delivered us the ECMWF wind and wave data.

REFERENCES

Claessens, E.J. and Dallinga, R.P. (1999). “The implementation of wind-wave models in ship design.” MARIN

memo, KIvI lecture, April 1999, Delft, The Netherlands. Dingemans, M.W., Petit, H.A.H. and Ris, R.C. (1998). “Application of SWAN in the Southern North Sea.” Report

no. H3292 WL|Delft Hydraulics, Delft, The Netherlands. Holthuijsen, L.H., Booij, N. and Ris, R.C. (1993). “A spectral wave model for the coastal zone.” Proceedings of 2nd

International Symposium on Ocean Wave Measurements and Analysis, New Orleans, USA, 630-641. Holthuijsen, L.H., Booij, N., Ris, R.C., Haagsma, IJ.G., Kieftenburg, A.T.M.M. and Padilla-Hernandez, R. (1999).

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Komen, G.J., Cavaleri, L., Donelan, M., Hasselmann, K., Hasselman, S. and Janssen, P.A.E.M. (1994). Dynamics and modelling of ocean waves. Cambridge University Press, Cambridge, United Kingdom, ISBN 0-521-493291-X.

Ris, R.C., Holthuijsen, L.H. and Booij, N. (1994). “A spectral model for waves in the coastal zone.” Proceedings of 24th International Conference Coastal Engineering, Kobe, Japan, Volume I, 68-78.

Ris, R.C. (1997). Spectral modelling of wind waves in coastal areas. PhD Thesis, Delft University of Technology, Communications on Hydraulic and Geotechnical Engineering, Report No. 97-4, ISBN 90-407-1455-X.

Van den Bos, L. (1998). “Bepaling van de werkbaarheid van materieel offshore”, Master Thesis, Delft University of Technology, Delft (in Dutch).

Wichers, J.E.W. (1987). Handbook of Coastal and Ocean Engineering, Volume 3, Chapter 7. “The behavior of dredging equipment operating in waves”, ISBN 0-87201-452-5.

WMO (1998). Guide to wave analysis and forecasting. Second edition. WMO report no. 702.