Probabilistic Design Tools

The DUKC (Dynamic UnderKeel Clearance), CADET (Channel Analysis and Design Evaluation Tool) and UNDERKEEL are examples of existing probabilistic design tools that are presented in this section. Many laboratories and government agencies have

equivalent probabilistic design tools for deep draught navigation in entrance channels. In the future, one can expect that these types of technology will become the norm rather than the exception as channel design is optimised for safe, economical and efficient navigation. The designer needs to be careful in judging the input and evaluating the output of such models. The dynamics of the channel bed and the human element in causing events of risk should be carefully taken into consideration, preferably by experienced engineers. The final decision on the depth of the navigation channel should be determined using as many quantified and qualified risk factors as realistically possible, in addition to economic and environmental considerations.

Dynamic UKC Technology

The key to probabilistic design lies in the derivation and construction of accurate and representative probability distributions of the various UKC factors. Incorrect assumptions about independence of UKC factors or the shape of their distributions lead to errors in the assessment of the risk of bottom touches. One method of reducing the impact of these assumptions is by combining statistical and deterministic methodologies in the evaluation of an entrance channel design. An example of this type of probabilistic design tool is the DUKC technology [Atkinson and O’Brien, 2008 ; O’Brien et al., 2012]. The DUKC system deterministically assesses the UKC of a vessel with a known load condition and speed and track under specific met-ocean conditions. By simulating vessel movements over many years of use it is possible to assess the risk of bottom touching, waterway capacity and optimised depths through statistical analysis of the simulated UKC data.

Aside from the reduced need for accurate and representative probability distributions, the advantages of a combination of deterministic simulations with statistical analysis methodologies are:

 Allows the entrance channel design to be evaluated against one or more UKC (or other safe navigation) criteria simultaneously. The DUKC primarily evaluates UKCNet

and Manoeuvrability Margin as outlined in sections 2.1.2.7 and 2.1.2.8, but other criteria affecting safe navigation may be included. For example, one could select (a) minimum vessel separation distances or (b) maximum allowable wind and current speeds for safe vessel operations

 Allows the entrance channel design to be optimised to specific needs of its users. For example, rather than considering vessel sailings in isolation it is possible to optimise an entrance channel design to allow multiple deep draught sailings on a single tide.

Not only does this permit the assessment of UKC safety, but also economic design aspects such as waterway capacity and throughput.

Channel Analysis and Design Evaluation Tool (CADET)

Another example of a probabilistic design tool is the CADET described by Briggs et al.

(2006, 2012, 2013), Briggs and Henderson (2011), and Briggs et al. (2013). It predicts channel accessibility for acceptable levels of risk based on Gaussian and Rayleigh distributions and an Ochi extremal analysis of UKC from ship motion allowances for different wave, ship and channel combinations. Wave conditions are usually based on historical record of local waves through either hindcast or measured values. This historical record is composed of the persistence of joint distributions of wave height, period and direction on an annual basis. Accessibility is determined by calculating the risk of a ship impacting a project depth given the wave conditions in the channel.

Deterministic methods might allow 100 % accessibility, but at a cost of additional dredging and an overly conservative channel design. The CADET predictions allow the designer to choose a channel depth with reduced accessibility for an acceptable level of risk.

CADET does not include the effects of heeling due to wind on ship UKC or channel width design elements. The interested user should refer to the references listed above for additional details of CADET.

Example CADET Application

CADET was applied to the modification of the entrance channel at Savannah, Georgia (USA). The goal of the Savannah Harbor Expansion Project (SHEP) was to evaluate three proposed channel options to accommodate next-generation post-Panamax (New Panamax) ships. The proposed Outer Channel is subject to waves and has a length of up to 37.5 km, width of 183 m, and maximum project or dredge depth of 14.9 m beneath the reference level of Mean Lower Low Water (MLLW). The project depth is restricted due to buried utilities, dredging costs, offshore reefs and environmental and political considerations. Each channel option consisted of six reaches, where a reach is required when changes in channel width, depth, or alignment occur.

The design ship was the Susan Maersk container ship with a capacity of 8,680 TEUs, Lpp = 331.6 m, B = 42.8 m and typical Vk = 8 to 14 knots. Two loading conditions with corresponding draughts were evaluated: light-loaded T = 14.0 m and fully-loaded T = 14.5 m. During right whale season, a maximum Vk = 10 knots is allowed in the Outer Channel to reduce the risk of collisions with a whale. Ship inputs included ship lines or hull offsets from the keel to deck-at-edge at 21 equally spaced stations between the forward and aft perpendiculars and bow and stern profiles. Additional inputs included longitudinal and vertical centre of gravity; roll damping factor; roll and pitch gyradii; wave frequencies for calculating response amplitude operators for heave, pitch, and roll; and critical point locations along the keel for evaluating UKC.

The US Army Corps of Engineers requires a minimum Gross UKC of 1.2 m. Because of environmental constraints on the maximum project depth, the tidal range up to 2.4 m is required to ensure safe navigation. Water depths in 30 cm increments were evaluated from a low tide value of 14.6 m up to a high tide value of 17.4 m MLLW (i.e. this range includes starting at existing depth, 2.4 m high tide maximum increase in depth and small increase at high end in case additional dredging is allowed). Of course, these tide heights only occur for limited durations and days each year so that the pilots will have limited sailing windows during any given day of a year.

Ninety-nine directional wave spectra were simulated using a TMA (Texel, Marsden and Arsloe) frequency spectrum and a cosⁿ directional spreading function. The parameters for these spectra were obtained from a joint probability distribution of wave height and period that was obtained from a WIS (Wave Information Study) 20-year hindcast at the nearby WIS370 deepwater buoy. A coefficient of variation is used to account for uncertainty in the wave measurements or predictions. Also, the probabilities of occurrence for each wave are used in the CADET predictions. The spectral wave heights were reduced at each reach along the Savannah channel according to wave transformation study results.

Ship squat was included using the Beck-Newman-Tuck (BNT) algorithm that is incorporated in CADET. The BNT is based on the dynamics of a slender ship in a finite-width inner channel with an infinitely wide outside channel of shallow depth. Uncertainty in ship sinkage and trim is included in CADET. Additional comparisons of squat were made with Ankudinov and PIANC squat predictors. The BNT squat predictions were included in the CADET UKC analysis.

The CADET tidal analysis indicated that a depth of 15.2 m MLLW would be present for durations of 8 hours and a depth of 15.8 m MLLW for durations of 6 hours every day of

every year. These durations are continuous time spans where the water level is at or above the indicated threshold each day. Water depths of 16.1 m to 17.4 m MLLW would have continually decreasing durations from 4 hours (365 days per year) to 1 hour (7 days per year). Of course, the durations must be long enough to allow the ship to safely transit the Outer channel as well as the 31 km-long Inner Channel. For the Outer Channel, transit times range from 1 to 3 hours based on channel length and ship speed from 8 to 14 knots, so that the 6 to 8 hours durations should be sufficient.

CADET predicted days of accessibility for light- and fully-loaded ships, inbound and outbound transits, speeds of 6 to 14 knots and depths of 14.6 to 17.4 m MLLW. To account for uncertainty and risk, CADET includes a motion risk factor α and a channel reach risk level β in its predictions. Both of these risk factors are adjustable by the user.

Values of α = 0.01 and β = 0.01 were used in this application. The α = 0.01 means that the ship has a 1 in 100 probability that the predicted motions allowance will be exceeded for the given set of wave conditions. The general rule is that if the probability of ship touching a flat channel bottom is less than 1 in 100 (i.e. this α) for each wave in a climatology during a given transit, then the channel is considered accessible for that depth. Similarly, the β = 0.01 represents the probability of one of the critical points on the ship (i.e. bow, stern, amidships) touching the project depth in a particular reach. It takes into account the uncertainties in depth measurements, dredge variability and over-dredge allowance. In general, the days of accessibility increase for slower ship speeds, outbound transits, interior reaches and light load conditions.

The days of accessibility assume the water depth is available 100 % of the time. When using tides, however, this is usually not the case as water levels have the limited durations discussed above. Therefore, the days of accessibility predicted by CADET were reduced by the relative percentage of the tide level. For example, a tide level occurring only 25 days per year is equivalent to only 6.8 % (i.e. 25/365). Thus, the CADET-predicted number of days of accessibility is multiplied by this tide level percentage to obtain the reduced days of accessibility when the tide level is occurring less than 365 days per year (i.e. every day of a year). Of course, this is somewhat simplistic and conservative as it assumes that the tide and waves are in phase, which could, but is not likely to occur simultaneously in a real-world situation. As a design tool, however, it is probably acceptable to interpret the results in this fashion as it makes the comparisons uniform. During actual transits, the pilots would need to take the wave and tide conditions into account to ensure safe navigation during the entire transit.

The light-loaded ship is the most realistic ship expected to use the Savannah Channel as full design-draught ships rarely occur at this location. For the light-loaded ship, a minimum depth of 15.2 m will have 358 days of accessibility per year with 8-hour durations during inbound transits at 10 knots. Since this tidally-adjusted depth is available for durations up to 8 hours every day of the year, it is not necessary to reduce the CADET days of accessibility by the tide level percentage. However, if a longer duration is required, then the days of accessibility would be reduced by the tidal percentage of the desired duration since it decreases from 9 hours for 331 days (i.e. 331/365 = 90 %) to 12 hours for only 64 days (i.e. 64/365 = 17 %). Also, increased ship speed requiring deeper draughts can be accommodated if willing to accept decreasing durations of 8 hours or less as the tide level increases. For instance, at this 15.2 m depth, an 8-hour duration is possible for 338 days per year during inbound transits at 14 knots. Finally, if a larger depth is required for any ship speed, the duration will decrease along with the days per year since the tide level will not be available year round. The CADET predicted days of accessibility will be decreased by multiplying by the tidal percentage for the desired depth.

For the fully-loaded ship at a minimum depth of 15.8 m, durations up to 6 hours are available for 360 days per year during inbound transits at 10 knots. A longer duration of 8 hours is possible, but only for a reduced days of accessibility of 24 days per year (i.e.

360*25/365) since the tide is only available 25 days per year for this water depth and duration. Increased ship speed is possible at this depth for durations of 6 hours or less for 357 days per year for inbound transits at 14 knots. As before, deeper channel depths are also attainable, but result in shorter durations and reduced days of accessibility. For a ship moving at 14 knots, a channel depth of 16.1 m is possible to achieve with durations up to 4 hours for 362 days per year. A longer duration up to 6 hours of increased water depth is available, but results in reduced days of accessibility of 143 days per year. This is due to the tide level being at that height for 6 hours only 144 days per year (i.e.

362*144/365).

CADET uses wave-induced ship motions due to heave, pitch and roll in the prediction of days of accessibility. These motions are output for each ship loading condition, channel reach, water depth, wave condition, transit direction, ship speed and critical point. The 99 wave conditions represent the entire range of exposure over a 20-year design life.

Extreme wave conditions produce the largest vertical motions, but also have very small probabilities of occurrence. The user can examine individual, average, typical, extreme, or specialised ranges of wave conditions. One specialised range includes only the highest 3 % to 5 % of waves since it gives a more realistic view of design wave conditions during transits. Ships would not be affected by routine smaller waves and would not use the channels during extreme storm events. Thus, only the larger waves that would have a significant effect on the ship are retained in the analysis, although they would have very low probabilities of occurrence.

As a comparison with the Concept Design (CD) recommendations, the Savannah Channel could not be used for such large ships if a purely deterministic requirement was enforced. The user can refer to Appendix C to observe that the Susan Maersk dimensions correspond well with Table C-1. According to the CD recommendations in Table 2.2, a Gross UKC (including squat, wave response, and MM) of at least 2.1 m is required for the Outer Channel (i.e. 15 % of T). Therefore, a water depth up to 16.1 m MLLW for the light-loaded ship and 16.6 m MLLW for the fully-loaded ship is required according to the CD procedure. Although the CD predictions are reasonably close to the CADET required depth, including tide elevation, of 15.2 m MLLW for the light-loaded ship and 15.8 m MLLW for the fully-loaded ship, the CD predictions are overly conservative.

Thus, by using the CADET probabilistic predictions, the port does not have to dredge the channel as deep as the CD procedure would require. This represents a large saving in dredging costs, especially in this case of a long access channel, compared to probably minor delay costs of shipping.

In summary, both ship loading conditions can be accommodated using the available tide depending on ship speed, desired UKC, and water level duration. Transits with the deeper draught ships will require tidal assistance at all times for safety. Since the tidal water levels only occur for a fraction of any day, there may be some instances where ships will need to wait on the tides to ensure safe navigation. However, since these large ships will not be calling on the port very frequently, this should not be a problem for efficient use of the channel. The interested reader should refer to the report by Briggs and Henderson (2011) for additional technical details. For more detail on the analysis of the economic aspects of deep-draught channel optimization, the reader is referred to the report of the US National Economic Development group of USACE and IWR: ’Manual for Deep Draught Navigation’, IWR Report 10-R-4, April 2010.

UNDERKEEL

The UNDERKEEL computational model has been developed for the study of ship motions and wave forces on ships, specifically in shallow water. It employs the standard linearised wave theory with potential flow applied in the frequency domain (i.e. regular waves) to represent the behaviour of waves and water flows in the vicinity of the ship. This is implemented in conjunction with a strip or slender body theory treatment of boundary conditions at the hull adapted to allow accurately for flows underneath the keel. All six components of the vessel’s motion are computed and all components of wave force and moment. The model has been verified by comparing computed values against field measurements and measurements of the movements of physical model vessels. A typical application is the estimation of vertical motions of ships underway in a navigation channel in order to estimate the likely minimum dredged depth needed for safe transit in waves Although the model operates in the frequency domain, superposition principles can be applied. UNDERKEEL can thus be used to compute motions of a vessel or wave-induced forces acting the vessel for any given required random wave input, including short-crested (multi-directional) sea conditions. This is for both first and second-order effects and so it reproduces the full range of wave, wave-induced flow and wave force phenomena.

Second-order forces are those due to:

 Surface stress

 The Bernoulli pressure effect

 Force rotation

 Pressure displacement

 Second-order wave diffraction effects

 Set-down and associated diffracted wave fields

These force effects are proportional to wave height squared and although often small in magnitude compared to first order waves, they are important because the horizontal motions of a large ship may be dominated by low frequency components.

A particular feature is that UNDERKEEL computes forces due to set-down bound waves (which are known to be the dominant forcing effect in many shallow water cases) without resorting to an approximate treatment of wave diffraction.