Screwed-up Riprap: Sizing Rock Linings to Resist Ship Propeller-jets by David C. Froehlich and Conor C. Shea Downloaded from ascelibrary.org by North Carolina State University on 09/01/13. Copyright ASCE. For personal use only; all rights reserved. Parsons Brinckerhoff Quade and Douglas, 909 Aviation Parkway, Suite 1500, Morrisville, North Carolina 27560 (tel: 919-468-2 131, e-mail: froehlich@pbworld.com). 2Parsons Brinckerhoff Quade and Douglas, 301 North Charles Street, Suite 200, Baltimore, Maryland 21201 (tel: 410-385-4182, e-mail: shea@pbworld.com). Prologue The only underwater international vehicular (automobile) tunnel in the world owes its existence to Fred W. Martin, a Windsor, Ontario Salvation Army Captain who said he was inspired by God to have the tunnel under the Detroit River built. It was not God, however, but the New York City engineering firm Parsons, Klapp, Brinckerhoff and Douglas (designers and builders of the Holland Tunnel in New York) who Martin visited one day in 1926 to see if such a tunnel could be built and operated profitably. Confident that the project was indeed feasible, and with urging from Martin who suggested that it would probably be six dozen Sundays or more before the politicians would agree on anything, so how about taking a flyer on this as a private project? the engineers not only agreed to design the tunnel but to guarantee its costs. The privatelyfinanced, privately-built, and privately- Figure 1. Section of the submerged tube portion of the Detroit-Windsor Tunnel being prepared. operated 2.4 km (1.5 mi) tunnel connecting Detroit, Michigan and Windsor was completed in 1930 after 26 months of construction, and to this day is a major border crossing and a vital socio-economic link between the United States and Canada. The engineering firm, now Parsons Brinckerhoff (PB), designed the tunnel to be built by three methods: cut-and-cover work for the entrances, shield-driven tunnels from the entrances to the river, and submerged tube for the half-mile river section. Approach sections, about 180 m long at each end, were built similar to subway tunnels in New York City. Figure 2. The 2,4 km (1.5 mi) tunnel connecting Detroit, Michigan and Windsor, Ontario, completed in 1930 after 26 months of construction, is the only subaqueous international vehicular (automobile) tunnel in the world. The shield-driven sections were the first to use welded structural steel segments instead of bolted cast iron as primary lining. The submerged section was built of nine steel tubes each 76 m long which were floated into place and then sunk in an excavated trench. 1
Their construction required 65 miles of arc welding, its first major use in tunneling history. Ownership of the Canadian half of the Detroit-Windsor Tunnel reverted to the city of Windsor in 1990, ending a 60-year franchise agreement with the Detroit & Canada Tunnel Corporation, which still maintains control of the Detroit side of the tunnel. Introduction Whatever their source of power, modern large ships (Figure 3) are moved through water by one or more propellers Figure 3. Inland cargo ships continue to increase in size and power, expanding the potential for erosion of waterway beds by propeller jets. (Figure 4). Propellers act in water as screws act in wood (in fact, ship propellers are called screws), propelling a vessel forward as they rotate and generating fast-moving turbulent streams of water (called jets or races) that have axial, radial, and tangential velocity components. As ships become larger and more powerful the potential for erosion of waterway beds by propeller jets increases. When combined with large vessel drafts, high-speed propeller jets having axial velocities of more than 12 m/s can scour sediment from around the foundations of marine structures, and remove essential cover from buried pipelines, tunnels, and aquatic disposal sites. Propeller-induced scour is a serious factor to be considered when designing marine structures or submerged river crossings where ship traffic is present, and is often most severe when a stationary ship begins to move in a shallow waterway. As a ship propeller draws fluid into itself, large inflow velocities can occur near the waterway bed directly under the propeller within a circular area of approximately twice the propeller diameter. In the jet formation region downstream of the propeller, fluid accelerates for a distance of from two to three times the propeller diameter, rotating about the core as well as moving axially (Figure 5). Velocity is Figure 4. Ship propellers act in water like screws, propelling a vessel forward as they rotate by generating fast-moving streams of water called jets or races. nonuniform in this region, with fluid passing close to the blades moving faster than the remainder of the flow, and the jet diameter decreases in the downstream direction. Finally, the jet begins to spread, gradually entraining more of the surrounding fluid. As the jet expands it becomes more uniform circumferentially and resembles closely the flow due to a simple axial jet issuing from a pipe. Because of the spreading, the jet will eventually impinge on the waterway bed.
A common method of protecting waterways against erosion from propeller jets is to dump rock riprap (Figure 6) on beds and banks of channels. The loose rock forms a flexible facing or lining that typically does not fail catastrophically and can be repaired during regular maintenance. Although several empirical formulae for estimating the rock size needed to resist propeller jet erosion have been proposed, they are implicitly connected to other relations for estimating near-bed velocities and bed shear stresses. A consistent approach for sizing dumped rock riprap needed to resist large bed shear stresses produced by ship propeller races is described and is tested using scale-model experimental data. The resulting expression for sizing riprap, which is based on a combination Expanding jet - 3n h qn - I,/I-+ L Propeller jet origin (x = 0) Figure 5. Definition sketch of a propeller jet showing the formation region immediately behind the jet, and the expansion region beginning approximately two to three propeller diameters away from the propeller. of theory and empiricism, is substantiated by the experimental data but is not conclusive. Propeller Jets The expanding jet begins approximately two to three propeller diameters from the propeller, where the velocity field becomes similar to the field produced by a momentum jet. Considering the propeller to be an actuator disk (White 1994, pages 682-683) having a diameter equal to the propeller diameter, axial velocity at the origin of the expanding jet region is given by Figure 6. 4 common method of protecting waterways against erosion from propeller jets is to dump rock riprap on the beds and banks of channels. U. = 1.6npDp& (1) where np = number of propeller revolutions per second, Dp = propeller diameter, and KT = propeller thrust coefficient for a stationary vessel. Values of KT depend on propeller properties, whether the propeller is ducted or open, and the ratio of propeller pitch Pp to propeller diameter. Recommended values of KT for ducted and open propellers for several pitch to diameter ratios are given in Table 1. When the thrust coefficient and propeller speed are not known, U, can be approximate using the formula given by Blaauw and van de Kaa (1978) as PO U. = 1.48 - (2) PD,2 I I *
Table 1. Propeller Thrust Coefficient K, as a Function of Propeller Pitch/Diameter Ratio for Stationary Vessels. 0.6 0.26 0.24 0.8 0.37 0.37 10 0.48 0.51 1.2 0.57 0.67 1.4 0.54 0.82 where P/, = installed engine power in watts, and p = water mass density. Axial velocity of an expanding stationary propeller jet is calculated by Fuehrer et al. (1987) as follows: whert 3 22.22 Ur=Umme x2 (3) u max I AU, afrom Presser (I 986). is the maximum velocity along the jet axis, D, = initial jet diameter, r = jet radius (that is, the perpendicular distance to the propeller axis), x = axial distance form the jet origin, and A, a = empirical coefficients. The initial jet diameter can be found as a fraction of the propeller diameter, that is, Do = k,dp5 where k/, = 1.O for ducted propellers, and 0.71 for non-ducted or open propellers. Fuehrer et al. (1987) find the coefficient A to depend on the presence of a rudder immediately behind the propeller as follows: 88e - O.O92(H/DJ., without a rudder 1.88e - o 161 ~ Dp); with a rudder where H = water depth, and HP = vertical distance between the propeller axis and the waterway bed. The exponent a is given by Oebius (1984) as a = i u aexp - 1.2 Uo where U,, = ambient velocity and a = 0.6 for single-propeller vessels, 0.3 for single-propeller vessels with jet expansion limited by walls, and 0.25 for twin-propeller vessels (Fuehrer et al. 1987). Substituting (4) into (3) for U,,, and letting r = Hp gives maximum near-bed velocity as = Ae-0.5 a (4) (5) (6) (7) Sizing Rock Wiprap A relation between the bed shear stress that can be tolerated by a mixture of riprap particles and the bed shear stress imparted by a propeller jet is needed to find the size of rock riprap that resists erosion. For fully turbulent flow, velocity near the bed is given by the expression (Keulegan I 93 8) 4
J -- where U, = r,/p is the bed shear velocity, rr, = bed shear stress, p = water mass density, y = vertical distance above the bed, and k, = roughness height. Following Campbell (1966), near-bed velocity is calculated a distance y = k, above the channel bottom, which gives Ub = 8.52 Ut and zb= cjpull where cr== 0.0138. A relation for critical bed shear stress rc based on a static analysis of overturning and resisting moments acting on a single rock particle given by Froehlich (I 997) reduces to S t c = TT;c* t 1 -!- - 1 pgd,, SF for horizontal beds conditions with small water-surface slopes, where r,* = dimensionless critical bed shear stress or Shields parameter, S, = specific gravity of the rock, SF = safety factor against overturning (1 5 SF < S,), and D,, = median riprap particle diameter. Equating expressions for rh and r,, substituting (7) for lj, setting cr = 0.0138, and setting rcr = 0.045 yields the following expression for D,, /HP: - D50 z 0.3 0.15kp\l;-i $ H P P I a 2 u,z S ---!-- 1 SF Testing and Safety Factors Safety factors needed to assure stability of a protective riprap layer are evaluated in the based on a series of scale-model experiments carried out by Maynord (1984) to find the size of riprap needed to withstand the erosive action of towboat propeller jets common to deep-water ship channels in the Unjted States. The expression for median riprap diameter given by (10) for safety factors SF = 1.O, 12, and 1.5 with S, = 2.65 is shown in Figure 7 along with the experimental data for stable and unstable (failed) conditions. Although the data do not reveal a distinct difference between stable and unstable conditions, the largely theoretical relation given by(lojwithsp= 1.0 provides a good fit to the region of overlapping stable and unstable measurements The riprap relation with SF = 1.5 shown in Figure 7 completely envelops the failed measurements, while the relation for SF = I.2 yields a stable solution that is likely to yield a riprap layer that will remain stable under the action of a high-speed propeller jet, provided adequate filters are installed and the layer is of sufficient thickness. Some displacement of riprap particles is likely if smaller safety factors are used. However, the results of this analysis are not conclusive and additional experimental studies are needed to provide more accurate descriptions of propeller jet development and jet-induced bed shear stress. (8) (9)
Example Application Size of riprap needed to resist erosion from propeller jets created by the 300-m (1000-i?) class cargo vessel shown in Figure 8 and described in Table 2 is calculated to show how the formula is applied. The ship s propellers are assumed to be initially stationary in an average downstream river current of 0.6 m/s, and then accelerated to full speed, creating the most extreme jet forces. Riprap specific gravity S, = 2.65, and safety factor SF = 1.O are assumed. Calculated near-bed velocities U, and median riprap diameters D,, for water depths ranging from 8.5 m (maximum vessel draft) to 15 m (maximum channel depth) are shown in Figure 9. Riprap diameters range from 0.4 m, for the deepest river flows, to 1.2 m for the shallowest. Large in 0.6 0.5 0.4 D50iHp 0.3 0.2 0.1 p i -1 0.0 0.0 0.5 1.0 1.5 Figure 7. The expression for median riprap diameter given by (10) for safety factors SF = 1.0, 1.2, and 1.5 with S, = 2.65 is shown along with experimental data for stable (blue circles) and unstable or failed (red circle) conditions. comparison to riprap commonly used to protect channel beds and banks from river currents occurring during large floods, the calculated sizes provide grounds for believing in the erosive power of high-speed ship-propeller jets. Calculations with PB Riprap Calculation of riprap diameters using (10) is laborious. However, the computational procedure is included in the PB Riprap computer program which allows rapid stability assessment of existing riprap layers, or design of new protective surfaces based on hydraulic and riprap properties. A screen capture of the PB Riprap Propeller page is shown in Figure 10. Hydraulic parameters that describe the propeller and the channel are entered on the tabbed notebook page titled Hydraulic Properties on the left of the screen. Riprap parameters describing the gradation, specific gravity, angularity, and median diameter (for analysis calculations) are entered on the tabbed Figure 8. 300-m class cargo vessel traveling upstream on the Riprap Properties page also located on the left side of the screen. Detroit River in the vicinity of the Detroit-Windsor Tunnel. 6
Table 2. looo-ft (300-m) Class Vessel Information for Propeller Jet Analysis Vessel Parameter (1) Draft Length Beam Propeller diameter Number of propellers Propeller speed Maximum propulsion thrust Description (2) 8.5 m 310m 32 m 5.2 m 2 110-120 revs/minute SOOO-brake horsepower per shaft For analysis of an existing lining check the analysis mode button and specify D,, on the Riprap Properties page. When designing a new riprap lining, check the design mode button on the top right of the screen and enter the desired safety factor on the tabbed method page (preferably the Froehlich and Shea page) located on the right of the screen. Once all needed data have been entered, a simple click on the Calculate button generates the solution (the safety factor SF for analysis mode, or the median riprap diameter D,, for design mode.) Summary and Conclusions Distance from propeller 3m Sizes of loose dumped rock riprap axis to keel needed to withstand bed shear stresses caused Maximum propeller 4.9 m by high-speed jets created by ship propellers pitch are evaluated based on a combination of Propeller ducts Non-ducted hydraulic theory and experimental evidence. Rudder type Central rudder on each Experimental data support stability predictions propeller - given by the derived expression and are used to establish safety factors needed to provide rock sizes suitable for design, 41though evidence indicates good prediction of stable riprap sizes, the data are limited in scope and, therefore, the findings are not conclusive. Additional studies are needed to corroborate the results given here, test other propeller and rudder configurations, improve estimates of propeller jet characteristics, and establish more reliable safety factors. qpw 8 7 6 5 1.2 1.0 0.8 0.6 D,, (m) 4 0.4 8 IO 12 14 16 Water Depth, H (m) Figure 9. Calculated near-bed velocities U,, and median riprap diameters Di,, for water depths ranging from $3 m (maximum vessel draft) to 15 m (maximum channel depth) for the example vessel. 7
Figure 10. PB Riprap Propeller page. Hydraulic parameters that describe the propeller and the channel are entered on the tabbed notebook page titled Hydraulic Properties on the left of the screen. Riprap parameters describing the gradation, specific gravity, angularity, and median diameter (for analysis calculations) are entered on the tabbed Riprap Properties page also located on the left side of the screen. Epilogue In addition to connecting the United States and Canada, the Detroit-Windsor Tunnel links PB S past and present. From design in the late 1920s to construction to maintenance and preservation, during the past 70-plus years PB has played key roles in the history of the tunnel. When the protective subaqueous cover began to erode as a result of water movement generated by propellers of ever larger and more powerful cargo ships, PB began a major underwater inspection and rehabilitation of the tunnel. Project manager Vahan Tanal coordinated PB s effort, which involved staff in New York and Baltimore, as well as local staff in Detroit. The PB team paid special attention to the Detroit River environment to ensure the rehabilitation would not endanger aquatic habitat. Placing new fill and large riprap atop the tunnel was PB s solution to the erosion. We used a simple, effective and economical method, explains Tanal. The client appreciated PB s focus on quality, schedule and budget. Lou Romano, the Windsor Tunnel Commission s assistant commissioner of works, asserts that the fast-tracking of the design and construction staging saved time without increasing costs on this vital project. Donald Vuchetich, president, Detroit & Canada Tunnel Corporation, says, The thoroughness of PB s analysis gives us comfort that all engineering issues were assessed, and conclusions and recommendations were well-conceived. 8
References Blaauw, H. G., and van de Kaa, E. J. (1978). Erosion of bottom and sloping banks caused by the screw race of maneuvering ships. Publication No. 202, Delft Hydraulics Laboratory Delft, The Netherlands. Campbell, F. B. (1966). Hydraulic design of rock riprap. Miscellaneous Paper No. 2-777, U.S. Army Waterways Experiment Station, Vicksburg, MS. Froehlich, D. C. (1997). Riprap particle stability by moment analysis. Managing Water. Coping with Scarcity and Abundance: Proceedings of Theme A. ASCE, New York, NY, 172-177. Fuehrer, M., Pohl, M., and Riimisch, K. (I 987). Propeller jet erosion and stability criteria for bot.tom protections of various constructions. Bulletin No. 58, PIANC, Brussels, Belgium, 45-56. Keulegan, G. H. (1938). Laws of turbulent flow in open channels. Journal of Research, National Bureau of Standards, Washington, D.C., 7-l to 7-22. Maynord, S. T. (1984). Riprap protection on navigable waterways. Technical Report HL-84-3, Waterways Experiment Station, Vicksburg, MS. Oebius, H. U. (1984). Loads on beds and banks caused by ship propulsion systems. Flexible Armoured Revetments Incorporating Geotextiles, Thomas Telford Limited, London, United Kingdom, 13-23 = Prosser, M. J. (1986). Propeller induced scour. Report No. RR2570, The British Port Association, London, United Kingdom. White, F. M. (1994). Fluid mechanics ( 3rd edition). McGraw-Hill, New York, NY. 9