Ic-23 Optimization of a Rolling And
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Joint International Conference on Computing and Decision Making in Civil and Building Engineering June 14-16, 2006 - Montréal, Canada OPTIMIZATION OF A ROLLING AND FLOATING LOCK GATE FOR THE ANTWERP PORT T. Richir1, J.-P. Pecque 2, C. Toderan3, F. Bair4 and P. Rigo5 ABSTRACT The Antwerp port authority recently decided to convert one of its shipping locks into a dedicated inland navigation lock to improve the traffic between the port and the Scheldt River. The rolling gate, considered for this lock, has to float to be led into the port for maintenance and repairing operations. Two partitioned floating tanks are used inside the gate. Water ballast can be pumped from the floating tanks to float the structure or to restore the mass equilibrium in case of damage due to ship impact. This paper presents a methodology to minimi e the weight of the gate by optimi ing simultaneously the height of the floating tanks, the number of their watertight partitions and the gate scantling while considering the floating stability (Pecquet 2005). KE, WORDS multi-ob(ective optimi ation, LBR-5 software, floating lock gate INTROD-CTION Antwerp (Belgium) is less than 100 km away from the embouchure of the Scheldt River into the ,orth Sea so that the Scheldt River is there still sensitive to the tides. To keep a constant water level inside the Antwerp port, seven shipping locks are used (-igure 1). The Antwerp port authority recently decided to convert one of these shipping locks (the .an Cauwelaert lock) into a dedicated inland navigation lock to improve the traffic between the port and the Scheldt River. A rolling gate, so-called 0wheelbarrow1 or 0lateral displacement gate1 (P2A,C 1385), is considered for this lock (-igure 2). 2ts dimensions are 35 7 8 7 13 m (length 7 width 7 height). 9oreover this gate has to float to be led into the port for maintenance and repairing operations. Two partitioned floating tanks are thus used inside the gate. Water ballast can be pumped from the floating tanks to float the structure or to restore the mass equilibrium in 1 Ph.D. Student, -.R.2.A. Scholarship, A,AST, University of Liege, Bat. B52/3, Chemin des Chevreuils 1, B-4000 Liege, Belgium, Phone +32-4-3554853, -a7 +32-4-3553133, thomas.richir? ulg.ac.be 2 Pro(ect Engineer, Study and Engineering Affice, SBE, Slachthuisstraat 81, B-3100 Sint-,iklaas, Belgium, Phone +32-3-8883513, -a7 +32-3-8883883, (p.pecquet? sbe.be 3 Research Engineer, A,AST, University of Liege, Bat. B52/3, Chemin des Chevreuils 1, B-4000 Liege, Belgium, Phone +32-4-3553341, -a7 +32-4-3553133, catalin.toderan? ulg.ac.be 4 Research Engineer, A,AST, University of Liege, Bat. B52/3, Chemin des Chevreuils 1, B-4000 Liege, Belgium, Phone +32-4-3553521, -a7 +32-4-3553133, f.bair? ulg.ac.be 5 Professor, -.,.R.S. Research Director, A,AST, University of Liege, Bat. B52/3, Chemin des Chevreuils 1, B-4000 Liege, Belgium, Phone +32-4-3553355, -a7 +32-4-3553133, ph.rigo? ulg.ac.be Page 155 Joint International Conference on Computing and Decision Making in Civil and Building Engineering June 14-16, 2006 - Montréal, Canada case of damage due to ship impact. Solid ballast is placed at the bottom of the gate to ensure floating stability. Dandvliet lock Berendrecht lock Baudewi(n lock .an Cauwelaer loc1 Eallo lock Royens lock Eattendi(k lock -igure 1: 2mplantation of the Shipping Locks of the Antwerp Port E7ceptional high tide level Usual level PORT OF ANTWERP 3.00 m Constant level 4.50 m 13.13 m E7ceptional low tide level 1 Abservation tube 2 2 2 -loating tanks 1 12.34 m SCHELDT RI.ER 3 Water ballast 3 3 4 Solid ballast 10.13 m 4 1.00 m 8.12 m -igure 2: Cross-Section of the .an Cauwelaert Lock Cate Page 156 Joint International Conference on Computing and Decision Making in Civil and Building Engineering June 14-16, 2006 - Montréal, Canada The floating stability analysis of the gate is e7plained in the first part of the paper. The LBR-5 software (Rigo 2001a, Rigo 2001b, Rigo 2003) used to optimi e the gate scantling is described in the second part. The third part presents the way to minimi e the weight of the gate by optimi ing simultaneously the height of the floating tanks, the number of their watertight partitions and the gate scantlings while considering the floating stability. FLOATING STABILIT, The rolling gate considered for the .an Cauwelaert lock has to float to be led into the port for maintenance or repairing operations. 9oreover the gate has still to float with a ma7imum 8 m wide hole in one floating tank caused by a boat impact. WATER BALLAST Two partitioned floating tanks are filled partially with water ballast which can be pumped out to float the structure and to restore the mass equilibrium in case of damage. The minimum height of water ballast is thus given by -igure 3 and Equations 1 to 4: L F 35.43 m B F 8.12 m Ht Hwb Lp BOAT B F 8.12 m Bb F 8.00 m Li (a) (b) -igure 3: E7ample for Damaged -loating Tanks (a) Plan .iew (b) Cross-Section .olume of income water: .i F B/2 7 (Ht H Hwb) 7 Li I1J .olume of water ballast to pump out: .o F B/2 7 Hwb 7 (L H Li) I2J Water ballast height (I1J F I2J): Hw2 3 H 4 Li 5 L I3J Length of income water: Li F Kroundup (Bb / Lp) + 1L 7 Lp I4J with Lp distance between two transverse watertight partitions Ht height of the floating tanks SOLID BALLAST The floating stability is assessed through the metacentric height, which is given by Equation 5: GM = KB + BM − KG − ∆GM I5J with C9 metacentric height Page 157 Joint International Conference on Computing and Decision Making in Civil and Building Engineering June 14-16, 2006 - Montréal, Canada E* distance between the gate bottom (E) and the buoyancy center (B) EC distance between the gate bottom (E) and the gravity center (C) BM metacentric radius F 2T / ∇ where 2T water plane moment of inertia ∇ under water volume (displacement) ∆C9 0free surface effect1 due to water ballast F i / ∇ where i free surface moment of inertia The role of solid ballast is to lower the gravity center and thus to increase the metacentric height. 2n case of damage the mass equilibrium is restored by pumping out water ballast but the gravity center goes up so that the metacentric height decreases. The minimum height of solid ballast is thus given by Equation 5 in case of damage and by considering a minimum 40 cm metacentric height as floating stability condition. The considered density of solid ballast is 80 k,/mM (steel blocks). SCANTLING OPTIMIZATION The .an Cauwelaert lock gate is composed by steel stiffened plates. A least weight optimi ation of the gate scantling (profile si es, dimensions and spacing) can be performed with the LBR-5 software (Rigo 2001a, Rigo 2001b, Rigo 2003). LBR-5 SOFTWARE Structural design is always defined during the earliest phases of a pro(ect. 2t is thus not difficult to understand why a preliminary design stage optimi ation tool is attractive. This is precisely the way the LBR-5 optimi ation software for stiffened structures was conceptuali ed. LBR-5 is an integrated package to analy e and optimi e naval and hydraulic structures at their earliest stages: tendering and preliminary design. 2nitial scantling is not mandatory. Designers can start directly with an automatic search for optimum si ing (scantling). Design variables (plate thicknesses, stiffener dimensions and spacing) are freely selected by the user. LBR-5 is composed of 3 basic modules (APT2, CA,STRA2,T and CAST). The user selects the relevant constraints (geometrical and structural constraints) in e7ternal databases. When the optimi ation deals with least construction costs, unitary material, welding, cutting and labor costs must be specified by the user to define an e7plicit ob(ective function (not empirical). -or least weight, these unitary costs are not used and the ob(ective function depends only on the geometrical parameters. Using all these data (constraints, ob(ective function and sensitivity analysis), the optimum solution is found using an optimi ation algorithm based on conve7 lineari ations and a dual approach (-leury 1383, Rigo and -leury 2001). 2ndependent of the number of design variables and constraints, the number of iterations requiring a complete structural re-analysis is limited to 10 or 15. MODELLING DESCRIPTION The LBR-5 mesh model (-igure 4) of the .an Cauwelaert lock gate includes: • 25 stiffened panels with 3 design variables each, i.e.: Page 158 Joint International Conference on Computing and Decision Making in Civil and Building Engineering June 14-16, 2006 - Montréal, Canada o Plate thickness o -or longitudinal stiffeners and transverse frames: ° Web height and thickness ° -lange width ° Spacing • 155 design variables (some design variables of stiffened panels are not considered) • 35 equality constraints, e.g. to impose uniform frames spacing and transverse symmetry • 213 geometrical constraints • 1400 structural constraints (280 per loading case), such as: o Plate yielding (.on 9ises) o Stiffener yielding (web and flange) o -rame yielding (web and flange) o Stiffener ultimate strength • 1 constraint imposing the gravity center cannot go up during the optimi ation process 1 6 6 13 6 2 12 23 24 25 (a) 3 6 6 6 6 11 6 6 4 10 18 13 6 6 6 5 22 3 (b) 20 21 6 6 6 5 8 8 14 6 6 15 15 6 6 18 -igure 4: LBR-5 9odelling (a) 9esh 9odel of the .an Cauwelaert Lock Cate (b) Stiffened Panel Element -ive loading cases are considered during the optimi ation process: • Three different levels of the Scheldt River (-igure 2), • Emptying of the port when the Scheldt River is at the average level, • 240 k,/mN test pressure in each floating tank when the gate is not yet in the water.