Study on coastal bridge under the action of extreme wave

Transcription

1 Study on coastal brdge under the acton of extreme wave Bo Huang Bng Zhu Jawe Zhang School of Cvl Engneerng, Southwest Jaotong Unversty, Chengdu , Chna Abstract In order to research the catastrophc damage problem of coastal brdge under the acton of extreme wave, combne the numercal smulaton wth tan experment and based on RANS and equaton, a brdge-wave nteracton model s establshed. The free surface locatons n the model are represented by the Volume of Flud method. Confrmed the wave parameters and the cross-secton form of the grder brdge of tan experment reference the Pngtan Strats Ral-cum-Road Brdge and the Hong Kong-Zhuha-Macau Brdge. The tan experment was conducted for verfcaton of the calculatons of numercal smulaton. The smulaton results show that the constrant condtons between the box grder and per has an mportant nfluence n horzontal translocaton damage of the box grder under the extreme wave. Wth ncreasng the submerged coeffcent, the buoyancy force ncreases frst and the decreases. Wth ncreasng the submerged coeffcent, the horzontal force decreases. 1 Introducton Wth the development of economy and socety, the bay brdge has become an ndspensable part of rapd coastal transportaton networ. Snce the last decade, several large-scale tsunams, hurrcanes and typhoons occurred around the world, especally Hurrcanes Ivan and Katrna n the U.S. had caused a great deal of coastal brdge destructon [1, 2]. Now, the world-class brdge engneerng n chna s Hangzhou bay sea-crossng brdge and zhoushan cross-sea brdge, the hongong-zhuha-macao brdge and across the Tawan strats pngtan channel brdge are under constructon. Most of these brdges n the eastern and southern part of chna, vulnerable to the typhoon attac, whch causes great damage on the constructon of sea-crossng brdge and brdge constructon. Studyng the coastal brdge s behavour n acton of extreme wave have sgnfcant meanngs n desgn, constructon and protecton of t In the past decades, many mportant results on the research of under the extreme wave sea-crossng brdge damage were obtaned. Ghamry s [3] dec wave lft expermental study ponts out that the varaton n lftng force of horzontal plate are depend on the wave perod and plate clearance. Robertson [4] used the extng data and method to calculate the hydrodynamc lft and hydrostatc lft of damage to hurrcane Katrna brdge, show that the destroy brdge s lft s greater than ts own gravty. Xao [5, 6] used the Volume of Flud (VOF) and a numercal wave-load model based on the ncompressble Reynolds averaged Naver-Stoes equaton and equatons has been used to nvestgate dynamc wave force exerted on the brdge dec. Dfferent brdge dec elevatons submerged at dfferent water depths were nvestgated. But untl now, they ddn t do the numercally smulatng and flume experment research to the brdge structure under the same wave envronment, use the flume experment to test the numercal model. In ths paper, a numercal wave-load model based on the ncompressble Reynolds averaged Naver- Stoes equaton and equatons has been used to nvestgate dynamc wave force exerted on the

2 brdge dec and the Volume of Flud (VOF) s adopted n the model to descrbe dynamc free surface. Choosng the actual cross secton form and wave parameters based on the hongong-zhuha-macao brdge and across the Tawan strats pngtan channel brdge. Studyng the coastal brdge s behavour n acton of dfferent brdge dec elevatons submerged and wave envronment through the numercal smulaton and flume experment. 2 Governng Equatons 2.1 Governng Equatons For the wave-structure-nteracton, the RANS equatons are used to solve the mean flow velocty and the second=order RANS equaton: turbulent model s used for the closure of RANS equatons. u x 0 (1) model: u u p uj t x x x 1 j g j j (2) t uj G t x j x j x j (3) Where: 2 t u j C1 G C2 t x j x j x j (4) 2 2 1u u j j 2 Cd j j, j, 3 2xj x C 2 u, G2 x t d t j j s turbulent netc energy, t s eddy vscosty, u s velocty vector of the men flow, s turbulent dsspaton rate, 0.09, d C C2 1.44, 1.0, 1.3, j s rate of stran tensor, p s pressure of the mean flow, g s th component of the gravtatonal acceleraton. 2.2 Numercal Method In the numercal model, used the two-step projecton method [7] to solve the RANS equatons (1) -

3 (2).Frst, ntroduce an ntermedate velocty n1 u, ts can carres the correct vortcty, there has: Where the t n1 n n n u u u n j j uj g t x j x j (5) s tme step, the equaton (5) ddn t have the pressure gradent term and the ntermedate velocty ddn t satsfy the contnuty equaton. The second step s to project the ntermedate velocty feld onto a dvergence free plane to obtan the fnal velocty: n1 n1 n1 1 n t x u u p (6) u x n1 0 (7) Consder the pressure gradents at the n+1-tme step, combne the equaton (6) and (7), the RANS almost satsfed. 3 Numercal Smulaton 3.1 Numercal model Based on the actual box secton of the hongong-zhuha-macao brdge structure, usng the establshed mathematcal model of box secton to smulate the wave force and wave of torque. Box secton sze as shown n fgure 1. Fg.1 Box secton sze The wave parameters of the box secton references the measurement of wave parameters on the the Tawan strats pngtan channel brdge ste locaton. Calculaton for dfferent water depths, dfferent submerged depth and dfferent wave heghts, a total of 70 nds of box secton under the condton of wave force and moment. Usng the second order stoes wave theory to generaton wave, and the Volume of Flud (VOF) s adopted n the model to descrbe dynamc free surface, whch s capable of smulatng complex dscontnuous free surface durng wave-dec nteracton. Horzontal drecton wth non-unform grd parttonng and n dense mesh sze near the structure. In order to mae the wave actoned on the

4 brdge fully developed, placed the center of the structure at least three wavelengths away from the boundary locaton. A sponge layer s set n front of the outflow boundary wave area to absorb the wave energy. Computatonal doman arrangement s shown n fgure 2. Fg.2 Computatonal doman arrangement 3.2 Numercal model Valdaton Accordng to the gravty smlarty crteron and the requrements of wave model test procedures, n harbor engneerng nsttute of Tanjn hydraulc research nsttute, a 1:30 scale model test n no reflecton wave machne to verfy the above the accuracy of the numercal model. The length, wdth and heght of the water tan are 68m, 1m,1.6m, respectvely. Accordng to fgure 1 box secton sze to mae the box grder model, model geometry sze error of the dmensons and elevaton must be controlled at + / mm. In order to ensure the rgdty of test model, box grder structure made of organc glass, hollow nsde and outsde closed. In the central secton of beams, use 3-component dynamometer to measure the total force. Consderng the demands of test depth and wave cycle, breawater model set up on the horzontal secton at the bottom of the tan drectly. Model was settled sx tme the sze of the wavelength away from the wave machne, the dstance from the rear wave sponger slope must greater than 2 tmes the wavelength. Physcal model and test nstallaton s shown n fgure 3: Fg.3 Test model nstallaton plan Fgure 4 shows the model of submerged coeffcent of 2.0, bottom elevaton of m, wave heght s 6 m; the bottom elevaton of m, wave heght s 2 m; the bottom elevaton of m, wave heght s 6 m, comparson of the buoyancy of box grder n these three worng condtons. Numercal results are n good agreement wth experment results, show that the results of numercal smulaton can

5 well reflect the real stress dstrbuton of box grder under wave load. Y=11.94,H=6 Y=15.99,H=2 Y=15.99,H=6 Fg.4 The tme curve of buoyancy 3.3 Wave Force Calculaton of Box Grder Wth the box grder secton as the research object, numercal model for wave forces actng on the box grder secton were smulated. Calculaton for dfferent water depths, dfferent submerged depth and dfferent wave heghts, a total of 70 nds of box grder cross secton under the condton of wave force. The worng condton of wave elements shown n the table:

6 Table.1 Wave elements of numercal smulaton NO The heghts of model bottom Y (m) Water depth d Submerged coeffcent model (m) Wave heght H (m) Perod T Dtto Dtto Dtto Dtto Dtto Dtto Dtto Dtto Dtto Dtto Dtto Dtto (s) Fgure 5 shows the curve of box grder per lnear meter of pea buoyancy the rato of ts own gravty per lnear meter change wth submerged coeffcent at the 15 nds of worng condton. Fgure 6 shows the curve of box grder per lnear meter of pea horzontal force the rato of ts own gravty per lnear meter change wth submerged coeffcent at the same worng condton.

7 Fg.5 The curve of buoyancy and the gravty rato changes wth the submerged coeffcent Fg.6 The curve of horzontal force and the gravty rato changes wth the submerged coeffcent As the fgure 5 shows, the box grder per lnear meter of pea buoyancy the rato of ts own gravty per lnear meter wll ncrease frst and then decrease as the submerged coeffcent ncrease, because when the submerged coeffcent s less than 1.0, wth the box grder gradually snng, causng dranage volume ncreased, then buoyancy ncreased. When submerged coeffcent greater than 1.0 and less than 1.5, the box grder s fully mmersed n water, but because of the nfluence of the wave, buoyancy at ths tme contnue to ncrease, gradually ncrease to the maxmum value. As the submerged coeffcent contnues to ncrease, the nfluence of the waves to the box grder wll gradually weaen, the buoyancy s decreased. As the fgure 6 shows, wth the ncrease of submerged coeffcent, box grder s gradually snng, wave effect on box grder secton gradually weaen, then the horzontal forces are present decreasng trend. Accordng to document [9], the frcton coeffcent between brdge abutment and box grder was 0.3, the brdge beam body wll damage because the horzontal dsplacement under the extreme wave load. By the damage formula of horzontal dsplacement (8): ( G F) N (8) Where: 0.3, G s weght of box grder, F s buoyancy, N s horzontal force.

8 Can be concluded: when submerged coeffcent s greater than 0.5, the box grder damage of horzontal dsplacement wll easy happen. 4 Concluson In ths paper, usng the ncompressble Reynolds averaged Naver-Stoes equaton and equatons to establsh wave-brdge nteracton numercal model, and verfed the accuracy of the numercal model by tan test. Through numercal smulaton of 70 nds of worng condtons, obtaned the followng concluson: (1) The numercal model establshed n ths paper, through the scale tan test under the condton of same contrast, proved to be accurate. The establshed numercal model can better smulate the actual engneerng of the brdge problem under the extreme wave acton, t can provde effectve numercal smulaton tools on desgn and constructon of sea-cross brdge. (2) When submerged coeffcent s greater than 0.5, the box grder damage of horzontal dsplacement wll easy happen. It has the gudng role on the sea-crossng brdge elevaton desgn, especally n low elevaton desgn. (3) The type of bearng between box grder and per plays a decsve role n the damage of seacrossng brdge under the extreme wave acton. Strengthen vertcal and lateral constrant between box grder and per can effectvely avod the damage of beam horzontal dsplacement. References 1.Fang Q (2012). Study on Extreme Wave Loads of Coastal Hghway Brdges. Harbn Insttute of Technology, School of Cvl Engneerng. 2. Zhu B, Kang A, Xng F et al (2013). Numercal Smulaton of Interacton Between Three-Dmensonal Wave and Round-End Boxed Cofferdam. Brdge Constructon, 43(6): Ghamry EI. Wave Forces on a Doc. Hydraulc Engneerng Laboratory, Insttute of Engneerng Research Techncal Report HEL-9-1, Unversty of Calforna, Bereley, Calforna, 206pp. 4. Robertson IN, Rggs HR, Ym SCS (2007). Lessons from hurrcane atrna storm surge on brdges and buldng. Journal of Waterway, Port, Coastal, and Ocean Engneerng. 133(6): Xao H, Huang W, Chen Q (2010). Effect of submerson depth on wave uplft force actng on blox bay brdge decs durng hurrcame atrna. Computers&Fluds. 39(4): Xao H, Huang W, Tao J et al (2013). Numercal modelng of wave-current forces actng on horzontal cylnder of marne structures by VOF method. Ocean Engneerng. 67(3): Huang W, Xao H (2009). Numercal modelng of dynamc wave force actng on escamba bay brdge dec durng Hurrcane Ivan. Journal of Waterway Port Coastal &Ocean Engneerng. 135(4): Kang A,Zhu B,Xng F(2014).Numercal Smulaton of Wave Force on Large Crcular Cylnder Based on - Coordnate and Immersed Boundary Method. Journal of Southwest Jaotong Unversty, 49(2): Wu Y,L A,Wang H (2015). Parameter Analyss and Optmzaton of Frctonal Pendulum Bearngs for Contnuous Grder Brdge. Brdge Constructon, 45(1):20-25.