A Discussion on Formulas of Seismic Hydrodynamic Pressure
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1 Interntionl Forum on Energy Environment Science nd Mterils (IFEESM 2017) A Discussion on Formuls of Seismic Hydrodynmic Pressure Liu Himing1 To Xixin2 1 Cin Mercnts Congqing Communiction Reserc & Design Institute Co. Ltd Stte Key Lortory of Bridge Engineering Structurl Dynmics Congqing Cin 2 Scool of Civil Engineering Hrin Institute of Tecnology Hrin Cin liuiming@cmk.com toxixin@liyun.com Keywords: Hydrodynmic pressure Seismic design Higwy ridge Guidelines Astrct. Te origin nd simpliction of formuls for seismic ydrodynmic pressure in te existing guidelines for seismic design of igwy ridges of Cin is reviewed. Five dferences from Jpnese specictions tt is Cinese guidelines come from re pointed out. A suggestion to mody te formuls is finlly presented. Introduction Recently some resercers mentioned te fct tt vlues of seismic ydrodynmic pressure from te existing guidelines for seismic design of igwy ridges of Cin [1] re muc lower tn tose from Jpnese design specictions for igwy ridges prt V seismic design [2]. Te utors of tis pper review te codes serc te origin of te formuls point out te cuse of te dference nd ten present modiction suggestion. Origin of te formuls in seismic design code of igwy engineering of Cin Te seismic ydrodynmic pressure ws firstly tken into ccount for te sitution wit wter dept lrger tn 5 meters in seismic design code of igwy ridges of Cin in 1989 []. Te formuls for tree vlue intervls of pier size to wter dept rtio re s following. Ew = 0. 15( 1 - )Ci Kξ γ w 2 Ew = 0.075Ci K ξ γ w 2 Ew = 0.2Ci K γ w 2.1 > were Ew is te resultnt force of totl seismic ydrodynmic pressure cted on te pier t eigt of /2 (kn) Ci is importnce fctor K is te design lterl seismic coefficient defined s te rtio of design orizontl sic ccelertion to grvity ccelertion is te wter dept (m) is te pier widt in te direction perpendiculr to te direction of ydrodynmic pressure (m) ξ is section spe fctor wit vlue 1.0 for rectngulr nd 0.8 for circulr γ w is unit weigt of wter (kn/m). One cn know from te commentry of te specictions tt te origin of tese formuls comes from Jpnese 1980 design specictions for igwy ridges Prt V seismic design []. Te formuls in Jpnese code re s follows [5]. k w0 A0 ) Copyrigt 2018 te Autors. Pulised y Atlntis Press. Tis is n open ccess rticle under te CC BY-NC license (ttp://cretivecommons.org/licenses/y-nc/.0/). 1788
2 k w0 A0 (0.7 ) 10 9 k w0 A < 5 6 were P is te sme s Ew in Eq. 1 ut t eigt of /7 k is te product of K in Eq.1 wit compreensive fctor Cs nd n importnt fctor s Ci in Eq. 1 in ddition of regionl nd site fctor w0 is te sme s γ w in Eq.1 A0 is re of te pier section t te eigt of /7 nd re te sme s in Eq. 1 is te lengt of oter side of rectngulr section of te pier. Origin of te formuls in Jpnese design specictions for igwy ridges According te commentry of Jpnese design specictions for igwy ridges Prt V seismic design [2 5] te ove formuls come from te suggestion y te Goto nd Toki [6]. From te following integrting eqution on velocity potentil in cylindricl coordinte system Eq.7 nd te oundry conditions in Eq.8 Eq. 9 Eq.10 nd Eq.11 dynmic pressure on rigid cylinder surfce in tree dimensionl nlysis cn e evluted y Eq φ 1 1 2φ 2φ 1 2φ =0 r 2 r r r 2 θ 2 z 2 c 2 t 2 (7) y ( )r = = cos θ r t (8) ( )θ =0 = ( )θ =π = 0 r θ r θ (9) ( ) z =0 = 0 z 0) (g 2φ ) z = = 0 z t 2 1) m 1 K1 (α m ) ( 1) cos α m z m =1 α m α m K 0 (α m ) K z (α m ) Py = k0γ wπ 2 2) were k0 is te lterl seismic coefficient γ w nd re te sme s in Eq.1 is te rdius of te cylinder oters re coefficients nd functions not illustrted ere. In simpliction cuic expression is tken for distriution of te ydrodynmic pressure wit te ordinte y in te cse of te cylinder moving in finite mss of wter te following formul is ten derived. 1789
3 Py = koγ wπ 2 z ) 1 2 ) Integrl of te term contining z from 0 to cn e otined s z 0 1 dz = ) Te formul of ydrodynmic pressure is ten finlly derived s follows. k 0γ wπ ) One cn see tt it is exctly te sme s Eq. ere equls /2 in Eq. π 2 equls A0= in Eq.. Formuls in te existing guidelines for seismic design of igwy ridges nd some tougts for modiction Te formuls on ydrodynmic pressure stipulted in te existing guidelines for seismic design of igwy ridges of Cin [1] re te following tree. Ew = 0.15 )Ci Aξ γ w 2 / g Ew = 0.075Ci Aξγ w 2 / g E w = 0.2 C i Aγ w 2 / g >.1 18 were ll prmeters ere re te sme s in Eq. 1 Eq. 2 nd Eq. respectively except for te A is orizontl design sic pek ground ccelertion nd tere must e /g te grvity ccelertion dded from te definition of seismic coefficient in Eq. 1. Py ttention on te fct tt A0= for pier wit rectngulr section one cn see from te ove formuls tt te formuls in Cinese guidelines re lmost te sme s in Jpnese specictions wit five dferences. First te vlue of te first consistent t te rigt side in Eq. is five times s one in Eq.1 since compreensive fctor Cz=0.2 is tken for ot seismic lod nd ert pressure in Cinese code. Second te second cutoff vlue of te tree rtio intervls is.0 in Eq. 5 little it lrger tn.1 in Eq. 17. Tird te incresing of te force in Eq. 5 is little slower tn tt in Eq.17. Fourt te vlue of te first consistent t te rigt side in Eq. 6 is little it lower tn te vlue of 0.2 in Eq. 18. Ft te eigt of /7 in Jpnese speciction is lso little it lower tn /2 in Cinese one. One cn find tt te second tird fourt nd ft dferences mke Cinese guidelines more conservtive y compring te force vlues from te two sets of formuls. Regrettly tere is misprint in Eq. 18 te rigtmost term tere must e 2[1]. Fortuntely Eq.18 is seldom pplied te rtio of.1 nd wter dept 5.0 m require quite lrge pier size sy dimeter t lest 15 meters for sitution wit sllow wter. 1790
4 One of te most signicnt improvements of te existing Cinese guidelines from te previous one is tt te compreensive fctor s een deleted completely since two level design procedure is dopted. Terefore te vlue of te first consistent t te rigt side in Eq.16 sould e multiplied y 5. A modiction of te formuls wit consulting Eq. Eq. 5 nd Eq.6 is suggested s following. E W= 0. 75( 1. 0 )Ci Aξγ W 2 / g E W= 0. 75Ci Aξ γ W 2 / g 2. 0 < 9) (20) were ll prmeters re te sme s in Eq. 16. One cn see tt Eq. 19 is te sme s Eq. nd Eq. 20 is conservtive wit rtio vlue from 1.0 to 1.6 for pier size 20 m to 0 m in wter dept less tn 5 m to 7.5 m compring wit Eq. 5. Te resultnt force is not signicnt for sitution in tis rnge compre wit te corresponding seismic effect. Tese formuls re simple nd convenient for igwy ridge design prctice. Conclusions Te origin of formuls for seismic ydrodynmic pressure on pier in wter in guidelines for seismic design of igwy ridges in Cin is reviewed. It is cler tt te formuls re simplied from n nlyticl solution of integrting eqution on velocity potentil on surfce of rigid cylinder in finite wter mss in tree dimensionl nlysis nd te oundry conditions. Tere re two errors from misprint nd slip up to witdrw te compreensive fctor in te process modying te design procedures wit te two level design strtegy. Te fct is pointed out tt te formuls in Cinese guidelines re conservtive in totl y comprison wit tose in Jpnese specictions. Finlly two formuls re suggested for modiction wit considering simple nd convenience in design prctice of igwy ridges. Acknowledgements Tis work ws finncilly supported y grnt of Ntionl Key R&D Progrm of Cin 2017YFC nd of Ntionl Nture Science Foundtion of Cin; open funds of Stte Key Lortory of Bridge Engineering Structurl Dynmics nd Key Lortory of Bridge Ertquke Resistnce Tecnology Ministry of Communictions PRC. References [1] Ministry of Trnsport of te People's Repulic of Cin: Guidelines for Seismic Design of Higwy Bridges (JTG/T B in Cinese) [2] Jpn Rod Assocition: 2012 Design Specictions for Higwy Bridges Prt V Seismic Design (2012). [] Ministry of Trnsport of te People's Repulic of Cin: Specictions of ertquke resistnt design for Higwy Engineering (JTJ in Cinese). [] Jpn Rod Assocition: 1980 Design Specictions for Higwy Bridges Prt V Seismic Design 980). [5] Jpn Rod Assocition: 2002 Design Specictions for Higwy Bridges Prt V Seismic Design (2002). 1791
5 [6] Goto H. nd K. Toki: Pro. of te rd World Conference on Ertquke Engineering New Zelnd II 965) 1792
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