CALCULATION OF CUMULATIVE DAMAGE OF TETRAPOD ARMOR LAYER

Transcription

1 Proceedng of the 7 th Internatonal Conference on an and Pacfc Coat (PC 13) Bal, Indonea, epteber 4-6, 13 CLCULIO OF CUMULIVE DMGE OF ERPOD RMOR LYER K-D. uh 1, M. K and -W. K 3 BRC: In the perforance-baed degn of a breakater aror layer, t often neceary to calculate t daage accuulated over the lfe cycle of the breakater. o ethod for calculatng the cuulatve daage have been propoed; one by Melby and Kobayah n 1998 and the other by Hanzaa et al. n In th paper, coparon ade beteen the to ethod for a etrapod aror layer. For the daage progreon of etrapod aror unt, hydraulc experent are ade. In the cae here a evere daage occur at the begnnng of the lfe cycle of the breakater, the to ethod do not ho gnfcant dfference, but n general the latter predct a larger cuulatve daage than the forer. For a etrapod aror layer, t recoended to ue the average of the to ethod. Keyord: ror layer; Breakater; Cuulatve daage; etrapod. IRODUCIO he extng tablty forula for aror unt calculate the degree of daage of the aror layer durng the peak of a degn tor. In the perforance-baed degn of the breakater aror layer, hoever, t often neceary to calculate t daage accuulated over the lfe cycle of the breakater. here are to ethod appeared n lterature to calculate the cuulatve daage; Melby and Kobayah (1998) and Hanzaa et al. (1996) (hereafter referred to a Method 1 and Method, repectvely). he Method 1 a propoed for tone aror layer for hch the daage level a ued, the phycal decrpton of hch the nuber of cubc tone th a de of D n5, eroded thn the dth (along the breakater algnent) of one nonal ze D n5. On the other hand, the Method a propoed for etrapod aror layer for hch the daage expreed n ter of relatve daage, hch defned a the nuber of dplaced etrapod thn the dth of one D n. nce and have eentally the ae phycal decrpton, the to ethod could be ued for both tone and concrete aror unt. Melby and Kobayah (1998) conducted hydraulc experent for daage progreon of quarry tone. Hoever, the experent for concrete aror unt are carce. uh and Chang (3) copared the to ethod th the experental reult of Melby and Kobayah (1998) for tone aror unt, but they copared only nuercal reult for etrapod aror unt. In the preent tudy, e conduct hydraulc experent for daage progreon of etrapod aror unt. he to calculaton ethod are then copared for etrapod aror unt. CLCULIO MEHOD Method 1 Baed on the tablty forula of Van der Meer (1987), Melby and Kobayah (1998) expreed the daage level a (1) b 5 here a ( H / ( Dn 5)), H = gnfcant ave heght, a / 1th a = denty of aror unt and = flud denty, = nuber of attackng ave, and a and b = eprcal coeffcent. Wth the duraton of ave attack gven by t, here = ean ave perod, Eq. (1) can be rtten a t b o calculate the cuulatve daage level n real tuaton of H and varyng th te, Melby and Kobayah (1998) propoed an eprcal procedure, n () 1 Departent of Cvl and Envronental Engneerng, eoul atonal Unverty, 1 Ganak-ro, Ganak-gu, eoul , REPUBLIC OF KORE Global Envronent yte Reearch Dvon, atonal Inttute of Meteorologcal Reearch, 61 Yeoeudaebang-ro, 16-gl, Dongjak-gu, eoul 156-7, REPUBLIC OF KORE 3 Coatal and Hydraulc Laboratory, U ry Engneer Reearch and Developent Center, 399 Hall Ferry Road, Vckburg, M , U 397

2 Calculaton of Cuulatve Daage of etrapod ror Layer hch the daage level at arbtrary te t, expreed a b b b 1 1, a ( t t ) (3) here 1 = knon daage level at t t 1, and = ean ave perod durng the perod fro t t 1 to t t. Baed on the eprcal forula of uh and Kang (1), the counterpart of Eq. (3) for etrapod can be rtten a ( t t ) (4) he coeffcent H D etated a n c f H.45.4 (cot ).85 D n f c 5. (5) (6) here tan = lope of the aror layer, tan / H / L th L g / ( ), and c 9. / /.85 (cot ) o calculate c ung Eq. (7), neceary, hch a pror unknon. We calculated c ung and 1 / t 1 1 n Eq. (7) and calculated ung Eq. (4)-(6). h and t / ere then ued n Eq. (7) to calculate c, and a re-calculated ung Eq. (4)-(6). Daage to the etrapod aror layer aued to occur under rough ea condton of the gnfcant ave heght greater than a crtcal value, H c, hch ay be defned a the ave heght correpondng to zero daage n a tablty forula. Method Hanzaa et al. (1996) propoed a lghtly dfferent ethod. uppong the ave heght durng the perod fro t t 1 to t t H and the cuulatve daage level up to t t 1 1, the nuber of ave hch attacked the breakater up to t t 1, ', deterned ung H and 1, repectvely, n place of H and n Eq. (1) a 1.5 (7) ' 1 1/ b he cuulatve daage level up to t t,, calculated by Eq. (1) th ' and H H here = nuber of ave beteen t t 1 and t t. Wth ( t t 1) /, gven by 1/ b t t 1 1 Ung the lar procedure, the cuulatve relatve daage of etrapod calculated by t t b (8) (9) (1) HYDRULIC EXPERIME Hydraulc experent for daage progreon of etrapod ere conducted n the ave flue at the Hydraulc and Coatal Engneerng Laboratory n eoul atonal Unverty that a 36- long, 1.- de, and 1.- deep. Fg. 1 ho the experental etup. horzontal bed th a 1/5 forehore lope a ntalled at the elevaton of c fro the botto of the flue. he breakater odel a placed at a dtance of 5 fro the ave aker th the breakater toe at a fe centeter fro the begnnng of the horzontal bed. he tet ecton a dvded nto to channel by a vertcal all along the ave flue, each havng a dth of.6 and.4, repectvely. he breakater a ntalled n the der channel and the other channel a left epty. Irregular ave baed on the odfed Bretchneder-Mtuyau pectru (Goda 1) ere generated th a pton-type ave aker. he ater depth a.6 at the ave paddle and.4 at the toe of the tructure. o eaure the ncdent ave, three ave gauge ere ntalled n the epty channel. he free urface dplaceent eaured by thee ave gauge ere ued to eparate the ncdent and reflected ave ung the ethod of uh et al. (1). Even though the channel epty, ave reflecton occur fro the lopng bed and the ave aborber located at the dontrea end of the flue. he ethod of uh et al. (1) etate the te ere of urface elevaton of the ncdent and reflected ave. he gnfcant ave heght H a calculated by the zero-crong analy of the te ere of the ncdent ave profle. 398

3 K-D. uh, et.al Fg. 1 ketch of ave flue and experental etup. Fg. Cro-ecton of breakater 399

4 Calculaton of Cuulatve Daage of etrapod ror Layer Fg. ho the cro-ecton of the breakater. he an charactertc of the etrapod ere: heght H 6. c; nonal ze Dn 4.3 c; a.3 g/c 3 ; eght W 15.5 g; and layer thckne 8. c. he underlayer conted of tone of daeter.-.5 c and thckne of 6. c, hle the core conted of tone of nonal ze Dn c. he lope of the tructure a cot 1.5. lttle ave overtoppng occurred hen the gnfcant ave heght a greater than 18 c. etrapod ere placed n to layer: randoly placed upper layer on the regularly placed loer layer. nce the etrapod n contact th the deall of the flue have le degree of nterlockng, they ere fxed not to ove and ere not ncluded n the calculaton of daage. Eght dfferent rregular ave tran of 15 n duraton th unque cobnaton of ave heght and ave perod ere ued to ulate tor of everal hour duraton. able 1 uarze the ncdent ave charactertc at the toe of the tructure. he nuber of ave n the 15 n burt a approxately 45 to 71 dependng on the ave perod. he urf larty paraeter baed on and H, 1/ tan [ g / ( H)], a n the range On the other hand, the urf larty paraeter for collapng ave, c, calculated by Eq. (7) ung varou cobnaton of =.,.5, 1. and = 15, 3, 45 a n the range of h prove that the ave lted n able 1 produce ntene collapng breaker at the tructure. able 1 et ave condton. Wave H (c) () Fve tet ere ere conducted a hon n able. Each ere cont of the eght ave cae lted n able 1 n dfferent equence, latng h th approxately 455 ave. he tet ere ere ntended to copare cuulatve daage caued by dfferent equence of tor a lted n able. In ere, the tor ntenty ncreaed onotoncally fro ave 1 to ave 8. In ere B and C, trong tor occur n the ddle of the equence, hle n ere D and E, trong tor occur at the begnnng and end of the equence. For each tet ere lted n able, tet ere repeated nne te. he tet of the axu and nu fnal daage ere dcarded, and the reanng even tet ere ued to calculate the ean and tandard devaton of daage. able Wave equence n tet ere. er. er. B er. C er. D er. E COMPRIO WIH EXPERIMEL REUL he calculaton ethod are appled to ulate the cuulatve daage of the etrapod aror layer n the preent experent. Fg. 3 ho the relatve daage calculated by Eq. (4) and (1) along th the experental data for ere to E. he experental data are repreented by error bar ndcatng 1 tandard devaton. he data of zero tandard devaton ndcate no daage progreon fro the prevou daage. he te nterval of calculaton a 15 n, hch the ae a the duraton of each ave cae n the experent. In general, the Method predct larger daage than the Method 1 except ere E n hch the frt ave the larget o that evere daage occurred at the begnnng of the ulaton. h trend the ae a that for tone aror layer (ee Fg. 5 n uh and Chang 3). In ere here the tor ntenty ncreae onotoncally, both ethod ntally over-predct the cuulatve daage, but the agreeent beteen predcton and eaureent becoe better n the lat tage here trong tor occur. In ere B and C here trong tor occur n the ddle of the equence, the eaured daage locate oehere beteen the to predcton. In ere D and E here trong tor occur at the begnnng and end of the equence, both ethod ell predct the cuulatve daage, epecally n ere E here the frt ave the larget o that evere daage occurred at the begnnng of the ulaton. a hole, t dffcult to judge hch ethod better predct the eaureent. nce the eaured daage locate oehere beteen the to predcton except the cae of large ntal daage n hch the to ethod yeld lar predcton, t recoended to ue the average of the to ethod. 4

5 K-D. uh, et.al (a) (b) (c) (d) (e) Fg. 3 Coparon beteen calculated and eaured relatve daage of etrapod aror: (a) ere ; (b) ere B; (c) ere C; (d) ere D; (e) ere E. 41

6 Calculaton of Cuulatve Daage of etrapod ror Layer In the tablty forula for aror unt, the daage level or the relatve daage proportonal to o that the coeffcent b ut be.5. hee equaton ere developed to calculate the daage of aror unt durng a ngle tor of relatvely hort duraton. For rock aror, Van der Meer (1987) and Melby and Kobayah (1998) hoed that b.5 for long-duraton tet. Melby and Kobayah (1998) obtaned b.5 by calbratng Eq. (3) th ther longduraton experental data. In the coparon hon n Fg. 3 here evere daage occurred three or four te n each ere, b.5 a ued. h ple that the tablty forula for etrapod developed for a ngle tor can be ued for calculaton of cuulatve daage by everal tor. If the ethod are ued for ore nuber of tor, a calbraton for the coeffcent b ay be neceary. Hoever, the probablty that a rubble ound breakater ll be everely daaged ore than everal te durng t lfete ut be very lo. COCLUIO Coparon a ade beteen the to ethod for calculatng the cuulatve daage of etrapod aror unt; Method 1 (Melby and Kobayah 1998) and Method (Hanzaa et al. 1996). In the cae here evere daage occurred at the begnnng of the lfete of the breakater, the to ethod dd not ho gnfcant dfference, but n general the Method predcted larger cuulatve daage than the Method 1. he to ethod ere copared agant the experental data of the preent tudy. Dependng on the te of occurrence of large tor, each ethod over- or under-predct the eaureent o that t dffcult to judge hch ethod ake a better predcton. nce the eaured daage locate oehere beteen the to predcton except the cae of large ntal daage n hch the to ethod yeld lar predcton, t recoended to ue the average of the to ethod for a etrapod aror layer. CKOWLEDGEME h tudy a upported by the Bran Korea 1 Project and the Project for Developent of Relablty- Baed Degn Method for Port and Harbor tructure ponored by Korea Mntry of Land, ranport and Marne ffar. REFERECE Goda, Y. (1). Rando ea and Degn of Marte tructure, 3rd ed., World centfc. Hanzaa, M., ato, H., akahah,., hoako, K., akayaa,. and anoto, K. (1996). e tablty forula for ave-dpatng concrete block coverng horzontally copote breakater. Proc. 5th Int. Conf. Coatal Eng., Melby, J.. and Kobayah,. (1998). Progreon and varablty of daage on rubble ound breakater. J. Wateray, Port, Coatal and Ocean Eng. 14, uh, K.D., Park, W.. and Park, B.. (1). eparaton of ncdent and reflected ave n ave-current flue. Coatal Eng. 43, uh, K.-D. and Chang, E.-. (3). Coparon of calculaton ethod of cuulatve daage of breakater aror layer. Ocean and Polar Re. 5(3), (n Korean). uh, K.-D. and Kang, J.. (1). tablty forula for etrapod. J. Wateray, Port, Coatal and Ocean Eng. 138, Van der Meer, J.W. (1987). tablty of breakater aror layer-degn forulae. Coatal Eng. 11,