Design of concrete armour layers

Transcription

1 Deig of cocrete armour layer J.W. va der Meer ead Coatal Structure. Ifram. PO Box 8, 389 AB Zeewolde, NL, ABSTRACT: Mot rubble moud breakwater i the world have a armour which coit of two layer of uit. Well kow example are rock, cube, tetrapod ad doloe, but there are may more. The Accropode i the firt uit that ha bee ued i may applicatio a a radomly placed oe-layer ytem. Recetly the Core-loc ha bee added a a imilar ytem. Alo cube i oe layer have bee teted ad gave a imilar behaviour with repect to damage developmet. Stability formulae have bee preeted for all thee uit ad advatage ad diadvatage dicued. Geeral tability formulae for cube ad tetrapod will be treated firt. The ifluece of cret height o tability wa ivetigated recetly by chagig the cret height of a breakwater with tetrapod. Thi ifluece ca be decribed by a expoetial fuctio ad ca be added to the exitig tability formula. Aother ifluece o tability i the packig deity. Thi ifluece ha alo bee ivetigated for tetrapod, leadig to a additio to the geeral formula. I fact, the additio for cret height ad packig deity ca alo be added (a a firt gue) to the tability formula for cube. Oe-layer ytem are dicued, tartig with a tability formula for the accropode. A compario i made with the Core-loc. Recet iteret ha bee focued o armour layer with a igle layer of cube or tetrapod. The tet for tetrapod howed very low tability, but the tet o cube were very promiig. Fially, all the cocrete uit have bee compared. INTRODUCTION The udo formula, writte a a fuctio of the tability umber, i very ofte a part of a more recet tability formula cotaiig more parameter. It i decribed by: / 3 / K (cotα) f (cotα) () D The tability formulae for rock layer, give by Va der Meer (988a ad b), give the followig relatiohip: / 5 f (cotα, T ( orξ ), N, P, S) () m where: igificat wave height i frot of tructure, relative ma deity, D 5 omial diameter (cubic ize), α lope agle, T m mea period, ξ m urf imilarity or breaker parameter, N umber of wave, P otioal permeability factor ad S damage level (for rock). Exteded reearch by Va der Meer (988c) o breakwater with cocrete armour uit wa baed o m above goverig variable foud for rock tability. The reearch wa limited to oly oe cro-ectio (i.e. oe lope agle ad permeability) for each armour uit. Therefore the lope agle, cotα, ad coequetly the breaker parameter, ξ m, are ot preet i the tability formulae developed o the reult of the reearch. The ame hold for the otioal permeability factor, P. Thi factor wa P.4. Breakwater with armour layer of iterlockig uit are geerally built with teep lope i the order of :.5. Therefore thi lope agle wa choe for tet o cube ad tetrapod. Accropode are geerally built o a lope of :.33, ad thi lope wa ued for tet o accropode. Cube were choe a thee elemet are bulky uit which have good reitace agait impact force. Tetrapod are widely ued all over the world ad have a fair degree of iterlockig. Accropode were choe a thee uit could be regarded a the latet developmet at that time, howig high iterlockig, trog elemet ad a oe-layer ytem. A uiform :3 forehore wa applied for all tet. Oly for the highet wave height which were

2 geerated, ome wave broke due to depth limited coditio. Damage to rock armour wa meaured by coiderig the eroded area aroud the water level. It i ot uual to meaure profile for cocrete armour layer. Very ofte damage i baed o a actual umber of uit. Therefore, aother defiitio ha bee uggeted for damage to cocrete armour uit. Damage there ca be defied a the relative damage, N od, which i the actual umber of uit diplaced related to a width (alog the logitudial axi of the tructure) of oe omial diameter D. For cube D i the ide of the cube, for tetrapod D.65 D, where D i the height of the uit, for accropode D.7D ad for Doloe D 4D (with a wait ratio of.3). The defiitio of N od i comparable with the defiitio of S, although S iclude diplacemet ad ettlemet, but doe ot take ito accout the poroity of the armour layer. Geerally S i about twice N od. Further, N od ca be eaily related to a percetage of damage. If the umber of uit i a cro-ectio i kow with a legth of D, the percetage of damage to a tructure i imply the ratio of N od ad thi umber. N od give the actual damage, where a percetage i alway related to the actual tructure. A imilar damage may, therefore, give differet percetage of damage if the cro-ectio are differet. The followig example may illutrate thi. Suppoe a breakwater with 5 to cube with a D of.84 m ad coider a tretch m log. Damage N od umber/ m. uit 7 uit. 54 uit. 9 uit If a cro-ectio, oe omial diameter wide, coit of uit, N od give /*%.5% damage. A loger cro-ectio coitig of 4 uit give oly.5% damage. A oly oe lope agle wa ivetigated, the ifluece of the wave period hould ot be give i formulae by ξ m, a thi parameter iclude both wave period (teepe) ad lope agle. The ifluece of wave period, therefore, will be give by the wave teepe om π /( gt p ). Geeral formulae for tability of cocrete uit iclude the relative damage level N od, the umber of wave N, ad the wave teepe, om. It i give by: f (, N, N ) (3) / m od The ext chapter give tability formulae for ome type of cocrete uit. Traditioal deig are treated a two-layer ytem ad the ew uit a oe-layer ytem. TWO-LAYER SYSTEMS. Cube ad tetrapod Baic reearch wa decribed by Va der Meer (988c). The formula for cube i give by: D N 6.7 N.4 od.3 For tetrapod: +.. om (4) N od +.85 om (5) N. For the o-damage criterio N od, equatio 4 ad 5 reduce to: -.. om om (6) (7) No damage at all i a very trict criterio ad armour layer deiged o thi criterio will get large cocrete uit. For rock layer ome ettlemet ad mall diplacemet i icluded i the tart of damage defiitio S-3. For N od a imilar ituatio i foud ad thi i a more ecoomical criterio tha o damage at all. Equatio 4 ad 5 give decreaig tability with icreaig wave teepe. Thi i imilar to the plugig area for rock layer. Due to the teep lope ued, o traitio wa foud to plugig wave. De Jog (996), however, aalyed more data o tetrapod from tet performed at Delft ydraulic ad he foud a imilar traitio a for rock. i formula for plugig wave hould be coidered together with equatio 5, which ow act for urgig wave oly, ad become: om Nod N (8) Both equatio 5 ad 8 are how i Figure for three differet damage level of N od. It i poible, ad it might eve be expected, that a imilar traitio ca be foud for cube. No data are available, however, o that apect.

3 tability umber / D N od N od N od.5 Eq. 5 urgig wave Eq. 8 plugig wave Va der Meer (988) De Jog (996) wave teepe m Figure Stability formulae for tetrapod.8 Ifluece of cret height f(r c/d) cret at wl high cret Relative freeboard R c /D Figure Ifluece of cret height o tability of tetrapod. Ifluece of cret height De Jog (996) alo ivetigated the ifluece of cret height ad packig deity o tability of tetrapod. Equatio 5 ad 8 regard to a almot o-overtopped tructure (le tha 5% overtoppig). Stability icreae if the cret height decreae. With the cret freeboard defied by R c, he foud that the tability umber i equatio 5 ad 8 could be icreaed by a factor f(r c /D ), with repect to a lower cret height. The cret height i the defied by the umber of omial diameter above or below till water level. Alo the packig deity, decribed i the ext ectio, ca be ivolved i the equatio by a factor f(φ). The geeral tability formulae for tetrapod become the: for urgig wave: N od 3.75 N f ( φ ) om f ( Rc / D ) (9). for plugig wave: N 8.6 od f ( ) om f ( R c / D ) D φ () N 3

4 Damage level N od φ. φ.95 φ.88 φ Stability umber / Figure 3 Stability of tetrapod for variou packig deitie The factor f(r c /D ) i how i Figure a a fuctio of the cret height R c /D. Thi factor ca be decribed by: f ( Rc / D ) +.7 exp(.6rc / D ) () If the cret i at the till water level, ie. R c /D, f(r c /D ).7. It mea that the tability umber icreae by a factor.7, or that the omial diameter required ca be decreaed by a factor / O the required weight thi i a factor Similar factor were foud for rock tructure, ee Va der Meer (993). The factor o the omial diameter there wa.5 ad o the weight..3 Ifluece of packig deity The packig deity ca be decribed i it implet way a a umber of placed uit per quare omial diameter: N A φ D () a / / where: N a the umber of uit; A urface area ad φ the packig deity. Packig deitie are give i the Shore Protectio Maual (984). The ormal packig deity ued i the tet amouted to φ.. Lower packig deitie of φ.95 ad.88 were ued to ivetigate the ifluece of φ. The packig deity give i the Shore Protectio Maual (984) i φ.4 for tetrapod (ad.7 for cube). It ideed appeared that a lower packig deity lead to lower tability, ee Figure 3. The damage level i give a a fuctio of the tability umber. The wave teepe wa the ame for all tet. Accordig to Va der Meer (988c) each data poit i a idepedet tet (o cumulative damage by icreaig the wave height i coecutive tet ru). 4 Three poit are added to Figure 3. d Agremod et al. (999) performed tet o armour uit i a igle layer. Oe of thee uit wa the tetrapod. It appeared that tetrapod i oe layer are ot table at all. The tability reult are how i Figure 3. The packig deity wa oly φ.48. Neverthele, the data are very ueful to fid a expreio for the ifluece of the packig deity o tability, the factor f(φ). Firt of all geeral curve through the data poit i Figure 3 would have more or le the ame hape. I order to decribe the packig deity, the average hift with repect to o damage N od i take ito accout. Thi i the reao why i equatio 9 ad f(φ) i placed behid the umber.85 ad Fially the packig deitie give i the Shore Protectio Maual (984) were take a referece: φ SPM. The actual packig deity i the decribed by φ/φ SPM, which give uity if the packig deitie of the Shore Protectio Maual are ued. Figure 4 give the reult. The factor f(φ) i give a a fuctio of φ/φ SPM. Icludig the reult of a igle layer of tetrapod, a traight lie i the oly correct iterpretatio of the reult. The ifluece of the packig deity o tability ca be decribed by: f ( φ ).4 +.6φ / φ SPM (3) I cocluio, equatio 9 ad, i combiatio with equatio ad 3, give the tability of a armour layer of tetrapod, icludig the ifluece of cret height ad packig deity. It might be poible that equatio ad 3 ca alo be applied to the tability formula 4 for cube, but more reearch i required to prove that. I order to give a firt gue of the ifluece of cret height ad packig deity o the tability of cube, equatio 4 become:

5 Reductio coefficiet f( ) Packig deity φ/φ φ/φ SPM Figure 4 Ifluece of packig deity o tability (of tetrapod) D N 6.7 N.4 od.3.4 Cumulative damage. +. f ( φ ) om f ( Rc / D ) (4) With regard to cumulative effect of multiple evet, the lope i each tet of all the reearch decribed above wa rebuilt after each tet. Cumulative damage for differet wave height wa ot meaured. I practice, however, a tructure like a breakwater i very ofte teted i a wave flume or bai by coecutive tet ru with icreaig wave coditio. If damage tart at a certai wave height, a ext tet ru will icreae thi damage. The formulae ca alo be ued to calculate uch cumulative damage. The procedure i a follow: calculate the damage for the firt wave coditio calculate for the ecod wave coditio how may wave would be required to give the ame damage a caued by the firt wave coditio add thi umber of wave to the umber of wave uder the ecod wave coditio calculate the damage uder the ecod wave coditio with the icreaed umber of wave calculate for the third wave coditio how may wave would be required to give the ame damage a caued by the ecod wave coditio, etc. Actually, the ifluece of the umber of wave o tability ha bee decribed i a very imple way. I fact the formula are oly valid for umber of wave betwee about 7 ad 5. Oe may improve the rage i the followig way, alo baed o exteive experiece with rock lope (Va der Meer, 988a): The ifluece of the umber of wave i accordig to above give formulae i the rage N 7. Betwee N the damage icreae liearly from to the damage foud for N. Further, for N > 7 the damage i limited to the damage foud for N 7. Thi procedure hould be ued i combiatio with the above procedure for calculatig cumulative damage. 3 ONE-LAYER SYSTEMS 3. The ytem The covetioal two-layer ytem ha bee ued for may year ad i till very popular. A firt layer i placed with o top aother layer. The uit have more or le iterlockig, depedig o the hape, but i fact the tability of uch a layer deped maily o tability of idividual uit. If damage tart, thi damage will icreae if the wave height icreae. The problem with very heavy uit (ay heavier tha -3 to) might be that placig ad rockig may lead to breakage of the uit ad coequetly to large damage to the tructure. Doloe ad tetrapod are fairly eitive for breakage if they become too large. The bet kow uit i a oe-layer ytem i the accropode. More recetly the core-loc wa iveted. Geerally they have imilar behaviour although ome differece exit. Accropode are radomly placed i oe layer, but o a very trict placig patter. The uit are placed a cloe a poible to each other. Core-loc are placed le trict ad are eve propoed to be ued for repair of damaged layer with doloe. Both accropode ad core-loc are trog uit. Eve if a leg break, till 9% of it origial weight i left, icludig mot of it iterlockig with other uit. 5

6 3 damage N od.5.5 accropode tart damage failure deig KD core-loc KD6 tetrapod tability umber / Figure 5 Stability of accropode The behaviour of thee uit uder wave attack i differet from covetioal two-layer ytem. Firt wave attack after cotructio will give ome ettlemet to the layer. Thi caue a complete packed layer where every uit make cotact with ome eighbour. I fact looe uit do ot exit aymore ad rockig ca hardly be oberved. I fact a oelayer ytem react a a itegral layer, where a twolayer ytem react o tability of idividual uit. Stability tet how (reult are dicued later) that accropode ad core-loc are table to a very high wave height. A oo a damage tart for thee high wave height a fairly udde failure of the whole tructure occur. I firt itace, uch a progreive failure may look quite dagerou. But thi behaviour may tur ito a advatage if a proper afety factor i ued for deig. If a afety factor of.3 i ued o the tability umber for tart of damage, it mea that if the deig wave height i uderpredicted by or %, othig will happe! Thi i cotrat to two-layer ytem, where damage icreae with icreaig wave height. Oe of the mai reao to chooe for a oe-layer ytem i a ecoomical factor. A oe-layer ytem mea a large avig i cocrete for the armour layer. It hould be oted that the differece i volume of cocrete required for both ytem i ot really the actual avig i cot. A the dimeio of the breakwater will be more or le imilar, the avig i volume of cocrete ha to be ubtituted by (cheaper) rock. Still a ubtatial avig i poible. Oe of the mai argumet agait a ew uit ha alway bee the lack of experiece. But with more tha breakwater built with accropode, thi i ot loger a valid argumet. For core-loc it i till valid a oly a few tructure have bee built with thee uit. But core-loc ad accropode are quite imilar ad their behaviour i imilar too. All together oe may coclude that a oe-layer ytem with accropode or core-loc give cheap ad reliable tructure. Therefore, it i recommeded to compare a covetioal deig alway with a oelayer ytem. 3. Accropode Figure 5 give the tet reult for accropode a foud by Va der Meer (988c). Tet are oly valid for a lope of :.33, but a imilar behaviour i expected for :.5. The torm duratio ad wave period howed o ifluece o the tability of accropode ad the "o damage" ad "failure" criteria were very cloe. The tability, therefore, ca be decribed by two imple formulae, ie. a fixed tability umber: tart of damage, N od : 3.7 failure, N od > : 4. (5) (6) Compario of equatio 5 ad 6 how that tart of damage ad failure for accropode are very cloe, although at very high / D -umber. It mea that up to a high wave height accropode are completely table, but after the iitiatio of damage at thi high wave height, the tructure will fail progreively. Therefore, it i recommeded that a afety coefficiet for deig hould be ued of about.5 o the / D -value. Thi mea that for the deig of ac- 6

7 cropode oe hould ue the followig formula, which i cloe to deig value of cube ad tetrapod: for deig:.5 (7) Thi i alo a value that i ued by Sogreah to deig accropode layer (K D ). Although accropode may fail i a progreive way for high wave height, ue of a afety coefficiet chage it to a afe tructure which ha the followig advatage with repect to other uit. If the deig wave height for cube or tetrapod i uder-etimated, a higher wave height tha expected may lead to icreaed ad udeirable damage. If the wave height for a accropode layer i uder-etimated up to 5%, i fact othig happe. No damage i expected a the tability umber i till lower tha the oe for tart of damage. The 5% i of coure baed o ideal tetig coditio. But i practice oe may rely at leat o -3% afety beyod give deig coditio. 3.3 Core-loc The recetly developed core-loc ha a imilar tability behaviour a accropode, although limited tet reult have bee publihed. It might be that the core-loc i eve a little more table tha the accropode. Thi wa dicued at the coferece after the preetatio of thi paper. Some reearcher had teted both accropode ad core-loc ad foud that core-loc howed le movemet i the layer (after ettlemet) tha accropode. Reult have ot yet bee publihed. The deig value give for core-loc i K D 6 which i a little higher tha for accropode. The tability umber for a :.33 lope become: for deig:.78 (8) Thi value i give i Figure 5 too. Although the differece with accropode (equatio 7) look mall, the differece i weight i a avig of 7%. The mai advatage of accropode at thi momet i the large experiece i cotructio of breakwater. Oly a few tructure have bee built with core-loc. But core-loc may be more uitable for le trict placig which mea that repair of local damage could be eaier with core-loc. 3.4 Cube The experiece of may reearcher, who have built tet ectio of breakwater with a double layer of cube, i that it i ot eay to place thee two layer radomly. The mai reao i that, due to the hape of a cube, cube like to lay i oe layer. Bhageloe (998) teted oe-layer ytem with rock, tetrapod ad cube. The reult have alo bee publihed by d Agremod et al. (999). The mai cocluio wa that a igle layer of cube wa remarkably table. Reearch wa cotiued with cube. The fial reult ca be foud i thi proceedig, the paper by Va Get et al. (999). The teted tructure had a lope of :.5. Oe remark hould be made a a warig: a igle layer of cube i table o the eaide, but ca ot withtad heavy wave attack o the cret. A igle layer of cube hould oly be coidered if the overtoppig i limited to ay le tha %. damage N od oe layer tw o layer tart damage failure deig KD tability umber / Figure 6 Stability of a igle layer of cube 7

8 For ifluece of packig deity, water depth ad ize of uder layer oe i referred to Va Get et al. (999). The fial reult are ummarized i Figure 6. A imilar behaviour i foud for a igle layer of cube a for accropode ad core-loc. The tructure i table up to a fairly high tability umber, but fail for oly little higher wave height. Thi behaviour ca be decribed by: tart of damage: 3. D failure: 3.75 D (9) () Both value are give i Figure 6. The mai item to be decided o i the required afety factor for deig purpoe. Figure 6 give alo reult for a covetioal double layer of cube (from Va der Meer, 988c), icludig 9% cofidece bad. It i clear that a igle layer i more table tha the covetioal tructure. O the other had, oe ca ot accept a lot of damage to a igle layer of cube a uder layer rock will diappear after iitial damage: there i oly oe layer! A covetioal double layer of cube will ofte be deiged for limited damage, ay N od. I Figure 6 thi i for about / D., which i imilar to K D 7. If a igle layer of cube will be deiged for thi value it mea that a covetioal double layer ad a igle layer will require the ame weight. The afety factor with repect to actual tart of damage i for the igle layer of cube 3./..36. Thi i lower tha the factor.5 foud for accropode. The afety factor with repect to failure i 3.75/..7, which i a little higher tha for accropode: 4./ I average imilar afety factor are foud. Therefore it i cocluded that above propoed deig value for a igle layer of cube give imilar afety a for accropode. Thi mea: for deig:. ( 4 OVERALL COMPARISON The brochure of accropode give a table with ome characteritic of a few uit. That table ha bee exteded to iclude all the uit treated i thi paper ad ha bee exteded by a few more characteritic value. Table give a good compario of variou cocrete uit which are available to protect breakwater uder wave attack. The table i baed o uit with a weight aroud 3 to. Table how that covetioal layer are deiged for ome damage, where the igle-layer ytem ue o damage. O the other had le damage hould be accepted for the thee igle layer. With the packig deity φ it i poible to calculate the required volume of cocrete per m o the lope a a fuctio of the igificat wave height, uig a ma deity for cocrete of 4 kg/m 3. The relative volume of cocrete ca be calculated if the differet lope are take ito accout. ere % i equal to the required volume for accropode. It i clear that accropode ad core-loc give large avig i required volume of cocrete. Oe hould remember, however, that geerally the cocrete volume aved hould be ubtituted by (cheaper) rock. The relative avig i volume of cocrete i ot equal to the actual avig i total cot. Table. Compario of variou cocrete uit for deig of armour layer Accropode Core-Loc Tetrapod Cube Cube umber of layer lope :4/3 :4/3 :,5 :,5 :,5 K D (breakig wave) / D N,5,8,,, damage N od,5,5 damage % 5 5 packig deity φ,6,56,4,7,7 cocrete per m o lope,8,48,35,37,36 relative volume of cocrete % 8% 8% % 4% 8

9 The igle layer of cube i alo a attractive olutio. The productio of mould for cube i eaier ad probably cheaper tha for the complicated uit hape of accropode ad core-loc. It may alo be eaier to place a igle layer of cube, although practical experiece i lackig. The mai limitatio of a igle layer of cube i that oly o-overtoppig tructure ca be deiged. REFERENCES Bhageloe, G.S Golfbreker met ee ekele toplaag (breakwater with a igle-layer). MSc-thei, Delft Uiverity of Techology, alo Delft ydraulic Report d Agremod, K., E. Berede, G.S. Bhageloe, M.R.A. va Get ad J.W. va der Meer 999. Breakwater with a igle-layer. Proc. COPEDEC- V, Capetow. De Jog, R.J Wave tramiio at low-creted tructure. Stability of tetrapod at frot, cret ad rear of a low-creted breakwater. MSc-thei, Delft Uiverity of Techology. Shore Protectio Maual 984. US Army Corp of Egr, CERC, US Govt. Pritig Ofice, Wahigto, DC Va der Meer, J.W. 988a.. Rock lope ad gravel beache uder wave attack. Doctoral thei, Delft Uiverity of Techology. Alo DELFT YDRAULICS Publicatio o Va der Meer, J.W. 988b.. Determiitic ad probabilitic deig of breakwater armour layer, Proc. ASCE, Joural of WPC ad OE, Vol. 4, No.. Va der Meer, J.W. 988c. Stability of Cube, Tetrapod ad Accropode, Deig of Breakwater, Thoma Telford. Proc. Breakwater '88 Coferece, Eatboure. Va der Meer, J.W., Coceptual deig of rubble moud breakwater, DELFT YDRAULICS Publicatio umber 483. Va Get, M.R.A., S.E. Plate, G.B.. Spaa, J.W. va der Meer & K. d Agremod 999. Sigle-layer rubble moud breakwater. Proc. Coatal Structure 99, Satader. 9