Stability of Rock Berm under Wave and Current Loading

Transcription

1 The Proeeding of The Tenty-third (13) International OFFSHORE AND POLAR ENGINEERING CONFERENCE Anhorage, Alaka, USA, June 3-July 5, 13, Paper TPC_61 Stability of Rok Berm under Wave and Current Loading N. I. Thuyanthan 1, S. Jegandan, D. J Robert 3 1 CAPE Group, Singapore; Inteea UK, 3 Monah Univerity, Autralia ABSTRACT Rok berm are ued for many different offhore appliation. Thee appliation inlude ue of rok berm for protetion of offhore pipeline from anhor and traler; for mitigating upheaval bukling of pipeline, for mitigating lateral bukling of pipeline; for our protetion. In order for the rok berm to perform it funtion, it i vital that the rok berm i table under the deign ave and urrent ondition. Thu it i vital that rok berm tability i aeed orretly. Thi paper preent an overvie of fundamental of rok berm tability aement under ave and urrent ondition. Reult preented in thi paper ill benefit the pipeline engineer involved in rok berm deign for Front End Engineering Deign (FEED) and detailed deign. KEY WORDS: Rok berm; eabed tability; Chézy oeffiient; hield parameter; threhold of motion; ave and urrent loading INTRODUCTION There are thouand of kilometer of offhore pipeline around the orld, forming a netork for the extration and tranportation of the oil and ga produt. Rok berm are ued for many different offhore appliation; ued for protetion pipeline from anhor and traler; for mitigating upheaval bukling of pipeline, for mitigating lateral bukling of pipeline; for our protetion. The rok berm tability aement determine the minimum partile ize of rok that ould be table under a given berm onfiguration and under deign ave and urrent ondition. The fundamental for the tability of rok berm alulation ome from threhold of motion of ediment. The tati tability of the eabed partile/ediment i determined by threhold of motion of the partile and the hear tree indued on the partile by the ave and urrent ation. For very lo flo, the rok/grain remain immobile. A the flo rate inreae, the hear tree applied on the partile inreae and reah a threhold value at hih fe rok/grain begin to move. Thi hear tre i knon a the threhold bed hear tre. The orreponding value of urrent peed or the ave height i knon a the threhold urrent peed or the threhold ave height. For table eabed, D 5 of the eabed partile need to be greater than the D 5 orreponding to the threhold of motion. Thi paper revie the fundamental of threhold of motion and preent the importane of Shield parameter and Chézy oeffiient in rok beam tability aement. Parametri tudy of eabed mobility (or rok berm tability) a undertaken for varying ave and urrent ondition. Reult of the tudy are preented in graphial form to implify the rok berm tability aement and determine the table rok izing for a given rok berm geometry. SEABED MOBILITY The eabed mobility depend on the prevailing flo ondition. The flo ondition an be laified a; Current alone dominant (ite deeper than about 4 m) Wave alone dominant (near-hore zone in depth le than 5 m) Combined ave and urrent (ite in depth beteen 5 m and 4 m) Seabed feature and ubtrate are influened by the prevailing flo ondition and hene an hange patially and in time. Hoever, the eabed ediment on the ontinental helf are in long-term equilibrium (at leat deadal) ith the prevailing hydrauli limate. Gravel ubtrate orrepond to thoe area experiening the tronget urrent, hilt muddy ediment orrepond to eak urrent and area of and orrepond to intermediate urfae urrent trength of.3 to.8 m/. ROCK BERM STABILITY METHODOLOGY Over the year, there ha been lot of reearh publiation on threhold of motion and rok berm tability alulation. Thi ha led to many uer referring to uh publiation and uing the equation propoed in the literature ithout fully undertanding the overall limitation and boundarie of thoe equation. Different ymbol ued in literature for the ame parameter alo lead to unneeary onfuion among pratiing engineer. Thu ymbol and equation in thi paper follo

2 the original referene and in ome oaion the ame equation i provided tie ith different ymbol to avoid any onfuion. Thi paper aim to provide the to main fundamental methodologie that an be ued for the eabed mobility aement. Thee are; 1. Methodology 1- baed on Shield parameter (Soulby, 1997). Methodology - baed on CIRIA Rok Manual (7) METHODOLOGY 1 In thi methodology, the tability of the rok-berm i determined by threhold of motion hear tre of the rok partile and the hear treed indued on the rok partile by the ave and urrent ation. For table rok-berm, the D 5 of the rok-berm need to be greater than the D 5 orreponding to the threhold of motion. Threhold Bed Shear tre The threhold bed hear tre i ommonly expreed in nondimenional form a ritial Shield parameter. r r g ( 1) d Where r = threhold bed hear tre (N/m) = denity of ater (kg/m3) = ratio of denity of eabed partile to denity of ater d = partile diameter (taken a D 5 ) g = aeleration due to gravity (9.81 m/) D 5 = alo knon a median diameter or medium value of partile diameter, it i partile diameter value at hih umulative ditribution perentage reahe 5%. The ritial Shield parameter for and on initially flat horizontal bed an be alulated a belo..3 r.55[1 exp(.d* )] 11.3D* () here 1/ 3 g( 1) D* d, = kinemati vioity of ater m/ The reearh in eabed movement, Panagiotopoulo et al,(1997) ha hon that the oheive material generally inreae the eroion threhold of andy depoit. The ritial bed hear tree required to diplae fine-grained and inreaed by up to 9% ith the addition of ~1% lay. For higher lay ontent the threhold hear tre an inreae by -3 fold, hene eabed ith ilty layey and are le ueptible than pure and to ave and urrent indued movement. If the eabed mobility aement i for mixture of mud and and, then Mithener et al, 1996, preented the equation belo for ritial bed hear tre (3) r b here b i the bulk denity (kg/m 3 ) of ediment. (1) If the bed i loping or tability i for a rok-berm ith a lope, then gravity provide a omponent of the fore on the grain hih may inreae or dereae the threhold hear tre required for mobility depending of the lope diretion. The threhold bed hear tre, τ βr, for a grain on a bed loping at an angle, β, to the horizontal in a flo making an angle, ψ, to uplope diretion an be related to the threhold ritial hear tre value for the ame grain on a flatbed by the folloing equation. r r here ψ β o in [o tan in in tan inident angle to lope angle of repoe (taken a 3 deg in thi paper) lope angle Fig. 1. Rok Berm lope ] 1/ Bed hear tre The bed hear tre ating on the bed i made up from ontribution due to Skin frition Form drag Sediment-tranport (aued by momentum tranfer) It i important to note that only kin frition ontribution at diretly on the ediment grain and it i therefore thi ontribution hih i ued to alulate the threhold of motion, bedload tranport and pik-up rate for grain in upenion. On the other hand, it i the total bed hear tre that orrepond to the overall reitane of the flo and determined the turbulene intenitie hih influene the diffuion of the upended ediment to higher level in ater olumn. When the bed i flat and ediment tranport i not too intene, then the total bed hear tre i equal to the kin-frition ontribution. 1. Bed hear tre due to urrent Note that the hear tre due to urrent (τ ) an be alulated uing different method (There an be 5% differene beteen the larget and loet alulated value of τ etimate). In thi paper, the hear tre due to urrent, τ, i alulated uing frition veloity, u *, a belo. u * here 1/ 7 d5 u*.11 U ( z) z z i ditane from eabed ρ = denity of ater (kg/m 3 ) d 5 = D 5 partile diameter (taken a D 5 ) (4) (5)

3 Alternatively, drag oeffiient an be ued to alulate the hear tre a hon belo. (6) C D U here U = depth averaged veloity C D = drag oeffiient, (thi an be taken a.5 if no information i available) C D an be alulated either baed on a logarithmi veloity profile in urrent, or by relating to Chezy oeffiient C. A. Baed on a logarithmi veloity profile in urrent, C D alulated a belo..4 an be C D 1 ln ( z / h) (7) Where z d 5 /1 and h i ater depth. B. Baed on Chezy oeffiient C, C D an be alulated a belo. g C D C (8) here C 18 log(11h / k ) k i hydrauli roughne (made of grain roughne and bed form roughne), for flat bed, k an range from D 5 for fine ediment to 4D 5 for oare ediment. k i taken a.5 D 5. Bed hear tre due to ave Shear tre due to ave an be alulated a belo. 1 f U here U f = bottom orbital veloity U rm ( here U rm i obtained from JONSWAP petrum) = ave frition fator, 1.39 (A/z ) -.5, here z d 5 /1, and emi orbital exurion A = U T p /π. (T p i the period aoiated ith the peak of the ave energy petrum). 3. Bed hear tre due to ombined urrent and ave The bed hear tree beneath ombined ave and urrent are enhaned beyond the value hih ould reult from a imple linear addition of the ave- alone and urrent alone tree. Thi i beaue of a non-linear interation beteen the ave and urrent boundary layer. There are more than different theorie and model hih aim to apture thi interation. The bet fit to mot model and data have been aptured by the folloing mean hear tre, τ m m Where = bed hear tre due to urrent alone (9) (1) = bed hear tre due to ave alone The maximum bed hear tre i then obtained by, 1/ max [( m o ) ( in ) ] (11) Where θ i angle beteen urrent diretion and diretion of ave travel. τ max i ued for the alulation of threhold of motion and entrainment rate of ediment. When the ave and urrent indued τ max i equal to or greater than the threhold bed hear tre, τ βr, the bed i mobile. METHODOLOGY The traditional deign method for the hydrauli tability of rok fill i baed on the inipient motion or ritial hear onept. For unidiretional teady flo the initial intability of bed material partile on a horizontal, plane bed i deribed by the Shield riterion ame a Eq (1), but in etion of CIRIA Rok Manual the equation i preented ith different format ith different ymbol a belo, Shear tre parameter (1) r gd here i the hear tre (N/m²); r i the apparent ma denity of the tone (kg/m³); D i the ieve ize (m) taken a D 5. Threhold Bed Shear tre Thi riterion eentially expree the ritial value of the ratio of the de-tabiliing fluid fore (that tend to move the partile) to the tabiliing fore ating on a partile. The fore that tend to move the bed material partile are related to the maximum hear tre exerted on the bed by the moving fluid; the tabiliing fore are related to the ubmerged eight of the partile. When the ratio of the to fore, repreented by the hear tre (Shield) parameter, ψ, exeed a ritial value, ψ r, movement i initiated. ψ r =.3.35 for point at hih tone firt begin to move ψ r =.5.55 for limited movement 1. Bed hear tre due to urrent CIRIA Rok Manual alulate urrent-indued hear tre, τ, (N/m²), ating on the bed in teady flo uing the folloing equation, baed on Chézy roughne equation: U C g (13) here U i the depth-averaged urrent veloity (m/) and C i the Chézy oeffiient (m 1/ /) (18 Log (1 +1h/k )). When the bed i hydraulially rough ( u*k /ν > 7; a for rok) the value of C depend only on the ater depth, h (m), and the bed roughne, k (m). For uniform ediment the range of grain roughne i given by = 1 to. Depite atter, on average the bet reult eem to be k D 5 obtained uing k = D 9 x D 5 for fine ediment and k =

4 x D 9 4 x D 5 for oare material, auming no bed-form roughne. Thu, k = 4 x D 5 an be ued for rok.. Bed hear tre due to ave CIRIA Rok Manual reommend the folloing equation beteen maximum hear tre under oillatory flo, (N/m²), and the relevant hydrauli parameter. 1 f u (14) here f i the frition fator (-) and u i the peak orbital veloity near the bed (m/²), hih may be determined, a a firt approximation, by linear ave theory. f i determined auming z = k /3 uing.5 a f.37 (15) k Where a (m) i the amplitude of horizontal orbital ave motion at the bed a defined belo (T i ave period). T a u (16) 3. Bed hear tre due to ombined urrent and ave For the inipient motion of oare material in oillatory flo, the Shield riterion for the initiation of motion i taken a =.3 and r the average oillatory hear tre i ued to alulate the ritial hear tre, (N/m²), evaluated uing (.5 ). Thu baed on thi methodology, the partile tart to be mobile hen (.5 ) gd..3 r 5 PARAMETRIC STUDY ON STABILITY Baed on methodology 1, parametri tudy a undertaken to determine the table D 5 under ave and urrent ondition in flat eabed. H (ignifiant ave height) a ranged from 1m to 1m, T p a taken a 8 (T p i period aoiated ith the peak of the ave energy petrum, T z hih i zero roing period =.781 T p ). U (urrent veloity at 1m from eabed) a varied from.5m/ to 3m/. Reult of parametri tudy are preented in graphial form from Fig. to Fig. 9. Thi paper introdue an Amplifiation fator (AF). The AF i multiplied by the table D 5 for flat eabed (from Fig. to Fig. 5) in order to obtain the table D 5 for rok berm ith ide lope (1:4 or 1:3). WORKED EXAMPLE Let u aume e have to find out the table D 5 in ater depth of m ith U of.5 m/, H of 4m and T p of 8. We an ue Fig. to find the table D 5, it an be een that the table D 5 i ~7.5mm. Let u aume that e no need to find out, hat hould be the table D 5 for a rok berm ith 1:3 ide lope under the ame ave and urrent ondition. We already kno that the table D 5 flat eabed i ~7.5mm. We need to ue Fig. 8 to onlude that the amplifiation fator (on D 5 ize ) i ~4.5. Thu the D 5 for 1:3 rok berm i ~ 33.75mm (7.5 x 4.5). If e ue the equation, e ill derive 34.5mm. Thu the ue of hat i a quik ay to obtain D 5 for rok beam deign. If e ue Method to find out the table D 5 for the ame enario onidered above, the reulting D 5 for flat bed i ~7.88mm, hih i loe to the value obtained from Method 1. Here, k ha been onidered a x D 5 a the partile ize i more appropriate to be taken a fine partile. DISCUSSION Stability of eabed grain i baed on omparing the ave and urrent indued hear tre on the eabed ith ritial bed-hear tre. Thi onept i the ame for both methodologie 1 &, but the evaluation of ritial tre and the method of ombining urrent indued hear and ave indued hear are different in the methodologie. Thu it i vital that the to methodologie are not mixed and they hould be applied independently under the limitation of the methodology. The methodology baed on CIRIA Rok Manual produe loer indued hear tree than Methodology 1 (baed on Soulby, 1997). But it i important to note that thi differene i offet by three fat that are key for uing the CIRIA methodology orretly. 1. Indued hear tre the CIRIA Rok Manual tate, (pg 548) here the ritial hear tre i baed on the average hear tre under oillatory flo ( = ½ ), the hield parameter hould have a value of.3, to agree ith the reult Rane and Warren (1968) Wherea, the methodology 1 (Soulby, 1997) provide the hield parameter baed on D* and not fixed at.3, thu it methodology of ombining ave and urrent to obtain the indued hear tree i different to that of methodology.. Limitation of Methodology (CIRIA Rok Manual) It i to be noted that the CIRIA Rok Manual equation i appliable only under the ondition,. 4 (17) If equation (16) i not atified (i.e in relatively trong ave ombination ith eak urrent), CIRIA Rok Manual reommend the ue of Methodology Amplifiation fator in Methodology. CIRIA Rok Manual provide an Amplifiation fator ( k, equation of the rok manual) for the bed hear tre a a reult of ave uperimpoing upon urrent.. k 1 C u 1 f g U (18)

5 Wave breaking limit H =1 m H =1 m Fig.. Stable D 5 under U =.5m/, Tp= 8, H = 1m to 1m. Wave breaking limit H =1 m H =1 m Fig. 3. Stable D 5 under U =1m/, Tp= 8, H = 1m to 1m.

6 Wave breaking limit H =1 m H =1 m Fig. 4. Stable D 5 under U = m/, Tp= 8, H = 1m to1m Wave breaking limit H =1 m H =1 m Fig. 5. Stable D 5 under U = 3 m/, Tp= 8, H = 1m to 1m.

7 Fig. 9. Amplifiation on table D 5 for rok berm of 1:4 & 1:3 under U =.5m/,1m/ Tp= 8, H = 3m. Fig. 6. Effet of Tp on table D 5 under U =1 m/, H = 1m to 3m. Fig. 6 ho the effet of Tp on the D 5 for given H. It an be onluded that effet of Tp i only prominent for ater depth belo ~5m. Fig. 7 and Fig. 8 are amplifiation fator (AF) to be applied to the D 5 obtained for flat eabed (from Fig. to Fig. 5) for rok beam ith ide lope 1:4 and 1:3 repetively. Fig. 9 ho the effet of U on the amplifiation fator. A U inreae (U i the urrent veloity 1m above eabed), the AF dereae for ater depth belo ~15m and inreaed for ater depth above ~15m. CONCLUSION Thi paper preented to fundamental methodologie (Methodology 1- baed on Shield parameter (Soulby, 1997) and Methodology - baed on CIRIA Rok Manual (7)) for tability aement of rok beam. Fig. 7. Amplifiation on table D 5 for rok berm of 1:4 under U =.5m/, Tp= 8, H = 1m to 1m. Key fator to be onidered in uing the methodologie orretly ere highlighted in thi paper. Parametri tudy (baed on Methodology 1) a undertaken for ranging ater depth, ave height and urrent ondition. The reult ere preented in graphial form uh that thee an be ued a deign hart by engineer to eaily and quikly obtain the table D 5 ize for rok on flat eabed or rok berm of 1:3 or 1:4 lope ith varying ater depth (-3m). REFERENCES Fig. 8. Amplifiation on table D 5 for rok berm of 1:3 under U =.5m/, Tp= 8, H = 1m to 1m. CIRIA Rok Manual C683, 7. Mithener, H. and Torf, H., Eroion of mud/and mixture, Journal of oatal engineering, Volume 9, page 1-5. Panagiotopoulo, G. Voulgari, M. B. Collin, The influene of lay on the threhold of movement of fine andy bed, Coatal Engineering, Volume 3, Iue 1, Otober 1997, Page Soulby, R, 1997, Dynami of marine and - a manual for pratial appliation, HR Wallingford, Thoma Telford, 1998.