Optimization of pile design for offshore wind turbine jacket foundations

Size: px

Start display at page:

Download "Optimization of pile design for offshore wind turbine jacket foundations"

Darren Walton
6 years ago
Views:

1 Downloae from orbit.t.k on: May 11, 2018 Optimization of pile esign for offshore win trbine jacket fonations Sanal, Kasper; Zania, Varvara Pblication ate: 2016 Docment Version Peer reviewe version Link back to DTU Orbit Citation (APA): Sanal, K., & Zania, V. (2016). Optimization of pile esign for offshore win trbine jacket fonations. Paper presente at 12th EAWE PhD seminar on Win, Lyngby, Denmark. General rights Copyright an moral rights for the pblications mae accessible in the pblic portal are retaine by the athors an/or other copyright owners an it is a conition of accessing pblications that sers recognise an abie by the legal reqirements associate with these rights. Users may ownloa an print one copy of any pblication from the pblic portal for the prpose of private sty or research. Yo may not frther istribte the material or se it for any profit-making activity or commercial gain Yo may freely istribte the URL ientifying the pblication in the pblic portal If yo believe that this ocment breaches copyright please contact s proviing etails, an we will remove access to the work immeiately an investigate yor claim.

2 OPTIMIZATION OF PILE DESIGN FOR OFFSHORE WIND TURBINE JACKET FOUNDATIONS Kasper Sanal 1 DTU Win Energy Roskile, Denmark Varvara Zania 2 DTU Civil Engineering Kgs. Lyngby, Denmark ABSTRACT The aim of this sty is to se nmerical methos of strctral esign optimization to esign piles for offshore win trbine jacket fonations. Pile mass is minimize with constraints on axial an lateral capacity. Reslts inicate that accrate knowlege abot soil characteristics can translate into significant cost rections. i l t = External iameter of the pile (m) = Internal iameter of the pile (m) = Length of the pile (m) = Thickness of pile wall (m) NOMENCLATURE INTRODUCTION Fonation an sbstrctre for offshore win trbines can amont to more than 20 % of the capital expenitre in a project. Pile-anchoring a jacket fonation to the seabe reqires to first perform a geological srvey to map the soil characteristics an then esign a pile with sfficient capacity to carry the loas from the sbstrctre. Strctral optimization [1] is the science of achieving the optimal loa carrying strctre. Given an objective sch as compliance or cost, an some constraints sch as limitations on the maximm stress or isplacement, the optimal strctre is efine as the one that minimizes the objective fnction while satisfying the constraints. A pile fonation is a slener hollow cyliner that is inserte into the soil. Anchoring by riven piles has been se extensively in the oil an gas instry, an in the last ecae also for offshore win trbines sing either monopiles or pile jacket fonations. Pile fonation esign is consiere in this sty accoring to the crrent state of practice for offshore fonations, see eg. [2], [3]. Axial an lateral capacities are calclate base on shaft friction an en bearing resistance an lateral resistance respectively. The obtaine ltimate loas formlate the esign basis. MODEL An analysis an optimization tool for jacket esign, JADOP, has been evelope at DTU Win Energy. In this sty JADOP is expane to incle pile esign. JADOP is a finite element package evelope in Matlab, with specific featres for esign optimization of win trbine spport strctres. The tower an sbstrctre are escribe by Timoshenko beam elements, an the loa set is applie by noal forces at the tower top (rotor loas), throghot the strctre (self-weight), an throghot the sbmerge part of the jacket (wave loas). The piles are assme to be slener hollow cyliners with constant iameter an thickness. For sch piles, the Ranolph formlation [4] provies an analytic relationship between forces an isplacements at the pile hea: F x F y F z M x M y [ M z ] K s K sθ 0 x 0 K s 0 K sθ 0 0 y 0 0 K = v z 0 K m 0 K mθ 0 0 θ x K m K mθ 0 θ y [ K T ] [ θ z ] (1) 1 PhD stent, Department of Win Energy, Technical University of Denmark, kasp@t.k 2 Associate Professor, Department of Civil Engineering, Technical University of Denmark, vaza@byg.t.k EAWE PhD Seminar

3 All the entries in the pile stiffness matrix are continos ifferentiable fnctions of soil properties an pile esign variables: K s = G s ( E eq G s ) K T = G p 3 ( πl ), 1 7 2, K sθ = K m = ( E eq G s ) K v = 2G p (1 υ)π (1 + 1 υ ζ E eq = E si s + E p I p, I I s + I p = π(2 i p 64 2 ) 3 7 ( 2 ) 2 l tanh μl μl, (μl) 2 = 2G p ( 2l 2 ζe p ) 5l(1 v), ζ = ln, K mc = ( E 5 3 eq 7 ) ( G s 2 ) (2) ) (3) where E s, G s, I s, E p, G p, an I p are the Yong s mols, shear mols, an inertia of soil an pile, respectively. v is the Poisson ratio of the pile material. Axial pile capacity can be ivie into friction capacity, Q f, an en bearing capacity Q b. The pile capacity in compression an tension are efine as Q c = Q f + Q b an Q t = Q f, respectively. Q f an Q b are given for clay, see eqations (5-6), an for san, see eqations (7-8), where b φ, f max,φ, N q,φ, an q b,max,φ are efine with respect to friction angle φ in Table 1 [3]. Q f clay (, l) = z=0 π 1 2 ( s 1 γ z ) 2 s z L + π 1 2 ( s 1 γ z ) 4 s z, = s γ (5) 2 ) Q clay b (, t, l) = min ( 9s π2 4, 9s π(2 i + Q 4 f ( i ) ) (6) L Q san f (, l) = πb φ γ z z + πf max,φ z, = f max,φ z=0 b φ γ (7) Q san b (, t, l) = min ( min(n q,φ γ L, q b,max,φ ) π2 4, min(n q,φγ L, q b,max,φ ) π i 4 + Q f( i, l) ) (8) Lateral resistance is assme to be the yiel bening moment of the pile cross section: Q M (, t) = 2σ yi p (, t) D (9) where σ y = 350 MPa is the yiel stress of the pile. Eqivalent lateral loa is compte by Broms theory [5]: 2 (4) M clay eq (, t, l) = 0.5 9s F F + M, M san eq (, t, l) = (K p γ ) 0.5 F1.5 + M, K p = tan 2 (45 + φ 2 ) (10) The esign basis is now efine as Q t F z Q c an Q M M eq Q M for each of the for piles, an lateral capacities in both x- an y-irections. Since this esign basis is only vali for slener piles, we constrain the length to be at least 10 times the iameter. For riven piles, API also recommens the pile thickness t D (m) [3]. OPTIMIZATION PROBLEM Let the variables be efine as iameter, thickness, an length of a pile, an let the for piles be ientical. The variables are then bone above an below to avoi nrealistic esigns. The objective fnction is pile mass, since this is assme to be the main cost river. The constraints are the esign basis for the piles. 100 minimize c(x) = ρπ( 2 ( 2t) 2 )l x=(,t,l) R 3 sbject to F z,i (x) Q t (x) 0, i = 1,,4 F z,i (x) Q c (x) 0, i = 1,,4 M eq (x) Q M (x) 0, i = 1,,4 M eq (x) + Q M (x) 0, i = 1,,4 l 0 10 (12) EAWE PhD Seminar

4 t 0 x x x 12 th EAWE PhD Seminar on Win Note that both the forces an the capacities are fnctions of the esign variables. In the capacities there are some non-smooth fnctions, bt this can in all cases be taken care of by splitting the non-smooth constraint into mltiple constraints that are smooth. The sensitivities are compte analytically for all fnctions, bt for brevity they are not written ot here. The problem is formlate as a simltaneos analysis an esign (SAND) problem. This means that i) the finite element system oes not have to be solve in every iteration, bt is impose as a constraint, an ii) any soltion that has not converge is in general not a soltion at all. In the nmerical examples shown here, all optimization rns have converge, so this is not a problem. NUMERICAL EXAMPLES Three nmerical examples are presente in this sty to emonstrate the feasibility of pile esign optimization an how it can be se to gain frther insight abot the engineering process: 1. The optimization problem in eqations (12) is solve once, see Figre The optimization problem in eqations (12) is solve a nmber of times with incremental change in the soil properties of clay. 3. The optimization problem in eqations (12) is solve a nmber of times with incremental change in the soil properties of san. The strctre above the piles is moelle to replicate the Innwin reference jacket [6], an is not moifie in the optimization. Note also that the initial pile esign is an average of the variable bons, an oes not represent any reference esign. JADOP comptes analysis an sensitivities, an the optimization problem is solve in IPOPT [7]. Figre 1. Overview of nmerical example #1. The strctral moel an variable bons are also se in nmerical examples #2 an #3. Table 1. Soil properties of san which epen on the friction angle of the soil. See eqations (2-4) for san capacities. φ [ ] b φ [ ] f max,φ [kpa] N q,φ [ ] q b,max,φ [MPa] RESULTS AND DISCUSSION 1. The optimize mass was 153 tons for the for piles in total, an the iameter, thickness, an length was 2080 mm, 27.1 mm, an 28.0 m respectively (Figre 1. The optimization converge after 20 iterations in less than 10 secons. This example shows that the optimization problem (12) can be se to optimize the pile esign for a given strctre EAWE PhD Seminar

5 when the geotechnical ata is known. Withot any preconceptions abot the esign, except that it shol be a slener hollow cyliner, the soltion to (12) generate a pile esign that has low mass an satisfies the esign basis. 2. Nmerical example #2 (Figre 2, clay) shows how sensitive the pile esign is to the weight an shear strength of the soil. All ata points represent a pile esign that has been optimize in the same way as nmerical example #1. Pile esign in clay is very sensitive to nraine shear strength, an the higher the strength, the lower the pile mass. 3. Nmerical example #3 (Figre 2, san) is similar to nmerical example #2. Pile esign in a sany soil is sensitive both to the weight of the soil, an to the angle of friction. For average soil conitions it appears that sany soil reqires heavier piles. The nmerical examples show that changes in soil properties can change the reqire pile mass with a factor of as mch as 2 or 3. For a large offshore win farm site with varying soil properties, there can therefore be a large cost rection potential if one maps the geotechnical ata all over the site. Then one can optimize the pile esign specifically for each trbine, an avoi expensive conservative esigns. In sch sitation, the avantage of an atomatic pile optimization methoology as presente here is particlarly sefl. Figre 2. Reslts of nmerical example #2 (clay) an #3 (san). See Table 1 for parameters epening on the friction angle in sany soil. The non-smooth behavior of the pile mass with respect to nraine shear strength of clay is assme to be e to a local minimm in the optimization. CONCLUSION It is emonstrate that preliminary pile esign can be atomate sing strctral optimization. We observe that in clay, the pile esign is highly sensitive to the shear strength of the soil. For piles in san, we observe that both nit weight an angle of friction has a high inflence on the total mass of the piles. The pile mass can change with a factor of 2 or 3 when the soil parameters change. This implies that the geotechnical ata shol be mappe for each win trbine in the offshore win trbine site. Frthermore, if the piles are esigne specifically for each trbine, one can obtain significant cost rections compare to the case where the worst conition is se for all pile esigns. The main limitation of this sty is that the esign basis assmes only one soil layer, while mltiple layers is often the case in reality. ACKNOWLEDGEMENTS This work is part of the Danish strategic research project ABYSS ( fne by Innovation Fn Denmark. Collaboration with Dr. Alexaner Verbart in the evelopment of JADOP is mch appreciate. REFERENCES [1] Bensøe, MP, Sigmn, O (2004). Topology optimization, Springer Verlagt [2] DNV (2010). Design of offshore win trbine strctres. Offshore Stanar DNV-OS-J101 [3] API (2011).. Geotechnical an fonation esign consierations. ANSI/API RP 2GEO 1st eition Petrolem an natral gas instries: Specific reqirements for offshore strctres, Part 4 [4] Ranolph, MF (1981). The response of flexible piles to lateral loaing, Geotechniqe, 31(2), [5] Broms, BB (1964), Lateral Resistance of Piles in Cohesive Soils, Proceeings of the American Society of Civil Engineers, Jornal of the Soil Mechanics an Fonations Division, Vol. 90, SM2 [6] Ramboll (2013), Design Report Reference Jacket, INNWIND.EU [7] Wächter A, Biegler, LT (2006). On the Implementation of a Primal-Dal Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming 106(1), pp EAWE PhD Seminar

A Blue Lagoon Function

A Blue Lagoon Function Downloaded from orbit.dt.dk on: Oct 11, 2018 A Ble Lagoon Fnction Markorsen, Steen Pblication date: 2007 Link back to DTU Orbit Citation (APA): Markorsen, S., (2007). A Ble Lagoon Fnction General rights