Prof. Dr.-Ing. Martin Achmus Institute of Soil Mechanics, Foundation Engineering and Waterpower Engineering Monopile design Addis Ababa, September 2010
Monopile design Presentation structure: Design proofs required Calculation method (p-y) Consideration of large pile diameters Consideration of cyclic loading effects 2
Monopile foundations Foundation Substructure Superstructure Up to now mostly monopile foundations in North and Baltic Sea Pile diameter initially around 3m, recently 5m and more Usual requirement: maximum permanent inclination < 0.5 Effect of cyclic loading? Special for offshore windmills: large diameters, large H/V ratio
Projects carried out until 2008 4
Required design proofs for Monopiles Bearing capacity and Serviceability under lateral (and axial) loads Consideration of cyclic effects (strength degradation / cyclic stability, accumulation of displacements) Worst- and best case-analyses regarding the stiffness under operational loads (calculation of natural frequency) 5
Design of horizontally loaded piles: Subgrade reaction method 1 p = k y e ph 2 z= L p E z= 0 ph, d DIN 1054: k s = E s /D, but admissible only for determination of bending moments and for max w < 2 cm Design proof is obsolete if: 1) Pile is fully embedded in soil and 2) Horizontal load in LC 1 is less than 3% of vertical load and in LC 2 maximum 5% of vertical load
p-y- method according to API RP 2A-WSD, 2000 Non-linear load-displacement curves (p-y curves) p-y curves are based on field tests with up to 1m pile diameter with up to 100 load cycles
p-y curves for sand acc. to API p/p u 1,0 10 5 k z / A p u = 1.0 k z p = A p y u tanh A pu y With: p = Soil resistance [kn/m] p u = maximum soil resistance [kn/m] y = pile deflection (lateral) [m] k = bedding modulus, dependent on ϕ [kn/m 3 ] A = Calibration factor [ - ] static : cyclic : z A = 3.0 0.8 0.9 D A = 0.9 Initial stiffness Relative Density (API RP-2A WSD, 2000)
p-y curves for sand acc. to API Max. lateral soil resistance p u [kn/m] : 1) ( C z + C D) γ z pus = 1 2 2) = C D γ z (deep) pud 3 (near to surface) the smaller value is relevant with: z = Depth below soil surface [m] D = average pile diameter [m] γ = effective unit weight of soil [kn/m 3 ] C 1, C 2, C 3 = empirical coefficients, dependent on ϕ [-] ϕ = angle of internal friction [ ] Coefficients Coefficient Angle of internal friction (API RP-2A WSD, 2000)
p-y curves for soft clay acc. to API p/p u with: 1,0 0,72 0,5 p p static y = 0,5 u y c 1 3 p/p u y/y c 0 0 0,5 1,0 0,72 3,0 1,0 8,0 p = Soil resistance [kn/m 2 ] p u = maximum soil resistance [kn/m 2 ] y = pile deflection [mm] y c = 2,5 ε c x D [mm] 1,0 3,0 8,0 y/y c 1,0 ε c = Strain at 0.5 σ max in undrained uniaxial compression tests p/p u 1,0 0,72 0,5 static cyclic p/p u y/y c 0 0 0,5 1,0 0,72 3,0 Deep if z > z R 0,72 1,0 3,0 8,0 15,0 y/y c 1,0 p/p u static p/p u y/y c 0 0 0,72 0,5 cyclic 0,72 z R /z 0,5 1,0 0,72 3,0 0,72 z/z R 15,0 0,72 z/z R Near to surface - z < z R 1,0 3,0 8,0 15,0 y/y c
p-y curves for soft clay acc. to API Max. lateral soil resistance p u [kn/m]: 1) 2) p u = 3c + γz + p u = 9c cz J D (Near to surface - if z < z R ) (Deep - if z z R ) With: z = Depth below soil surface [m] z R = Depth of the zone of reduced soil resistance (near to surface) [m] 6D z R = γd + J c c = undrained shear strength of undisturbed samples [kn/m 2 ] D = Pile diameter [m] γ = effective unit weight of the soil [kn/m 3 ] J = Dimensionless empirical constant between 0.25 (medium stiff clay) and 0.5 (soft clay) [ - ]
p-y curves for cohesive soils O Neill und Gazioglu (1984): Integrated Clay Model no distinction between soft and stiff clay based on 21 field tests at 11 different locations p ult = F N p c u D F empirical soil degradation - factor N p bearing capacity coefficient N N p p = 3+ 6 = 9 z z crit for z z crit for z > z crit F (Failure)Strain ε from UU- triaxial test < 0.02 0.02 0.06 > 0.06 F s (static) 0.50 0.75 1.0 F c (cyclic) 0.33 0.67 1.0 z L crit c = L c 4 EI = 3,0 E D 0,5 0,286 critical depth Critical pile length pile length, from which the length has no further influence on pile behavior
API-Method for Monopiles? Horizontal force in MN Horizontal force in MN Displacement w in cm Rotation in H-w-/H-φ-curves: Comparison API-FEM p-y-method acc. to API underestimates deflections Unmodified application is not recommended
Effect of large diameter Proposal of Soerensen et al. (2010) and results of Augustesen et al. (2010) for monopiles in sand Significant effect Estimation from numerical simulations 14
Piles under cyclic horizontal loads Test results Alizadeh & Davisson (1970) Hettler (1981): Model tests y K, N y K,1 = 1+ C N ln N
Cyclic Loading Offshore guidelines (GL, DNV) demand consideration of cyclic load effects BSH-Standard Soil Investigations : Cyclic laboratory tests should lead to a prediction of cyclic deformations and stability of the foundation structure. Loading Time
Usual requirement: Rigid clamping under design load But: for large-diameter monopiles this leads to extreme lengths! IGBE: Coupling of FE-simulations with cyclic triaxial tests (SDM-stiffness degradation method)
SDM method FE-Model Cyclic triaxial test device Principle: Result (Monopile D = 7.5m, dense sand, H=15 MN, h=20m)
E E a ε sn cp, N = 1 a s1 ε cp, N Degradation of secant modulus under cyclic loading in the pile-soil model (schematic) Degraded stiffness: E E sn s1 ε = ε a cp, N = 1 a cp, N = N b b 1( X ) 2 (Huurman 1996) with X σ = σ 1, cyc 1, sf b 1 and b 2 are cyclic parameters to be determined in triaxial tests 19
Timmerman & Wu (1969) Achmus et al. (2007) Simulation of plastic strain response in a cyclic triaxial test with dry sand using the degradation stiffness model Simulation of lateral pile deflection in a 1-g laboratory test using the degradation stiffness model 20
Variation of stiffness in two pile-soil systems dependent on the number of load cycles 21
On the effect of rigid clamping Depth below sea bed in m Deflection in cm Dimensionless pile deflection y k,n / y k,1 in 1 Number of load cycles N in 1 Rigid clamping ( vertical tangent or zero toe kick ) must not always secure favourable behavior under cyclic loads. For very large-diameter monopiles the requirement leads to too large embedded pile lengths.
Investigation regarding the minimum embedded length of Monopiles Pile deflection lines calculated with the FE method Dependence of the pile head deflection on different loading conditions 23
Accumulation of horizontal pile deflections at seabed level for monopiles D = 5 m Pile deflections under cyclic loading (D = 5 m, H = 15 MN, h = 15 m) 24