Evaluation of sand p–y curves by predicting both monopile lateral response and OWT natural frequency

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Adopted values for computing the 1st NF at North Hoyle_

α	m	Substructure mass mS (ton)	Substructure bending rigidity EIS (GN m2)	Tower top bending rigidity EItop (GN m2)	Soil Young’s modulus Es (MPa)	λav
0.905	1.739	34.138	254.162	33.547	110.0	3.808

Soil strength and deformation parameters at North Hoyle site_

Cohesion c (kN/m2)	Angle of friction ϕ (°)	Young’s modulus Es (MPa)	Poisson’s ratio νs	Shear modulus Gs (MPa)	Reference
0.0	40.0	644.0	0.40	230.0	Arany et al. [20]

Soil strata for each soil layer at Horns Rev_

Soil layer	Type	Depth (m)	Es (MPa)	γ(γ′) (kN/m3)	ϕ (°)	ψ (°)	νs
1	Sand	0.0–4.5	130.0	20(10)	45.4	15.4	0.28
2	Sand	4.5–6.5	114.3	20(10)	40.7	10.7	0.28
3	Sand to silty sand	6.5–11.9	100.0	20(10)	38.0	8.0	0.28
4	Sand to silty sand	11.9–14.0	104.5	20(10)	36.6	6.6	0.28
5	Sand/silt/organic	14.0–18.2	4.5	17(7)	27.0	0.0	0.28
6	Sand	>18.2	168.8	20(10)	38.7	8.7	0.28

Proposed formulae to enhance p–y curves_

The initial stiffness E*py	Parameters involved	Nature of sand	Reference
kAPIz	As in equation (2)	Silica	API [4], DNV [5]
kWz=z kAPI(DprefDp)4(1-a)4+a {{\boldsymbol{k}}_{\boldsymbol{W}}}{\boldsymbol{z = z}}\,{{\boldsymbol{k}}_{{\bf{API}}}}{\left({{{{\boldsymbol{D}}_{\boldsymbol{p}}^{{\bf{ref}}}} \over {{{\boldsymbol{D}}_{\boldsymbol{p}}}}}} \right)^{{{{\boldsymbol{4(1 - a)}}} \over {{\boldsymbol{4 + a}}}}}}	a=0.6 for a medium dense sanda=0.5 for a dense sandDpref=1.0 m	Silica	Wiemann et al. [12]
kS1 z=a(ZZref)b(DpDpref)c ϕd {{\boldsymbol{k}}_{{\boldsymbol{S1}}}}\,{\boldsymbol{z = a}}{\left({{{\boldsymbol{Z}} \over {{{\boldsymbol{Z}}_{{\bf{ref}}}}}}} \right)^{\boldsymbol{b}}}{\left({{{{{\boldsymbol{D}}_{\boldsymbol{p}}}} \over {{\boldsymbol{D}}_{\boldsymbol{p}}^{{\bf{ref}}}}}} \right)^{\boldsymbol{c}}}\,{\phi ^{\boldsymbol{d}}}	a=50,000, zref=1 m, Dpref=1.0 mb=0.6, c=0.5, d=3.6, ϕ in radians	Silica	Sorensen et al. [13]
kK z=kAPIzref(ZZref)m(DpDpref)0.5 {{\boldsymbol{k}}_{\boldsymbol{K}}}\,{\boldsymbol{z =}}{{\boldsymbol{k}}_{{\bf{API}}}}{{\boldsymbol{z}}_{{\bf{ref}}}}{\left({{{\boldsymbol{Z}} \over {{{\boldsymbol{Z}}_{{\bf{ref}}}}}}} \right)^{\boldsymbol{m}}}{\left({{{{{\boldsymbol{D}}_{\boldsymbol{p}}}} \over {{\boldsymbol{D}}_{\boldsymbol{p}}^{{\bf{ref}}}}}} \right)^{{\boldsymbol{0}}{\boldsymbol{.5}}}}	m=0.6, zref=2.5 m, Dpref=0.61 m	Silica	Kallehave et al. [14]
kS2 z=a(ZZref)b(DpDpref)c (EsEsref)d {{\boldsymbol{k}}_{{\boldsymbol{S2}}}}\,{\boldsymbol{z = a}}{\left({{{\boldsymbol{Z}} \over {{{\boldsymbol{Z}}_{{\bf{ref}}}}}}} \right)^{\boldsymbol{b}}}{\left({{{{{\boldsymbol{D}}_{\boldsymbol{p}}}} \over {{\boldsymbol{D}}_{\boldsymbol{p}}^{{\bf{ref}}}}}} \right)^{\boldsymbol{c}}}\,{\left({{{{{\boldsymbol{E}}_{\boldsymbol{s}}}} \over {{\boldsymbol{E}}_{\boldsymbol{s}}^{{\bf{ref}}}}}} \right)^{\boldsymbol{d}}}	a=1 MPa, zref=1 m, Dpref=1 mEsref=1 MPa, b=0.3, c=0.5, d=0.8	Silica	Sorensen [15]

North Hoyle OWT’s structural details_

OWT component	Symbol (unit)	Value
Tower height	LT (m)	67.0
Substructure height	Ls (m)	7.0
Structure height	L (m)	74.0
Tower top diameter	Dt (m)	2.3
Tower bottom diameter	Db (m)	4.0
Tower wall thickness	tT (mm)	35.0
Substructure diameter	Ds (m)	4.0
Substructure wall thickness	ts (mm)	50
Tower material Young's modulus	ET (GPa)	210.0
Tower mass	mT (ton)	130.0
Top mass	Mtop (ton)	100.0
Monopile diameter	Dp (m)	4.0
Monopile wall thickness	tp (mm)	50
Monopile material Young's modulus	Ep (GPa)	210.0
Monopile depth	Lp (m)	33.0
Measured frequency	fmeasured (Hz)	0.35

Stiffness coefficients, interaction factors, and the different 1st NFs computed for the OWT at North Hoyle_

Parameters	ABAQUS FE Analysis	WILDPOWER 1.0
		Reese et al. (1974)	O’Neil and Murchison (1983)	Kallehave et al. (2012)	Sorensen et al. (2010)	Sorensen (2012)	Wiemann et al. (2004)
KL (MN/m)	771.64	1293.02	1471.54	2307.26	744.07	1335.67	1101.32
KR (MN m/rad)	54,172.94	63,519.50	66,491.98	74,640.81	50,676.57	63,667.97	60,458.79
KLR (MN)	5065.43	7109.84	7770.27	10,061.80	4689.59	7141.61	6412.90
CR	0.8693	0.8859	0.8900	0.9072	0.8703	0.8901	0.8802
CL	0.9977	0.9986	0.9988	0.9993	0.9978	0.9987	0.9984
Fixed base NF fFB (Hz)	0.417
1st NF f1 (Hz)	0.361	0.369	0.371	0.378	0.362	0.371	0.367
Measured NF f measured (Hz)	0.35
Deviation (%)=|fmeasured−f1fmeasured| 100 {\rm{Deviation}}\,(\%) = \left| {{{{f_{{\rm{measured}}}} - {f_1}} \over {{f_{{\rm{measured}}}}}}} \right|\,100	100 3.14	5.43	6.00	8.00	3.43	6.00	4.86

Monopile head flexibility coefficients_

Flexibility coefficients	ABAQUS FE analysis	WILDPOWER 1.0
		Reese et al. (1974)	O’Neill and Murchison (1983)	Kallehave et al. (2012)	Sorensen et al. (2010)	Sorensen (2012)	Wiemann et al. (2004)
IL (m/MN)	0.003356	0.002011	0.001775	0.001052	0.003225	0.001871	0.002375
IR (rad/MN m)	0.000048	0.000041	0.000039	0.000033	0.000047	0.000039	0.000043
ILR (1/MN)	0.000314	0.000225	0.000207	0.000142	0.000298	0.000210	0.000252