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

*The initial stiffness E_py**	Parameters involved	Nature of sand	Reference
k_APIz	As in equation (2)	Silica	API [4], DNV [5]
$k_{W} z = z k_{API} {(\frac{D_{p}^{ref}}{D_{p}})}^{\frac{4 (1 - a)}{4 + a}}$	a=0.6 for a medium dense sand a=0.5 for a dense sand D_p^ref=1.0 m	Silica	Wiemann et al. [12]
$k_{S 1} z = a {(\frac{Z}{Z_{ref}})}^{b} {(\frac{D_{p}}{D_{p}^{ref}})}^{c} ϕ^{d}$	a=50,000, z_ref=1 m, D_p^ref=1.0 m b=0.6, c=0.5, d=3.6, ϕ in radians	Silica	Sorensen et al. [13]
$k_{K} z = k_{API} z_{ref} {(\frac{Z}{Z_{ref}})}^{m} {(\frac{D_{p}}{D_{p}^{ref}})}^{0.5}$	m=0.6, z_ref=2.5 m, D_p^ref=0.61 m	Silica	Kallehave et al. [14]
$k_{S 2} z = a {(\frac{Z}{Z_{ref}})}^{b} {(\frac{D_{p}}{D_{p}^{ref}})}^{c} {(\frac{E_{s}}{E_{s}^{ref}})}^{d}$	a=1 MPa, z_ref=1 m, D_p^ref=1 m E_s^ref=1 MPa, b=0.3, c=0.5, d=0.8	Silica	Sorensen [15]

FE mesh used to analyze soil–monopile interaction.

Monopile at Horns Rev: (a) monopile structural details, (b) soil layers.

Table 2

Soil strata for each soil layer at Horns Rev.

Soil layer	Type	Depth (m)	E_s (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

Histograms for the monopile head stiffness coefficients provided by the different models.

(a) (Substructure/tower/monopile) system, (b) Tower modeling with three springs representing the soil–monopile interaction, (c) Details of substructure and tower.

Table 3

Soil strength and deformation parameters at North Hoyle site.

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

Table 4

North Hoyle OWT’s structural details.

OWT component	Symbol (unit)	Value
Tower height	L_T (m)	67.0
Substructure height	L_s (m)	7.0
Structure height	L (m)	74.0
Tower top diameter	D_t (m)	2.3
Tower bottom diameter	D_b (m)	4.0
Tower wall thickness	t_T (mm)	35.0
Substructure diameter	D_s (m)	4.0
Substructure wall thickness	t_s (mm)	50
Tower material Young's modulus	E_T (GPa)	210.0
Tower mass	m_T (ton)	130.0
Top mass	M_top (ton)	100.0
Monopile diameter	D_p (m)	4.0
Monopile wall thickness	t_p (mm)	50
Monopile material Young's modulus	E_p (GPa)	210.0
Monopile depth	L_p (m)	33.0
Measured frequency	f_measured (Hz)	0.35

Table 5

Adopted values for computing the 1st NF at North Hoyle.

α	m	*Substructure mass m_S* (ton)**	*Substructure bending rigidity EI_S* (GN m²)**	Tower top bending rigidity EI_top (GN m²)	*Soil Young’s modulus E_s* (MPa)**	λ_av
0.905	1.739	34.138	254.162	33.547	110.0	3.808

Monopile head movements in terms of monopile head applied loading: (a) H-*u_L*, (b) M-*θ_R* and (c) H-*θ_R* curves.

Table 6

Monopile head flexibility coefficients.

Reese et al. (1974)	O’Neill and Murchison (1983)	Kallehave et al. (2012)	Sorensen et al. (2010)	Sorensen (2012)	Wiemann et al. (2004)
I_L (m/MN)	0.003356	0.002011	0.001775	0.001052	0.003225	0.001871	0.002375
I_R (rad/MN m)	0.000048	0.000041	0.000039	0.000033	0.000047	0.000039	0.000043
I_LR (1/MN)	0.000314	0.000225	0.000207	0.000142	0.000298	0.000210	0.000252

Table 7

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

Reese et al. (1974)	O’Neil and Murchison (1983)	Kallehave et al. (2012)	Sorensen et al. (2010)	Sorensen (2012)	Wiemann et al. (2004)
K_L (MN/m)	771.64	1293.02	1471.54	2307.26	744.07	1335.67	1101.32
K_R (MN m/rad)	54,172.94	63,519.50	66,491.98	74,640.81	50,676.57	63,667.97	60,458.79
K_LR (MN)	5065.43	7109.84	7770.27	10,061.80	4689.59	7141.61	6412.90
C_R	0.8693	0.8859	0.8900	0.9072	0.8703	0.8901	0.8802
C_L	0.9977	0.9986	0.9988	0.9993	0.9978	0.9987	0.9984
Fixed base NF f_FB (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
$Deviation (%) = \| \frac{f_{measured} - f_{1}}{f_{measured}} \| 100$	100 3.14	5.43	6.00	8.00	3.43	6.00	4.86

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DOI: https://doi.org/10.2478/sgem-2022-0003 | Journal eISSN: 2083-831X (formerly 0137-124X) | Journal ISSN: 0137-6365

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Language: English

Page range: 66 - 81

Submitted on: May 20, 2021

Accepted on: Nov 27, 2021

Published on: Feb 10, 2022

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Keywords:

offshore wind turbines,

natural frequency,

soil–monopile stiffness

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2022 Douifi Amel, Amar Bouzid Djillali, Bhattacharya Subhamoy, Amoura Nasreddine, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 44 (2022): Issue 1 (March 2022)

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

Figures & Tables

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