Complicated environmental issues combined with the growing harm of the greenhouse gas emission placed the environmentalists in a challenging situation all over the world. The search for clean energy from renewable resources became an urgent need. This has been confirmed during the United Nations climate change and energy policy framework conference where it was agreed on the target that 27% of the total energy consumed in the EU must be renewable by 2030 (EUCO 169/14) [1]. To reach this prospective goal, more significance is given to the development of offshore wind parks as the wind energy produced by offshore wind turbines (OWTs) is considered more attractive for the availability of large offshore areas, where consistent winds are steadier and stronger than those in onshore lands.
The most widely adopted foundation is the monopile, which is a largediameter hollow steel driven pile with a diameter
It is well recognized that the Winkler model that uses the nonlinear p–y curves proposed by the standards, currently in use [4,5] for monopile design, has gained broad confidence over many decades. However, as this model has been developed on the basis of field testing investigations performed on smalldiameter piles (
The main objective of this paper is to assess the performances of the currently used p–y models (API and DNV) and the enhanced p–y curves recently proposed to design monopiles under lateral loading. This is achieved by a comparative study between the results supplied by a computer program called WILDPOWER 1.0 [8] and those of the Finite Element (FE) analysis obtained using the commercial package ABAQUS.
Two case studies are considered in this paper to evaluate the Beam on a Nonlinear Winkler Foundation (BNWF) model and to study its performances when applied to largediameter monopiles. The first, which consists of an OWT embedded at Horns Rev (Denmark), is believed to constitute a severe test to both computer programs involved in the comparative study. The monopile lateral behavior is examined, and the assessment is carried out through the profiles of displacements, bending moments, shear forces, and soil reactions.
It is generally accepted that the dynamic characteristics, especially the first natural frequency (1st NF) of an OWT, are affected by the soil–monopile interaction [2,3]. When the BNWF model fails to adequately capture the lateral behavior of a largediameter monopile, an inaccurate monopile head stiffness is produced, and consequently the OWT design is unsafe. In this context, a second case study consisting of an OWT supported by a monopile at North Hoyle (UK) is studied. This case is selected for the availability of the OWT tower structural details along with the geotechnical and monopile data required for Winkler and FE modeling, and most importantly for the existence of the OWTmeasured 1st NF, which forms a key element in this assessment study.
Three work steps are necessary for reaching the 1st NF and then assessing the performance of each p–y model implemented in WILDPOWER 1.0. Firstly, an analytical expression for the 1st NF encompassing the monopile head stiffness (lateral, rocking, and crosscoupling coefficients) is provided and detailed. Secondly, the monopile head stiffness quantifying the soil–monopile interaction is described. Thirdly, the natural frequencies supplied by both FE and Winkler analyses are compared to the measured ones. Comments are given at the end of the paper.
In current geotechnical practice, analysis of laterally loaded piles is commonly conducted using an approach in which the soil foundation system is modeled as a BNWF with a series of uncoupled nonlinear springs representing the soil. This model involves the resolution of fourthorder differential equation:
In this equation,
To perform accurate design of piles supporting platforms in gas and oil offshore industry, Reese et al. [6] carried out a total of seven (two static and five cyclic) load tests on two identical instrumented piles installed at Mustang Island, Texas. In the static tests, both piles had a diameter of 0.61 m and a slenderness ratio of 34.4 and were installed in a medium sand. Based on these field tests, Reese et al. (1974) proposed a semiempirical p–y curve consisting of three straight lines and a parabola (Figure 1a). For lack of space, the different parameters involved in Figure 1a are not given here. However, for a detailed explanation, the reader can refer any article from the overwhelming number of papers that have been dedicated to this important subject (see, e.g. [9]).
To improve Reese et al.’s formulation which has been characterized by a significant amount of empiricism, O’Neill and Murchison [7] proposed a hyperbolic p–y curve in the form:
The initial stiffness of the API p–y curve
It is quite clear from equation (4) that the initial stiffness is independent of monopile properties (diameter and bending stiffness) and is linearly dependent on the depth
The ultimate resistance
The first expression corresponds to the wedge mode of failure, whereas the second one corresponds to the flow pattern. The coefficients
As building OWTs supported by monopiles became a necessity, the monopile designers extrapolated the API methodology to design largediameter monopiles. However, poor predictions were observed, and therefore, the abovementioned p–y curves were deemed no longer appropriate for this kind of foundations. A detailed critical review of the API method can be found in [8]. This situation prompted many researchers to suggest analytical p–y curves formulae in an attempt to improve the analysis by accounting for the monopile diameter and sometimes for monopile bending flexural rigidity. Hence, most of the suggested formulations alter the p–y curves at the level of initial stiffness, whereas the ultimate soil resistance
Proposed formulae to enhance p–y curves.
As in equation (2)  Silica  API [4], DNV [5]  
 Silica  Wiemann et al. [12]  
 Silica  Sorensen et al. [13]  
 Silica  Kallehave et al. [14]  
 Silica  Sorensen [15] 
The analytical formulations appearing in Table 1 are all for silica sands and the only input soil parameter required is the sand internal friction angle
The multisegment p–y formulation proposed by Reese et al. [6] (Figure 1a), the hyperbolic form by O’Neill and Murchison [7] (Figure 1b), and the other formulations suggested to enhance the p–y curves described in Table 1 have been encoded in a Fortran program called WILDPOWER 1.0. This has been conceived as a general name which stands for
The performances of p–y curve models implemented in WILDPOWER 1.0 are assessed against the FE results provided using ABAQUS [17].
The FE mesh used to model the monopile and its surrounding medium is illustrated in Figure 2. Due to the existence of a plane of symmetry in the considered problem, only half of the domain is meshed as shown in Figure 2. The soil domain is discretized using 4600 twentynoded hexahedral displacementbased isoparametric elements type C3D20R. The vertical boundaries are placed at a distance of 15
To disregard any installation effects, the monopile was assumed to be wishedinplace. Using the same type of elements as those used to model the soil, 3230 twentynoded quadratic hexahedral elements were employed to model the pile. Furthermore, the pile was treated as a linear elastic material with a Young’s modulus of
The accuracy of the monopile response to lateral loading is estimated by studying a monopile embedded at a site called Horns Rev, which is situated in the Danish sector of the North Sea. The monopile design parameters, which consist of displacement, bending moment, shear force, and soil reaction profiles, are computed first by both WILDPOWER 1.0 using the six p–y curves and ABAQUS and then compared. The monopile considered in this subsection has been chosen from one of the 80 installed OWTs type Vestas V80. It has an outer diameter of 4 m, a length of 31.6 m, and a wall of variable thickness inducing a variable flexural stiffness (
The identification of soil strata crossed by the monopile has been carried out by Augustesen et al. [10]. The Cone Penetrometer Testing (CPT) experiments revealed that the lithology was mostly formed of sand with roughly six layers. Details of layer thicknesses and their physical and strength properties are summarized in Table 2. The nature and thickness of each layer are illustrated in Figure 3b.
Soil strata for each soil layer at Horns Rev.
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 
The monopile in this first case study was subjected to a static horizontal load of
Figure 4 shows the variation of the monopile displacements with depth. Augustesen et al. [10] had previously studied the monopile at Horns Rev using FLAC_{3D}. The obtained displacement profile is included in Figure 4 for comparison. With the exception of small deviations observed at both monopile head and tip, a perfect agreement is noticed between FLAC_{3D}’s displacement profile and that of ABAQUS for almost the entire length of the monopile. This is somehow a validation of the FE analyses carried out by ABAQUS in this paper.
At the first glance, it easy to notice that the pattern exhibited by the Winkler model, when both Reese et al. and the API p–y curves are used, differs from that of ABAQUS. This confirms that these methods are not able to predict correctly the monopile displacements, especially at the top and bottom of the monopile. However, in Figure 4b, almost a perfect match is observed between the FE displacements and those of Winkler model for the upper part of the monopile when WILDPOWER 1.0 employs Sorensen et al. (2010) p–y curve, albeit a significant deviation is noticed at the monopile tip.
The Winkler model using both Sorensen (2012) and Wiemann et al. (2004) p–y curves reveals an underestimation of pile displacements along the entire monopile length, thus showing a deformation pattern close to that exhibited by the API method. The profile of displacements shown by Kallehave et al. (2012) failed to capture the behavior of a rigid monopile completely.
The different bending moment profiles are plotted in Figure 5. With the exception of Kallehave et al.’s model which underestimates the bending moment on almost the entire monopile length, it is clearly seen that all methods exhibit an identical tendency with nearly the same value of maximum bending moment, which differs slightly from that of ABAQUS. This gives a confirmation that the bending moment cannot be considered as a performance indicator to assess the BNWF model. The profiles of shear forces are shown in Figure 6. With respect to shear forces, all the methods capture well the monopile behavior over the upper third length, while a significant ovestimation of shear force values is observed in the middle part, where the absolute maximum efforts are expected to take place.
Figure 7 shows the distribution with depth of soil reaction for all studied models. Three important key points are worth indicating. Firstly, both FE and Winkler models exhibit a similar variation pattern, where the magnitudes of deviations are identical to those observed in the displacement profiles. This is because the lateral displacements and soil reactions are the direct solutions of the differential equation representing the Winkler model. Secondly, the depth locations at which the soil reaction becomes zero differ from one model to another. For the API’s group (Figure 7a), the zero soil reaction is situated slightly above that of ABAQUS, whereas in the Sorensen’s group (Figure 7b), the depth of zero soil reaction almost coincides with that of FE analysis. However, Kallehave et al. (2012) model in Figure 7c shows a point located well above the depth of zero soil reaction provided by ABAQUS. Thirdly, the soil reaction increases in the part of the soil located beneath the soft layer (formed of organic clay) and extending to the monopile tip. This is observed in all methods with the exception made for both API and Kallehave et al. models which show a decreasing pattern.
The soil–monopile interaction is a necessary ingredient for a rigorous assessment of the vibration characteristics of an OWT whose quantification relies fundamentally on monopile head stiffness coefficients. In this regard, the load deformation curves for the monopile studied in this section were established first, fitted by sufficiently higherdegree polynomials, and then the first derivative was evaluated at the origin for the determination of flexibility coefficients. The obtained coefficients were inverted to get the stiffness coefficients. Histograms of Figure 8 show the values of the stiffness coefficients of the three groups previously seen in this case study. As it has been expected, the values of stiffness coefficients confirm the tendency of lateral displacements of Figure 4. In the API’s group (Figure 8a), values of
The most significant element in this subsection is the 1st NF, which is a parameter of importance in the safe design of slender structures such as offshore wind towers. Therefore, and before performing the comparisons based on the 1st NF of each model, three preliminary steps are worth to be described. In the first step, the different terms constituting the analytical expression describing the natural vibration of an OWT are given and explained. In the second step, the structural details of the North Hoyle OWT selected for this study are given and the site geotechnical data are provided as well. The soil–monopile interaction in terms of flexibility coefficients and then the resulting monopile head stiffness coefficients necessary for the natural frequency computation are established by both ABAQUS and WILDPOWER 1.0 using all Winkler models in the third step. The 1st NF computed by the FE analysis and by the Winkler models are compared to the measured natural frequency supplied by the OWT manufacturer to assess the performance of each p–y curve.
The natural frequency of an OWT is highly dependent on the material properties employed in its fabrication and is significantly affected by the stiffness provided by the soil–monopile system.
The structure mounted on the monopile is usually formed by a substructure and tower in an OWT (Figure 9). A rigorous expression for the fixed base natural frequency, taking into account the variation of the tower cross section with elevation, has been proposed in [18] as:
In this kind of structures, the monopile head stiffness quantifying the soil–monopile interaction can be better represented by three springs. This is because the translation and the rotational modes of vibration are cross coupled, which requires an additional spring. In this context, Arany et al. [19] derived the expressions of natural frequency of an OWT on threespring flexible foundations by means of two beam models: Bernoulli–Euler and Timoshenko. The natural frequency in both cases was obtained numerically from the resulting transcendental equations. They proposed a closed form expression containing a lateral stiffness coefficient
The geotechnical investigations at the North Hoyle site revealed a lithology formed mostly of sand layers. The adopted soil strength and deformation parameters are summarized in Table 3. The North Hoyle OWT structural data and measured 1st NF supplied by the manufacturer are presented in Table 4.
Soil strength and deformation parameters at North Hoyle site.
0.0  40.0  644.0  0.40  230.0  Arany et al. [20] 
North Hoyle OWT’s structural details.
Tower height  67.0  
Substructure height  7.0  
Structure height  74.0  
Tower top diameter  2.3  
Tower bottom diameter  4.0  
Tower wall thickness  35.0  
Substructure diameter  4.0  
Substructure wall thickness  50  
Tower material Young's modulus  210.0  
Tower mass  130.0  
Top mass  100.0  
Monopile diameter  4.0  
Monopile wall thickness  50  
Monopile material Young's modulus  210.0  
Monopile depth  33.0  
Measured frequency  0.35 
Based on the data provided in Table 4, other parameters necessary for the 1st NF computation are given in Table 5 in detail. Here, an important point is worth noting. The value of soil Young’s modulus reported in Table 5 was deemed extremely high for such a soil and a value of
Adopted values for computing the 1st NF at North Hoyle.
0.905  1.739  34.138  254.162  33.547  110.0  3.808 
The last step leading to the comparative study is to evaluate the OWT natural frequency using FE by ABAQUS on one hand and the 1st NF using WILDPOWER 1.0 for each p–y curve model on the other hand. FE computations using ABAQUS are based on the same FE mesh used for the first case study in Section 3.1. Although finding
Monopile head flexibility coefficients.
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 
The stiffness matrix elements are determined by simply inverting the flexibility matrix of equation (11):
The monopile head stiffness coefficients,
Stiffness coefficients, interaction factors, and the different 1st NFs computed for the OWT at North Hoyle.
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  
1st NF  0.361  0.369  0.371  0.378  0.362  0.371  0.367 
Measured NF  
 100 3.14  5.43  6.00  8.00  3.43  6.00  4.86 
Although successful in designing smalldiameter piles, the extension of the p–y method already included in the piling regulation codes to the design of largediameter monopiles supporting OWTs resulted in unsatisfactory predictions and showed that the API p–y curves are not able to predict the correct deformation pattern of this kind of stiff foundations. Therefore, many researchers have been prompted to propose other formulations of p–y curves which have the ability to produce better performances.
To assess the performances of recently proposed p–y curves, two case studies were considered in this paper. The first case study, which consisted of a monopile embedded in multilayered sandy soil at Horns Rev (Denmark), was considered to illustrate the evolution of all the monopile design parameters with depth. A monopile supporting an OWT at North Hoyle (UK) was chosen as a second case to evaluate the Winkler model performances by computing the 1st NF. The major conclusions reached from this Winkler model assessment were as follows:
The BNWF models based on either Reese et al. (1974) or O’Neill and Murchison (1983) p–y curves have been found inappropriate to design largediameter monopiles for two main reasons. Firstly, they overestimated the monopile stiffness by exhibiting a deformation pattern similar to that of slender, smalldiameter piles. Secondly, they failed to quantify the monopile head stiffness by giving high values of 1st NF.
The improvements brought by the BNWF models based on Wiemann et al. (2004) and Sorensen (2012) procedures were deemed insufficient, and consequently, their p–y curves are not acceptable as methods for designing monopiles. However, an excellent agreement was observed between ABAQUS and WILDOPER 1.0 when using Sorensen et al. (2010) p–y curve for the upper part of the monopile length. Therefore, the values of the 1st NF predicted by both WILDOPER 1.0 and ABAQUS which are very close to each other, match also the measured natural frequency.
In the assessment of both OWT monopile lateral response and its tower 1st NF, the BNWF model based on Kallehave et al. (2012) p–y curve failed in predicting a correct behavior, and therefore, it does not have the ability to design a largediameter monopile under horizontal loadings.
Adopted values for computing the 1st NF at North Hoyle.
0.905  1.739  34.138  254.162  33.547  110.0  3.808 
Soil strength and deformation parameters at North Hoyle site.
0.0  40.0  644.0  0.40  230.0  Arany et al. [ 
Soil strata for each soil layer at Horns Rev.
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.
As in 
Silica  API [ 


Silica  Wiemann et al. [ 


Silica  Sorensen et al. [ 


Silica  Kallehave et al. [ 


Silica  Sorensen [ 
North Hoyle OWT’s structural details.
Tower height  67.0  
Substructure height  7.0  
Structure height  74.0  
Tower top diameter  2.3  
Tower bottom diameter  4.0  
Tower wall thickness  35.0  
Substructure diameter  4.0  
Substructure wall thickness  50  
Tower material Young's modulus  210.0  
Tower mass  130.0  
Top mass  100.0  
Monopile diameter  4.0  
Monopile wall thickness  50  
Monopile material Young's modulus  210.0  
Monopile depth  33.0  
Measured frequency  0.35 
Stiffness coefficients, interaction factors, and the different 1st NFs computed for the OWT at North Hoyle.
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 

1st NF 
0.361  0.369  0.371  0.378  0.362  0.371  0.367 
Measured NF 


100 3.14  5.43  6.00  8.00  3.43  6.00  4.86 
Monopile head flexibility coefficients.
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 
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