Numerical Study on Lateral Response of Offshore Monopile in Sand under Local Scouring Conditions

Abstract

Currently, p-y models have been broadly adopted for estimating the lateral bearing capacity of large-diameter monopiles in offshore engineering. However, the existing p-y curves cannot reflect the effect of pile diameter D on the lateral response of monopiles under local scouring conditions. In order to extend the existing p-y model to a large-diameter pile, a well-calibrated three-dimensional pile-soil model performed by ABAQUS is used to study the effect of the pile diameter D on the ultimate soil resistance P and the initial stiffness k of the Lin’s p-y model. Based on the numerical simulation results, two diameter-related parameters A and B, which represent the relationships between the ultimate soil resistance and the initial stiffness obtained by the numerical model and the Lin’s p-y model, respectively, are proposed and introduced into the Lin’s p-y model to present a modified p-y model. The comparison results show that the proposed modified p-y model is capable of providing a better estimation of the lateral response of large-diameter monopiles than the existing p-y model under a scouring condition.

1. Introduction

As global warming become progressively prominent, it is essential to find alternative renewable energies to minimize the use of fossil fuels [1]. The offshore wind farm is a green energy source and offers sustainable means of electrical power generation [2,3].

Currently, monopiles have been widely used in offshore engineering [4], accounting for 75% of offshore wind turbine foundations [5,6]. The lateral loads from wind, wave, and current are the dominant load acting on the monopile foundation [7]. Consequently, the bearing capacity of a monopile foundation must be precisely predicted.

Scour is a process of removing soils around foundations by waves and currents in a river or ocean environment [8,9]. The research showed that the scour depth around monopiles in offshore wind power engineering could be up to 1.5 times pile diameter or even higher [10]. Therefore, scour can have a critical effect on the large-diameter monopile lateral capacity, which is mainly related to the soils at shallow depths and they usually can be scoured away by waves and currents [11,12,13].

The most widely used method of evaluating the lateral response of piles for an offshore wind turbine is the analytical p-y model [14,15]. In this method, the pile’s lateral deflection in response to a lateral load is measured by the deflection of y. The force per unit length from the soil against the pile which develops as a result of the pile deflection is known as soil resistance p. A typical p-y model consists of the initial stiffness and the ultimate soil resistance.

The p-y model was first proposed by Mcclelland and Focht [16]. Then, based on the results of the field small-diameter monopile test, Matlock [17] and Reese et al. [18] proposed a p-y model suitable for soft clay and sand foundations, respectively. However, the lateral response of an offshore wind turbine supported by a large-diameter monopile cannot be accurately predicted by conventional p-y models [19,20,21,22]. Many researchers used centrifuge tests [23,24] and finite element methods (FEM) [25,26] to study the lateral response of the large-diameter monopole. Their research revealed that large-diameter monopiles (D = 1 to 6 m) behaved significantly more softly than that predicted using API’s [14] p-y model. That means the latter’s initial stiffness was greatly overstated, while the eventual soil resistance was greatly underestimated at a shallow depth.

Up to date, limited attention has been paid to analyze the effect of local scour on the lateral capacity of piles based on the p-y model. Lin et al. [11] proposed a p-y model to analyze the effect of scour-hole dimensions on the lateral response of piles. This Lin’s p-y model was further developed by many researchers [5,27]. A rational nonlinear distribution of the soil strain throughout the length of the pile in the wedge was used by Yang et al. [5] to modify the Lin’s p-y model and it was then expanded to account for the pile under scouring conditions. Tseng et al. [27] combined the initial stiffness of the Kallehave’s p-y model [28] and the ultimate soil resistance of the Lin’s p-y model to propose a new p-y model, which can reflect the effect of local scour on the lateral capacity of piles.

However, the existing p-y model considering local scouring conditions was based on the monopile with a small pile diameter (D = 0.61 m). However, currently, the large diameter piles (D > 5 m) have been increasingly used in an offshore wind farm. Therefore, the existing p-y model may not be capable of reasonably predicting the lateral response of large-diameter monopiles under local scouring conditions.

In this research, a well-calibrated three-dimensional pile-soil ABAQUS numerical model was used to investigate the effect of pile diameter on the initial stiffness and the ultimate soil resistance of monopiles with various diameters. Based on the numerical simulation results, the diameter-related parameters are introduced into the Lin’s p-y model to present a modified p-y model that can provide a reasonable lateral response of a large-diameter monopile in the sand under a scouring condition.

2. The Analytical p-y Models

Based on the p-y model proposed by Reese et al. [18]. Lin et al. [11] proposed a method to investigate the effects of local scour hole dimensions on the responses of laterally loaded piles in sand.

2.1. The Reese’s p-y Model

With the help of the field tests data [19], Reese et al. [18] proposed a p-y model to calculate the ultimate soil resistance per unit length P and the initial stiffness k at each depth z, as shown in Equations (1)-(3).

$$P_{st}=\gamma ’z\left[\begin{array}{l}\frac{K_{0z}\tan \phi ’\sin \beta }{\tan \left(\beta -\phi ’\right)\cos \alpha }+\frac{\tan \beta }{\tan \left(\beta -\phi ’\right)}\left(D+z\tan \beta \tan \alpha \right)+\\ K_{0z}\tan \beta \left(\tan \phi ’\sin \beta -\tan \alpha \right)-K_{a}D\end{array}\right]$$

(1)

$$P_{sd}=K_{a}D\gamma ’z\left({\tan }^8\beta -1\right)+K_{0}D\gamma ’z\tan \phi ’{\tan }^4\beta$$

(2)

$$k_{\mathrm{Reese}}=k_0\times z$$

(3)

where, P_st and P_sd are the ultimate soil resistance per unit length near and well below the soil surface, respectively; k_Reese is the initial stiffness of the p-y curve at depth z; φ’ is the effective internal friction angle of soil; γ’ is the effective weight of soil; D is the pile diameter; α and β are parameters related to the failure zone; K₀ and K_a are the static and active lateral earth pressure coefficient, respectively; and k₀ is an empirical coefficient related to the relative density of sand.

The transition depth can be obtained with the help of Equations (1) and (2), then the ultimate soil resistance per unit length P_s at a certain depth z is determined. Once the value of P_s is calculated, the soil resistance at lateral displacements of D/60 and 3D/80 at that depth can be obtained by multiplying the depth-controlled parameters A_s and B_s, respectively. A typical p-y curve is shown in Figure 1.

2.2. The Lin’s p-y Model

Based on the Reese’s p-y model, Lin et al. [11] proposed Equations (4)–(7) to calculate the post-scour ultimate soil resistance F_u at a certain depth z using the force equilibrium of the wedge at failure, as shown in Figure 2. The corresponding applicable conditions are summarized in Equations (8)–(10).

$$\begin{array}{l}{F}_{u0}=\frac{\gamma ’K_0\tan \beta z^3}{3\cos \alpha }\left[\cos \alpha \sin \beta \tan \phi ’-\sin \alpha +\frac{\tan \phi ’\cos \beta }{\tan \left(\beta -\phi ’\right)}\right]+\\ {{\displaystyle }}^{}\stackrel{}{{{\displaystyle }}^{}}\frac{\gamma ’z^2}{\tan \left(\beta -\phi ’\right)}\left(\frac{D\tan \beta }{2}+\frac{z{\tan }^2\beta \tan \alpha }{3}\right)-K_a\frac{\gamma ’D{z}^2}{2}\end{array}$$

(4)

$$\begin{array}{l}{F}_{u1}=\frac{\gamma ’K_0\tan \beta }{3\cos \alpha }\left\{\begin{array}{l}\left[z^3+3D_1\left(z^3-z^2{S}_w/\tan \beta \right)+2D{1}^2{\left(z-Sw/\tan \beta \right)}^3\right]\times \\ \left[\cos \alpha \sin \beta \tan \phi ’-\sin \alpha +\frac{\tan \phi ’\cos \beta }{\tan \left(\beta -\phi ’\right)}\right]\end{array}\right\}+\frac{1}{\tan \left(\beta -\phi ’\right)}\\ {{\displaystyle }}^{}{{\displaystyle }}^{}\left(\begin{array}{l}\frac{\gamma ’\left(1-\tan \beta \tan \theta \right)\tan \beta }{6}\left\{\begin{array}{l}3D{\left[z\left(1+D_1\right)-Sw{D}_1/\tan \beta \right]}^2+\\ 2\tan \beta \tan \alpha {\left[z\left(1+D_1\right)-Sw{D}_1/\tan \beta \right]}^3\end{array}\right\}+\\ \frac{\gamma ’S{w}^2\tan \theta }{6}\left(3D+2S_w\tan \alpha \right)\end{array}\right)-K_a\frac{\gamma ’D{z}^2}{2}\end{array}$$

(5)

$$\begin{array}{l}{F}_{u2}=\frac{\gamma ’K_0}{3\cos \alpha }\left\{\begin{array}{l}\left[{\left(z+S_d\right)}^3\tan \beta -3\left(S_w+S_d/\tan \theta \right)S{d}^2+2S{d}^3/\tan \theta \right]\times \\ \left[\cos \alpha \sin \beta \tan \phi ’-\sin \alpha +\frac{\tan \phi ’\cos \beta }{\tan \left(\beta -\phi ’\right)}\right]\end{array}\right\}+\frac{1}{\tan \left(\beta -\phi ’\right)}\\ {{\displaystyle }}^{}{{\displaystyle }}^{} \left\{\begin{array}{l}\frac{\gamma ’{\left(z+S_d\right)}^2\tan \beta }{6}\left[3D+2\left(z+S_d\right)\tan \beta \tan \alpha \right]-\gamma ’\frac{{\left(S_w\tan \theta +S_d\right)}^2}{\tan \theta }\times \\ \left[\frac{D}{2}+\frac{1}{3}\left(S_w+S_d/\tan \theta \right)\tan \alpha \right]+\gamma ’S{w}^2\tan \theta \left(\frac{D}{2}+\frac{S_w\tan \alpha }{3}\right)\end{array}\right\}-K_a\gamma ’D\frac{{\left(z+S_d\right)}^2-S{d}^2}{2}\end{array}$$

(6)

$$D_1=\frac{\tan \beta \tan \theta }{1-\tan \beta \tan \theta };H_1=\frac{S_w}{\tan \beta };H2=\frac{S_w}{\tan \beta }+\frac{S_d}{D_1}$$

(7)

$$F_u=F_{u0} \theta <{90}^{°}-\beta , 0<z\le H_1; \theta \ge {90}^{°}-\beta , 0<z\le H_1$$

(8)

$$F_u=F_{u1}; \theta <{90}^{°}-\beta , H_1<z\le H_2$$

(9)

$$F_u=F_{u2}; \theta <{90}^{°}-\beta , z>H_2; \theta \ge {90}^{°}-\beta , z>H_1$$

(10)

$$F_u={\displaystyle {\int }_0^z{P}_{st}{d}_z}$$

(11)

where F_u0, F_u1, and F_u2 are the ultimate soil resistance corresponding to different scour hole dimensions; z is the depth below the post-scour soil surface; S_d is the scour depth; S_w is the scour width and θ is the slope angle; and D₁, H₁, and H₂ are intermediate parameters.

While F_u at a certain depth z is determined, the value of Z, which is the equivalent depth below the post-scour soil surface, can be obtained from Equations (11) and (1) or (2). Then, the post-scour ultimate soil resistance per unit length P_Lin and the initial stiffness k_Lin of the p-y curve at the post-scour depth z can be described by the p-y curve proposed by Reese et al. [18]. The details of derivation of Equations (4)–(11) can be found in the paper by Lin et al. [11].

3. Numerical Analyses on the Lateral Response of Monopile with Scour

3.1. Three-Dimensional Pile-Soil Model in ABAQUS

Three-dimensional numerical models were used to estimate the lateral response of monopiles. The pile lateral-load test data in Mustang Island [19], which have been widely adopted by researchers to test the reliability of their numerical models [11,29], were used in this research to calibrate the parameters used in ABAQUS numerical model without scouring. Considering the symmetry of the geometrical shape of the model, half of the model, which has 67,134 elements, was selected for numerical simulations, as shown in Figure 3. The region of the model is defined as a half cylinder with a radius of 10D and the bottom of the model is located 10D below the pile toe.

The pile was simulated as an equivalent solid cylinder of a linear elastic material and the corresponding elastic modulus was converted based on the equivalent bending stiffness of the section. The parameters of the pile used in the ABAQUS model are presented in

Table 1. Parameters of the pile used in the ABAQUS model.

Pile Parameters	Value
Diameter, D (m)	0.61
Thickness, t (m)	0.01
Embedded depth, L (m)	21
Equivalent elastic modulus, Ep’ (GPa)	26.2
Density, ρ (kg/m3)	7850
Poisson’s ratio, ν	0.3

.

The analytical models, proposed by Reese et al. [18] and Lin et al. [11], were obtained by the theory of elasticity and the limit theory based on the Mohr-Coulomb (MC) model. In this research, we adopt the same plastic MC model in the ABAQUS as the existing analytical models to represent the behavior of soils.

Table 2. Parameters of the soil used in ABAQUS.

Soil Parameters	Values
Effective weight, γ’ (kN/m3)	10.4
Internal friction angle, φ’ (degrees)	39.0
Dilation angle, ψ (degrees)	9.0
Poisson’s ratio, ν	0.3
Cohesion, c (kPa)	0.1
Coefficient of static lateral earth pressure, K0	0.4
Reference modulus, E0 (MPa)	120.0
Exponent factor, $n$	0.5

presents the parameters of the soil used in the ABAQUS model. The internal friction angle φ’, the coefficient of static lateral earth pressure of soil K₀, and the effective weight γ’ were selected from the test data of Reese et al. [18]; the values of soil cohesion c and dilation angle ψ were determined by Wang et al. [29]; and the constitutive model parameters of soil (E₀ and n) were obtained from Lin et al. [11].

The Coulomb friction model was adopted to represent the shear behavior of the pile-soil interface and the value of the interface friction coefficient was set to be tan (0.5φ’). Once the numerical model was built, the pile was laterally loaded at 0.3 m above the soil surface with various concentrated loads (20, 50, 100, 150, 200, 240, and 272.16 kN) and the corresponding lateral displacements and bending moments of the pile were recorded, as shown in Figure 4a,b, respectively. Overall, the pile-head displacements at the soil surface and bending moments along the pile estimated from the ABAQUS were similar to those measured by the field test.

3.2. Pile-Soil Numerical Model with Scour

The numerical model presented in Figure 3 was “scoured” to generate a conical hole around the monopile, as shown in Figure 5a. The geometries of the pile with scouring are shown in Figure 5b. The calibrated parameters of the soil presented in Table 2 were used in the numerical model with scour. The parameters of piles and scour holes used for numerical simulations are presented in

Table 3. Parameters of piles used in numerical model with scour.

D (m)	L (m)	L/D	ρ (kg/m3)	ν	t (m)	Ep’ (GPa)
3	24	8	7850	0.3	0.04	21.5
4	24	6	7850	0.3	0.05	20.2
6	24	4	7850	0.3	0.07	18.9
8	24	3	7850	0.3	0.09	18.3

and

Table 4. Parameters of scour holes.

Diameter, D (m)	Scour Depth, Sd (m)	Top Scour Width, Sw (m)
3	4.5	6
4	6	7.5
6	9	12
8	12	16

, respectively.

3.3. p-y Curves Obtained from ABAQUS

The pile-soil model (D = 3 m) was selected as an example to illustrate how to obtain the p-y curves from the lateral response of a monopile with a scour hole in ABAQUS numerical modeling. By using the displacement loading method with the lateral displacement of 0.2D applied at the head of the pile, the lateral reaction force corresponding to the lateral displacement and under each time step is obtained, as well as the displacement and shear force profile of the pile at the same time. Figure 6 shows the displacement profiles of the pile under every 0.2 time step (i.e., the lateral displacement at the pile head increased by 0.04D in each time step). An obvious plane rotation of the pile with a turning point at about 13.5 m below the sour hole, which is equal to 0.7L_scour below the post-scour soil surface, is observed.

Figure 7 shows the shear force profiles of the pile under every 0.2 time step. In this research, the polynomial fitting method is used to fit five shear force data. The obtained fitting equation is then differentiated to calculate the soil resistance p at the central data. In addition, the lateral displacement y along the pile can be derived from Figure 6. Then, the p-y curves at a given depth can be determined, as shown in Figure 8.

3.4. Values of P and k Obtained from Numerical and Analytical Models

It is well-known that the ultimate soil resistance and initial stiffness are two important parameters for controlling the shape of the p-y curve. In this research, the lateral displacement of 0.2D at the pile head [30,31] was selected to derive the ultimate soil resistance P at each depth z. The initial stiffness k is the slope of the straight line of the p-y curves.

Table 5. Comparisons of soil resistance and initial stiffness (D = 3 m).

z/Lscour	Numerical Model		Lin’s Model		Ratios
	P (MN/m)	k (MN/m2)	PLin (MN/m)	kLin (MN/m2)	P/PLin	k/kLin
0.16	5.53	124	3.23	65.4	1.71	1.90
0.35	2.90	97.6	6.75	80.8	0.43	1.21
0.59	0.50	84.6	13.2	97.2	0.04	0.87
0.67	0.15	74.2	15.8	102	0.01	0.73
0.84	−1.85	245	21.6	111	−0.09	2.21
0.92	−2.86	201	24.9	115	−0.11	1.75

presents the obtained P and k values from ABAQUS numerical simulations. On the other hand, values of P_Lin and k_Lin were calculated from the Lin’s p-y model presented in Section 2.2. Equation (10) was used to calculate the post-scour ultimate soil resistance F_u at this depth. Then, the corresponding equivalent depth Z can be obtained by equating Equations (11) and (1). Finally, values of P_Lin and k_Lin of the p-y curve at the post-scour depth z were described by the p-y curve at the equivalent depth Z using Equations (1) and (3). The calculated P_Lin and k_Lin values at various post-scour depths are also summarized in Table 5.

The values of the ultimate soil resistance and the initial stiffness calculated from the numerical model and the Lin’s model are also shown in Figure 9 and Figure 10, respectively. The values of P obtained by the numerical model decrease with the increase in z/L_scour. A turning point around z/L_scour = 0.7 is observed, that is the value of P is positive when z/L_scour < 0.7 and P turns negative when z/L_scour > 0.7, as shown in Figure 9a. The values of k decrease with the increase in z/L_scour when z/L_scour < 0.7 and increase significantly with further increase in z/L_scour, as shown in Figure 9b. However, the values of P_Lin and k_Lin increase with the increase in z/L_scour, as shown in Figure 10, which is quite different from those obtained by the numerical model.

Such differences could be explained by various failure mechanics of soil foundations. The Lin’s model assumes there are two types of failure modes for the monopile under lateral loading conditions, namely, the wedge failure near the soil surface and lateral flow soil failure at deep depths. However, the failure of monopole pile presented in Figure 11 shows that the rotation failure appeared near the pile toe rather than the lateral soil flow. The center point of the rotation failure zone is located near z/L_scour = 0.7 (i.e., the turn point O in Figure 6). Similar phenomenon was also obtained by Wang et al. [29]. This is the reason why there is a significant difference between the p-y curves obtained by the numerical model and the Lin’s model.

In summary, the Lin’s model has some deficiencies in calculating the lateral response of the monopile with a large diameter. Consequently, in order to extend the Lin’s model to the monopile with a large diameter, the effects of the pile diameter on the lateral response of the monopile need to be considered in the Lin’s model.

4. The Modified p-y Model under a Scouring Condition

4.1. P and k Values for Monopiles with Various Diameters

Four pile-soil numerical models (D = 3, 4, 6, and 8 m and L/D = 8, 6, 4, and 3, respectively) were built in ABAQUS to study the effect of the pile diameter on the lateral response of monopiles considering local scour conditions. The values of the ultimate soil resistance and the initial stiffness obtained from the ABAQUS numerical model and the Lin’s model at various depths of these four pile-soil scour models were estimated. Figure 12 summarizes the ratio of initial stiffness k/k_Lin and the ratio of ultimate soil resistance P/P_Lin for these four pile-soil scour models. It is found that values of P/P_Lin decrease significantly with the increase in z/L_scour when z/L_scour < 0.7 and then decrease slightly with a further increase in z/L_scour. The values of k/k_Lin decrease with the increase in z/L_scour, however, there is a turning point around z/L_scour = 0.7.

4.2. The Modified p-y Model

Based on the results presented in Figure 12, a function P/P_Lin expressed by z/L_scour and L/D was proposed. Firstly, an elliptic function (Equation (12)) and a linear function (Equation (13)) were selected to express the relationships between P/P_Lin and z/L_scour, when z/L_scour ≤ 0.7 and z/L_scour > 0.7, respectively.

$$A=\frac{P}{P_{Lin}}=C_R\times \left[1-\sqrt{1-{\left(\frac{z/L_{scour}-0.7}{0.7}\right)}^2}\right];z/L_{scour}\le 0.7$$

(12)

$$A=\frac{P}{P_{Lin}}=Ck\times \left(z/L_{scour}-0.7\right);z/L_{scour}>0.7$$

(13)

where C_R and C_k are fitting parameters.

Table 6. Fitting parameters for piles with various diameters.

L/D	CR	Ck
3	9.90	1.29
4	6.63	1.27
6	4.59	0.95
8	4.25	0.55

presents values of coefficient C_R and C_k for the various sizes of piles.

Then, an exponential function and a linear function were further used to build relationships between fitting parameters (C_R and C_k) and L/D, as shown in Figure 13.

$$C_R=120{(L/D)}^{-2.70}+3.75$$

(14)

$$C_k=-0.023{\left(L/D\right)}^2+0.095\left(L/D\right)+1.23$$

(15)

Put Equations (14) and (15) into Equations (12) and (13) to obtain the proposed modified model that builds up equations of A expressed by L/D and z/L_scour, see Equations (16) and (17), respectively.

$$A=\frac{P}{P_{Lin}}=\left[120{\left(L/D\right)}^{-2.7}+3.75\right]\times \left[1-\sqrt{1-{\left(\frac{z/L_{scour}-0.7}{0.7}\right)}^2}\right];z/L_{scour}\le 0.7$$

(16)

$$A=\frac{P}{P_{Lin}}=\left(-0.023{\left(L/D\right)}^2+0.095\left(L/D\right)+1.23\right)\times \left(z/L_{scour}-0.7\right);z/L_{scour}>0.7$$

(17)

The same fitting method was adopted to fit the data in Figure 12 to propose equations of B expressed by L/D and z/L_scour. The fitting results are shown in Equations (18) and (19).

$$B=\frac{k}{k_{Lin}}=-2.55\left(z/L_{scour}\right)+2.92+0.15\left(4-L/D\right);z/L_{scour}\le 0.7$$

(18)

$$B=\frac{k}{k_{Lin}}=-3.61\left(z/L_{scour}\right)+5.6+0.1\left(4-L/D\right);z/L_{scour}>0.7$$

(19)

where z is the distance from the post-scour soil surface; L is the pile embedded length before scour; L_scour is the pile embedded length after scour; and k_Lin and P_Lin are the initial stiffness and the post-scour ultimate soil resistance of the p-y curve at a certain depth obtained by the Lin’s model, respectively. The correction parameters A = P/P_Lin and B = k/k_Lin are used to represent the relationships between the ultimate soil resistance and the initial stiffness obtained using the numerical model and the Lin’s model, respectively. Finally, a hyperbolic form (Equation (20)), which has been adopted by many researchers [15,29] was used to describe the characteristic of the modified p-y curve.

$$p=\frac{y}{\frac{1}{B{k}_{Lin}}+\frac{y}{A{P}_{Lin}}}$$

(20)

4.3. Prediction Performance of the Modified p-y Model

In order to test the prediction performance of the proposed modified model, a beam on the nonlinear Winkler foundation (BNWF) model was built in ABAQUS to analyze the lateral response of laterally loaded piles by means of the modified p-y curves. In the BNWF model, the soil is described by a series of independent springs (i.e., p-y curves). For a given depth z, the soil resistance p is provided by the spring when the pile lateral displacement is y. The 3D linear beam elements (B31) with the element length Δl = 0.1 m in ABAQUS were used to represent the pile behavior and the parameters of the pile used in the numerical model are presented in Table 3.

The Lin’s model and the proposed modified model were coded into ABAQUS to simulate the lateral response of piles with scouring (D = 3, 4, 6, and 8 m and L/D = 8, 6, 4, and 3). The calculated lateral load–displacement curve of each pile is summarized in Figure 14. The absolute average relative error percentage (AAREP), as shown in Equation (21), was used as an indicator to evaluate the prediction performance of the p-y models. D_p is the relative difference between the predicted and numerical data and N is the number of testing data used.

$$AAREP=\frac{{\displaystyle \sum _{i=1}^N\left|D_{\mathrm{p}}\right|}}{N}$$

(21)

Overall, the prediction performance of the proposed modified p-y model is better than that of the original Lin’s model. The values of AAREP of the proposed model for monopoles with D = 3 m and 4 m are only 6.17% and 4.06%, which is much better than that of the original p-y model with AAREPs of 24.33% and 28.84%. However, we can also find that the prediction performance of the proposed and original models decreases with the increase in diameters. This is because the large-diameter monopiles were treated as a beam in the BNWF model. However, with the increase in diameter, whether the large-diameter monopile should be considered as a “beam” or a “structure” remains an open question.

A monopile foundation, which is located in the Zhugensha sea area, Jiangsu province, China, was used to illustrate the practical application of the proposed modified p-y model. The pile diameter of the monopile of the 6 MW offshore turbine is 6.0 m and the embedded depth is 46.1 m. The scour condition around the monopile is serious, with a typical scour hole shape as the “inverted conical”, as shown in Figure 15. The maximum of scour depth around the monopile is 8.6 m. Based on the measured scour hole data, a numerical model of the monopile under a local scour condition was constructed in ABAQUS, whose parameters are presented in

Table 7. Parameters of the 6 MW offshore turbine.

Parameters	Values
Diameter, D (m)	6
Thickness, t (m)	0.07
Embedded depth, L (m)	46.1
Equivalent elastic modulus, Ep’ (GPa)	18.9
Loading height, h (m)	6
Density, ρ (kg/m3)	7850
Poisson’s ratio, v	0.3
Scour depth, Sd (m)	8.6
Top scour width, Sw (m)	13.3

and

Table 8. Parameters of the soil in Zhugensha sea area.

Soil Parameters	Values
Effective weight, γ’ (kN/m3)	10.4
Internal friction angle, φ’ (degrees)	33.0
Dilation angle, ψ (degrees)	3.0
Poisson’s ratio, ν	0.3
Cohesion, c (kPa)	0.1
Coefficient of static lateral earth pressure, K0	0.4
Reference modulus, E0 (MPa)	240.0
Exponent factor, $n$	0.5

.

Figure 16 shows the lateral load–displacement curve at the pile head of the monopile under the lateral load of 6000 kN. It is found that the proposed modified p-y model is more accurate than that of the Lin’s model and the AAREP of the proposed modified p-y model and the Lin’s model are 4.82% and 17.33%, respectively.

5. Conclusions

In this paper, a modified p-y model that can be used to calculate the lateral response of a large-diameter monopile (D = 3, 4, 6, and 8 m) in the sand under local scouring conditions was proposed as an extension to the work by Lin et al. [11]. The main conclusions are as follows:

• Numerical simulation results show that the values of P and k obtained from the numerical model decrease with the increase in z/L_scour, when z/L_scour < 0.7, and then increase with a further increase in z/L_scour. Such results are quite different from those obtained by the Lin’s p-y model where the values of P_Lin and k_Lin monotonically increase with the increase in z/L_scour.
• Two diameter-related parameters, A = P/P_Lin and B = k/k_Lin, represent the relationships between the ultimate soil resistance and the initial stiffness obtained by the numerical model and the Lin’s p-y model, respectively, were developed and introduced into the Lin’s p-y model to propose a modified p-y model.
• The prediction performance of the modified p-y model is better than that of the Lin’s p-y model. The values of AAREP of the modified p-y model for monopiles with D = 3 m and 4 m are 6.17% and 4.06%, which is much better than that of the Lin’s p-y model with AAREPs of 24.33% and 28.84%.

The current pile-soil numerical model is based on the linear Mohr-Coulomb (MC) criterion that is difficult to capture the stress-dependent mechanical behaviors of soil foundations. Especially, scour holes would affect the stress states. Therefore, further research is required to adopt a nonlinear constitutive model of the soil in 3D numerical analysis to consider the stress history of the soil.