# Scour Effects on the Lateral Behavior of a Large-Diameter Monopile in Soft Clay: Role of Stress History

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{c}is the lateral displacement at half the maximum soil stress, which can be determined by:

_{50}is the strain at one-half the maximum stress.

_{u}is the ultimate soil resistance per length, which is equal to the smaller value of p

_{u1}and p

_{u2}calculated by:

_{u}is the soil undrained shear strength; J is a constant value; z is the depth below the post-scour mudline.

_{u}. The modification of p

_{u}depends on the change of the undrained shear strength and the effective unit weight of the remaining soils after scour, as follows [14]:

_{int}is soil void ratio before scour; S

_{d}is scour depth; C

_{c}and C

_{ur}denote the compression and swelling indexes obtained from the oedometer tests.

_{u}considering the stress history effect can be rewritten as follows:

## 2. Three-Dimensional Finite Element Analyses

#### 2.1. Three-Dimensional Finite Element Model

_{p}= 210 GPa and Poisson’s ratio of ν

_{p}= 0.3. An advanced hypoplastic clay model (to be presented in the following subsection) was used to represent the soil behavior. The interaction between the pile and the soil was simulated based on the Coulomb friction law. The frictional coefficient μ = 0.31 was adopted in this study based on the equation proposed by Randolph and Wroth [23]. The detachment between the pile and the clay was allowed [24].

#### 2.2. An Advanced Hypoplastic Model for Clay Considering Stress History Effect

**D**represent the objective stress rate and the Euler stretching tensor, respectively.

**L**is

**I**is a fourth-order identity tensor; a, c

_{1}, and c

_{2}are the three parameters, and can be calculated by

_{c}is a model parameter that denotes critical friction angle; ν is a model parameter that controls the soil shear stiffness at large strain; Parameter α can be calculated by

^{’}) plane, respectively. (e and p

^{’}denote void ratio and mean effective stress, respectively).

**N**is a second-order constitutive tensor and can be expressed as

**m**denote the degree of non-linearity and tensorial quantity, respectively, and have the following equations

_{r}= 1 kPa is a reference stress; N is a model parameter defining the position of the isotropic virgin compression line in the ln(1 + e) versus ln (p

^{’}) plane.

**D**due to the nonlinear form given by the Euclidian norm $\Vert \mathit{D}\Vert $, and thus there is no need to define yield surface when predicting nonlinear behavior.

_{c}, N, λ*, κ*, and ν. The parameters are equivalent to those defined in the modified Cam clay model.

**δ**is used as a new tensorial state variable and the normalized magnitude of

**δ**is:

**δ**is:

**u**is a fourth-order tensor that represents stiffness, and can be calculated using the following equation:

_{rat}is a model parameter that can be quantified by the ratio between initial small-strain stiffness upon a 90° strain path reversal and the initial stiffness upon a 180° strain reversal; m

_{R}represent the initial small-strain stiffness upon a 180° strain path reversal. m

_{R}can be calibrated to fit the initial stiffness G

_{0}, which is formulated by Wroth and Houlsby [30], as follows:

_{g}and n

_{g}are model parameters that reflect the stress dependency of small-strain stiffness.

**δ**is:

_{r}is a model parameter that controls the rate of stiffness degradation.

_{c}, N, λ*, κ* and ν are for the basic model. The six other parameters, i.e., R, m

_{rat}, β

_{r}, χ, A

_{g}, and n

_{g}are for the intergranular concept.

#### 2.3. Parameter Calibration and Model Validation

^{’}

_{c}, N, λ*, and κ* were obtained from Powrie [31] and Al-Tabbaa [32]. The parameters R, m

_{rat}, β

_{r}, and χ were calibrated against data reported by Benz [33] on small-strain stiffness of kaolin clay, as shown in Figure 3a. In order to calibrate the remaining parameters ν, A

_{g}, and n

_{g}, an undrained cyclic triaxial test was carried out. The kaolin clay sample was consolidated under an isotropic confining stress of 200 kPa, followed by 100 cycles of undrained cyclic compression. More details about the triaxial test can be found in He [34]. The confining stresses in the afore-mentioned elemental tests (for calibrating model parameters) generally do not exceed 200 kPa, except one case of 300 kPa in Benz [33]’s tests. This range of effective confining stress (i.e., p’ ≤ 200 kPa) is relevant to that considered in the numerical investigation reported herein, i.e., p’ value of the soil (γ’ = 8 kN/m

^{3}, K

_{0}= 0.625, where K

_{0}is the coefficient of lateral earth pressure) along the 30 m deep monopile fall within 180 kPa. It is worth noting that the Kaolin clay can differ a lot depending on the manufacture. The aforementioned databases for the calibration of the model parameters and the trixial test were all based on the same type of Kaolin, i.e., Speswhite Kaolin clay.

#### 2.4. Load Case

_{hub}was estimated as [37,38]:

_{a}is the density of air; A

_{R}is the rotor swept area; C

_{T}is the thrust coefficient, and U is the wind speed.

_{s}is shape coefficient which equals to 0.5 for the tubular tower; V

_{z}denotes the average wind speed as a function of height z. The normal wind speed profile is given by the power law [36]:

_{hub}is the wind speed at the height of the hub z

_{hub}; α is the power law exponent, which is assumed to be 0.2.

_{M}is the inertia coefficient; C

_{D}is the drag coefficient; ρ is the mass density of the sea water; D

_{t}is the diameter of each section; $\dot{x}$ and $\ddot{x}$ are the wave-induced velocity and acceleration in the horizontal direction. Since current force is relatively small compared to wind and wave force, thus loads due to current are not considered for analysis.

#### 2.5. Numerical Modelling Procedure

_{d}= 0.2 D (1 m) and S

_{d}= 0.5 D (2.5 m) were examined. The detailed procedures are as follows:

- (1)
- (2)
- Initial K
_{0}stress of the soil was generated by a spatial calculation method available in ABAQUS in a Geostatic step. In this step, an equivalent pressure that equals the vertical stress of the scour layer was then applied on the soil surface. Due to the equivalent pressure, the soil stress of the remaining soil after scour keep remained unchanged. Therefore, the soil shear strength and other soil properties of the remaining soil after scour were assumed to be the same with those before scour. This operation can model scour ignoring the stress history effect, which is similar to the method often used in practice, i.e., just simply removing the scour layer while keeping the soil properties of the remaining soil unchanged. - (3)
- Wished-in-place pile installation was achieved by changing appropriate elements to a linear elastic material of the pile. Pile installation effect was not considered for a reasonable simplification.
- (4)
- The loads described in Section 2.4 were applied on the structure.

- (1)
- A model without scour was first developed, and then the initial K
_{0}soil stress was achieved. - (2)
- Defining a special step for forming scour. In this step, the scour layer was removed by adding keywords in the ABAQUS input file, i.e., Model change, remove, as shown in Figure 5c. This operation models the unloading process when scouring, and thus takes accout of the stress history effect.
- (3)
- Changing appropriate elements to a linear elastic material of the pile, and the loads described in Section 2.4 were applied on the structure.

## 3. Numerical Results

#### 3.1. Undrained Shear Strength after Scour

_{u}) of the remaining clay after scour. When the stress history effect is ignored, the soil vertical stress and the OCR of the remaining soil keep unchanged. Therefore, the undrained shear strength of the remaining soil is almost the same as that in the condition of no scour, and could be fitted by a linear line, i.e., s

_{u}= 1.66 z. However, the undrained shear strength of the remaining soil which considers the stress history effect is found to be decreased when compared with that of ignoring the stress history. In this study, ᴧ = 0.78 in Equation (5) provides the best agreement with the computed results, as shown in Figure 6b.

#### 3.2. Lateral Load-Deflection Response

_{d}= 0.2 D and S

_{d}= 0.5 D, respectively. The results of the case of no scour are also presented in the figures. All the detailed values are summarized in Table 3. It should be noted that, at any given scour depth, the percentage increases in pile head deflection presented in Table 3 are relative to the values of that with ignoring the stress history effects.

_{d}= 0.2 D) and 49% (S

_{d}= 0.5 D) higher pile-head deflection compared with the case in which the stress history effect is ignored. The percentage increase in pile-head deflection between considering and ignoring the stress history effect is found to increase with increasing scour depth. Therefore, ignoring the stress history of the remaining soil is likely to cause an unconservative analysis of the laterally loaded pile under scour conditions. A similar conclusion is also made by Lin et al. [10] and Zhang et al. [12]. In addition, compared to the result of no scour, considering scour and the resulted stress history effect leads to a 16% (S

_{d}= 0.2 D) and 64% (S

_{d}= 0.5 D) increase in lateral pile-head deflection. It is recommended that scour and the accompanying stress history effect should be well treated when designing the monopile-supported wind turbines in clay.

_{d}= 0.2 D and S

_{d}= 0.5 D are also included in the Figure 7a and Figure 7b, respectively. Since scour has an insignificant effect on the change of the effective unit weight of the remaining soil [10,12], thus it was ignored in this study.

_{d}= 0.2 D) and 75% (S

_{d}= 0.5 D) compared with that of ignoring stress history effect. The differences are higher than those computed by 3D FE analysis, i.e., 13% for S

_{d}= 0.2 D and 49% for S

_{d}= 0.5 D. The comparison shows that Lin’s [10] p-y method overestimates the percentage difference in pile-head deflection between ignoring and considering stress history effect.

#### 3.3. Profiles of the Bending Moment

_{d}= 0.2 D) and 2% (S

_{d}= 0.5 D) higher maximum bending moment compared with the case in which stress history is neglected. It can also be found that the percentage difference in the maximum bending moment, between considering and ignoring stress history effect increases insignificantly with increasing scour depth. The results indicate that the stress history effect may have a minor influence on the maximum bending moment in the pile. Besides, when the scour depth increases to 0.2 D and 0.5 D, the maximum bending moment increases by approximately 2% and 5%, respectively, compared with that under no scour condition. To some extent, the scour and the stress history effect on the maximum bending moment in the pile can also be ignored.

#### 3.4. Soil Displacement Field

_{d}= 0.2 D and S

_{d}= 0.5 D, respectively. Two distinct soil flow mechanisms can be clearly identified for the large diameter monopile, namely a wedge mechanism near the ground surface and rotational soil flow near the pile toe. Similar failure mechanisms were also observed by Hong et al. [35] and Schroeder et al. [39]. When considering the stress history effect, the width of the wedge failure zone on the ground surface extends from 1.6 D to 1.8 D (S

_{d}= 0.2 D) and 1.7 D to 2.5 D (S

_{d}= 0.5 D). Meanwhile, the wedge failure zone is observed to extend to a greater depth, i.e., from 0.53 L (L = pile embedded length before scour) to 0.57 L (S

_{d}= 0.2 D) and 5.7 L to 6.7 L (S

_{d}= 0.5 D). As expected, the differences in the width and depth of the wedge failure zone between considering and ignoring stress history effect increase with increasing scour depth. As for the rotation center of the plane rotation zone, when considering stress history, it moves downward from 0.76 L to 0.78 L (S

_{d}= 0.2 D) and 0.78 L to 0.82 L (S

_{d}= 0.5 D). As a conclusion, soil failure mechanism of the large diameter monopile consists of two parts, namely wedge failure at shallow and rational soil flow at depth. Ignoring the stress history effect underestimates the width and depth of the wedge failure zone, while overestimates the location of the rotational soil flow zone.

#### 3.5. p-y Curves Derived from Finite Element Simulation Results

_{d}= 0.2 D) and 39.8% (S

_{d}= 0.5 D), which is lower than that when using the p-y curves proposed by Lin et al. [10], i.e., the percentage reduction is 36.2% (S

_{d}= 0.2 D) and 52.3% (S

_{d}= 0.2 D). The comparison demonstrates that Lin’s [10] p-y method overestimates the percentage reduction in ultimate soil resistance between considering and ignoring the stress history effect. The overestimation leads to a larger percentage difference in pile-head deflection when compared with that obtained from 3D FE analysis (see Table 3).

_{d}= 0.2 D and S

_{d}= 0.5 D are presented in Figure 14a,b, respectively. In this study, the secant modulus at a small displacement, i.e., y = D/1000, of the p-y curves were regarded as initial stiffness [44]. It can be clearly seen in the figure that considering stress history effect leads to a decrease in the initial stiffness of the p-y curves when compared with the results that ignoring the stress history. The percentage reduction in initial stiffness between considering and ignoring stress history effect is further examined in Figure 15. At any given scour depth, the percentage reductions in the initial stiffness of p-y curves in Figure 15 are relative to the values of that with ignoring the stress history effects. The figure reveals that the percentage reduction gradually decreases when the soil depth increases. On the other hand, the percentage reduction in the initial stiffness of p-y curves is found to increase with increasing scour depth. When the scour depth is 0.2 D and 0.5 D, the percentage reduction in the initial stiffness of the p-y curves can be up to 20.7% and 25.8%, respectively. The initial stiffness of p-y curves can affect the natural frequency of an offshore wind turbine directly. It was founded by Wang et al. [45] that 10–50% decrease in the initial stiffness of p-y curves could lead to a 4.6–6.6% drop in the natural frequency of the wind turbine, which has a dramatic effect on the wind turbine fatigue life [46]. Thus, it is recommended that the initial stiffness of p-y curves should be well evaluated.

## 4. Conclusions

- Scour significantly increases the overconsolidation ratio and reduces the undrained shear strength of the remaining soil, which contributes to the significant difference in pile behavior between considering and ignoring the stress history effect.
- When the scour depth is increased from 0.2 D to 0.5 D, consideration of the stress history effect is found to result in a maximum 30.1–39.8% and 20.7–25.8% reduction in the ultimate soil resistance and the initial stiffness of the p-y curves, respectively. These reductions lead to a 13–49% increase in lateral pile-head deflection and 1–2% increases in maximum bending moments in the pile. Ignoring the stress history effect leads to an unconservative analysis of laterally loaded piles under scour conditions.
- Soil failure mechanism of the large diameter monopile consists of two parts, namely wedge failure at shallow and rational soil flow at depth. Ignoring the stress history effect underestimates the width and depth of the wedge failure zone, while overestimates the location of the rotational soil flow zone.
- Modified p-y curves proposed by Lin et al. [10] for considering the stress history effect overestimate the percentage reduction in ultimate soil resistance. Consequently, Lin’s [10] p-y method will likely overestimate the percentage difference in pile-head deflection between considering and ignoring the stress history effect.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

L | embedded pile length |

D | pile diameter |

p | soil resistance per length |

y | lateral pile deflection |

y_{c} | lateral deflection at half the maximum soil stress |

ε_{50} | strain at one-half the maximum stress |

p_{u} | ultimate soil resistance per length |

γ′ | volume of the pore fluid |

s_{u} | undrained shear strength |

z | depth below the post-scour mudline |

σ′ | vertical effective stress |

OCR | overconsolidated ratio |

e | soil void ratio |

p^{‘} | mean effective stress |

S_{d} | scour depth |

C_{c}, C_{ur} | compression and swelling indexes, respectively |

E_{p} | Young’s modulus of pile |

ν_{p} | Poisson’s ratio of soil |

μ | friction coefficient |

$\stackrel{\circ}{T}$ | objective stress rate |

D | Euler stretching tensor |

L | hypoelastic tensor |

I | fourth-order identity tensor |

N | second-order constitutive tensor |

Y, m | degree of non-linearity and tentorial quantity, respectively |

N | position of the isotropic virgin compression line in the ln(1 + e) versus ln (p^{’}) plane |

λ*, κ* | slope of the isotropic virgin compression and unloading line in the ln(1 + e) versus ln (p^{’}) plane, respectively |

φ’_{c} | critical state friction angle |

ν | parameter controlling the shear stiffness |

δ | intergranular strain |

R | size of the elastic range |

$\hat{\mathsf{\delta}}$ | direction of the intergranular strain |

u | fourth-order tensor |

m_{rat} | path-dependent parameter |

β_{r}, χ | strain-dependent parameters |

A_{g}, n_{g} | stress-dependent parameters |

G_{0} | soil initial stiffness |

F_{hub} | wind load acting on the hub |

ρ_{a}, ρ | density of air and sea water, respectively |

A_{R} | rotor swept area |

C_{T}, C_{s} | thrust and shape coefficient, respectively |

F_{tower} | wind load acting on tower |

A_{tower} | wind pressure area on the tower |

V_{z} | average wind speed |

V_{hub} | wind speed at the height of the hub |

α | power law exponent |

φ | soil porosity |

F_{wave} | wave load |

c_{m}, c_{d} | inertia and drag coefficient, respectively |

$\dot{x}$,$\ddot{x}$ | wave-induced velocity and acceleration |

K_{0} | coefficient of lateral earth pressure |

k | initial stiffness of p-y curves |

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**Figure 2.**Diagram of: (

**a**) the offshore wind turbine supported on a monopile foundation modelled in this study; (

**b**) three-dimensional finite element mesh and boundary conditions.

**Figure 3.**Comparison between measured and computed of: (

**a**) small-strain stiffness; (

**b**) stress-strain relationship of soil element subjected to cyclic triaxial shearing.

**Figure 4.**Validation of the numerical model against the centrifuge test reported by Hong et al. [35].

**Figure 5.**Schematic diagram of numerical modelling procedures of: (

**a**) no scour; (

**b**) scour ignoring the stress history effect; (

**c**) scour considering stress history effect. Note: S

_{d}denotes scour depth; γ’ denotes soil effective weight.

**Figure 7.**Comparison between the computed and calculated lateral load-deflection relationships at the scour depth of: (

**a**) S

_{d}= 0.2 D; (

**b**) S

_{d}= 0.5 D.

**Figure 8.**Profiles of the bending moment at the scour depth of: (

**a**) S

_{d}= 0.2 D; (

**b**) S

_{d}= 0.5 D.

**Figure 9.**Computed soil displacement field and displacement vectors at the scour depth of S

_{d}= 0.2 D: (

**a**) ignoring the stress history effect; (

**b**) considering the stress history effect.

**Figure 10.**Computed soil displacement field and displacement vectors at the scour depth of S

_{d}= 0.5 D: (

**a**) ignoring the stress history effect; (

**b**) considering the stress history effect.

**Figure 11.**Comparison of the p-y curves at the scour depth of: (

**a**) S

_{d}= 0.2 D; (

**b**) S

_{d}= 0.5 D. Note: The depth of the p-y curve, z, was measured from the post-scour mudline.

**Figure 12.**Distributions of ultimate soil resistance at the scour depth of: (

**a**) S

_{d}= 0.2 D; (

**b**) S

_{d}= 0.5 D.

**Figure 14.**Distributions of the initial stiffness of the p-y curves at scour depth of: (

**a**) S

_{d}= 0.2 D; (

**b**) S

_{d}= 0.5 D.

Parameter | Value | Remark | ||
---|---|---|---|---|

Monotonic response at medium to large strain levels | Critical state friction angle | φ′_{c} | 22° | Powrie [31] |

Slope of the isotropic NCL in the ln(1 + e)-lnp’ space | λ* | 0.11 | Al-Tabbaa [32] | |

Slope of the isotropic unloading line in the ln(1 + e)-lnp’ space | κ* | 0.026 | ||

Position of the isotropic NCL in the ln(1 + e)-lnp’ space | N | 1.36 | ||

Parameter controlling the proportion of bulk and shear stiffness | ν | 0.1 | Calibrated against cyclic triaxial test | |

Small-strain stiffness upon various strain reversal | Strain range of soil elasticity | R | 10^{−4} | Calibrated against Benz’s [33] small-strain stiffness data |

Path-dependent parameter | m_{rat} | 0.7 | ||

Strain-dependent parameter 1 | β_{r} | 0.12 | ||

Strain-dependent parameter 2 | χ | 5 | ||

Stress-dependent parameter 1 | A_{g} | 650 | Calibrated against cyclic triaxial test | |

Stress-dependent parameter 2 | n_{g} | 0.65 |

**Table 2.**Environmental site conditions [20].

Parameter | Value |
---|---|

Wind speed Weibull distribution shape parameter | 1.8 |

Wind speed Weibull distribution scale parameter | 8 m/s |

Reference integral length scale | 18% |

Turbulence integral length scale | 340.2 m |

Density of air | 1.225 kg/m^{3} |

Significant wave height with 50-year return period | 8.5 s |

Peak wave height | 6.1 m |

Water depth | 10 m |

Density of sea water | 1030 kg/m^{3} |

Method | Condition | With No Scour | With Scour (S_{d} = 0.2 D) | With Scour (S_{d} = 0.5 D) |
---|---|---|---|---|

3D FE analysis | Ignoring stress history | 0.081 | 0.083 | 0.089 |

Considering stress history | 0.081 | 0.094 | 0.133 | |

Percentage increase | - | 13% | 49% | |

p-y method proposed by Lin et al. [10] | Ignoring stress history | 0.882 | 0.896 | 0.971 |

Considering stress history | 0.882 | 1.121 | 1.695 | |

Percentage increase | - | 25% | 75% |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

He, B.; Lai, Y.; Wang, L.; Hong, Y.; Zhu, R.
Scour Effects on the Lateral Behavior of a Large-Diameter Monopile in Soft Clay: Role of Stress History. *J. Mar. Sci. Eng.* **2019**, *7*, 170.
https://doi.org/10.3390/jmse7060170

**AMA Style**

He B, Lai Y, Wang L, Hong Y, Zhu R.
Scour Effects on the Lateral Behavior of a Large-Diameter Monopile in Soft Clay: Role of Stress History. *Journal of Marine Science and Engineering*. 2019; 7(6):170.
https://doi.org/10.3390/jmse7060170

**Chicago/Turabian Style**

He, Ben, Yongqing Lai, Lizhong Wang, Yi Hong, and Ronghua Zhu.
2019. "Scour Effects on the Lateral Behavior of a Large-Diameter Monopile in Soft Clay: Role of Stress History" *Journal of Marine Science and Engineering* 7, no. 6: 170.
https://doi.org/10.3390/jmse7060170