# Validation and Application of a New Software Tool Implementing the PISA Design Methodology

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## Abstract

**:**

## 1. Introduction

## 2. Method

_{out}), and wall thickness (t). This so-called calibration space or design space is used to provide some flexibility in optimizing the final design while ensuring the validity of the calibrated soil reactions, as long as the final design is within this space.

## 3. Validation of Monopile Designer for Dunkirk Sand

_{r}) in the range 45% ≤ D

_{r}≤ 90% were considered. Burd et al. describe the General Dunkirk Sand Model (GDSM) as a collection of soil reactions in which the coefficients in the dvf’s have been expressed in terms of D

_{r}. The GDSM has been validated for monopiles with an L/D ratio in the range 2–6 and a h/D ratio in the range 5–15.

_{r}= 75%, backed by the original 3D finite element calculations used for the calibration/validation of the GDSM with the Critical State constitutive model for sand by Taborda et al. [9]. The soil profile as defined in the monopile designer is listed in Table 1. For the Numerical Based Design (NBD), this soil profile was translated into a single soil layer when generating the PLAXIS 3D finite element models, using the Hardening Soil small-strain (HSsmall) model by Benz [10] with drained (effective) parameters as listed in Table 2. Parameter values are mostly based on correlations by Brinkgreve et al. [11], considering D

_{r}= 75%. The HSsmall parameter set was tested under drained triaxial compression test conditions at initial isotropic stresses of 50, 100, 150, and 400 kN/m

^{2}, and the stress–strain behavior was compared with triaxial test data on Dunkirk sand with an initial void ratio of e

_{0}≈ 0.64 (D

_{r}≈ 75%) from the PISA project, digitized from [9]. A dilatancy cut-off was imposed at a maximum void ratio of 0.72, equivalent to a volumetric strain (expansion) of nearly 5%, to account for Critical State. Results of the triaxial test simulations (HSsmall ###) in comparison with digitized lab test data (DTXC-###-64) are shown in Figure 1, where ### indicates the corresponding initial isotropic stress in kN/m

^{2}. Although HSsmall does not capture the softening behavior, the overall stress and strain response is quite accurate for these test conditions.

_{0}. In the HSsmall model, this parameter is stress-dependent and hence depth-dependent. With a reference value G

_{0}

^{ref}= 194,000 kN/m

^{2}for a reference confining pressure of 100 kN/m

^{2}this will give the G

_{0}-profile as depicted in Figure 2. The G

_{0}-profile is plotted over digitized data from [9]. It can be concluded that the modelled G

_{0}-profiles are quite similar.

_{max}is applied at the top of the pile (z = h) such that at mudline level (z = 0) a lateral displacement around 0.2 times the pile diameter is obtained in the last calculation phase.

^{6}kN/m

^{2}and Poisson’s ratio ν = 0.3. Between the pile wall and the soil and at the pile base, 12-node interface elements are used to model soil-structure interaction and to ‘collect’ the soil reactions. In absence of softening and Critical State behavior, the wall friction angle in the interface elements is assumed 29° and the dilatancy angle 0°. One of the used finite element models is shown in Figure 3.

_{max}); (Phase 4) applying prescribed displacement for large displacement solution (v

_{max}). It is the idea that Phase 3 provides accurate data to calibrate the small-strain response, which is needed for any Fatigue Limit State (FLS) design criterion, while Phase 4 provides data to calibrate the large strain response and bearing capacity, which is needed for any Ultimate Limit State (ULS) design criterion.

## 4. Validation Results

- Overall, the small displacement solutions of the calibrated 1D models (1D Calibrated) are similar as the corresponding 3D finite element solutions (3D FE), whereas they are conservative compared to the GDSM solutions (1D GDSM).
- For large displacements, the 1D Calibrated solutions are more ‘curved’ than the corresponding 3D FE solutions. In most cases, this results in a higher load in the mid displacement range, but also a ‘bearing capacity’ at maximum displacement that is closer to the corresponding 3D FE solution (some are even lower).
- For large displacements, the 3D FE solutions overall show a lower stiffness and bearing capacity compared to the GDSM solutions, but the corresponding 1D Calibrated solutions are generally closer to GDSM solutions.
- Following points 2 and 3 (for large displacements), distinction can be made between the lower and higher L/D ratios: for the higher L/D ratios (L/D = 4; Models 3, 4, 6, 7, and 9), the 1D Calibrated solutions tend to be stiffer than the 3D FE solutions and show a better correspondence to the GDSM solutions than for the lower L/D ratios (L/D = 2; Models 1, 2, 5, and 8). A further nuance for the low L/D ratios can be seen in that the 1D Calibrated solutions tend to be better (at least in terms of bearing capacity) for larger diameter piles (Models 1 and 2).
- No clear trend can be observed with respect to the h/D ratio.

## 5. Application Case: 11 MW Wind Turbine in the North Sea

## 6. Design Optimization

_{0}, smaller φ′, smaller OCR). The loading involves a static lateral load H = 15 MN acting at a height h = 35 m, resulting in a bending moment M = 525 MNm at mudline level.

- Serviceability Limit State (SLS) criterion: under a lateral load H acting at height h, the average rotation at mudline must be less than 0.25°.
- Ultimate Limit State (ULS) criterion: considering a global safety factor of 1.5 according to the Working Stress Design approach, the working load shall be increased by this factor to obtain the design load, and the resulting lateral displacement at mudline must be less than 0.1 times the monopile diameter.

- There is a significant difference between the embedment depth resulting from the SLS design criterion and the ULS design criterion.

## 7. Discussion of Results

- Increasing the pile diameter D.
- Relax the rotation requirement.

## 8. Conclusions

- Results from the monopile designer, both from 3D finite element calculations as well as from 1D Calibrated soil reactions, are in line with previous results from the PISA research team.
- Although the response from the 1D Calibrated soil reactions is more or less similar as the response from the 3D finite element (FE) calculations, they could be closer if the so-called second-stage optimization would be used to calibrate the soil reactions.
- For normally consolidated sandy soils, as considered in the validation case, the results from the calibrated soil reactions are in line with (although a bit conservative compared to) the results from the General Dunkirk Sand Model (GDSM). For over-consolidated sandy soils, as considered in the application case, the GDSM is more conservative, but could still serve for concept design purposes. Nevertheless, the PISA numerical based design and use of calibrated soil reactions has the advantage of providing a site-specific calibrated response.
- According to the PISA approach, in sandy soils, the SLS design criterion is often decisive as it leads to the largest embedment depth.
- The curve describing the pile rotation as a function of the embedment depth can become rather horizontal near the SLS design criterion. This means, a small reduction in pile rotation requires a significant increase in embedment depth to fulfill the SLS design criterion (if it can be fulfilled at all), which is undesirable. Very competent soil conditions, as considered in [12], seem to be less ‘sensitive’ with respect to the SLS design criterion, although in those cases the SLS criterion still prevails.
- To avoid the undesirable situation as mentioned above, it might be considered to allow for a more relaxed (increased) rotation requirement, since otherwise it may make the monopile unnecessarily expensive. A larger rotation of, for example, 0.50° would seem tolerable, provided the ULS criterion is fulfilled. This would also bring the embedment depth L based on SLS design closer to L based on ULS design.
- Given that the API design method does not explicitly consider the (very) high soil stiffness at small deformations, care must be taken when using this method for FLS design.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A1.**Load-displacement curves for Models 1–9 as listed in Table 3.

Model | η (-) (FLS) | η (-) (ULS) |
---|---|---|

1 | 0.963 | 0.950 |

2 | 0.952 | 0.958 |

3 | 0.923 | 0.835 |

4 | 0.931 | 0.823 |

5 | 0.958 | 0.956 |

6 | 0.971 | 0.891 |

7 | 0.983 | 0.897 |

8 | 0.971 | 0.952 |

9 | 0.954 | 0.835 |

## References

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**Figure 1.**Triaxial test results for HSsmall model in comparison with PISA (Pile Soil Analysis) data, digitized from [9].

**Figure 4.**Load-displacement curves for Model 1 (

**a,b**) and Model 3 (

**c,d**) as listed in Table 3. Results from the other models are available in Appendix A.

**Figure 7.**Embedded length analysis. (

**a**) Bearing capacity as a function of embedment depth L considering Ultimate Limit State (ULS) conditions. (

**b**) Pile rotation as a function of embedment depth L considering Serviceability Limit State (SLS) conditions.

**Figure 8.**Load-deflection behavior for L = 24 m for different design methods; (

**a**) Fatigue Limit State (FLS); (

**b**) Ultimate Limit State (ULS).

**Table 1.**Soil profile, as defined in the monopile designer, representing Dunkirk sand with D

_{r}= 75%.

Top (m) | Bottom (m) | γ′ (kN/m^{3}) | G_{0,mid} (MN/m^{2}) | φ′ (°) | Ψ (°) | K_{0} (-) |
---|---|---|---|---|---|---|

0 | −90 | 10.09 | 205.3 | 39 | 9 | 0.37 |

**Table 2.**Parameters of the Hardening Soil small-strain (HSsmall) model, representing Dunkirk sand with D

_{r}= 75%.

Parameter | Symbol | Value | Unit |
---|---|---|---|

Effective unit weight | γ′ | 10.09 | kN/m^{3} |

Reference secant stiffness in triaxial compression | E_{50}^{ref} | 45,000 | kN/m^{2} |

Reference tangent stiffness in primary oedometric loading | E_{oed}^{ref} | 45,000 | kN/m^{2} |

Reference triaxial unloading/reloading stiffness | E_{ur}^{ref} | 135,000 | kN/m^{2} |

Stress-dependency of stiffness | m | 0.5 | - |

Effective cohesion | c′ | 0.1 | kN/m^{2} |

Effective friction angle | φ′ | 39 | ° |

Dilatancy angle | Ψ | 9.0 | ° |

Strain at which G has reduced to 70% | γ_{0.7} | 0.000125 | - |

Reference small-strain shear modulus | G_{0}^{ref} | 194,000 | kN/m^{2} |

Reference stress | p^{ref} | 100 | kN/m^{2} |

Unloading/reloading Poisson’s ratio | ν_{ur} | 0.2 | - |

K_{0} stress ratio in normally consolidated condition | K_{0}^{nc} | 0.3707 | - |

Friction ratio | R_{f} | 0.906 | - |

Tensile strength | σ_{t} | 0.0 | kN/m^{2} |

Model | h (m) | L (m) | D_{out} (m) | h/D (-) | L/D (-) | t (m) | v_{max} (m) |
---|---|---|---|---|---|---|---|

1 | 50 | 20 | 10.0 | 5.0 | 2.0 | 0.091 | 9.9 |

2 | 75 | 20 | 10.0 | 7.5 | 2.0 | 0.091 | 14.0 |

3 | 100 | 40 | 10.0 | 10.0 | 4.0 | 0.091 | 7.8 |

4 | 75 | 40 | 10.0 | 7.5 | 4.0 | 0.091 | 10.8 |

5 | 25 | 10 | 5.0 | 5.0 | 2.0 | 0.045 | 5.1 |

6 | 25 | 20 | 5.0 | 5.0 | 4.0 | 0.045 | 4.3 |

7 | 50 | 20 | 5.0 | 10.0 | 4.0 | 0.045 | 6.1 |

8 | 75 | 15 | 7.5 | 10.0 | 2.0 | 0.068 | 7.5 |

9 | 37.5 | 30 | 7.5 | 5.0 | 4.0 | 0.068 | 6.0 |

**Table 4.**Soil strata and corresponding relative density (D

_{R}) and over-consolidation ratio (OCR) at the project site.

Top (m) | Bottom (m) | D_{R} (%) | OCR (-) |
---|---|---|---|

0 | −2 | 82 | 1.0 |

−2 | −3.9 | 65 | 10.0 |

−3.9 | −6.5 | 62 | 10.0 |

−6.5 | −9.6 | 61 | 10.0 |

−9.6 | −13.2 | 59 | 8.0 |

−13.2 | −17.3 | 64 | 6.1 |

−17.3 | −20.7 | 65 | 5.1 |

−20.7 | −23.8 | 57 | 4.4 |

−23.8 | −25.8 | 68 | 4.1 |

−25.8 | −30.0 | 73 | 3.7 |

−30.0 | −31.0 | 72 | 3.5 |

−31.0 | −32.5 | 61 | 3.3 |

−32.5 | −60.0 | 70 | 3.2 |

Top (m) | Bottom (m) | γ′ (kN/m^{3}) | G_{0} (MN/m^{2}) | φ′ (°) | Ψ (°) | K_{0} (-) |
---|---|---|---|---|---|---|

0 | −2 | 7.9 | 51.89 | 41 | 11 | 0.3 |

−2 | −3.9 | 9.1 | 50.08 | 39 | 9 | 1.6 |

−3.9 | −6.5 | 9.6 | 52.44 | 39 | 9 | 1.6 |

−6.5 | −9.6 | 9.9 | 66.19 | 39 | 9 | 1.6 |

−9.6 | −13.2 | 10.0 | 87.50 | 38 | 8 | 1.4 |

−13.2 | −17.3 | 10.2 | 122.01 | 39 | 9 | 1.2 |

−17.3 | −20.7 | 10.4 | 150.85 | 39 | 9 | 1.0 |

−20.7 | −23.8 | 10.1 | 161.33 | 38 | 8 | 1.0 |

−23.8 | −25.8 | 10.6 | 185.13 | 40 | 10 | 0.9 |

−25.8 | −30.0 | 10.9 | 196.30 | 40 | 10 | 0.8 |

−30.0 | −31.0 | 11.0 | 212.42 | 40 | 10 | 0.8 |

−31.0 | −32.5 | 10.6 | 196.46 | 39 | 9 | 0.8 |

−32.5 | −60.0 | 11.0 | 299.31 | 40 | 10 | 0.8 |

Model | h (m) | L (m) | D_{out} (m) | t (m) | v_{max, z = h} (m) |
---|---|---|---|---|---|

1 | 30 | 24 | 6.0 | 0.08 | 4.5 |

2 | 72 | 24 | 6.0 | 0.08 | 9.0 |

3 | 30 | 12 | 6.0 | 0.08 | 6.0 |

4 | 72 | 12 | 6.0 | 0.08 | 13.0 |

5 | 63 | 36 | 9.0 | 0.08 | 8.5 |

6 | 90 | 36 | 9.0 | 0.08 | 12.0 |

7 | 63 | 18 | 9.0 | 0.08 | 12.0 |

8 | 90 | 18 | 9.0 | 0.08 | 16.5 |

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**MDPI and ACS Style**

Brinkgreve, R.; Lisi, D.; Lahoz, M.; Panagoulias, S. Validation and Application of a New Software Tool Implementing the PISA Design Methodology. *J. Mar. Sci. Eng.* **2020**, *8*, 457.
https://doi.org/10.3390/jmse8060457

**AMA Style**

Brinkgreve R, Lisi D, Lahoz M, Panagoulias S. Validation and Application of a New Software Tool Implementing the PISA Design Methodology. *Journal of Marine Science and Engineering*. 2020; 8(6):457.
https://doi.org/10.3390/jmse8060457

**Chicago/Turabian Style**

Brinkgreve, Ronald, Diego Lisi, Miquel Lahoz, and Stavros Panagoulias. 2020. "Validation and Application of a New Software Tool Implementing the PISA Design Methodology" *Journal of Marine Science and Engineering* 8, no. 6: 457.
https://doi.org/10.3390/jmse8060457