6
Simplified Hand Calculations

6.1 Flow Chart of a Typical Design Process

It is often necessary to take a bird's‐eye view of a design process highlighting the different ingredients. Figure 6.1 shows a typical flowchart of a foundation design.

Flowchart of a design process from Obtain the loads on the foundation and classify them, Obtain Site Investigation Report, and Design criteria to Select a foundation and choose dimensions to satisfy the ULS…, etc.

Figure 6.1 Flowchart of a design process.

As may be observed, the main ingredients for foundation design are:

  1. (a) Loads on the foundation under different scenarios
  2. (b) Site investigation, i.e. ground conditions
  3. (c) Criteria for design

This chapter provides the following examples:

  1. Target frequency of a turbine
  2. Stiffness of a monopile foundation using three types of method: simplified, standard, and advanced methods
  3. Stiffness of a mono‐caisson
  4. Estimation of loads on a monopile foundation through the use of spreadsheet type program
  5. Natural frequency of a monopile‐supported wind turbine
  6. Design of a monopile‐supported wind turbine
  7. Design of jacket‐type wind turbine system
  8. Design of a spar buoy type wind turbine

The aim of this chapter is to present some example problems on the different concepts.

6.2 Target Frequency Estimation

6.3 Stiffness of a Monopile and Its Application

To estimate foundation stiffness, the following methods are used:

  • Simplified method. Closed‐form solutions for foundation stiffness can be obtained for simple ground profiles. Any spreadsheet programs or even a simple calculator can be used to compute them and typically take only few minutes. This method can be useful in the preliminary design and during the optimization stage or even financial feasibility study.
  • Standard method. In this method, pile‐soil interaction is represented by a set of discrete Winkler springs where the spring stiffness is obtained through py curves available in different design standards. Standard software is available at reasonable costs to carry the analysis and will only take few hours to carry out an analysis. Complex ground soil profiles can be analysed. Few soil parameters are required, and the effects of cyclic load are taken empirically.
  • Advanced methods. These are continuum models and advanced 3D finite element (FE) software packages or programs are necessary. Such packages are expensive, computationally demanding, and require experienced engineer to carry out the simulations. However, such models are versatile and can model complex ground profile and any type of soils with different constitutive relations. Cyclic loading can also be applied and pore‐water pressure accumulation can also be accounted for.

6.3.1 Comparison with SAP 2000 Analysis

The system was modelled using SAP 2000 and a modal analysis is carried out to obtain the natural frequency. Nonprismatic beam elements of varying diameter were assigned to the tower while the soil structure interaction was represented by discrete linear Winkler springs. The spring stiffness values were taken from the soil properties ( Table 6.2) and are a function of modulus of elasticity at the location of the spring and the spacing between two adjacent springs. A lumped mass was assigned at the tower head to model the dead mass of the RNA (rotor‐nacelle assembly). The first natural frequency recorded was 0.351 Hz. Figure 6.11 shows the first mode of vibration.

Schematic of first mode of vibration depicted by a shaded vertical bar attached to an ascending curve. The top portion of the bar has an xz plane.

Figure 6.11 First mode of vibration.

6.4 Stiffness of a Mono‐Suction Caisson

6.5 Mudline Moment Spectra for Monopile Supported Wind Turbine

In the frequency diagram (Figure 2.13) shown in Chapter 2and Example 6.1, the PSD magnitudes are normalised to unity as they have different units and thus the magnitudes are not directly comparable. In Chapter 2, a generalised method is presented to evaluate the relative magnitudes of four loadings (wind, wave, 1P, and 3P) by transforming them to bending moment spectra using site and turbine specific data. This formulation can be used to construct bending moment spectra at the mudline, i.e. at the location where the highest fatigue damage is expected. Equally, this formulation can also be tailored to find the bending moment at any other critical cross section, e.g. the transition piece (TP) level. This example case study is considered to demonstrate the application of the proposed methodology. The constructed spectra may serve as a basis for frequency based fatigue estimation methods available in the literature.

6.6 Example for Monopile Design

Monopiles are the most commonly used foundations. This section of the chapter provides a example based on a method proposed by Arany et al. (2017) titled ‘Design of monopiles for offshore wind turbines in 10 steps’. The method can be presented in the form of a flowchart (see Figure 6.15).

Flowchart from Establish design criteria, Obtain basic turbine…, Obtain Metocean data, Obtain geological and geotechnical data to Guess pile dimensions, to Is the long term behavior acceptable?, if Yes, to Finish, etc.

Figure 6.15 Flowchart.

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