Finite element modelling

The influence of finite element modelling of the NREL 5MW wind turbine was studied using beam and solid element models, as shown in Figures 4-1(a) and (b). In the beam element models, the effect of discretisation of the soil profile into layers, represented by springs, was studied. These are shown in Table 4-1. The effect of soil block/cylinder boundaries was examined in the 3D solid element model of the wind turbine. The block diameters considered are presented in Table 4-2, expressed in terms of the pile diameter (Dpile=6m).

Table 4-1. Soil profile discretisation in the beam element model of the NREL 5M W wind turbine.

Model Number of springs Discretised layers’ depths (m) BE-1 3 15 BE-2 5 9 BE-3 9 5 BE-4 15 3 BE-5 30 1.5

Table 4-2. Soil block/cylinder boundaries in the solid element model of the NREL 5M W wind turbine.

Model Soil block diameter Soil block depth below monopile

SE-1 3Dpile 2.5Dpile

SE-2 6Dpile 2.5Dpile

SE-3 12Dpile 2.5Dpile

76 As stated in Chapter 3, Timoshenko beam elements of 0.5m length were implemented for the modelling of the offshore wind turbine support structure in the beam element models. Eight-node linear solid elements were used for the modelling of the 3D models. In the 3D models, the pile and tower parts were meshed using two elements through thickness with a length of 0.5m. The size of elements in the soil cylinder (block) was variable based on the dimensions of the block. In the soil cylinder size of 3Dpile, the outer boundaries were meshed using 0.8m elements. For the larger soil blocks, the size of elements at the outer boundaries scaled up more or less proportionally (e.g. the 6Dpile block was meshed using approximately 1.5m elements at the outer boundaries and so on). The interface between the soil and pile in all blocks was meshed with approximately 0.5m elements at the circumference. The sensitivity of offshore wind turbine’s stiffness to smaller mesh size was examined and found to be negligible. The bottom boundary of the soil block was 15m below the pile and was supported on pins, while roller was used for the side boundaries.

In practice, a soil profile may consist of different soil types. A homogeneous soil profile was considered in this analysis for the sake of simplicity. A uniform assumption to study soil-pile interaction is commonly implemented in the literature (Achmus and Abdel-Rahman, 2005; Alexander and Bhattacharya, 2011; Kuo, Achmus and Abdel-rahman, 2012; Byrne et al., 2015; Zdravković et al., 2015). As shown in Table 3-1, the soil profile at the location of the NREL 5MW wind turbine mostly consists of cohesionless soil. Thus, in this study, the various cohesionless soil types that were present at this site (from loose to dense sand) were considered homogeneously to investigate the profile numerical modelling effects on the lateral and rotational stiffness of the wind turbine. Table 4-3 shows the types of soil considered for this analysis, where φ is the angle of friction, ɣsat is the saturated unit weight, E50 is the elastic modulus, and υ is the Poisson ratio of

the soil. The soil properties presented here are based on the data given by Nehal (2001). As this information is not complete in some cases, the best estimates for the soil parameters (e.g. elastic modulus) were used. In the following, the angle of friction of the soil will also be used as a representative for the soil type.

Table 4-3. Different soil profiles considered in this research based on the types of soil at the location of the NREL 5M W wind turbine.

Soil types φ (˚) γsat (kN/m3) E50(MPa) υ

Loose sand to medium- dense sand-1

27.5 17 20 0.3

30.0 18 45 0.3

Medium dense sand-2 to dense sand

32.5 19 60 0.3

35 19 80 0.3

Figures 4-1(a) and (b) show the beam and solid element models of the wind turbine in ABAQUS, respectively. The lateral springs in the beam element model are highlighted in Figure 4-1(a). Two point loads of 1MN were applied: one at the mean sea level representing the waves, one at the

77 rotor height representing the wind, as shown in Figures 4-1(a) and (b). In the solid element models, the point loads were uniformly distributed at the surface of the support structure at the respective levels. The vertical load from turbine weight, which is positioned at the top of the tower, was also taken into consideration by the application of gravity. In this research, the longitudinal stress in the pile, the lateral displacement at the mudline and tower top along with tower top rotation were measured, as indicated in Figure 4-1(c).

(a) (b)

(c)

Figure 4-1. Sketch of (a) the beam element model of the wind turbine with lateral springs and the applied loads, (b) the solid element model of the wind turbine with the soil block/cylinder and the applied loads and (c) the deflected shape and measurements’ locations.

General static step was used in the static studies, in which the load was ramped up in one second and the incrementation of the step was controlled by setting a maximum limit of 0.1s. The monopile and tower were modelled using elastic materials. This is mainly because yielding of the steel section under operational loads is very unlikely to occur (Kampitsis et al., 2015). In the beam element models, the nonlinear p-y curves were defined according to DNV (2013) recommended practice (shown in Appendix-A). Elastic and Mohr-Coulomb material definitions were used in turn to investigate the effects of soil nonlinearities on the lateral and rotational stiffness of the wind turbine structure in the 3D models. A small amount of cohesion (c) of 0.1kPa was applied in the Mohr-Coulomb models to stabilise the 3D models initially, similar to Abdel-Rahman and

Fwind=1M N

Fwave=1M N

Fwind=1M N

Fwave=1MN

Mudline Lateral displacement at the mudline Tower top displacement

Tower top rotation

Soil springs Soil

cylinder/block

Longitudinal stress along the tension side of the pile

78 Achmus (2005). The interface between soil and pile was modelled using the Coulomb friction with μ=0.4, which is typically used for the soil-pile interaction (Achmus and Abdel-Rahman, 2005). The inside of the pile was filled with soil of the same type as the soil used in the soil block. For the contact region at the bottom of the monopile with the soil, normal (i.e. perpendicular surface) contact was assumed to be sufficient. In all surface interactions the selection of the master and slave surface determines which surface penetrates the other between the nodes, with the slave surface being the penetrable surface. The choice of master and slave surfaces was made based on the relative elastic moduli of the sections in contact following ABAQUS documentation (2012).