ta-original="//html.scirp.org/file/5-8102527x37.png" />Monopile cross sectional area,
Constant relating to pile installation equipment setup,
Constant relating to faceted monopile test energy scaling,
Constant relating to circular monopile test stress scaling.
Relating to test faceted monopile,
Relating to full scale faceted monopile,
Relating to test conventional circular monopile,
Relating to full scale conventional circular monopile.
The test hammer impact energy was based on data gathered from a commercial installation. A pile driving history for a similar full scale conventional monopile design is illustrated in Figure 4. The data shows that a
Figure 4. Piling log histogram.
significant number of impactsoccur around 1000 kNm per blow. Above 800 kNm per blow there are approximately 2000 blows. Therefore the pile driving history was simplified to 1000 kNm per blow at 2000 blows.
From the geometrical dimensions of the full scale and test size monopiles presented in Table 1, the test hammer blow energy and other test scaling parameters are calculated and presented in Table 2. The scaled down piling installation test was conducted at the constant impact energy of 38 KNm.
3. Results and Analysis
Typical resistive strain gauge measurement requires that the stress field prior to measurement is qualitatively understood. Strain gauges are then aligned to the principal strains in that field. However due to the complex nature of impact loading, the use of R rosette was warranted, which was described in more detail in the previous section. From the measurement of such rosette, magnitude of principal stresses in any direction can be calculated and it is not necessary to align the strain gauge with the principal strains.
An example of results from measurement point 1i is presented. Figure 5(a) illustrates the principal stresses during a single impact. Figure 5(b) illustrates the angular orientation of the maximum principal stress σ1 for the same time range. The reference for the angular orientation is the axis running through the centre of the test piece. The minimum principal stress orientation is +90˚ from. The data shows that during the main impulse is almost 90˚, which means that the maximum principal stress is in the circumferential direction of the monopile. The minimum principal stress is in the longitudinal direction of the test piece which coincides with the direction of the hammer impact. Immediately after the main impulse, ringing of the test piece is observed. Stress waves travelling up and down the test piece superimpose to produce a complex stress field with unstable orientation.
Data across the range of measurement points and across the full number of 34 impacts observed, shows that the minimum principal stress, during the main impulse, is always aligned with the direction of the hammer impact, as was expected. The maximum deviation from the direction of the hammer impact is around ±10˚ near the faceted test piece corners and is less elsewhere. Since the cosine of 10˚ results in the error of less than 2%, minimum principal stress, during the main impulse, will effectively be regarded as acting in the longitudinal direction of the test piece. The magnitudes of the maximum principal stress σ1, during the main impulse will effectively be regarded as acting in the circumferential direction of the test piece.
The polymer dolly and cap assembly was used to evenly transfer the impact from the hammer to the test piece, however an amount of misalignment was still expected. Because of the limited number of measurement points it was feared that the maximum stressed regions would be missed. Hence the layout of the measurement points was planned in such a way so as to allow an estimation of the hammer impact misalignment with the minimum number of measurement points. Once the misalignment is understood the position and magnitude of maximum stress can be estimated. The gauges were placed around the circumference of both test pieces (see Figure 2). To estimate the impact misalignment, stress between circumferential gauges was extrapolated. An example of the extrapolation for the circular test piece is illustrated in the polar plot of Figure 6. The angular axis corresponds
Table 1. Monopile dimensions.
Table 2. Test Scaling parameters.
Figure 5. (a) Principal stresses; (b) Maximum principal stress orientation.
Figure 6. Stress distribution due to impact misalignment.
to the position on the circular test piece if viewed from the top. The magnitude of the stress is plotted on the radial axis. Gauges placed near the 270˚ position measure the highest stresses. This corresponds to the free end of the hammer assembly with the support being at the opposite end or the 90˚ position. Extrapolation of the stress distribution displays as a circle offset from the centre of the polar plot. From the extrapolated distribution, position and magnitude of the estimated maximum stress is calculated.
Mean results of the extrapolation over the 34 impacts are presented in Table 3. Extrapolations for both circular and faceted test pieces are shown. It is noteworthy that the ratio of maximum over minimum extrapolated
Table 3. Stress extrapolation due to impact misalignment.
stresses highlights large amounts of misalignment for some principal stresses. The ratio of maximum extrapolated over maximum measured stresses allows an estimation of stress increase due to misalignment. This is used later for fatigue damage calculations.
A notch at the weld root or toe creates a high stress concentration resulting in a steep stress gradient and possible stress singularity. Strain gauges on the other hand average the strain field across the measurement matrix and hence should be placed in regions of moderate stress gradients. To accommodate high stress gradients, the “hot spot” method recommended by the relevant design standard was employed  . The method uses two stress values, at 0.5 times the plate thickness and 1.5 times the plate thickness perpendicularly away from the weld notch. From these two stress values, stress to the weld notch is linearly extrapolated and it is named the hot spot stress. Obviously this extrapolation does not reflect the real stress at the notch, however it forms a comparison system to the S-N fatigue data formulated using the same method.
The hot spot stress can be formulated mathematically by linear extrapolation to the weld toe  :
Extrapolated hot spot stress,
Stress measured at 0.5 times plate thickness perpendicularly away from the weld notch,
Stress measured at 1.5 times plate thickness perpendicularly away from the weld notch.
This method was used to determine the hot spot stresses at the facet corner weld. Measurement points 1i and 1ii were placed at 0.5 and 1.5 times plate thickness perpendicularly away from the weld notch, respectively. In order to calculate the stress ratio as shown in Equation (12), two values from the measurement point at the same time must be used. The signals were very dynamic, with natural frequency ringing superimposed onto primary impact. The signal was therefore filtered to allow determination of the comparative peak stress values. Raw and filtered signal for a single impact are illustrated in Figure 7. Results over the 34 impacts were calculated and the mean values are presented in Table 4. It is a curious result since the maximum principal stress decreases towards the weld notch, possibly indicating superposition of positive and negative stresses with the negative stress rapidly increasing towards the corner weld notch.
Typically stress cycles with tensile components produce crack initiation and propagation, leading to fatigue damage. Rare circumstances of crack propagation under compressive stress loading are documented  , however there is lack of information about the compressive stress components associated with S-N fatigue data used  . It has been decided to only focus on stress cycles with significant tensile stress component, hence narrowing the fatigue analysis down to maximum principal stresses.
To calculate the fatigue damage which gives the most conservative value, the critical position with the largest stresses must be identified. The largest tensile stress occurs at the inner side of the facet corner of the faceted test piece. As for the circular test piece, the largest tensile stress occurs on the inside cylindrical surface.
The stress spectrum is complex, composed of the initial impact and the proceeding ringing. A way to deal with this is to use the “rainflow” counting method, which decomposes a complex stress spectrum into a series of
Figure 7. (a) Raw stress measurement; (b) Filtered stress measurement.
Table 4. Hot spot stress.
simple stress cycles  . This method was used to calculate the fatigue damage at four locations. Three were on the inside corner of the facet and correspond to measurement points 1i, 2i and 3i. The fourth position was on the inside surface of the circular test piece and corresponds to the measurement point R1i.
The stress spectrum at these four positions of interest is presented in Figure 8. Stresses at the faceted test piece measurement points 1i, 2i and 3i have been factored in line with the hot spot method and stress increase due to impact misalignment. Stress at the circular test piece measurement point R1i has been factored by the scaling constant (see Equations (9) & (10) and Table 2) and stress increase due to impact misalignment. The number of stress cycles has been extended to the anticipated 2000 hits for the full duration of the installation procedure.
The position 1i suffers the largest magnitude stress cycles since it is closest to the hammer impact zone. The stress range at the other positions 2i and 3i are somewhat smaller indicating more general loading throughout the length of the monopile. The stress range at the position R1i referring to circular cross section geometry, is smaller than at positions 2i and 3i which refer to the faceted corner geometry. This illustrates the stress concentration of the faceted as compared to the circular geometry. This result would also depend on the number of facets in the geometry, with fewer sides likely having a more adverse effect.
Miner’s summation was used to deal with variable amplitude fatigue damage  . This damage function defines failure due to variable amplitude loading by:
In this failure criteria, represents the number of cycles to failure and is the actual number of cycles spent at cyclic stress range. The damage is summed for all stress ranges i. can be obtained from S-N
Figure 8. Stress spectrum histogram.
data provided by the reference  :
where plate thickness t is taken into account. Other parameters are based on material and weld classification. The large scale monopile is to be manufactured from structural steel S235 or similar. The weld is classified based on the direction of the principal stress incurring the damage. In our case it is the maximum principal stress which acts in the direction parallel to the longitudinal welds and perpendicular to the circumferential welds of the structure. The perpendicular is more damaging than parallel stress loading, resulting in a reduced fatigue life. Therefore the analysis is performed for perpendicularly loaded circumferential welds. Parameters associating with this weld classification are presented in Table 5. The plate thickness t was presented previously in Table 1.
Applying the damage function to the stress range spectrum yields a measure of damage incurred due to the monopile installation procedure. The damage is expressed as the percentage of the total life used up. Results for the four positions 1i, 2i, 3i and R1i are presented in Table 6. The fatigue damage is below 1% and is larger for the faceted geometry.
As was noted previously, the stress spectrum of position 1i displays the largest stress ranges as compared to other positions, since the position 1i is closest to the hammer impact zone. However the damage at position 2i is similar to but slightly larger than damage at position 1i. This is counter intuitive but can be explained. There are 283 and 508 stress cycles between 25 - 90 MPa for positions 1i and 2i, respectively. There are also 34 and 0 stress cycles above 90 MPa for positions 1i and 2i, respectively. Therefore there are approximately twice as many medium level stress cycles at position 2i than at position 1i, which is shown to be more significant than the lack of a low number higher level stress cycles.
Piling trials were conducted to simulate a full scale monopile installation. Scaled down test pieces were used with the equipment representative of the full scale procedures. Two types of test pieces were used, conventional
Table 5. S-N curve parameters.
Table 6. Fatigue damage.
circular and faceted. Both test pieces were instrumented with resistive strain gauges in attempt to quantify possible fatigue damage resulting from the full scale operation. It has been shown that the damage of the faceted geometry is larger than that experienced by the circular geometry but is still negligible in comparison with the full fatigue life available.
Fatigue damage calculations were based on the relevant design standard. The S-N data therein is general for a range of applications. Although the fatigue damage was shown to be negligible, there have been cases of monopile damage resulting from the piling installation. Therefore tests to failure may provide an understanding about the failure mechanisms and subsequent prediction of failure.
The approach used to link the test to the full scale conditions involved many scaling parameters. These parameters were estimated via dimensional analysis with stated assumptions. Strict validity of these scaling parameters should be investigated to gain more confidence in the results obtained.
There are currently no analytical or numerical models describing localised stressing of monopiles during the pile driving installation. This would require a 3D stress wave propagation model, perhaps implemented through the finite element method. Data gathered in this study can inform development of such a model; on the other hand, the model itself could shed light on various aspects of the test conducted, for example, the best measurement point placement in order to capture the most critical stressing of the welds. It could also provide a better understanding with regards to impact misalignment which will inform the relationship between nominal and peak stressing.
This work was performed in collaboration with TWI Ltd., Gardline, BSP International Foundations Ltd., Scottish Power Renewables, Tata Steel and OGN, with support from the Regional Growth Fund and Narec. The authors specifically acknowledge the support of TWI in producing the scaled down test piece and BSP for providing the facilities necessary to carry out the pile driving test.
 Da Costa, L.M., Danziger, B.R. and Lopes, F.D.R. (2001) Prediction of Residual Driving Stresses in Piles. Canadian Geotechnical Journal, 38, 410-421.
 Koulin, G., Sewell, I. and Shaw, B.A. (2015) Faceted Monopile Design Suitable for Mass Production and Upscaling. Procedia Engineering, 114, 385-392.
 Bhattacharya, S., Lombardi, D. and Wood, D.M. (2011) Similitude Relationships for Physical Modelling of Monopile- Supported Offshore Wind Turbines. International Journal of Physical Modelling in Geotechnics, 11, 58-68.
 Fleck, N.A., Shin, C.S. and Smith, R.A. (1985) Fatigue Crack Growth under Compressive Loading. Engineering Fracture Mechanics, 21, 173-185.
 Downing, S.D. and Socie, D.F. (1982) Simple Rainflow Counting Algorithms. International Journal of Fatigue, 4, 31-40.