Uncertain parameters of the propagation path in 3D pile driving noisemodelling
Jonas VON PEIN(1) , Johannes SEIDEL(1) , Elin KLAGES(1) , Stephan LIPPERT(1) , Otto VON ESTORFF(1)(1) Hamburg University of Technology (TUHH), Institute of Modelling and Computation, Germany, mailto: mub@tuhh.de

Abstract
Nowadays, offshore constructions are mainly mounted to the sea bed by steel piles. These piles are driven into
the soil by percussive pile driving. This process leads to high underwater sound pressure levels. Therefore,
limiting values have been set in many countries for the protection of the marine fauna. In order to get a profound prognosis of the emitted sound levels, numerical models are essential. These models are often rotationallysymmetric and based on a finite-element formulation for the close vicinity of the pile and a far-field propagation
model for ranges further away. In the current contribution the far-field model is a full 3D parabolic equation
model. A major problem in pile driving noise radiation modelling is to derive a reliable description of the acoustical properties of the sea bottom. However, due to the inhomogeneous character of the soil these parameters
are always subjected to variability. To quantify the effects of this uncertainty in the acoustical soil parameters, asensitivity analysis is performed for a pile driving scenario assuming a flat and a heavily changing bathymetryboth with and without noise mitigation. Furthermore, the sensitivity analysis is performed with Nx2D and 3D
simulations.
Keywords: Pile driving, underwater acoustics, 3D modelling, parameter uncertainties

1

INTRODUCTION

Piles are the state-of-the-art foundation for fastening offshore constructions to the sea bed and percussive piledriving is mainly used to bring the pile to its dedicated penetration depth. During the installation process soundpressure waves are emitted into the water, which lead to sound pressure levels reaching potentially harmful
amplitudes for marine mammals [1]. To protect the marine fauna, limits have been set by some authorities,e.g., for the German Exclusive Economic Zone [2]. There, they are defined at 750 m distance to the pile forthe sound exposure level (SEL) as 160 dB and the peak pressure level (SPLpeak ) as 190 dB. The SEL can bederived with the pressure time series p(t) within the time interval t2 − t1 = T0 = 1 s and the reference pressurep0 = 1 µPa by 1 Z t2 p(t)2 
SEL = 10 log10
dt dB .
(1)
T0 t1 p20
While the SEL is based on the average of the pressure time series, the max(p(t)2 ) 
SPLpeak = 10 log10
dB
p20

(2)

only depends on the maximum amplitude of p(t). Predictions of sound pressure levels are often obligatory
prior to construction in order to check for the necessity of noise mitigation measures. These prognoses can be
performed by numerical or analytical models. The advantages of numerical models are the ability of improving
the noise mitigation set-up and the high physical insight. There are different modelling approaches, see [3], andmany of them have been shown by the developers during the benchmark scenario workshops COMPILE I andII [4, 5]. The models presented therein all have in common, that the bathymetry is considered as rotationallysymmetric. However, the authors of this contribution have shown that for locations with heavily changing
bathymetry the consideration of 3D-effects is necessary to get profound results [6, 7].

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An important aspect of the modelling process of pile driving noise is the estimation and derivation of theacoustical properties of the soil. In real-life the sea bed is of non-homogenous material with layers of changing
thickness. Moreover, the wave speeds within the soil may vary with range and depth, while seasonal changes
lead to differences of the sound speed in water. The importance of uncertain soil parameters for a 2D scenario
has been shown by Lippert and von Estorff [8]. The authors identified that the layer thickness and compressional
wave speed within the soil are the dominating parameters in a scenario without noise mitigation.
Within this contribution the influence of uncertain parameters on the sound pressure levels is investigated within
three steps. First, a flat 2D scenario is considered. These results can directly be compared to [8]. Second, a 3D
scenario with a heavily changing bathymetry is computed with full 3D and Nx2D simulations and the according
influences are compared to the flat scenario. Third, the influence of the uncertain parameters on the difference
between 3D and Nx2D results, the 3D-effects, is evaluated. All computations are performed without "reference"
and with "mitigated" noise mitigation.

2

MODELLING APPROACH

2.1 Pile driving noise
The pile driving noise is computed with a hybrid modelling approach. It is based on a finite element model(FEM) for the close-range and a parabolic equation (PE) model for the far-field. The FE-model is split intoa pre-calculation considering only the hammer pile interaction and the main acoustical model. Within the precalculation the detailed geometry of the relevant hammer parts and the pile are used to derive the pile headexcitation, e.g. velocity or force. For details on the pile-hammer-model, compare Klages et al. [9]. The derived pile head excitation is used as a boundary condition within the acoustical model. Therein, the pile, thelayered soil, and the water are discretized. The soil is assumed to be of linear-elastic material. The sea surface is modelled as a zero-pressure boundary condition and the domain is enclosed by non-reflecting boundary
conditions.
The FE-model is rotationally symmetric. However, there are pile driving locations where 3D-effects have to betaken into account due to a varying bathymetry, as shown in Fig. 1. Therefore, a 3D PE model based on the
split-step Padé technique is used to incorporate horizontal diffraction. A detailed description and validation of
the FE/PE model is given in [6].

ϕ

750 m

1500 m30

25

water depth [m]3520

Figure 1. Measured bathymetry data at a real-life pile driving location.

2.2 Uncertainties
The consideration and computation of the influence of uncertain soil parameters as well as the influence ofa changing sound speed in water is done by applying the Fuzzy Arithmetic [10]. A detailed description andapplication of the used Fuzzy Arithmetic scheme is given by Lippert [11] and Seidel et al. [12].

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3

PILE DRIVING SCENARIO

1
0.8
0.6
0.4
0.2
0
1700

µ (c1 )

1
0.8
0.6
0.4
0.2
0
1480

1490

1500
1510
cw [m/s]

1520µ (∆z1 )µ (ρ1 )µ (cw )

The considered pile is a conical monopile with a maximum diameter of 8.7 m, an averaged constant wall thickness of 81 mm, an overall length of 69 m, and a penetration depth of 32 m. The used hammer is an IHC S-3000
at a strike energy of 2000 kJ. The mitigated case is computed with a noise mitigation system placed at a radiusof 10 m from the pile center-line. The water-depth of the considered location is shown in Fig. 1. The same piledriving set-up has previously been considered in [7].
The analysis of the influence of uncertain parameters of the propagation path on the pile driving noise radiationis performed with the sound speed of water cw , the compressional wave speed c1 and density ρ1 of the firstsoil layer, and with the thickness ∆z1 of the first soil layer. Due to the high computational effort of full 3D
simulations, the focus within this contribution is on the acoustical properties of the first soil layer and the soundspeed of water. Depending on season and location the sound speed in the water cw is assumed to be between
1480 m/s and 1520 m/s with a modal value of 1500 m/s. The modal value of the compressional wave speed c1
in the first layer of the soil is 1600 m/s. The lower boundary is assumed to be higher than the highest soundspeed in water and is therefore chosen to be 1530 m/s. The upper boundary is set to 1700 m/s. The density of
the first layer ρ1 is set to 1800 kg/m3 with a range of ±100 kg/m3 . Finally, the thickness ∆z1 of the first layer
is 4.6 m±2.8 m. The according Fuzzy number representation is chosen to be triangular for all parameters withthree α-cuts and is depicted in Fig. 2.

1800

1750
ρ1

[kg/m3 ]

1850

1900

1
0.8
0.6
0.4
0.2
0

1
0.8
0.6
0.4
0.2
0

1550

2

3

1600
1650
c1 [m/s]1700

4
5∆z1 [m]7

6

Figure 2. The Fuzzy Number representation of the considered parameter set with membership level η.

4

2D RESULTS

In order to assess the influence of the considered parameters, a comparison of the results is done for a simplified 2D scenario without any changes of the bathymetry. Therefore, the water depth is constantly 38 m. The
previously shown parameter set is used for the computation of the following results. For a first estimation of theinfluence of each parameter, the results of the maximal difference between the SEL of the α-level 3 result andthe results computed varying only one parameter at a time within its range is shown in Fig. 3 for the reference
and the mitigated scenario. From the results in Fig. 3 it can be seen, that the variation within the pre-defined
limits of the sound speed in water cw , the sound speed in the soil c1 , and the thickness of the first layer ∆z1
are clearly in the same range, whereas the density ρ1 of the first soil layer has a rather small influence. In
both cases cw has the highest influence, followed by ∆z1 and c1 . Generally, the variation of the SEL is slightly
higher in the mitigated case.

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|∆SEL| [dB]

c1
∆z1

1

0
100

200

300

400 500
range [m]

600

700

2
|∆SEL| [dB]

cw
ρ1

2

cw
ρ1

c1
∆z1

600

700

1

0
100

200

300

400 500
range [m]Figure 3. The variation ∆SEL between the α-level 3 result and the maximium difference over range for thereference (left) and mitigated (right) scenario evaluated 2 m above the soil.
The domination of c1 and ∆z1 compared to ρ1 was also identified by Lippert and von Estorff [8], whereas cw
was not considered in their publication.
The sound speed of water cw is one of the dominating factors. It affects the reflection factor between water and soil for the reference case and between soil to water for the mitigated case. Furthermore, it directly influences the angle of the Mach-cone, which is defined with the compressional wave speed of steel
as ϕMach = sin−1 (cw /csteel ) [13]. This angle is valid for the reference scenario and is directly linked to thereflection coefficient. The high influence of cw is unexpected due to the small difference of ±20 m/s that istaken into account. However, in real-life this margin can also be much smaller with a high degree of certainty.
Depending on the layer thickness ∆z1 , different positively or negatively interfering ray paths are possible, whichlead to differences in the results. The layer thickness is also important for the tunneling of noise mitigation systems. The effect of the layer thickness is comparably small, considering the relatively big spread of 4.6±2.8 m.
However, the influence of the thickness of the first soil layer also heavily depends on the properties of thesecond layer. The difference between the acoustical properties of layer 1 and layer 2 define the reflection coefficient at their interface. Compared to the soil properties in [8] the difference between layer 1 and layer 2 isρ1ρ1c1
rather small with nominal values of c1
c2 ≈ 0.92 and ρ2 ≈ 0.9 compared to c2 ≈ 1.16 and ρ2 ≈ 1.43 [8].
The compressional wave speed in the soil c1 directly contributes to the reflection coefficient between water andsoil and soil to water as well as the reflection between the first and the second soil layer. Furthermore, it isrelevant for the critical angle, and therefore has a non-linear effect, similar to cw . The considered range (−3.7%
to +6.25%) is comparably small. However, the results clearly indicate the importance of c1 .
The density of the first layer ρ1 only contributes to the impedance of the layer and not to the incidental angle.
The span is chosen to be ±100 kg/m3 , which can be considered as a real-life measure. However, the influenceof the density ρ1 is rather small, as has been shown in [8].
In order to identify ranges of the computed results that incorporate the interplay of the different uncertain soil
parameters, the fuzzy results are shown in Fig. 4 for the mitigated and the reference scenario, respectively. The
computations of the different α-levels allow a representation of the sound pressure levels with upper and lower
bounds of the computed α-level. Thereby, the red curve depicts the SEL derived at α-level 3, which stands forthe nominally chosen parameter configuration. The black line indicates the minimum and maximum values ofthe α-level 2 and the gray curves show the same for α-level 1. In both cases, the variation of the results isgenerally highest around 300 m. Furthermore, the span of the SPLpeak is greater than of the SEL.
To get a better insight into the distribution of the results at a specific position, the results from Fig. 4 are plotted
at 750 m with their according α-level in Fig. 5. The results of α-level 2 vary about 1 dB for the mitigated andthe reference case. The reference results of the α-level 1 have a higher deviation at this location, especially thereference scenario shows a few comparably low results of the SEL. However, most of the values are centeredaround 177.5 dB for the reference scenario and around 165.5 dB for the mitigated case.

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200

190

180
100

200

300

400 500
range [m]600

sound pressure levels [dB]sound pressure levels [dB]SEL
SPLpeak

700

SEL
SPLpeak
190

180

170
100

200

300

400 500
range [m]

600

700

1

1

0.8

0.8
µ(SEL)µ(SEL)

Figure 4. The fuzzy result of the SEL and SPLpeak over range for the reference (left) and mitigated (right)
scenario evaluated 2 m above the soil.

0.6
0.4
0.2

0.6
0.4
0.2

0
174.5 175 175.5 176 176.5 177 177.5
SEL at 750 m [dB]

0
164.5

165

165.5
166
SEL at 750 m [dB]

166.5

Figure 5. The fuzzy result of the SEL at 750 m distance for the reference (left) and mitigated scenario (right)
evaluated 2 m above the soil.
The fuzzy arithmetics allow several evalutations of the computed data. To show the influence of the parameterson the sound pressure levels, the averaged deviation coefficient [10] is weighted with the membership level ηof Fig. 2, averaged and normalized, leading to the membership level weighted, normalized, averaged deviation(i)coefficient ∆z of parameter i. Within Fig. 6 the resulting deviation coeffcients of the considered parameters are
depicted over range for the reference and mitigated case. Due to the different interference patterns, the influenceof the parameters is varying with range. However, it can clearly be seen, that the influence of the density ρ1 isnegligible. Computing the average deviation of the parameters leads to the following order of importance: For
(c )
(∆z )
the reference scenario the averaged deviation coefficents for the parameters are: ∆z 1 = 0.42, ∆z 1 = 0.32,
(c )

(ρ )

∆z w = 0.18, ∆z 1 = 0.08. For the mitigated case, the order is changing, with a higher influence of the
(∆z )

(c )

(c )

(ρ )

thickness of layer 1: ∆z 1 = 0.37, ∆z 1 = 0.29, ∆z w = 0.25, ∆z 1 = 0.08. The difference in the importanceof the layer thickness and the sound speed of water between the two considered scenarios is directly related
to the noise propagation path. In the mitigated case, the presure waves in the water are induced via the soil.
Therefore, the thickness of layer 1, which is also important for the tunneling of a noise mitigation system, andthe sound speed of water, which influences the transmission at the interface between soil and water, are gainingof importance.

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200
400
range [m]

(i)

cw
c1
ρ1
∆z1

∆z

(i)

∆z

1
0.8
0.6
0.4
0.2
0
100

600

1
0.8
0.6
0.4
0.2
0
100

cw
c1
ρ1
∆z1

200
400
range [m]600

Figure 6. The membership level weighted, normalized averaged deviation coefficient of each parameter for the
SEL over range for the reference (left) and mitigated (right) scenario evaluated 2 m above the soil.

5

3D RESULTS

0

0

10

10

20

20

174

30

30

172

40

40

0

90

180
270
azimuthal angle ϕ

360

178
176

SEL [dB]

depth [m]In this section, the real-life bathymetry as shown in Fig. 1 is considered within Nx2D and 3D computations.
Within Fig. 7 the SEL of the reference scenario is shown together with the bathymetry over the azimuthal
angle ϕ at a distance of 750 m. Within these results it can clearly be seen, that with the chosen parameter
configuration a high-noise zone could be identified at around 220◦ . Furthermore, the influence of 3D-effects isclearly visible and these effects lead to a higher sound pressure level. In the following, this scenario is used forthe investigation of the influence of uncertain soil parameters on the sound pressure levels at a location with aheavily changing bathymetry. In order to decrease the computation time only azimuthal angles of 180◦ < ϕ <360◦ are considered.

170
0

90

180
270
azimuthal angle ϕ360

Figure 7. The 3D (left) and Nx2D results (right) of the SEL over depth and azimuth at 750 m for the reference
scenario (as shown in [7]).
(i)The evaluation (not shown) of the ∆z for the 3D and Nx2D results over range clearly indicated the sameorder of importance of the considered parameters as for the flat 2D results.
The fuzzy results of the SEL at the range of 750 m evaluated in a depth of 28 m is shown in Fig. 8 with theminimum and maximum of the considered α-levels. It can clearly be seen, that the influence of the uncertainties
stays constantly in the same range independent of the occurrence of 3D-effects. Moreover, the location of theidentified high-noise zone does not rely on the varied parameters. Furthermore, the 3D-effects are independentof the use of a noise mitigation system and lead in both cases to differences of ±3 dB. As shown before in
Fig. 5, the lower boundary of α-level 1 is much lower in the reference scenario. Within Fig. 9 the influenceof the parameters on the 3D-effects (SEL3D -SELNx2D ) is shown. As shown before in fig 6, the most importantfactor is c1 for the reference scenario and ∆z1 for the mitigated scenario. However, the sound speed of water
has the second highest influence in both cases.

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360

170
168
166
164
162
180

SEL [dB]
360

170
168
166
164
162
180

270
azimuthal angle ϕ [◦ ]

180
178
176
174
172
180

SEL [dB]

SEL [dB]
SEL [dB]

180
178
176
174
172
180

270
azimuthal angle ϕ [◦ ]270
azimuthal angle ϕ [◦ ]

360

270
azimuthal angle ϕ [◦ ]

360

c2
c1
ρ1
∆z1

270
azimuthal angle ϕ [◦ ]

360

(i)

1
0.8
0.6
0.4
0.2
0
180

∆z

∆z

(i)

Figure 8. The Nx2D (upper) and 3D (lower) fuzzy results of the SEL over azimuth for the reference (left) andmitigated (right) scenario evaluated in 28 m water depth at 750 m range.
1
0.8
0.6
0.4
0.2
0
180

cw
c1
ρ1
∆z1

270
azimuthal angle ϕ [◦ ]

360

(i)

Figure 9. The ∆z for the difference of the 3D and Nx2D results over azimuth for the reference (left) andmitigated (right) scenario evaluated in 28 m water depth at 750 m range.

6

CONCLUSIONS AND OUTLOOKWithin this contribution the fuzzy results of sound pressure levels derived with a hybrid FEM/PE model ofa real-life pile driving scenario are shown. The uncertain parameters are the sound speed of water, as wellas the sound speed, the density, and the thickness of the first soil layer. The results clearly indicate that the
influence of the density can be neglected while the other three parameters have similar influences. In thereference scenario the sound speed of the first layer is the most important parameter, whereas in the mitigatedcase the thickness of the first layer has the highest influence. These results are derived with a flat soil as wellas with a heavily changing bathymetry. The occurring 3D-effects are influenced in the same way, however,in both cases the sound speed of water is the second most important parameter. Furthermore, the locationof occurring 3D-effects and their contribution to the sound pressure levels are independent of the considered
uncertain parameters.
The next step in the consideration of uncertain parameters in pile driving noise radiation is to link probability
density functions to the Fuzzy Number representation in order to derive probability distributions of the computed
sound pressure levels. Furthermore, other parameter sets can be considered and one more α-cut could be used
for a higher reliability of the results.

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ACKNOWLEDGEMENTS
The authors would like to thank the company Ørsted Wind Power A/S for their friendly and fruitful cooperationand valuable support.

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