ABSTRACT: A steel monopile is the most common foundation type of a wind turbine installed offshore and is driven into place with the help of vibratory or impact hammers. Underwater noise generated during the installation of steel monopiles has recently received considerable attention from international environmental organizations and regulatory bodies in various nations. Collected data regarding underwater noise measurements indicate that pile driving operations, especially when impact hammers are used, can be potentially harmful for the marine ecosystem. In this paper, a linear semi-analytical model is developed for the study of the vibroacoustic behaviour of a coupled pile-soil-water system. The hammer is substituted by an external force applied at the head of the pile. The pile is described by a thin shell theory, whereas both soil and water are modelled as three-dimensional continua. The solution is based on the dynamic structuring technique. The total system is divided into two sub-systems namely, the shell structure and the soil-fluid medium. The response of each sub-domain is expressed as a summation over a complete set of eigenfunctions. The orthogonality of the shell modes in vacuo and the bi-orthogonality of the acousto-elastic modes is utilized in order to meet the displacement compatibility and the force equilibrium at the interface of the two sub-systems. With the developed model, the wave radiation due to vibratory and impact pile driving is analysed. The influence of soil elasticity and soil stratification on the dynamics of the coupled system is examined. In addition, the energy launched by the hammer into the water and into the soil is investigated for both excitation types in order to highlight the main differences in the generated wave field.
KEY WORDS: Vibroacoustics; Pile driving; Underwater noise; Soil-fluid interface; Scholte waves; Dynamics of shells
1 INTRODUCTION
To meet today’s increasing energy demand, a large number of offshore wind farms are planned for construction in the near future. Although several foundation concepts have been developed so far, in order to support the tower and the nacelle of offshore wind power generators, the most common of those is a steel monopile. Steel monopiles are driven into the sediment offshore with the help of large impact or vibratory hammers. During the piling process, the generated underwater noise levels are very high. Measurements indicate that the noise levels close to the pile due to the impact hammers can be in the order of 105 Pa [1].
Such high noise levels have naturally drawn the attention of regulatory bodies in various nations. The Dutch government permits pile driving only from the first of July till the end of December of each year in order to avoid disturbance of the breeding season of the harbour porpoises [2]. In the United Kingdom, an evaluation per project takes place. Measures like seal scarers are used together with a few low energy blows of the impact hammer mainly aiming at intimidating the mammals in the neighbourhood of the construction site [3]. The German Federal government, on the contrary, adopts certain sound level criteria. These have been set to 160 dB re 1 μPa for the sound exposure level (SEL) and to 190 dB re 1 μPa for the sound peak pressure level (SPL), both at a distance of 750m from the sound source [4]. Even though there is yet no overall consensus upon the most appropriate way of quantifying the level of noise which can be potentially harmful for marine species, all the involved parties recognise
that certain measures have to be taken in order to protect the marine ecosystem. In the scientific literature, there are several studies which actually investigate the impact of pile driving operations and other anthropogenic noise emissions in the marine species [5-8]. In this context, one can realise that the problem examined here is multidisciplinary in nature, in the sense that scientists of various background as well as international environmental organizations are strongly involved.
In Figure 1, a typical installation setup of a large monopile is shown. During impact piling, a stress wave is generated which travels from the top to the bottom of the pile. As soon as this wave enters the fluid zone, part of the energy is irradiated in the form of pressure waves into the water. Another part of the energy enters the soil and radiates outwards in the form of compressional and shear waves. This paper aims to shed some new light on the physics associated with noise induced by pile driving and to highlight the contribution of various parameters to the total acoustic field. Such parameters can be, for example, the input energy and the hammer type, the soil conditions and the soil layering as well as the pile dimensions. The present paper is largely based on previous work by the same authors [9-10], but here the main focus is placed on a thorough parametric study as described above.
To reach this objective, the paper is divided into four main sections. In section 2, the necessary theoretical background is given together with a brief description of the semi-analytical model developed in this work. In sections 3 and 4, the
Wave radiation from vibratory and impact pile driving
in a layered acousto-elastic medium
A. Tsouvalas1, A.V. Metrikine11Department of Civil Eng., Faculty of Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN
Delft, The Netherlands
acoustic field is examined for the case of an impact hammer and for the case of the vibratory hammer, respectively. Finally, in section 5, some conclusions are drawn on the basis of the obtained results together with some recommendations which, to the authors’ opinion, require further investigation.
Figure 1 Installation of a pile with an impact hammer (left) and with a vibratory hammer (right)
2 THEORETICAL BACKGROUND
In this section, the governing equations which are used to describe the vibroacoustics of the coupled system are briefly introduced. A detailed description of the model and the solution procedure can be found in [10].
2.1 Statement of the problem
The total system consists of the pile and of the soil-fluid exterior (to the pile) domain as shown in Figure 2. The hydraulic hammer is substituted by an external force applied at the pile head. The pile is described by an appropriate thin shell theory which includes the effects of both shear deformation and rotational inertia [11]. The shell is of finite length and occupies the domain from 0 ≤ z ≤ L. The constants E, ν, R, ρ and 2h correspond to the complex modulus of elasticity in the frequency domain, the Poisson ratio, the radius of the mid-surface of the shell, the density and the thickness of the shell respectively. The fluid is modelled as a three-dimensional inviscid compressible medium with a pressure release boundary describing the sea surface. The fluid occupies the domain z1 ≤ z ≤ z2 and r > R. The soil is
described as a three-dimensional elastic continuum and is terminated at a certain depth with a rigid boundary. The soil can consist of a number of layers with varying properties, all of them horizontally stratified. The constants λs,k and μs,k define the Lamè coefficients for the soil material and ρs,k is the soil density. The index k=1,2,3,… refers to the different soil layers.
2.2 Equations of motion and boundary conditions
The solution of the system of coupled partial differential equations is based on the dynamic sub-structuring technique in which the total system is divided into two sub-systems: the shell structure and the soil-fluid domain. The linearity of the model allows for the representation of the response of each
subsystem in the form of a superposition over appropriate eigenfunctions. The completeness of the modal sum for the layered soil-fluid domain is guaranteed by the introduction of a rigid boundary at a certain depth as shown in Figure 2.
Figure 2 Geometry of the model
The governing equations that describe the linear shell vibrations in the time domain are:
(
)
(
)
(
)
(
)
f e s p m p z z H z z H z z H f p t u I u L + − − − + + − − = + 2 1 2 && (1)In the equation above, up(z,θ,t) is the displacement vector of the mid-surface of the shell. The terms L and Im are the stiffness and modified inertia matrix operators of the shell, respectively, which are based on the applied thin shell theory. The term ts(R,z,θ,t) represents the boundary traction vector that takes into account the reaction of the soil surrounding the shell at z2 ≤ z ≤ L. The term pf(R,z,θ,t) represents the fluid pressure exerted at the outer surface of the shell at z1 ≤ z ≤ z2.
The functions H(z-zj) are the Heaviside step functions which are used here to account for the fact that the soil and the fluid are in contact with different segments of the shell.
The fluid is treated as a three-dimensional inviscid compressible medium with a pressure release boundary describing the sea surface. The motion of the fluid is fully characterized by a velocity potential φf(r,z,θ,t):
(
, , ,)
1(
, , ,)
0 2 2 − = ∇ r zt c t z r f f f θ ϕ θ ϕ && , (2)in which cfis the sound speed in the exterior fluid domain. The soil is described as a three-dimensional elastic continuum able to support both dilatational and shear waves and is terminated at a certain depth with a rigid boundary. The body waves generated at the pile tip are not accounted for in the framework of this model. These waves are not expected to contribute significantly to the acoustic field since they will consist of shear and compressional body waves with a spherical front spreading outwards into the soil region below the tip of the pile [12]. The motion of each soil layer can be described by the following set of coupled linear equations: sk 2 s,k s,k s,k s,k s,k s,k
, ⋅∇ u +(λ +μ )⋅∇∇⋅u =ρ ⋅u&&
μ , (3)
in which us,k(r,z,θ,t) is the displacement vector of the soil medium. The solution for the soil domain can be found using the Lamb’s decomposition.
2.3 Solution of the governing equations
The response of the system is sought for in the form of a modal expansion with respect to the in vacuo modes of the shell and to those of the soil-fluid domain. The analytical approach is based on the following steps: (i) solution of the eigenvalue problem of the shell without the presence of the soil-fluid medium; (ii) solution of the eigenvalue problem of the acousto-elastic domain; (iii) derivation of a relation between the unknown modal coefficients of the two sub-systems, i.e. the shell structure and the fluid-soil domain, by using the interface conditions and the orthogonality properties of the acousto-elastic modes and (iv) solution of the coupled system of equations by applying the orthogonality property of the shell structural modes.
For the shell in vacuo, the response can be expressed as:
(
)
∑∑
∞( )
(
)
= ∞ = − = 0 1 , , , , cos /2 ~ n m j p jnm nm p j z A U z n u θ ω δ θ π θ (4)with n=0,1,2,..∞ is the circumferential order and m=1,2,..∞ is the axial order. The functions Ujnm,p(z)with j=z,θ,r describe the axial distribution for the axial, circumferential and radial displacement fields respectively. Anm are the undetermined shell modal factors. For the exterior soil-fluid domain the response can be represented as:
(
)
∑∑
∞( )
= ∞ = = 0 1 ; , ; , , , , ( ) , n q nq f s jnq nq f s j r z C U z Y r u θ ω θ (5)The subscripts s and f refer to the soil and fluid respectively. The eigenfunctions Ujnk,s;f along the vertical coordinate are obtained by satisfying the set of boundary and interface conditions at z=zk with k=1,2,3,… corresponding to the different layers. The index q is used here to reflect the different modes along the vertical coordinate. In accordance with Figure 2, the following set of boundary and interface conditions is imposed. At z= the fluid pressure is set equal z1 to zero. At z=z2 the normal stress and displacement are continuous whereas the shear stress of the soil is set equal to zero (inviscid fluid). Finally, at z=L the displacements of the soil are set equal to zero. At all other interfaces between the various soil layers continuity of displacements and stresses is required. The functions Ynq(r,θ) are the Fourier-Bessel components, which appropriately describe the radial and circumferential dependence of the field.
By enforcing the force equilibrium and the displacement compatibility at the interface between the shell and the exterior domain, the original system of coupled partial differential equations is reduced to a system of coupled algebraic equations which can be solved with high accuracy. To achieve this, the orthogonality condition of the shell modes in vacuo and the one of the exterior soil-fluid domain are used to relate the unknown sets of modal coefficients (Anm, Cnq) and to solve the coupled problem. All the aforementioned steps are described in detail in [9] and will not be repeated here.
3 WAVE RADIATION FROM IMPACT PILE DRIVING
In this section, the generated acoustic field in the fluid and the elastic field in the soil is studied for the case of impact piling. At first, the case of a soft homogeneous soil is examined. Subsequently, the case of a harder soil sediment is analysed
with the aim to examine the sole influence of soil elasticity on the wave radiation at the surrounding domain. Finally, the more realistic case of a two-layered soil is studied in which the upper few meters consist of a relatively soft sediment. The latter is a typical soil stratification for offshore environments. 3.1 Soil domain consisting of a single soft soil layer At first, the case of a pile being driven into a homogeneous soil is studied. The pile dimensions, soil conditions and fluid characteristics are summarised in Table 1.
Table 1. System parameters (homogeneous soil)
Parameter Value Unit
E 2.1x1011 N m-2 ν 0.28 - ρ 7850 kg m-3 η 0.001 - R h L z1 z2 Es vs ρs ξs* cf ρf 2.50 0.03 60.0 7.00 27.0 7x107 0.40 1700 0.01 1500 1000 m m m m m N m-2 -kg m-3 - m s-1 kg m-3 *ξ
s denotes here a frequency independent soil material damping
which is equal to 1% of the correspondent elastic part, i.e. Es =
Es,elastic (1 + i·ξs).
Figure 3 Input force for the impact hammer
The input force is applied vertically at the head of the pile. For this example a smooth exponential in time force is considered. Several studies [13], have shown that such a force represents closely the one exerted by hydraulic impact hammers at the head of the pile. The time signal of the input force is shown in Figure 3 and its amplitude spectrum is shown in Figure 4. This input force corresponds to an energy input of about 900kJ.
In Figure 5, the sound pressure levels (dB re 1μPa) are shown in one-third octave bands for the locations depicted in Table 2.
Figure 4 Amplitude spectrum of the input force There is a distinct difference between the points positioned close to the sea surface and of the ones positioned close to the seabed. The latter contain a large amount of energy at frequencies lower than 50 Hz which is not present in the case of the upper points. As will be discussed in the sequel, this difference is mainly attributed to the presence of interface waves.
Table 2 Location of points in the water column Point Radial distance from
the pile surface (m) Depth (m) A B 2 18 4 4 C 2 19 D 18 19 Figure 5 Pressure amplitude spectra of the four locations in the case of a soft soil sediment In Figure 6, the calculated pressures in the fluid are shown for points A and C. The SPL- and SEL-values are summarised in Table 3 for all examined locations. As can be seen, the pressure levels are very high especially close to the pile surface. The small delay in the arrival time of the first peak of the pressure in the case of the lower point is related to the propagation angle of the pressure fronts in the fluid region. Table 3 Pressure levels at the examined locations Point SPL (dB re 1μPa) SEL (dB re 1μPa) A B 233 217 207 196 C 228 203 D (750m) 220 187 195 171
As will be discussed in the sequel (Figure 7), the pressure fronts in the fluid region are formed with an angle of about sin-1(c
f/cp)=160 to the vertical, in which cf is the sound speed in the fluid and cp is the speed of compressional waves in the pile. The vertical distance between points A and C equals 15m. The distance perpendicular to the wave fronts that needs to be covered between points A and C is approximately equal to 15·cos(900-160)=4.1m. To cover this distance the pressure
waves need approximately 2.7x10-3s, which is the time delay
observed between the peak at point A and C as shown in Figure 6.
Figure 6 Pressures in time at two depths close to the pile
Figure 7 Pressures in the fluid (top) and displacement norm in the soil (bottom) for two moments in time after the impact
As already mentioned, the maximum allowable underwater pressure levels according to the German national standards are set to 160 dB re 1 μPa for the sound exposure level (SEL) and 190 dB re 1 μPa for the sound peak pressure level (SPL), both evaluated at a distance of 750m from the sound source [4]. The evaluated -averaged over the water depth- pressure levels at a distance of 750m are shown in the last row of Table 3. It is clear that the maximum allowable SEL-limit is exceeded in this case.
In Figure 7, the pressures in the fluid together with the displacement norm in the soil, are shown for two moments in time after the hammer impact. The pressure conical fronts in the fluid region, commonly referred to as Mach cones, are formed with an angle of 160 to the vertical. These are clearly
visible at the initial moments in time after the hammer impact. In the soil region, both vertically polarised shear waves and compressional waves are generated, with the former being much stronger than the latter. This actually implies that the majority of the energy in the soil is carried by shear rather than compressional waves. In addition, Scholte waves are generated along the seabed-water interface, which induce pressure fluctuations in the water column close to the seabed. 3.2 Soil domain consisting of a single hard soil layer In this section, the effect of soil elasticity is examined. The soil domain is assumed homogeneous and the elasticity modulus is equal to Es = 250 MPa. The soil density is 1800 kg
m-3 and the Poisson ratio is equal to v
s=0.37. The rest of the
material properties are given in Table 1.
In Figure 8, the pressure amplitude spectra are shown for the case of the stiff soil. A comparison of Figure 5 with Figure 8 clearly shows that there is an increase of the pressure levels close to the seabed whereas the pressures close to the sea surface do not change. This difference is mainly attributed to the change in the behaviour close to the seabed-water interface.
Figure 8 Pressure amplitude spectra of the four locations in the case of a hard soil
To illustrate that this is indeed true, in Figure 9, the pressures are shown for point D and for the two soil conditions. The first pressure peak is almost identical regardless of soil elasticity. This is related to the first pressure cone (Mach cone) as discussed previously. As time advances, the two signals show large differences. A low frequency peak which occurs at approximately 0.10s in the case of the hard
soil, appears much later in time (0.18s) for the soft soil and with a reduced, by more than 60%, amplitude. This peak is caused by the slowly propagating Scholte wave along the seabed–water interface. The differences are more apparent if one compares the radial velocities in the fluid region for the same points (Figure 10). The high frequency peaks which occur early in time are almost identical for both cases whereas the low frequency peaks which appear later in time are caused by the Scholte wave and therefore are influenced significantly by soil elasticity.
Figure 9 Comparison of the pressures at point D for the case of a soft and a hard soil substrate
Figure 10 Comparison of the radial fluid velocity at point D for the case of a soft and a hard soil substrate
In Figure 11, the pressures in the fluid together with the velocity norm in the soil are shown for two moments after the hammer impact. The choice of the velocity norm allow us to expose a compressional front which advances in the soil region followed by the strong shear waves. One can also distinguish a head wave with a spherical front between the compressional and the shear waves. A comparison of Figure 11 with Figure 7 shows that the pressures close to the seabed are increased in the case of the hard soil and the penetration depth of the Scholte wave into the fluid region also increases in the latter case. The influence of soil elasticity on the penetration depth of Scholte waves into the fluid region has been observed by other researchers [14-15] and is also verified by the present model.
Figure 11 Pressures in the fluid (top) and velocity norm in the soil (bottom) for two moments in time after the impact 3.3 Case of a two-layered soil with a thin soft upper layer
and a hard soil substrate
Although the previously examined cases help to understand the basic physics associated with waves induced by pile driving, the case of a homogeneous soil is an oversimplification of reality. In this section, the above restriction is somewhat relaxed and the case of a two-layered soil is examined in which the top layer is relatively soft and has a thickness of 7m. The underlying soil is stiffer and extends to large depths. Such a soil stratification is not uncommon in realistic environments, in which the upper few meters consist of soil of relatively low stiffness whereas the underlying soil is much stiffer. The pile dimensions and fluid characteristics are already given in Table 1. The soil conditions are summarised in Table 4.
Table 4. Soil parameters (two-layered soil sediment) Soil layer Es
(MPa) (kgmρs -3) (-) vs Thickness (m)
Upper 70 1700 0.40 7.00
Lower 250 1800 0.37 100.00
In Figure 12, the pressures in the fluid region are shown together with the displacements in the soil domain for three moments in time after the hammer impact. On the basis of a comparison with the previously examined cases, the following conclusions can be drawn. The shear fronts in the soil region change slope at the interface between the two layers. The shear waves in the bottom layer travel with a speed which is equal to 225ms-1 whereas in the top layer the speed is lower
(121ms-1). This difference in the speed of propagation is
correctly captured by the present model. Stoneley waves propagate along the interface between the two soil layers as can be seen in the third plot. These waves are very slow and therefore they stay behind the shear fronts in the second soil layer. Nevertheless, the Scholte waves at the interface with the fluid are still the slowest waves in the domain. The pressures induced in the fluid by the Scholte waves influence only a narrow zone close to the seabed level (0.5m-1.0m penetration depth into the fluid region).
Figure 12 Pressures in the fluid (top) and displacement norm in the soil (bottom) for three moments in time
In Figure 13, a comparison of the pressure amplitude spectra for point D is shown. As expected, soil stratification and soil elasticity influence mainly the low frequency octave bands up to 160Hz. Higher octave bands show very similar pressure levels since they correspond to the pressure conical waves which remain largely unaffected by soil conditions.
Figure 13 Comparison of pressure spectra for point D In Figure 14, a comparison of the displacement amplitude spectra of the soil for a point positioned on the seabed surface at 18m from the pile is shown. For increasing soil stiffness, the peak of the amplitude spectrum moves towards higher frequencies. The case of the two-layered soil shows two distinct peaks in contrast to the homogeneous soil cases. The displacements in the case of the hard soil sediment are lower in magnitude compared to the other cases.
In Figure 15, the radial velocity of the fluid is shown for points B and D. Also included are the results obtained for point D in the case of the homogeneous soil for comparison. The absence of any effect of the interface waves for the point located close to the sea surface is apparent (point B). A
comparison between the case of the homogeneous soft layer and of the two-layered bottom shows that the presence of the hard substrate in the latter case results in a modification of the velocity field for time moments larger than 0.08s. This is probably caused by a reflection of the compressional waves in the pile once they reach the interface of the two soil media. The first Scholte wave occurs from the compressional waves travelling upwards the pile after reflection at the interface between the two media while the second one is caused by the reflected waves at the pile tip level.
Figure 14 Comparison of displacement amplitude spectra for a point positioned on the seabed surface and at r=18m
Figure 15 Radial velocity of the fluid for points B and D
4 WAVE RADIATION FROM VIBRATORY PILE
DRIVING
In contrast to the case of the impact hammer, vibratory hammers drive the pile into the soil in a different manner. The input force consists of low frequencies and has a periodic character. A typical input force from a vibratory hammer is shown in Figure 16 and its Fourier transform is depicted in Figure 17. In reality the force is applied for longer periods of time but here it is terminated after a few oscillations in order to obtain the transient response of the system. The application time is sufficient in order to develop the full radiation pattern as if the force was applied for longer periods.
In this example, the main driving frequency is around 20Hz which is a typical driving frequency for offshore vibratory
hammers. A small amount of energy in spread in a few sub- and super-harmonics of the fundamental driving frequency up to 120Hz. The magnitude of the input force is about 1MN. The analysis is limited to the case of a homogeneous soil with the material properties as introduced in Table 1.
Figure 16 Input force exerted by the vibratory hammer
Figure 17 Amplitude spectrum of the input force A typical radiation pattern as a result of the force applied in this case is shown in Figure 18. The generated wave field shows the following characteristics:
• The wave field in the soil consists mainly of vertically polarised shear waves with cylindrical fronts which spread outwards from the vibrating pile with the shear wave velocity. The shear velocity in this example is equal to 121ms-1.
• The Scholte waves, which propagate parallel to the seabed-water interface, attenuate much less in comparison with the shear waves in the soil. They
propagate with a speed of 105ms-1 which
corresponds to 86% of the shear velocity of the soil medium.
• The pressures in the fluid are localised close to the seabed. The typical Mach wave radiation pattern in the fluid region cannot be distinguished in this case. The results regarding the wave radiation in the soil are in full agreement with the ones presented in [12], in which the vibrations of concrete piles subjected to a vibratory hammer
excitation were examined. Due to the presence of the fluid layer on top of the soil domain in our work, Rayleigh waves at the surface of the soil are substituted by Scholte waves at the interface.
Figure 18 Pressures in the fluid (top) and displacement norm in the soil (bottom) for four moments in time
5 CONCLUSIONS
In this paper, the underwater noise generated from the offshore installation of steel monopiles is examined. The model is based on a semi-analytical formulation which allows to couple the vibrations of pile with the surrounding water-soil medium into an integrated model. The hammer is substituted by an external force applied at the head of the pile. The pile is described by a thin shell theory, whereas both soil and water are modelled as three-dimensional continua. The solution is based on the dynamic sub-structuring technique. The total system is divided into two sub-systems; the shell structure and the soil-fluid medium. The response of each sub-domain is expressed as a summation over a complete set of vertical eigenfunctions. The orthogonality of the shell modes in vacuo and the bi-orthogonality of the acousto-elastic modes are utilized in order to meet the displacement compatibility and the force equilibrium at the interface of the two sub-systems.
With the developed model, the wave radiation due to vibratory and impact pile driving is analysed. The influence of soil elasticity and soil stratification on the dynamics of the coupled system is examined. The main differences between the generated wave field with the two hammer types are qualitatively analysed.
Results from impact pile driving show that the pressure field in the fluid consists mainly of conical fronts (primary noise source) which are formed with an angle of 160 to the
vertical. In the soil region, both vertically polarised shear waves and compressional waves are generated, with the former being much stronger than the latter. In addition, Scholte waves are also present close to the seabed-water interface. They induce pressure fluctuations in the water column which can be of significant amplitude close to the seabed (secondary noise path). Soil elasticity and soil stratification influence mainly the secondary noise path as shown by the examined cases.
In contrast to the case of the impact hammer, in the case of the vibratory hammer, the force contains a fundamental frequency together with some sub- and super-harmonics. The results show that the wave field in the soil consists of vertically polarised shear waves formed in cylindrical fronts and spreading outwards from the vibrating pile. Scholte waves are also generated close to the seabed-water interface. Their attenuation is much smaller in comparison with the shear waves in the soil. The pressures in the fluid are mainly localised close to the seabed, consist of low frequency components and are in general much lower than the ones obtained by the impact hammer.
Although the basic features of the generated wave field can be obtained with the present model, some improvements are needed too. The radiation of waves from the tip of the pile needs to be accounted for since it is expected to have a dominant contribution when the penetration depth of the pile into the sediment is small. In addition, a linearized description of the shear friction at the pile-soil interface can be of some interest for future research.
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