Valentin Meyer

Laurent Maxit

Ygäal Renou

Christian Audoly

Ygaal Renou

Vibroacoustic modeling of submerged stiffened cylindrical shells with internal structures under random excitations

Keywords: Vibroacoustics, Cylindrical shell, Diffuse Sound Field, Turbulent boundary layer I-INCE Classification of Subjects Numbers: 54.3, 76.9

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INTRODUCTION

In many aeronautical or naval applications, ribbed structures are subject to random pressure fields such as Diffuse Sound Fields (DSF) or fluctuations due to the turbulent flow induced by their movement. These excitations yield vibrations, which knowledge is of primarily importance in practice. Many works can be found in the literature for plates under a Turbulent Boundary Layer (TBL). Strawderman [START_REF] Strawderman | Turbulence-induced plate vibrations: an evaluation of finite-and infinite-plate models[END_REF] reviews the first existing models of finite and infinite plates. He points out that none of the models fully agrees with experimental results but that the ones for the finite plate performs better. The complexity of the problem is successively increased by taking heavy fluid loading into account [START_REF] Strawderman | Turbulence-induced plate vibrations: Some effects of fluid loading on finite and infinite plates[END_REF][START_REF] Aucejo | Vibro-acoustique des structures immergées sous écoulement turbulent[END_REF] or by stiffening the plates [START_REF] Rumerman | Estimation of broadband acoustic power radiated from a turbulent boundary layerdriven reinforced finite plate section due to rib and boundary forces[END_REF]. Maxit and Denis [START_REF] Maxit | Prediction of flow induced sound and vibration of periodically stiffened plates[END_REF] use the wavevector-frequency analysis, earlier reviewed by Strawderman [START_REF] Strawderman | Wavevector-frequency analysis with applications to acoustics[END_REF], and the reciprocity principle to study the problem of a ribbed plate with heavy fluid loading. Their method consists in determining the second order moment of the response thanks to the wall pressure fluctuations and the sensistivity functions of the system. The sensitivity function at a point M of the system is estimated from the vibratory field induced by a point excitation at M . As the formulation of this method is not only valid for plates, the aim of the present work is to apply it to the case of submerged cylindrical shells with internal structures. Nevertheless, the aim of this paper is not to characterize the TBL on a circular cylinder and widespread models models such as Corcos' [START_REF] Corcos | Resolution of pressure in turbulence[END_REF] or Chase's [START_REF] Chase | The character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model[END_REF] will be used because of their simplicity of implementation. Indeed, in the case where the TBL thickness is small compared with the radius of curvature of the system, which is the case in this study, the boundary layer is similar to a planar one [START_REF] Blake | Aero-hydroacoustics for ships[END_REF][START_REF] Richard | Turbulent boundary layer on a cylinder in axial flow[END_REF].

A substructuring method is used to determine the sensitivity functions of the submerged cylindrical shell with internal structures. The Condensed Transfer Function (CTF) method, previously developed by the authors [START_REF] Meyer | A condensed transfer function method as a tool for solving vibroacoustic problems[END_REF][START_REF] Meyer | Prediction of the vibroacoustic behavior of a submerged shell with non-axisymmetric internal substructures by a condensed transfer function method[END_REF], is an extension of the classical admittance approach [START_REF] Firestone | The mobility method of computing the vibration of linear mechanical and acoustical systems: Mechanical-electrical analogies[END_REF] to allow coupling along lines. A set of orthonormal functions called condensation functions is used as a basis for approximating the displacements and the forces at the junctions between the subsystems. Condensed transfer functions are then defined and calculated for each uncoupled subsystems, and the superposition principle for passive linear systems leads to the vibroacoustic behavior of the coupled system. One of the main advantage of the CTF method is that the condensed transfer functions of the uncoupled subsystems can be described by different methods. In this case, the submerged shell CTFs are calculated by solving the Flügge equations in the spectral domain, whereas the internal frames are modeled by FEM, allowing flexibility on their geometry.

The paper is organized as follows:

• Section 2 presents the wavenumber-point (k,M) reciprocity technique.

• In section 3, the CTF method is applied to calculate the sensitivity functions of a submerged cylindrical shell with internal structures.

• An application to a complex cylinder under a DSF and a TBL is proposed in section 4. The influence of non-axisymmetric internal frames will be discussed.

• Conclusions are drawn in section 5.

THE WAVENUMBER-FREQUENCY (k, M ) RECIPROCITY TECHNIQUE

This section is based on the wavenumber-frequency formulation which can be found in the literature [START_REF] Aucejo | Vibro-acoustique des structures immergées sous écoulement turbulent[END_REF][START_REF] Strawderman | Wavevector-frequency analysis with applications to acoustics[END_REF][START_REF] Maxit | Wavenumber space and physical space responses of a periodically ribbed plate to a point drive: A discrete approach[END_REF]. The wavenumber-frequency (k, M ) reciprocity technique has been presented in details by Maxit and Denis [START_REF] Maxit | Prediction of flow induced sound and vibration of periodically stiffened plates[END_REF] and the general outline is briefly described in this section.

Let us consider a vibroacoustic system made of a structure coupled to a fluid domain. The surface Σ p is excited by a random pressure field. The wall pressure p b (x, t) is expressed in a point x ∈ Σ p as a function of the time t. The system is supposed to be linear and invariant in time, so that the displacement w at a point x can be expressed as:

w(x, t) = Σp +∞ -∞ h w (x, x, t -τ ) p b (x, τ ) dτ dx (1)
where h w (x, x, t) is the impulse response of the system at point x when excited by an impulse unitary force at point x.

The excitation being random, the quantity of interest is the second order moment of the displacement. Considering that the random process is ergodic, the inter-correlation function R ww (x, x , t) is defined as:

R ww (x, x , t) = +∞ -∞ w(x, τ )w(x , t + τ )dτ (2)
Injecting Eq. (1) into Eq. ( 2) and applying a Fourier transform in the time domain yields the space-frequencyspectrum S ww (x, x , f ):

S ww (x, x , f ) = Σp Σp H * w (x, x, f ) S pp x, x, f H w x , x, f dxd x (3)
where H w (x, x, f ) is the transfer function in displacement of point x when excited at point x, S pp x, x, f is the space-frequency spectrum of the wall pressure, and * denotes the conjugate. The space Fourier transform of S pp x, x, f can be written as a function of the wavenumber-frequency spectrum of the wall pressure φ pp (k, f ):

S pp x, x, f = 1 (2π) 2 +∞ -∞ φ pp (k, f )e -jk( x-x) d 2 k (4)
φ pp (k, f ) is a power spectrum density that characterizes the excitation and is supposed to be known. This value is expressed in Pa 2 .s and is defined for positive frequencies only. Let us define Hw (x, k, f ) as the frequency response at point x when the system is excited by a plane wave with wavevector k:

Hw (x, k, f ) = Σp H w (x, x, f ) e jkx dx (5)

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Thus, injecting Eq. ( 4) into Eq. ( 3) and using Eq. ( 5), the space-frequency spectrum of displacement can be written finally as:

S ww (x, x , f ) = 1 4π 2 +∞ -∞ H * w (x, k, f )φ pp (k, f ) Hw (x , k, f )d 2 k (6)
If one is interested only in the spectral power density of the displacement at point x (i.e. x = x), Eq. ( 6) can be written as follows:

S ww (x, f ) = 1 4π 2 +∞ -∞ | Hw (x, k, f )| 2 φ pp (k, f )d 2 k (7)
The same developments can be made for the spectral power density of the pressure at point z:

S pp (z, f ) = 1 4π 2 +∞ -∞ | Hp (z, k, f )| 2 φ pp (k, f )d 2 k ( 8
)
where Hp (z, k, f ) represents the pressure at point z in the fluid when the system is excited by a plane wave of wavevector k. It should be noted that this plane wave can be either propagating either evanescent, depending on its value compared to the acoustic wavenumber k 0 = 2πf c0 , with c 0 the sound velocity. When solving a problem numerically, integrals over infinite domains such as in Eqs. ( 7) and ( 8) are an issue. However, it can be shown on systems such as plates or shells that the transfer functions Hw (x, k, f ) and Hp (z, k, f ) tend to 0 when |k| → ∞. Thus, a cutoff wavenumber N k based on the response function of the system along the wavenumbers can be defined [START_REF] Maxit | Prediction of flow induced sound and vibration of periodically stiffened plates[END_REF], allowing the integration domain to be truncated. The difficulty now lies in the calculation of the transfer functions over the integration domain. In practice, it consists in determining the displacement at location x or the pressure at location z when the system is excited by all the wavenumbers included in the integration domain. The number of excitations can thus be large and leads to prohibitive computation time. To tackle this issue, the use of the Lyamshev reciprocity principle is proposed [START_REF] Fahy | Some applications of the reciprocity principle in experimental vibroacoustics[END_REF]. It consists in exploiting the property that the transfer function between two points remains the same if the observation and excitation point are exchanged:

H w (x, x, f ) = H w (x, x, f ) (9)
Eq. ( 5) can thus be written:

Hw (x, k, f ) = Σp H w (x, x, f ) e jkx dx ( 10
)
This equivalence is called the wavenumber-point (k, M ) reciprocity principle. It means that the power spectrum density of the displacement of the system at point x can be calculated through Eq. ( 7), knowing the vibratory field of the system excited by a point force at point x. Similarly, the Lyamshev reciprocity principle is also valid for a point z in the fluid domain. The pressure at point z for a point force at x is equal to the displacement at point x when the system is excited by an acoustic monopole at point z. Hence, the power spectrum density of the pressure at point z can be determined through Eq. ( 8), knowing the vibratory field of the system excited by a monopole in z. This paper focuses on the response of stiffened cylindrical shells with internal structures under random excitation. The reciprocity technique is illustrated for such a system in Fig. 1. In this case, the calculation of the power spectrum densities of displacement Hw (x, k, f ) and of pressure Hp (z, k, f ) used in Eq. ( 7) and ( 8) is not straightforward. Therefore, the Condensed Transfer Function (CTF) method presented in the next section is used to tackle this issue.

APPLICATION OF THE CONDENSED TRANSFER FUNCTION METHOD

Principle of the method

The Condensed Transfer Function (CTF) method is a substructuring method where the subsystems are modeled by plates and shells and coupled along lines [START_REF] Meyer | A condensed transfer function method as a tool for solving vibroacoustic problems[END_REF]. On each junction between subsystems, a set of orthonormal functions (ϕ n (s)) 1≥n≥N called condensation functions is defined, where s is the curvilinear abscissa along the junction. These functions are used to approximate the displacements and forces at the junctions for each uncoupled system α and to define the condensed transfer functions:

Y α nm = Ū α m,q,p , ϕ n F α m,q , ϕ m 1≤p≤4,1≤q≤4 = Ū α m,q,p , ϕ n p,q , (11)
where •, • is a scalar product. F α m is the vector of the efforts on the junction, where the components in each direction of space is equal to ϕ m . The indices p and q denote one of the four directions of space used in the case of a cylindrical shell (the three translations or forces and the rotation or moment around the tangential coordinate). Ūα m,q is the displacements vector of the junction when the subsystem is excited in the direction q by a force of magnitude F α m,q . Thanks to the superposition principle for linear passive systems, and to the forces equilibrium and displacements continuity, the coupling forces F c between two subsystems α and β are deduced by the following equation:

Y α + Y β F c = Ũβ -Ũα (12)
where

Ũα = Ũ α p , ϕ n n,p
, is the vector of free condensed displacements and is calculated by projecting the displacement in the direction p on the condensation function ϕ n when subsystem α is not coupled to the other subsystems and only excited by external forces.

Once the coupling forces have been calculated by inverting Eq. ( 12), the displacement at the point x of the coupled system can be deduced:

U α (x) = Ũα (x) + N n=1 Y α xn F c n ( 13
)
where Ũα (x) is the displacement at the point x when the subsystem α is uncoupled and excited by the external excitation. Y α xn is the condensed transfer function between the observation point x and the condensation

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function ϕ n (i.e. the displacement in x when the uncoupled subsystem is excited only by ϕ n ). Similarly, the pressure at the point z of the coupled system can be deduced:

p re (z) = pα re (z) + N n=1 Y α zn F c n ( 14
)
where pα re (z) is the pressure at the point z when the subsystem α is uncoupled and excited by the external excitation. Y α zn is the condensed transfer function between the observation point z and the condensation function ϕ n .

The advantage of this method is that the condensed transfer functions of each uncoupled subsystem can be calculated by different techniques. In the case of a submerged cylindrical shell with internal structures, the submerged shell admittances are calculated through the Flügge equations, while the internal structures are modeled by Finite Elements.

The excitation of the coupled system is taken into account in the free displacement term, on the right hand side of Eq. ( 12). In the case of a point force, the free displacements of the shell can be calculated using the Függe equations and the free displacements of the internal frames can be determined using the FEM. Examples and validations on a complex submerged shell are given in [START_REF] Meyer | Prediction of the vibroacoustic behavior of a submerged shell with non-axisymmetric internal substructures by a condensed transfer function method[END_REF]. In the case of an acoustical monopole, developments need to be done to calculate the free displacements of the shell. This is the aim of the next subsection.

Free displacements of the submerged shell for a monopole excitation

In the fluid domain surrounding the cylindrical shell, the pressure is decomposed as the sum of the blocked pressure p b and the reradiated pressure p re due to the system vibrations:

p = p b + p re (15)
The blocked pressure will be used as a source term in the spectral equations of movement of the submerged cylindrical shell without internal structures [START_REF] Maxit | Prediction of the vibro-acoustic behavior of a submerged shell non periodically stiffened by internal frames[END_REF]. The case of a monopole excitation outside the shell is considered, as seen in Fig. 2. The blocked pressure p b (x, r, θ) is solution of the non-homogeneous Helmholtz equation:

∆p b (x, r, θ) + k 2 0 p b (x, r, θ) = q exc (x, r, θ) (16)
where q exc is the source term. The rigid boundary condition (Neumann) on the shell surface is written thanks to Euler's relation:

∂p b ∂r (x, R, θ) = 0 (17)

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with R the radius of the shell. The blocked pressure p b is the sum of the incident pressure p i and the scattered pressure p s : p b = p i + p s . The incident pressure is known and the scattered pressure needs to be calculated. From the previous equations, one can write:

∆p s (x, r, θ) + k 2 0 p s (x, r, θ) = 0 (18) and ∂ ∂r p s (x, R, θ) = - ∂ ∂r p i (x, R, θ) (19)
Applying a 2D-Fourier transform along the axial and tangential coordinates to Eq. ( 18) and ( 19) yields:

∂ 2 ∂r 2 ps (k x , r, n) + 1 r ∂ ∂r ps (k x , r, n) + k 2 r - n 2 r 2 ps (k x , r, n) = 0 (20)
∂ ∂r ps (k x , R, n) = - ∂ ∂r pi (k x , R, n) ( 21
)
where ps is the 2D-Fourier transform of the scattered pressure, and k 2 r = k 2 0 -k 2 x . For a given k x and n, Eq. ( 20) corresponds to Bessel's differential equation, which solutions can be written with Hankel's functions of the first and second kind of order n, H (1) n and H (2)

n ps (k x , r, n) = A r H (1) n (k r r) + B r H (2) n (k r r) (22)
The constant A r and B r are calculated thanks to the Sommerfeld's radiation condition and the Euler's equation:

   A r = 0 B r = - 1 krH (2) n (krR) ∂ ∂r pi (k x , R, n) (23)
The incident pressure field for a monopole in (x s , r s , θ s ) can be expressed by:

p i = p 0 e jk0d d ( 24
)
with j 2 = -1, p 0 the source intensity and d the distance between the source and the observation point. Applying a 2D-Fourier transform yields [START_REF] Skelton | Acoustics of an anisotropic layered cylinder[END_REF]:

pi (k x , r, n) = jπp 0 H (2)
n (k r r s )J n (k r r)e -j(nθs+kxxs) for r < r s

Injecting Eq. ( 25) in Eq. ( 23) and then in Eq. ( 22) yields:

ps (k x , r, n) = -jπp 0 H (2) n (k r r s )J n (k r R) H (2) n (k r R) H (2) n (k r r)e -j(nθs+kxxs) (26)
The blocked pressure is deduced by summing the incident and scattered pressure:

pb (k x , R, n) = jπp 0 J n (k r R) - H (2) n (k r R)J n (k r R) H (2) n (k r R) H (2) n (k r r s )e -j(nθs+kxxs) (27)
Using that J n (z)H (2) n (z) -J n (z)H (2) n (z) = -2j πz , Eq. ( 27) can finally be written as:

pb (k x , R, n) = 2p 0 k r R H (2) n (k r r s ) H (2) n (k r R) e -j(nθs+kxxs) (28)
This expression can be used in the right-hand term of the spectral Flügge equations to determine the free displacements of the shell under a monopole excitation. This method is applied in the next section to discuss the influence of the internal structures on the vibroacoustic behavior of a submerged shell under a random excitation.

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TEST CASE APPLICATION

Description of the system

A 5 m radius, 42.3 m length and 30 mm thick cylindrical shell stiffened with 51 stiffeners and 2 spherical bulkheads (10 mm thick, 30 m curvature radius) is considered in this section, as shown in Fig. 3a. There are three different types of stiffeners and their spacing varies between 0.6 and 1 m. The whole system is made of steel (η = 0.02) and is immersed in water. Clamped boundary conditions are used at the ends of the shell, 2 m away from the first and the last stiffeners. A non-axisymmetric frame is linking the two stiffeners at x = 11.5 m and x = 21.5 m. A model of this internal structure is shown in Fig. 3b, with the colors representing the displacement magnitude of the eigenmode at 170 Hz. It consists in a plate assembly made of a horizontal floor, a vertical stiffening plate and two disc sections that are linked to the stiffeners. Displacements continuity is assumed at all the junctions.

In order to use the reciprocity principle, a point force is applied on the surface of the cylindrical shell at the point M 1 of coordinates (x, θ, r) = (11.5, 0, 5). Similarily, a monopole excitation is defined at the point M 2 of coordinates (x, θ, r) = (11.5, 0, 500). The response of the system is calculated through the CTF method for both excitations separately, and thanks to the reciprocity principle, the sensitivity functions are given by the response in the wavenumber-frequency space.

Examples of sensitivity functions

Sensitivity functions, i.e. accelerations of the shell in the wavenumber space, are calculated thanks to the CTF method under the point force and under the monopole excitation. The results are plotted in Fig. 4 for the point force at f = 207 Hz and in Fig. 5 for the monopole excitation at f = 568 Hz. These frequencies are chosen because differences can clearly ben seen in the spectra. Indeed, more circumferential orders tend to play a role in the response of the structure when there is a non-axisymmetry [START_REF] Meyer | Prediction of the vibroacoustic behavior of a submerged shell with non-axisymmetric internal substructures by a condensed transfer function method[END_REF][START_REF] Marcus | The effect of internal point masses on the radiation of a ribbed cylindrical shell[END_REF]. In Fig. 5, the white line represents the radiation circle. The spectral components inside this circle are the main contributors to the pressure radiated in the far-field [START_REF] Williams | Experimental investigation of the wave propagation on a point-driven, submerged capped cylinder using k-space analysis[END_REF]. No clear difference can be seen inside the radiation circle at this frequency, so no large difference is expected in the power spectral density of the pressure at M 2 .

Diffuse Sound Field

As the radius of curvature of the shell is large compared with the wavelength, the expression of a diffuse sound field (DSF) for a plate in the wavenumber-frequency space is taken as [START_REF] Marchetto | Caractérisation expérimentale de structures sous champ acoustique diffus : mesure des fonctions de sensibilité par principe de réciprocité[END_REF]:

φ pp (k x , k θ , f ) = π k0 Spp(f ) √ k 2 0 -(k 2 x +k 2 θ ) if k 2 x + k 2 θ < k in 0 0 if k 2 x + k 2 θ ≥ k in 0 ( 29
)
with S pp the frequency spectral density, taken constant equal to 1 Pa 2 .s in this example.

k in 0 = 2πf c in 0
is the acoustic wavenumber. As air is considered inside the cylindrical shell (with weak coupling only), the sound velocity is c in 0 = 340 m.s -1 . In this example, the DSF excites only the cylinder on the section between the two bulkheads at x = 9.5 and x = 23.5 m. According to the reciprocity principle and to Eq. ( 10), it consists in calculating the displacements of the structure under a point force at x only on x ∈ Σ p . Fig. 6 shows the power spectral densities of the radial acceleration at M 1 and pressure at M 2 as a function of the frequency with and without the non-axisymmetric internal frame. The red solid line shows the results in the case of the axisymmetric stiffened shell (i.e. the stiffened submerged shell without the internal frame) and the blue dashed line shows the case where the non-axisymmetric frame is taken into account. It can be said that the non-axisymmetric internal frame has an influence on the response of the structure when it is excited by the DSF. For the acceleration at M 1 , the power spectral density tends to decrease except for some frequency ranges. The decrease can be explained from the reciprocity principle, by saying that the amplitude of displacement is on average lower in the non-axisymmetric case [START_REF] Meyer | Prediction of the vibroacoustic behavior of a submerged shell with non-axisymmetric internal substructures by a condensed transfer function method[END_REF][START_REF] Meyer | Vibrations et rayonnement acoustique des coques cylindriques raidies : étude expérimentale de l'influence des structures internes nonaxisymétriques[END_REF]. The increases can be explained by looking at the sensity functions shown in Fig. 4 where more circumfenential orders play a role in the non-axisymmetric case. For the power spectral density of pressure at M 2 , an increase smaller than 2 dB can be seen.

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(a) (b) Figure 6: Power spectral density of the system excited by a diffuse sound field with and without the nonaxisymmetric internal structure as a function of the frequency of the (a) radial acceleration at M 1 and (b) pressure at M 2 .

Turbulent Boundary Layer excitation

A structure immersed in a flow can be excited by a Turbulent Boundary Layer which is characterized by the parameters shown in Table 1 [START_REF] Howe | Surface pressures and sound produced by turbulent flow over smooth and rough walls[END_REF]. These parameters can be calculated through CFD (computational fluid dynamics) calculations. This is however not the aim of the present work and the values have thus been arbitrarily chosen for naval applications, and used in simple models to calculate the wavenumber-frequency spectrum of the wall pressure. The strongest pressure fluctuations occur at the convective wavenumber k c and the acoustic wavenumber k 0 defined by:

k c = 2πf U c and k 0 = 2πf c 0 ( 30
)
where U c is the convection speed taken as U c = 0.6U ∞ [START_REF] Howe | Surface pressures and sound produced by turbulent flow over smooth and rough walls[END_REF][START_REF] Arguillat | Measured wavenumber: Frequency spectrum associated with acoustic and aerodynamic wall presure fluctations[END_REF] and c 0 = 1500 m.s -1 . The acoustic, convective and flexural wavenumbers are plotted as a function of the frequency up to 1000 Hz in Fig. 7a. The flexural wavenumber is calculated for a h = 0.03 m thick plate made of steel (density ρ s = 7800 kg.m -3 , Young modulus E = 210 GPa and Poisson coefficient ν = 0.3) through the following formula [START_REF] Junger | Sound, structures, and their interaction[END_REF]:

k f = 2πf h 12(1 -ν 2 )ρ s E 1/4 (31)
It can be seen in Fig. 7a that the convective wavenumber is much bigger than the acoustic and flexural wavenumbers for the parameters chosen for this study. On the other hand, the radial accelerations of a cylinder above the ring frequency, f r = 1 2πR E ρs(1-ν 2 ) = 173 Hz, present generally maxima for wavenumbers around the flexural wavenumber and then decreases when the wavenumber increases. Fig. 7b shows the module of the radial acceleration as a function of the axial wavenumber for the circumferential order n = 0 at the frequency f = 1000 Hz. It clearly shows that the amplitude is maximum at the flexural wavenumber k f , and then drops dramatically. It can thus be said that the structure acts as a filter on the high wavenumbers and that the vibrations are mainly due to the acoustic components of the TBL. As mentionned at the end of section 2, a cutoff wavenumber N k can thus be defined from the flexural waenumber and a margin coefficient to numerically calculate the integrals of Eqs. ( 7) and [START_REF] Chase | The character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model[END_REF]. In this example, the margin coefficients are taken equal to 4 for the axial wavenumbers and 1.2 for the circumferential wavenumbers.

In the present study, the wavenumber-frequency of the wall pressure φ pp (k x , k θ , f ) is expressed as:

φ pp (k x , k θ , f ) = S pp (f )Ψ pp (k x , k θ , f ) (32)
An empirical model proposed by Goody [START_REF] Goody | Empirical spectral model of surface pressure fluctuations[END_REF] is used for the frequency spectral density S pp (f ):

S pp (f ) = 4πC 2 τ 2 w (2πf ) 2 δ 3 U 3 ∞ C 1 + 2πf δ U∞ 0.75 3.7 + C 3 R -0.57 T 2πf δ U∞ 7 (33)
where C 1 , C 2 and C 3 are respectively 0.5, 1.5 and 1.1. R T = U 2 T δ ν0U∞ is the Reynolds number that takes into account the ratio of intertial forces to viscous forces. τ w = ρ 0 U 2 T is the shear constraint at the wall. The cross-spectrum Ψ pp (k x , k θ , f ) is deduced from a spatial Fourier Transform of the expression given by Corcos [START_REF] Corcos | Resolution of pressure in turbulence[END_REF] and yields:

Ψ pp (k x , k θ , f ) = 4αβ k x -2πf Uc 2 + 2πf α U c 2 k 2 θ + 2πf β U c 2 (34)
with α = 0.11 and β = 0.77 empirical values.

The power spectral density of the acceleration at M 1 and of the pressure at M 2 are plotted as a function of the frequency in Fig. 8a and 8b respectively. Similarily to the results from the diffuse sound field, it can be said that the non-axisymmetric internal frame has an influence on the response of the system when it is excited by a TBL. Differences up to 6 dB can be seen in Fig. 8a for the power spectral density of acceleration at M 1 between the axisymmetric and non-axisymmetric cases . For the power spectral density of pressure at M 2 shown in Fig. 8b, the differences between the two cases are smaller. No clear difference can be seen below 250 Hz, and the non-axisymmetric case is between 1 and 2 dB higher in the rest of the frequency range.

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CONCLUSION

The response of a submerged stiffened cylindrical shell with non-axisymmetric internal frames under random excitations has been calculated. For this purpose, the wavenumber-frequency (k, M ) reciprocity technique has been presented and is based on sensitivity functions, that are the result of deterministic calculations of the system under a point force or a monopole. They are estimated with the CTF method, that is a substructuring method that enables to take internal frames in a submerged shell into account. One of the main advantage of this approach is that once the sensitivity functions are stored in a database, it is easy to change the excitation by modifying the expression of the wall pressure spectrum φ pp .

An application on a test case taken from the naval industry under different random excitations (DSF, TBL) shows the versatility of the method. From the results it can be said that the non-axisymmetric internal frames can have an influence on the response of the system under random excitations. As more circumferential orders tend to play a role when the system is non-axisymmetric, the response tends to be higher in this case. The method can now be used to further investigate physical phenomena (Bloch-Floquet waves propagation for instance) involved in a stiffened submerged cylindrical shell under random excitation.

Figure 1 :

 1 The (k, M ) reciprocity technique applied to a stiffened submerged cylindrical shell with internal structures to evaluate (a) the displacement at a point on the shell surface or (b) the pressure at a point in the fluid domain.

Figure 2 :

 2 Sections of a stiffened cylindrical shell model including a non-axisymmetric internal frame and an acoustic monopole in the fluid domain. (a) View in the plane θ = 0. (b) View in the plane x = x A .

Figure 3 :

 3 Submerged cylindrical shell with axisymmetric stiffeners: (α) spacing 0.75 m, T-cross-section (mm): 300 × 60/60 × 300; (β) spacing 1 m, T-cross-section (mm): 200 × 15/15 × 200; (γ) spacing 0.6 m, T-cross-section (mm): 200 × 25/15 × 200. (a) Section in the plane θ = 0. (b) Mode at 170 Hz of the non-axisymmetric frame.

Figure 4 :Figure 5 :

 45 Sensitivity function (acceleration in dB ref gµm.s -2 ) in the wavenumber space for a point force at M 1 at f = 207 Hz. (a) Axisymmetric case. (b) Non-axisymmetric case. Sensitivity function (acceleration in dB ref gµm.s -2 ) in the wavenumber space for a monopole at M 2 at f = 568 Hz. (a) Axisymmetric case. (b) Non-axisymmetric case.

Figure 7 :

 7 (a) Acoustic (blue solid line), convective (black dotted line) and flexural (red dashed line) wavenumbers as a function of the frequency. (b) Radial acceleration as a function of the axial wavenumber k x at 1000 Hz for the circumferential order n = 0 and for a point force at M 1

Figure 8 :

 8 Power spectral density of the system excited by a turbulent boundary layer with and without the nonaxisymmetric internal structure as a function of the frequency of the (a) radial acceleration at M 1 and (b) pressure at M 2 .

Table 1 :

 1 Turbulent Boundary Layer parameters

	Parameter	Notation Value
	Flow speed	U ∞	15 m.s -1
	Friction velocity	U T	1 m.s -1
	Thickness	δ	0.01 m
	Kinematic viscosity (at 20 • C)	ν 0	1.005 µ Pa.s
	Fluid density	ρ 0	1000 kg.m -3

email: valentin.meyer@insa-lyon.frINTER-NOISE

ACKNOWLEDGMENTS

This work was funded by DCNS and performed within the framework of the LabEx CeLyA of Université de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ANR-11-IDEX-0007).


C Boutin

C Eme

Domestic Wastewater Characterization by Emission Source

Keywords: Domestic sanitation, faeces, greywater, biological treatment, source separated, urine

Historically, domestic wastewater has been split into two main categories: blackwater and greywater. We set out to characterize domestic effluent more finely in terms of specific pollution emission sources: urine, faeces, toilet paper, cooking, bathroom and laundry effluent, etc. This more detailed characterization helps to provide a more thorough knowledge of domestic wastewater composition and its variability. This literature review makes an inventory of scientific papers characterizing household effluents by emission sources in Western Europe, in contexts similar to France. A critical reading is made, covering analysis protocols and sampling methods.

Results are also compared with national data for small communities. In volume terms, greywater is the main contributor to domestic wastewater. Faeces and toilet paper supply most of the organic matter. Nitrogen comes mainly from urine, and phosphorus mainly from greywater generated by food-related and cleaning activities.

The nutrient balance of each effluent, represented in this study by the ratios BOD 5 :N,P, allows an estimation of its response potential with regard to biological treatment. The evaluation of nutrient balance reveals chronic nutrient deficits in greywater for a biological treatment. However, such treatment is favoured by the biodegradability and nutrient balance of human excreta in blackwater.

With the aim to optimize wastewater uses by treating or recycling specific domestic effluents, this work provides a database with ranges of variation and knowledge for a fuller understanding of processes.

INTRODUCTION

Wastewater characterization by emission source involves fine expertise with daily use surveys and robust field campaigns at household scale. These practices imply important studies costs and set limits to research activities. Knowledge of domestic wastewater and its range of variation enable to optimize treatment units design in a real-world context. Domestic wastewater from a collection network differs from domestic effluent generated by individual users and in that; it contains no clean water or rainwater intrusion, or agricultural or industrial contributions. Collected domestic wastewater is relatively well characterized, whereas the effluent actually released at habitat scale has been less described, owing to broad variability among users. In the context of the development of projects for reclaiming and re-using domestic wastewater, and in particular separation at source, this review describes a characterization of domestic effluents by emission source. To improve wastewater treatment and consider new alternatives in the French context, an improved understanding of wastewater emission sources is required. Here we present a bibliography review of domestic wastewater production and quality at household scale.

Classification

The characterization of domestic wastewater by emission source implies differentiating all source locations where wastewater is produced at household scale.

Figure 1. Classification of domestic wastewater

Blackwater. For blackwater, two modes of effluent collection are considered: classic collection of whole excretion and water from toilets, and selective collection from sourceseparating toilets which are usually composed of a faecal bin and an urine diverter. Unlike classical toilets, source-separating toilets allow a separate collection of yellow water (flush water and urine) and brown water (flush water or not, faeces and toilet paper). Contributions considered as accidental, such as cleaning water in toilets, cigarette butts, etc. are also taken into account.

Greywater. Greywater includes various emission sources. Effluent characteristics are linked to appliances used and to individual patterns: kitchen sink, dishwasher, washing machine, bathroom washbasin, shower, and bath. These uses are divided under two headings: (i) greywater from food-related activities and cleaning (kitchen and laundry activities), and (ii) greywater from personal care, bathroom effluents.

MATERIALS AND METHODS

The datasets presented (more than 80) come from scientific publications dealing with strict domestic effluent or medical characterization of human excreta. They all concern exclusively Western Europe. They cover only strict domestic water uses. Facing a broad diversity of published work, a critical reading was undertaken, which revealed variability in the methods for surveys and assessment used. Datasets considered in this study are not often detailed in their original publication. The statistical material presented offers only partially exploitable data. However, an inventory of the data averages allows the average composition of each emission sources to be established, with minima, maxima and range variations of this average. Each effluent is characterized by the quantification of loads in grams per person per day, implying the integration of the dweller's occupancy time to obtain a daily estimate over 24 h. Effluent concentrations were evaluated when dataset are adequate This article concerns mainly the classical parameters (COD, BOD 5 , DM, SS, N, and P), although the bibliography also covers some micropollutants, metals and sanitary indicators [START_REF] Eme | Composition des eaux usées domestiques par source d'émission à l'échelle de l'habitation[END_REF].

RESULTS AND DISCUSSION

Blackwater

Few (<10) consolidated datasets are available to separately characterize urine (whether hydrolysed or not), or faeces. Each contribution made by blackwater was evaluated in grams per person per day, given the difficulties in quantifying concentrations of faeces and toilet paper. The sum of all the flows slightly exceeded the overall measured composition of the blackwater. Blackwater flows are generally measured per inhabitant, without correcting for occupancy time, whereas a separate source is evaluated per person for a 24 h period. Analytical errors may add to this discrepancy.

Volumes of blackwater generated vary appreciably according to flush type. The identification of the different types of flush gave an average rate of dilution of excreta in blackwater of 1:27 for a classical toilet [START_REF] Eme | Composition des eaux usées domestiques par source d'émission à l'échelle de l'habitation[END_REF].

Figure 2.

Load distribution in blackwater in L.pers -1 .day -1 for the volume (without taking flushes into account), and in g .pers -1 .day -1 for the other variables The main contributors of suspended organic matter were faeces and toilet paper. Urine was the main contributor of nutrients. Toilet paper made up nearly 50% of SS. Heavy metals, when assayed, came mostly from service piping. The micropollutants identified came from pharmaceuticals and their metabolites, preferentially eliminated in urine. The presence of pathogens in the blackwater contributions is very often associated with faeces and the contamination of other sources by them.

About half the organic matter contained in blackwater comes from faeces and more than 30% from toilet paper. Hydrolysed nitrogen comes essentially from urine; phosphorus comes equally from urine and faeces.

Greywater 52 datasets were used to characterize greywater. They include effluents from personal care and effluents from food-related and upkeep activities. Data related to personal hygiene are more abundant. To evaluate of the contribution of each water end-use, various methods are implemented through bibliography. Long and fastidious surveys are generally required. Among them, some can use 'direct' monitoring by assessing the production of effluents combined by on-site sampling. Others imply 'indirect' monitoring by following selective consumption of drinking water uses by dairy surveys or flow meters and/or modelling the use of household fixtures and appliances.

Variability of greywater composition (Table 1) occurs at several scales, with main different habits at social, temporal and spatial scales. The average production of wastewater is 86 L per person per day, with about 47% attributed to personal care and 53% to food-related and cleaning activities. Physically and chemically, greywater composition presents low values of BOD 5 , COD, SS and nutrients, but with very broad ranges of variations. Comparing the different sources of greywater (bathroom, kitchen and laundry), a qualitative difference is seen for BOD 5 , COD and SS concentrations. Laundry effluents (BOD 5 : 567 mg.L -1 ) are more concentrated than bathroom effluents (BOD 5: 131 mg.L -1 ); even so, mass pollution from personal care represents 20% of greywater.

Reconstituted wastewaters

From all previous considerations, a proposal of domestic wastewater reconstitution is presented (table 2). Domestic wastewater reconstitution presented below is compared to National datas. A complementary reconstitution has been also realized [START_REF] Eme | Composition des eaux usées domestiques par source d'émission à l'échelle de l'habitation[END_REF] cumulating blackwater and greywater datasets. but is not presented here. This second reconstitution had permit to validate previous results. Domestic wastewater cumulated loads achieved respect the same order of magnitude as the average composition of domestic wastewater met in small communities (< 2000 PE) measured at the wastewater treatment plant.

Table 2. Reconstitution of the quantity and quality of domestic wastewater from collected data (expressed in L.pers -1 .d -1 and in g.pers -1 .d -1 ). Variable in L.pers -1 .d -1 or g.pers -1 .d

-1 .d -1 b) from Mercoiret, L., 2010 and considering 1 inhab.d -1 in BOD 5 = 1 Person Equivalent.d -1
The contribution of greywater is greater in volume. Faeces and toilet paper supply most SS and organic matter, with an appreciable contribution from greywater arising from food-related and cleaning activities. Nutrients mostly come from urine (nitrogen), and laundry water, faeces and urine (phosphorus).

This study underlines that greywater forms at least 25% of domestic wastewater pollution (except for nitrogen). Its volume contribution is always dominant, even when flush volume is not optimized.

Biodegradability and nutrient balance for biological treatment

Data presented come from the literature, and as complete datasets are lacking, only minima, means and maxima are considered. In the presence of nutrients, the COD/BOD 5 ratio is a measure of how much easily total biodegradable organic matter is present in effluent. The COD/BOD 5 ratios in the data collected suggest that urine is most easily biodegraded, followed by faeces and then greywater, with a broad dispersion of data for this last type of effluent.

The absence of data for BOD ultimate or inert residue limits the characterization of the overall biodegradability of the effluents. The biodegradability and balanced organic matter and nutrients of human excreta seem to favour biological treatment. However, additional analysis is necessary to integrate, in particular, BOD ultimate and inert residue. Figure 3 illustrates the TN/BOD5 and TP/BOD5 ratios for the different effluents generated at the domestic scale. An evaluation of the nutrient balance of effluents, represented by the ratios BOD 5 :N,P, indicates their suitability for treatment: the regular nutrient deficiency of greywater makes it a poor medium for the bacterial growth necessary for its biological treatment.

CONCLUSION

This domestic wastewater characterization considers maximum household uses such as human excretion (urine and faeces), toilet paper use, kitchen effluents, bathroom effluents and laundry effluents.

The reconstitution of domestic wastewater using cumulated data from emission source gives values of the same order of magnitude as those for domestic wastewater in small communities. However, care must be taken to differentiate between person and inhabitant: confusion is apparent in the studies considered, some taking into account occupancy of inhabitants, others not.

Protocol homogeneity between different studies would facilitate average wastewater characterization and improve the understanding of processes. Differences in protocols (in particular for the characterization of SS and for BOD 5 , with few publications stating whether or not allylthiourea (ATU) was used) must be more fully taken into account to make a finer estimation of true wastewater composition.

The evaluation of the nutritional balance of effluents, represented by the ratios BOD 5 :N,P, allows an estimate of their potential responsiveness to biological treatment: the regular deficiency in nutrients of such greywater makes it unable to support the bacterial growth necessary for its biological treatment.

These conclusions are drawn from the average and extreme values of existing datasets. Household consumption is changing: this database will need to be extended for each type of effluent to integrate changing user behaviour and new regulations, and refine the technical adaptations required for the treatment and gainful re-use of each of these effluents.

Figure 3 .

 3 Figure 3. Domestic effluents and biological treatment (all data collected)

Table 1 .

 1 Composition of greywater from data collected

				Data collected 1	Range of variation 2
	Parameter	Unit	average	number of values	minimum maximum
	pH		-	7.5	23	6.1	9.6
	Conductivity	µS.cm -1	561	11	65	3000
	Turbidity	NTU	69	18	5	462
	DM			582	7	44	879
	SS			89	20	20	361
	BOD 5			221	27	20	756
	COD			362	29	25	1583
	TOC			99	10	10	600
	TN			14	17	3	75
	OrgaN		7	1	7	7
	+ -N 2-N NH 4 NO 3	mg.L -1	3 3	2 11	1 0	13 10
	KN		1	9	0	27
	TP			4	10	0	11
	PO 4	3--P		12	15	0	101
	K			9	1	5	23
	S			72	1	18	72
	Surfactants		13	5	0	118
			1: averaged average literature values collected;
			2: minimum and maximum of all the data collected

13eme congres spécialisé IWA on Small Water and wastewater Systems, Athènes, Grèce, 14-16 sept 2016

ACKNOWLEDGMENTS

The authors thank Onema (the French National Agency for Water and Aquatic Ecosystems) for providing financial support for this work.


Maud Vanpoulle
email: maud.vanpoulle@wanadoo.fr

Being innovative regarding the sensitive question of accidents in mountain sports: prevention opportunities provided by experience feedback methods applied to accident and near-miss sequences

Introduction

The effectiveness of sport accidents prevention is often considered in terms of communication strategies, in relation with the good enunciation, the correct reception, and ideally, the appropriation of prevention messages and safe methods by participants.

The accuracy of these strategies depends on thorough knowledge of accident frequencies, of typical circumstances and risk factors, and of the origins of accident sequences [START_REF] Bahr | Understanding injury mechanism : a key component of preventing injuries in sport[END_REF][START_REF] Rasmussen | Proactive Risk Management in a Dynamic Society[END_REF].

Unfortunately, according to recent studies on mountain leisure and recreation [START_REF] Soulé | Accidentologie des sports de montagne : État des lieux, diagnostic et préconisations[END_REF], the knowledge of accident facts, causes, and consequences in mountain sports seems perfectible. More than the quantity of information produced, sometimes important, the fragmentation of sources, the heterogeneous methodologies used to collect information, and the data availability, are problematic for a meaningful use of accident data. Corporative, institutional, methodological or judicial stakes are pregnant when it comes to accidents and can partly explain this fragmented picture of accidentology (Soulé et al., 2015).

With this in mind, we present here an alternative way: incidentology. The study of not only accidents, but also of incidents (or near-miss sequences), is liable to lessen some of the blocks to accident reporting and to circumvent some of the stakes at play. It appears as a somewhat dedramatized way to improve knowledge of accident sequences. Inspired by experience feedback methods as used in industrial settings 1 , it consists in grasping the preventive value of problematic situations, which could have escalated to an accident but where worse outcomes have been avoided, without having to face the emotional and juridical charge inherent to accidents. Moreover, incidents, much more frequent than accidents (not to say commonplace), provide a greater pool of data to comprehend accidentology .

Accident reporting and feedback on outdoor and/or mountain accidents have a long history in North America where, to only cite the most famous, Accident in North American Mountaineering (ANAM) publishes reports every year from the American Alpine Club (AAC) and the Alpine Club of Canada (ACC). The purpose is to transform these stories into learning situations for anyone willing to grasp their preventive value; with the hope that the seldom fact of knowing about them will have a positive impact on the reader's behaviour.

Although all the existing accident and incident reporting systems provide interesting insights on accident sequences, most of them lack detailed information on the situations to enable thorough analysis of the data, and thus meaningful experience sharing and preventive approaches improvement.

After having detailed the theoretical and conceptual background of experience feedback methods regarding accident analysis, we will intend to offer a comprehensive, international overview of existing accident and near-miss reporting systems in the field of mountain sports. Based on the presented systems, on risk analysis theories, and on various test phases among participants, we will then propose recommendations to create a comprehensive accident and incident reporting system to allow in-depth, multi-1 Analysis of accidents or incidents to turn them into learning opportunities to improve safety.

Background theory on experience feedback methods applied to incidents and near-miss sequences

When applied to sport situations, cyndynics methods [START_REF] Kervern | L'archipel du danger : introduction aux cindyniques[END_REF] and system-based interpretations show complex forms of causality, allowing a deep understanding of accident situations [START_REF] Vignac | Les perspectives préventives offertes par l'incidentologie des sports pratiqués dans les milieux à risque[END_REF]. This multifactor, process, and systemic approach can be applied a posteriori (post-accident), or a priori, in an anticipation perspective [START_REF] Soulé | Cyndinique Sportive : Une Approche Interdisciplinaire Des Accidents De Sport[END_REF]. For [START_REF] Lagadec | La gestion des crises[END_REF], accidents always "give warnings", in forms of dysfunctions or incidents. It is thus important to look at these incidents, although they may seem meaningless or disturbing, as do experience feedback methods used in at-risk industrial settings (nuclear, aero spatial) or transports.

Experience feedback is a process composed of various steps: collecting and memorising information on accidents, treatment of this data, transmission of the results in order to share the experience thus formulated [START_REF] Valancogne | La défense en profondeur[END_REF][START_REF] Bal | Dossier sur la sûreté de fonctionnement[END_REF]. [START_REF] Wybo | Méthodologie de partage d'expérience de gestion d'incidents[END_REF] add the idea of collective learning, echoing the concepts of a learning organisation [START_REF] Argyris | Apprentissage organisationnel. Théorie, méthode, pratique[END_REF]: "Experience feedback consists in using the development of an event as an opportunity to collect individual experiences of several actors to join them into a collective experience. Experience feedback must allow grasping of the dynamic representation of situations to better understand past situations, and allow sharing of the so acquired experience in managing risks and crisis".

Experience feedback goes beyond the only awareness of accidents or incidents within an organization, it enables reflexing upon experience and formulating learnings via the added meaning provided by analysis. Although experience sharing is often already in place in an unofficial way within groups, Van Wassenhove and Garbolino ( 2008) stress the need to structure its cycle to enhance its preventive value. [START_REF] Weill-Fassina | Analyse des accidents du travail, gestion des risques et prévention[END_REF] mention that this work can be done on accidents as well as on incidents, which happened in normal or disorganised situations. Near-misses, also called close calls or incidents, are considered by [START_REF] Van Der Schaaf | Development of a near-miss management system at a chemical process plant[END_REF] as "any situation in which a sequence of events was interrupted, preventing the occurrence of potentially serious consequences ". In other words, when an incident occurs, one must keep in mind that slight circumstantial changes could have led to much more serious consequences [START_REF] Ives | Near miss reporting pitfalls for nuclear plants[END_REF][START_REF] Gambino | Near miss, an untapped database to find root causes[END_REF]. In an anticipation strategy, incidents should be considered as forerunner signs of hazards that must not be overlooked [START_REF] Vaughan | The Challenger launch decision: Risky culture, technology, and deviance at NASA[END_REF].

As the product of a non-completed accident sequence, incidents provide insights on accident causes, and circumstances, just as well as accidents themselves. They comprise, all, or part of the ingredients of an accident sequence, without the physical and emotional damages. Thus, they make the testimonials easier and lessen some of the judicial and emotional stakes involved with accident reporting. Furthermore, they are liable to enlighten which prevention barriers did work, allowing the situation to maintain a balanced state (in the sense of non-accidental, see [START_REF] Rasmussen | Proactive Risk Management in a Dynamic Society[END_REF], and which ones did not work.

Inspired of the Swiss cheese model [START_REF] Reason | Managing the Risks of Organisational Accidents[END_REF], the following figure sums up the learning opportunities of incidents. When an accident happens, it means that none of the prevention barriers worked. In the case of a near-miss, the danger crosses some of the barriers but is stopped by others, before reaching its goal. To finish, as already highlighted by Bird in 19742 , incidents are a lot more common than accidents, providing a greater pool of data to study accidentology from. More numerous than accidents, with less consequences, a lighter emotional and judicial charge, incidents make for an undeniable source of preventive inspiration [START_REF] Lecoze | Etude et recherche DRA 37 Retour d'expérience, rapport final d'opération b, presque accidents et risque d'accident majeur : état de l'art[END_REF].

Overview of mountain sports accident and incident reporting systems

Eight accidents and/or incidents reporting systems have been identified worldwide. In this section, they are synthetically described. The design of the forms, their degree of directivity, the categories used for sorting risk factors, and the type of analysis provided are tackled. The following table summarizes this information. The Canadian ANAM report form is very detailed, entailing a multifactor approach and questioning both environmental and human factors.

Some of the stories are very detailed, providing a blow by blow account of the whole incident/accident sequence. This reveals key precursor elements in the origin of accidents: unplanned separation of the group, delay in starting the climb, marginal route errors, unsuitable or insufficient equipment, etc. Such richness is paradoxically likely to entail a limit since the profusion of information may overwhelm readers.

On an analytic point of view, most reporting systems stick to descriptive facts and publish a very brief with few comments on appropriateness of decision, often for understandable liability concerns. Certain organisations (ANAM, Canadian Avalanche Center) publish a synthesis of accidental trends on a regular basis.

We either have really specific systems, which provide detailed environmental factors analysis, mostly on avalanche risks, or broad systems with few analytic elements.

Problematic

To base prevention measures on thorough accident and incident knowledge there is a need for a standardized, common, and broadly used experience sharing platform on accidents and incidents in mountain sports. We need to go from an invention, a method experienced in the industrial setting (experience feedback), to a practical tool used by mountain enthusiasts to report their accidents and near-misses, and to consult others'.

Integrating experience feedback methods, existing mountain accident-incident reporting systems, multi-factors, systemic approaches to accident analysis, and practitioners expectations, how can we create a functional, in depth, accident and incident reporting system? The stake is to go from theories and ideas to a practical tool, and to question the modalities of its socialization.

Proposing a new accident and incident reporting platform

Based on these different forms, on questionnaire methodologies in psycho-social sciences [START_REF] Peterson | Constructing effective questionnaires[END_REF][START_REF] Podsakoff | Common method biases in behavioral research: a critical review of the literature and recommended remedies[END_REF]Salancik, 1984), and on previous knowledge on most recurrent risk factors in mountainous accidents (Soulé et al., 2015;[START_REF] Mccammon | Evidence of heuristic traps in recreational avalanche accidents[END_REF][START_REF] Mccammon | Heuristic traps in recreational avalanche accidents: Evidence and implications[END_REF] American. Among them, 7 are mountain professionals, and the majority (55%) consider themselves able to take someone of lower experience with them in the concerned activity.

It starts with an introduction presenting the objectives of such a platform, its advantages and how it works. Then observable characteristics of the respondent and the event (experience level, nature of the event, activity, number of participants…) are tackled through close-ended questions.

Thirdly, the respondent is asked to openly describe what happened. According to Salancik (1984) and [START_REF] Peterson | Constructing effective questionnaires[END_REF], it is important to place open-ended, general questions first, and then go into more details, in order not to influence the respondent's first interpretation. Therefore, we then ask the respondent to deepen his interpretation by presenting potential risk factors (group dynamics, trip preparation, knowledge of conditions beforehand, risk assessment throughout trip…) to consider and comment on.

These aspects were defined based on human factors theories [START_REF] Mccammon | Evidence of heuristic traps in recreational avalanche accidents[END_REF][START_REF] Mccammon | Heuristic traps in recreational avalanche accidents: Evidence and implications[END_REF]Cierco & Debouck, 2013) and on the study of several hundreds accident reports (see Soulé et al., 2015). We followed a semi open-ended question format for this section, inspired of the ACC ANAM (Alpine Club of Canada form for Accidents in North American Mountaineering) report form, that allows guiding the respondent's attention on specific aspects without conforming his answers. These items were originally separated in two parts: before and during the trip, but the tests showed that it generated a lot of repetitions so they were gathered into one. Finally, a conclusion part was added, between the two test phases, following the same semi-open format, questioning the potential changes provoked by the event on the participant's practice. This part seems to allow for a focus on the preventive learnings drawn by the participant. It triggers interesting answers such as "I will be more aware of risks and careful about the conditions before going. I will be more patient to wait for good conditions and partner" or "I need to learn to read maps and practice avalanche victims search".

The questionnaire presented herein is a result of a compromise between:

-the camptocamp expectations and its former accident report form; this led, for example, to include accidents, instead of merely narrowing the scope to incidents innovation in terms of "any new approach, practice, or intervention, or any new product implemented to improve a situation or resolve a social problem, and having found takers at the institutions, organisations, and communities level" [START_REF] Bouchard | Recherche en sciences humaines et sociales et innovations sociales. Contribution à une politique de l'immatériel[END_REF]. It constitutes a social innovation in the sense that it aims at going from an invention, ideas, and theories (inspired by experience feedback methods), to an innovation, appropriated, used but also improved by practitioners. In facts "ordinary" users, partly formed by the camptocamp community, are to be considered actors of this innovation, and are involved at each stage of the project to co-create a platform transforming itself as it becomes a social practice. Users' feedback was sought to implement the form, which was transformed as the network evolved (decision to work with camptocamp, for example), and the platform is meant to keep evolving as users nourish it with new reports and use it as a tool to improve their own practices. Thus, innovations evolve with the configuration of the network of actors carrying them.

To socialize this project, the appropriation of the tool by the practitioners is an important stake. A focused communication about the platform objectives and advantages of participating needs to be done to involve mountain enthusiasts. In fact, being part of such a collaborative platform allows users to learn from others' experience, but also from experts: technical comments will be published (UIAA, Petzl), and a scientific analysis of the reports will be made available periodically.

This platform follows a double preventive objective. First, the reports will be public, eventually linked to a camptocamp topo or outing, to allow participants to know about specific environmental hazards in a route or area, grasping the raw preventive value of reports.

In a longer-term preventive goal, such a shared accident/incident reports bank provides a great pool of scientific data to study accidentology from. Scientific analysis will thus be able to bring a meaningful plus-value by modelling the hazardous trends identified in the reports, allowing to base preventive measures on accidentology knowledge.

A work on explaining near-misses, and on the advantages of sharing our experiences, in an accessible, easy to understand way, needs to be done in order to shift the view of accidents and incidents from something negative and sometimes shameful, to a learning opportunity that we, as a member of the mountain community, ought to share.

The current stake is therefore to transform an invention (experience feedback) into an innovation, appropriated, used and transformed by practitioners as a tool to improve their practices.

Conclusion

The work presented here gives a first version of an accident-incident experience sharing system in mountain sports, meant to keep evolving as it becomes socially used. It The question of giving back to the participants who share their experience, and thus a certain intimacy, with the community has to be raised. Beyond the direct use of the platform, where participant can learn from public reports, technical advices will be published and a periodical scientific analysis will be made. How can we generalize hundreds of extraordinarily heterogeneous tales without overwriting the heuristic value of each story? Can we draw general preventive conclusions without risking over generalization?

  factors and system-based analysis of reports, and ultimately propose a first version of such a system. On one hand, this applied research tackles methods that look innovative in the field of mountain hazards prevention; on the other hand, it constitutes in itself a social innovation, since it currently results in the implementation of an online, openaccess, participative platform enhancing the preventive use of gathered experience feedbacks. With the support of such institutions as the Petzl Foundation, the Camptocamp community and the UIAA (International Union of Mountain Federations), it eventually aims to provide an alternative way of improving the prevention of accidents in mountain areas.

Fig. 1 :

 1 Fig. 1: Prevention barriers and near-misses (Lecoze & Lim, 2004)

  we implemented the following report form: http://www.camptocamp.org/articles/697210/fr/base-serac-de-recits-d-incidents-etaccidents This questionnaire has gone through different test phases. It was first tested in an informal way, seeking one on one feedback from 5 participants (ski-mountaineers and rock-climbers). It was then tested online among 53 participants, both French and North

(

  as initially envisaged by the research team and the Petzl Fundation) -the Petzl foundation, which funded the new version of the camptocamp website.As a counterpart, the camptocamp association had to develop and implement, technically speaking, an ambitious, efficient, and users friendly platform dedicated to the accidentology of mountain sports -scientific expectations; the research team involved in this project intended to get sufficiently detailed data to make an in depth analysis possible -the contributors' acceptance in terms of time needed to submit a record (with the will to keep it as low as possible); in spite of the stakeholders' curiosity, the length needed to answer could reasonably not exceed 20 minutes overall…5. Socializing the innovation to implement a public accident-incident reports database in mountain sportsThis questionnaire, implemented by the L-Vis research laboratory, is eventually based on practitioners' reactions, on mountain professionals and federal organizers advices (national and international: Fédération française des clubs alpins de montagne, Alpine Club of Canada), with the support of the UIAA and the Petzl foundation. It is to be put online on the camptocamp website for any practitioner to report his experience and to openly consult others'. We have here a network integrating the university research field, the federal sport movement, a company foundation and the main collaborative website of the mountain community, forming a broad, plural, and solid collective. All of these actors seek general interest and are financially disinterested. The composition of this network allows sharing of technical (Internet and websites expertise, technical knowledge of mountain sports and practitioners, communication skills), of financial (Petzl Foundation), and of scientific (research team) means. With 44 400 members the camptocamp community constitutes a great base to launch what constitutes a social

  highlights the perspectives offered by studying near-misses as well as accidents, using experience feedback concepts and methods, and it allows basing a practical tool on theoretical concepts. It questions the modalities of socializing what constitutes an innovation.

Table 1 :

 1 Synthetic description of accident and incident reporting systems in mountain sportsTwo trends can be noticed. First, we find very open forms more or less narrowed to a general question on facts description. Second, there are some more directive forms,

		Alpine	near-	Alpine	Camptocamp (France)	ANENA	NWAC	CAC (Canadian	ANAM, AAM	ANAM, ACC (Alpine Club of
		miss (USA)	Sicherheit		(Association	(Northwest	Avalanche	(Accidents in North	Canada) (Canada)
				(Suisse)		Nationale pour l'Étude de la Neige	Avalanche Center) (USA)	Center) (Canada)	American Mountaineering,
						et des Avalanches)			American Alpine
						(France)			Club) (USA)
	Directivity	Low directivity.	Low directivity.	One descriptive open	Very directive.	Very directive.	Very directive	A very directive	Directive. Close-ended
		One descriptive	One descriptive	question	Close-ended	Close-ended	and fact-	first part on	questions followed by
		open question	open question		questions on	questions.	oriented. Close-	primary cause and	several semi-open and
		(what		and boxes on		numerous factors,		ended questions.	triggering event	open-ended questions
		happened?)	various risk		particularly on			followed by a
				factors to check.		snow stability and			descriptive open
						environmental			question.
						aspects.
	Taxonomies	No categories to	Possible risk	No categories. The	Classification of	Classification of	Environmental	No classification	Classification of risk
		fill in but		factors are listed	reports are classified by	causes and factors	risk factors	conditions		factors, attenuating factors
		suggestions	without an	activity (ski, rock-	through close-	(environment	(snow and		and rescue process (the
		upon risk		obvious	climbing, ice-climbing,…)	ended questions.	and snow, group,	weather) are		respondent is asked to
		factors to		categorization	and by primary cause		triggering	classified		comment the facts on the
		consider in the		(avalanche, rock/ice		events) through			following aspects:
		report			fall/wind/lightning, fall		close-ended			supervision, equipment,
		(leadership,		of a person, physical		question			environment, activity
		decision-			inability)					appropriateness
		making and							experience and training,
		exercise of								behaviour, group
		judgement)							dynamics, decision-
										making, communication,
										and leadership)
	Approach/analysis Suggests a		The reports are	No analysis provided	Multi-factor	Multi-factor	Human factors	Short analysis	Multifactor approach with
		multifactor	not public but		approach.	approach. The	are purposely	provided by	an emphasis on human
		approach but no	the Swiss Alpine		Analysis focused	respondent's	set aside. The	ANAM.	factors. It goes beyond
		analysis is		Club publishes		on environmental	interpretation is	focus is on snow		obvious factors, but the
		provided		short "safety		aspects	led by the	aspects.		analysis made is the same
				notes" based on			categories			than ANAM, AAM
				the reports.			proposed.

According toBird's pyramid (1974), established upon accident statistics in the American industry in 1969, the probability that an accident occurs increases with the number or incidents and close-calls. Each accident would then be linked to hundreds of minor accidents occurred previously; as many precursors which could have acted as alarm systems. Although developed for the industrial setting, this point of view suggests interesting perspectives.