### Strutt Help

Ground Attenuation    1/1

Strutt|Environmental Noise|Ground Attenuation inserts attenuation (dB) into the active row of the worksheet.

#### ISO9613.2

Input required is source and receiver heights, source to receiver distance and ground factors.

This method of calculating the ground effect is applicable only to ground which is approximately flat, either horizontally or with a constant slope.
Ground factors to be used are:
Hard ground: 0
Porous ground: 1
Mixed ground: 0 - 1

The ground effect is calculated by separating the distance between the source and receiver into 3 regions as:

The total ground attenuation for each octave band is calculated as:

A_(gr) = A_s + A_r + A_m

Where,
A_s is the source region attenuation
A_r is the receiver region attenuation
A_m is the middle region attenuation

A_s, A_r and A_m are calculated using:

Nominal midband frequency, Hz A_s or A_r*, dB A_m, dB
63 -1.5 -3q**
125 -1.5 + G xx a'(h) -3q(1 - G_m)
250 -1.5 + G xx b'(h)
500 -1.5 + G xx c'(h)
1000 -1.5 + G xx d'(h)
2000 -1.5(1 - G)
4000 -1.5(1 - G)
8000 -1.5(1 - G)

Notes:

a'(h) = 1.5 + 3.0 xx e^(-0.12(h-5)^2)(1-e^(-d_P//50)) + 5.7 xx e^(-0.09h^2)(1 - e^(-2.8 xx 10^-6 xx d_P^2))

b'(h) = 1.5 + 8.6 xx e^(-0.09h^2)(1-e^(-d_P//50))

c'(h) = 1.5 + 14.0 xx e^(-0.46h^2)(1-e^(-d_P//50))

d'(h) = 1.5 + 5.0 xx e^(-0.9h^2)(1-e^(-d_P//50))

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* For calculating A_s, take G = G_s and h = h_s. For calculating A_r, take G = G_r and h = h_r. See 7.3.1 (ISO 9613.2) for values of G for various ground surfaces.

** {:(q = 0 , when \ d_P <= 30 (h_s + h_r)),(q = 1 - (30(h_s + h_r))/d_P, when \ d_P > 30(h_s + h_r) ):}, where d_P is the source-to-receiver distance, in metres, projected onto the ground planes

#### CONCAWE

Note this correction is only valid for source-receiver distances greater than 100 m.

Ground effects, K_3, are calculated as a function of distance for each octave band where:

63 Hz: K_3 = 33.4 - 35.04log_10 d + 9.159(log_10 d)^2 - 0.3508(log_10 d)^3

125 Hz: K_3 = 8.96 - 35.8log_10 d + 20.4(log_10 d)^2 - 2.85(log_10 d)^3

250 Hz: K_3 = -64.2 + 48.6log_10 d - 9.53(log_10 d)^2 + 0.634(log_10 d)^3

500 Hz: K_3 = -74.9 + 82.23log_10 d - 26.921(log_10 d)^2 + 2.9258(log_10 d)^3

1 kHz: K_3 = -100.1 + 104.68log_10 d - 34.693(log_10 d)^2 + 3.8068(log_10 d)^3

2 kHz: K_3 = -7 + 3.5log_10 d

4 kHz: K_3 = -16.9 + 6.7log_10 d

#### CNOSSOS EU noise propagation model

CNOSSOS is developed for propagation above varying-height ground planes, and uses the concept of equivalent height z_s,z_r - i.e. the source and receiver heights are defined relative to the average height of the ground plane, and are not necessarily the same as the local source/receiver heights h_s,h_r:

As well as the source-receiver geometry, the CNOSSOS model uses the ground factor G over the ground plane (i.e. proportion of porous ground). In cases where the ground plane consists of multiple ground types, the average bar G (weighted by the extent of each ground type) should be used.

Typical values of G are as follows:

• Soft, uncompacted ground (pasture, loose soil); snow etc: G=1.0
• Compacted soft ground (lawns, park areas): G=0.7
• Compacted dense ground (gravel road, compacted soil): G=0.3
• Hard surfaces (asphalt, concrete): G=0.0
The ground factor G_S for the source region (the zone within a horizontal distance <= 30(z_S+z_R) from the source) is also required, to account for propagation where the source and receiver are close, where the reflection properties of the source region dominate.

In cases where the source and receiver are close (within 30(z_s+z_r) horizontal distance), Strutt modifies the user-entered average ground factor as follows:

bar G prime = bar G (d_(SR))/(30(z_S+z_R))+G_s (1-d_(SR)/(30(z_s+z_r)))

d_(SR) is the horizontal source-receiver distance along the average ground plane

The CNOSSOS model predicts the attenuation under neutral (or "homogenous") atmospheric conditions (constant sound speed where sound propagation paths are straight rays), as well as adverse (or "favourable") conditions where a sound speed gradient results in curved ray paths.

The effect of the curved ray paths is to increase the average propagation height and reduce the strength of the ground effect.

Under neutral conditions, the ground attenuation is calculated as:

A_(ground) = -"Max" {(-10 log_10 (4 k^2/d_(SR)^2(z_s^2-sqrt((2 C_f)/k) z_s + C_f/k)*(z_r^2-sqrt((2 C_f)/k)z_r + C_f/k))),(-3(1-bar G_w)) :}

where:
k is the wavenumber
C_f=d_(SR) (1+3 w d_(SR) e^(-sqrt(w d_(SR))))/(1+w d_(SR))
w = 0.0185 (f^2.5 bar G_w^2.6)/(f^1.5 bar G_w^2.6 + 1.3*10^3 f^0.75 bar G_w^1.3 + 1.16*10^6)
bar G_w is either the corrected ground factor bar G prime or the uncorrected ground factor bar G, depending on the calculation type:

(The CNOSSOS ground module is also used by the CNOSSOS diffraction module to calculate the ground reflection from the source to the diffraction edge Delta_(ground(S,O)) and from the diffraction edge to the receiver Delta_(ground(O,R); the ground factor term is taken as either the modified or the unmodified term as outlined in the table below)

Under adverse conditions, the ground attenuation is calculated as:
A_(ground) = -"Max" {(-10 log_10 (4 k^2/d_(SR)^2(hat z_s ^2-sqrt((2 C_f)/k) hat z_s + C_f/k)*(hat z_r^2-sqrt((2 C_f)/k) hat z_r + C_f/k))),(-3(1-bar G_m) \ " for " \ d_(SR)<=30(z_s+z_r)),(-3(1-bar G_m)*(1+2*(1-(30(z_s+z_r))/d_(SR))) " otherwise") :}

where:
hat z_s = z_s+ Delta z_s + Delta z_t is the effective source height under adverse conditions

hat z_r = z_r + Delta z_r + Delta z_t is the effective receiver height under adverse conditions

Delta z_s = a_0(z_s/(z_s+z_r))d_(SR)^2/2 is the change in effective source height due to the curvature of the sound paths

Delta z_r = a_0(z_r/(z_s+z_r))d_(SR)^2/2 is the change in effective receiver height due to the curvature of the sound paths

Delta z_t = 6*10^-3 d_(SR)/(z_s+z_r) is the change in effective source/receiver height due to atmospheric turbulence

a_0 is the inverse of the radius of curvature of the sound paths. A default value of a_0 = 2*10^-4 is provided in CNOSSOS, however this could potentially be user-modified in Strutt if required.

bar G_m is either the corrected ground factor bar G prime or the uncorrected ground factor bar G, depending on the calculation type.

References:

• ISO 9613-2 Acoustics - Attenuation of sound during propagation outdoors - Part 2: General method of calculation, pp5 - 7
• CONCAWE: Manning, C.J., The propagation of noise from petroleum and petrochemical complexes to neighbouring communities p.87
• CNOSSOS: Stylianos Kephalopoulos, Marco Paviotti, Fabienne Anfosso-Lédée (2012) Common Noise Assessment Methods in Europe (CNOSSOS-EU) EUR 25379 EN. Luxembourg: Publications Office of the European Union, 2012, 180 pp.