# Impact and Control of Reflected Noise from an Overpass Bottom
## 2 Materials and Methods
### Sound Field Simulation  
In this study, Cadna A v. 4.3.144 (DataKustik, Germany) was applied for sound field simulation and analysis via a 3D sound field model. The German RLS-90 traffic noise model adopted in Cadna A noise prediction and assessment software is an approved noise prediction model by the Technical Regulation for Road Traffic Noise Assessment Models promulgated by Taiwan Environmental Protection Administration (EPA). In RLS-90 traffic noise model, the Emission Level (L\({}_{\rm m,e}\)) at the position 25 m horizontally from the centerline of the outer lane and 4 m vertically from the road surface was calculated with traffic flow (M) and heavy vehicle ratio (P) and modified with maximum allowable speed correct value (D\({}_{\rm v}\)), pavement type correct value (D\({}_{\rm Stro}\)), road longitudinal slope correct value (D\({}_{\rm Stg}\)), and reflection on particular conditions correct value (D\({}_{\rm E}\)):  
\[{\rm L}_{\rm m,e}={\rm L}_{\rm m}{}^{(25)}+{\rm D}_{\rm v}+{\rm D}_{\rm Stro}+{ \rm D}_{\rm Stg}+{\rm D}_{\rm E}\]  
where the boundary conditions of L\({}_{\rm m}{}^{(25)}\) are described as follows:  
1. Twenty five meters horizontally from the centerline of the outer lane and 2.25 m vertically from the road surface;  
Figure 4: Site conditions and layout of Site C. (**a**) The different structure of road (the elevated road intersects with the bottom noise emission road); (**b**) plane view; and (**c**) cross section profile.  
The road was paved with non-corrugated mastic asphalt;  
3. The maximum allowable speed is 100 km/h;  
4. The road longitudinal slope is less than 5%;  
5. The free sound propagation on a flat and straight road is a straight line.  
The calculation formula is as follows:  
\[\mathrm{L_{m}}^{(25)}=37.3+10\times\log[\mathrm{M}\times(1+0.082\times\mathrm{ P})]\]  
where M is the average hour traffic flow (vs/h).  
P is heavy vehicle ratio (vehicles with a net weight of 2.8 tons and above) (%).  
The average traffic noise level on the straight lane (\(\mathrm{L_{m}}\)) was calculated with considerations of the following factors: Emission Level (\(\mathrm{L_{m,e}}\)), amount of change due to distance and air absorption (\(\mathrm{D_{s\perp}}\)), amount of change due to road surface and whether reduction (\(\mathrm{D_{BM}}\)), and amount of change due to terrain and construction measures (\(\mathrm{D_{B}}\)):  
\[\mathrm{L_{m}}=\mathrm{L_{m,e}}+\mathrm{D_{s\perp}}+\mathrm{D_{BM}}+\mathrm{D_ {B}}\]  
Input parameters for the software include: Terrain, ground level, road width, road elevation, number of lanes, average vehicle speed, traffic flow (light and heavy vehicles), road pavement type, obstacles (noise barriers and buildings), and bridge bottom reflection.  
This study included parameters of the surrounding terrain features of each site into 3D sound field modelling. The purpose of sound field model calibration was to make sure that the simulated results derived from this model were close to the actual situations (according to Taiwan's regulations, the difference between the simulated value and measured value should be less than \(\pm\)3 dB(A). Therefore, related traffic parameters were entered into RLS-90 road noise prediction model to simulate the noise level at various measurement sites. When the simulated noise levels produced by the software were close to the actual noise levels, it meant that the simulated results were credible. After taking into consideration of the parameters on the shape of the elevated road and sound path, as well as proving the credibility of the noise model after on-site measurement data verification, the noise model can serve as a reference for determining the influence level of reflected noise on nearby residence and planning and designing of absorbing material setups for the overpass bottom.