Appendix C Direct Wayside Noise Model
C1.
INTRODUCTION
This section details the wayside noise modeling for the potential operational railway noise impact from the KCRC Sheung Shui to Lok Ma Chau Spur Line. The direct wayside noise model adopted in the operational noise assessment for the proposed Spur Line was described. The airborne noise due to the railway operation was predicted using the computer model, which was subsequently energy summed with the structure-radiated noise to determine the total wayside noise level.
C1.1
Theory
The numerical modelling used by RAYNOISE Rev. 3.0 is based on the principles of geometrical acoustics which assumes that sound waves behave as sound rays. Acoustic rays are reflected by solid surfaces and lose part of their energy at each rebound. The classical computer algorithms used to predict the sound field produced by the sources and model the reflection from physical structures are Mirror Image Sources Method (MISM) and Ray Tracing Method (RTM).
The MISM uses virtual mirror image sources to trace back sound reflection paths from the receiver to the sound source. In the RTM, the energy emitted by the sound source is assumed to be distributed into discrete number of sound rays. Each ray travels at the speed of sound and collides with the walls, floor and surfaces where it is reflected in accordance with the law of specular reflection. The energy level of the rays decrease at reflections by means of wall absorption and progressively as it travels by means of air absorption. The energy contribution of the rays crossing the receiver defined give a measure of the sound pressure level. The method accounts for losses due to spherical divergence.
The computer model employs hybrid algorithms, namely the Conical Beam Method and the Triangular Beam Method, which are MISM/RTM mixtures. RAYNOISE Rev. 3.0 is based on these methods to simulate the acoustical behavior of any arbitrary enclosed or open space. In the analysis, 6000 rays per sphere with the maximum order of reflection of 70 are used to ensure accuracy in prediction. Furthermore, diffraction and transmission of sound are also accounted for in the model. Diffraction of sound is modeled by tracing first-order diffraction paths according to the dominant diffraction edges defined in the geometry model. The energy contribution is calculated with the Kurze-Anderson formula given as Equations C.1 and C.2:
(Equation
C.1)
where DLB is the attenuation due to screen obstruction(dB) ; and
N, the Fresnel number, is defined as
(Equation C.2)
with P.L.D. being the Path Length Difference between the direct and the diffracted sound paths.
C2.
MODEL CALIBRATION
The wayside noise
modeling focuses on the prediction of the direct airborne noise impact from the
passenger trains utilizing the computer model, "RAYNOISE Rev. 3.0".
The direct wayside noise component was quantified and added to the
structure-radiated component to assess the total noise impact on the wayside
due to train operation on the Spur Line.
C2.1
Direct Wayside Noise Model
The numerical
modeling used by RAYNOISE is based on the principles of geometrical acoustics
and described in Section 3.3.2.
A three-dimensional geometry model of the viaduct was built in accordance to the Spur Line initial trackform design for Sonneville Low Vibration Track Viaduct Trackform. For all the single train compartment modeled, the physical dimensions of the East Rail Mid Life Refurbished were adopted. Figure C.1 and C.2 detail the dimensions of the geometry models for the single and twin viaduct. Three material properties were defined for the model, namely Concrete for the viaduct, Reflector for the train bodies and Plenum for the plenum system. Suitable material properties were assigned to the respective elements of the model. The absorption coefficients adopted for the concrete and reflector are typical data as prescribed in the computer prediction model while for the plenum material, the absorption coefficients for the sound absorption treatments used on the West Rail Viaduct plena and parapet noise barrier [14] were used. The sound absorption coefficients for different materials used in the wayside noise model were tabulated in Table C1, C2 and C3.
Table C1 Sound
Absorption Coefficients, a, for
Concrete adopted in the Wayside Noise model
|
Frequency, Hz |
63 |
125 |
250 |
500 |
1000 |
2000 |
4000 |
8000 |
|
Absorption Coefficient, a |
0.03 |
0.04 |
0.05 |
0.06 |
0.06 |
0.07 |
0.09 |
0.09 |
Table C2 Sound
Absorption Coefficients, a, for
Reflector adopted in the Wayside Noise Model
|
Frequency, Hz |
63 |
125 |
250 |
500 |
1000 |
2000 |
4000 |
8000 |
|
Absorption Coefficient, a |
0.15 |
0.14 |
0.11 |
0.10 |
0.06 |
0.05 |
0.05 |
0.05 |
Table C3 Sound
Absorption Coefficients, a, for
Plenum adopted in the Wayside Noise Model
|
Frequency, Hz |
63 |
125 |
250 |
500 |
1000 |
2000 |
4000 |
8000 |
|
Absorption Coefficient, a |
0.20 |
0.20 |
0.60 |
0.75 |
0.85 |
0.90 |
0.90 |
0.90 |
C2.2
Calibration Procedure
The two major direct airborne noise sources, namely the noise due to wheel rail interaction and from the air-conditioning system on the train, were modelled as point sources with characteristics conforming to a free-field spherical source. Since the contribution of the auxilliary equipment on the train to the wayside noise impact was outweighed by that of the dominant noise sources, i.e. the wheel rail interaction and air-conditioning system, these minor sources were not included in the wayside noise model. In the calibration and the subsequent modeling, 6000 rays per source were used with the reflection order of 70. The model calibration enables the evaluation of effectiveness of the plenum noise reduction system incorporated and the mitigation measures proposed to alleviate the impact of the airborne noise on the wayside.
The source term of the air-conditioning system on the car used in the modeling was extracted from the results of measurement carried out by AEC in the noise study of the East Rail refurbished trains for KCRC[1]. The sound power levels of the air-conditioning units on the top of the train car are tabulated in Table C4 below.
Table
C4 Sound
Power Level of Air-Conditioning System
|
Frequency, Hz |
63 |
125 |
250 |
500 |
1000 |
2000 |
4000 |
8000 |
|
Sound Power Level Lw , dB |
95.1 |
97.2 |
102.6 |
96.7 |
97.8 |
95.2 |
89.1 |
80.7 |
The two air-conditioning units on the top of each train compartment and eight wheels of the bogies under each car were modelled as point sources. After consultation with KCRC, the location of the wheel rail interaction source was set at 150mm above the top of rail. The location of these ten noise sources according to the East Rail Refurbished train dimensions was detailed in Figure C.3 Figure C.4 shows the geometry model for the calibration with all the omnidirectional sources marked as black circles.
The model was calibrated to the reference direct wayside noise level of (Lmax) 86.3 dB(A) at 25m setback from the track centerline. The calibration result in terms of A-weighted spectrum was detailed in Figure C.5. The results as noise contour plots in horizontal and vertical planes, are available upon request. The calibrated set of sound power level for the wheel rail interaction to be adopted in the wayside noise modelling was as follows.
Table
C5 Sound
Power Level of Wheel Rail Interaction
|
Frequency, Hz |
63 |
125 |
250 |
500 |
1000 |
2000 |
4000 |
8000 |
|
Sound Power Level Lw , dB(A) |
94.8 |
99.5 |
103.7 |
105.4 |
111.1 |
114.2 |
104.1 |
93.5 |
C3.
PREDICTION OF WAYSIDE NOISE LEVEL FOR VIADUCT SECTIONS
C3.1
Single Viaduct Model Result
The geometry model for single viaduct section is illustrated in Figure C.6. The ten point sources for the air-conditioning system and wheel rail interaction were marked as black circles. From the modeling results, the noise level due to direct wayside noise component is (Lmax) 71.0dB(A) at Standard Reference Conditions (SRC), i.e. 25m from the track centerline level with top of rail, to the outboard side and (Lmax) 69.2dB(A) at SRC to the inboard side. The outboard side is determined as the wayside adjacent to the track carrying the train. The inboard side is defined as the trackside to the opposite direction. The predicted noise levels for the single viaduct model for the inboard and outboard side expressed as A-weighted spectrum is illustrated in Figure C.7.
The results in terms of noise contour plot in horizontal and vertical planes are available upon request. The sound field pattern at the plenum outlet and around the single viaduct is also available on request.
C3.2
Twin Viaduct Model Result
The geometry model for one car in twin viaduct section is illustrated in Figure C.8. The ten point sources for the air-conditioning system and wheel rail interaction were shown as black circles. According to the modeling results, the noise level due to direct wayside noise component is (Lmax) 72.7 dB(A) at SRC to the outboard side whereas at SRC to inboard side the direct wayside noise component is (Lmax) 69.7 dB(A). The attenuation resulted from the twin viaduct noise reduction system with under-walkway plenum and central plenum is 15.4 dB(A). The predicted noise levels for the single viaduct model for the inboard and outboard side expressed as A-weighted spectrum is illustrated in Figure C.9. The results in terms of noise contour plot in horizontal and vertical planes were detailed are available upon request. The sound field pattern at the plenum outlet and around the twin viaduct is also available upon request.
The geometry model for two cars in twin viaduct section is illustrated in Figure C.10. The ten point sources for the air-conditioning system and wheel rail interaction were illustrated as black circles. For the twin viaduct – two cars model, the noise level due to direct wayside noise component is (Lmax) 75.2 dB(A) at SRC to the outboard side and the inboard side. The predicted noise levels for the single viaduct model for the inboard and outboard side expressed as A-weighted spectrum is illustrated in Figure C.11. The results in terms of noise contour plot in horizontal and vertical planes sound field pattern at the plenum outlet and around the twin viaduct are available upon request.
C3.3
Wayside Noise Level
For the at-grade section of the Spur Line alignment, the conditions without mitigation measures as that of a ballast track will be used. The East Rail rolling stock reference noise level of (Lmax) 86.3dB(A) at 25m from track centerline level with top of rail for a train passby at 100 km/h was taken as the source noise level. Since the wayside noise for at-grade section is dominated by the airborne noise component, the correction applied to which with respect to the variation train speed is taken as 30log(speed/100).
For the viaduct section, the direct wayside noise level is determined by the calibrated computer model. In the wayside noise modelling for the Spur Line, it was assumed that the East Rail Mid Life Refurbished Trains (which is not equipped with bogie skirts and undercar absorption) operated on the viaduct utilizing Sonneville Low Vibration Track Viaduct Trackform was modeled. From the results, the highest noise level due to the direct wayside noise component modeled at the Standard Reference Conditions of 25 m setback from track centerline level with top of rail is (Lmax) 75.2 dB(A) for 2 trains passby on the twin viaduct section at the same time. Moreover, the noise attenuation achieved by the plenum system is estimated up to 15.3dB(A) for the direct wayside noise component alone. Since only one train compartment of the train is modelled, equation C.3 is applied to convert the modeling results to the direct wayside noise level due to passby of a 12-car train.
(Equation C.3)
The highest direct wayside noise levels modelled for the single viaduct is 73.6dB(A) in Lmax whereas for the twin viaduct is 75.3dB(A) in Lmax for the outbound side. Due to uncertainty of viaduct geometry, the higher air borne source noise level of the outbound plenum was adopted for both outbound and inbound as a worst case approach. The plenum attenuation achieved is 15.2 dB(A) for single viaduct and 13.5dB(A) for twin viaduct.
where lo = train length with known noise level (m),
l = train length for predicted noise level (m),
d = perpendicular distance from line source (m),
The total wayside noise level is obtained as energy sum of the direct noise and structure-radiated noise component. From the Study of the MTRC Lantau Airport Railway Measurement Study, the structure-radiated noise for the Sonneville Low Vibration Track Viaduct Trackform with dynamic stiffness of 13kN/mm is 66.5dB(A) at 25m from track centerline level with top of rail for a train passby at 100km/h. The correction for train speed variation assumed for the structure-radiated noise is 25log(speed/130). The wayside noise spectrum for train operation on viaduct obtained was shown in Figure C.12. The structure-radiated noise level estimated for the twin viaduct is applied to determine the total wayside noise for both the single viaduct and twin viaduct sections in view of the fact that it represents the worst case. The total wayside noise levels determined at 25m from nearest track centerline level with top of rail for a train passby at a speed of 100km/h are tabulated in Table C6. For twin viaduct sections, it is 75.8 dB(A) in Lmax.
Table C6 Total
Wayside Noise Level at Standard Reference Conditions determined for Viaduct
Sections
|
Viaduct Type |
Direct Noise, Lmax, dB(A) |
Structure-radiated Noise, Lmax,
dB(A) |
Total Wayside Noise at SRC, Lmax,
dB(A) |
|
Single |
73.6 |
66.5 |
74.4 |
|
Twin |
75.3 |
66.5 |
75.8 |