Road traffic noise prediction model ASJ RTN-Model 2008 proposed by the Acoustical Society of Japan - Part 3: Calculation model of sound propagation

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1 Road traffic noise prediction model AJ RTN-Model 2008 proposed by the Acoustical ociety of Japan - art 3: Calculation model of sound propagation hinichi akamoto a Institute of Industrial cience, The University of Tokyo Komaba Meguro-ku Tokyo Japan Akinori Fukushima b NEW Environmental Design Inc Mizuki-dori Hyogo-ku Kobe Hyogo Japan Kohei amamoto c Kobayasi Institute of hysical Research Higashi-Motomachi Kokubunji Tokyo Japan ABTRACT As the third part of AJ RTN-Model 2008, calculation model of sound propagation is presented. The model is an up-grade version of the previous model that was proposed in This model is basically developed as a practical calculation model based on Geometrical Acoustics and it contains effects of shielding by barriers or buildings, ground surface, air absorption and meteorological condition. Based on newly obtained knowledge, several improvements were made on the calculation method of sound diffraction and reflection to develop the model. The procedures of application to roads with special cases such as interchange, signalized intersection, double deck viaduct, road tunnel, semi-underground road and roads with built-up areas are also included. 1. INTRDUCTIN The road traffic noise prediction model AJ RTN-Model 2008 employs an engineering method for the calculation of sound propagation. The method, by which continuous equivalent A- weighted sound pressure levels at roadside areas are calculated, was developed by modifying the previous model named AJ RTN-model 2003 based on newly obtained knowledge. As for correction for diffraction effect, the calculation methods for dense asphalt concrete and drainage asphalt concrete were improved based on the spectral characteristics of recent road traffic noise and the correction for structure borne noise of viaduct was newly provided. a address: sakamo@iis.u-tokyo.ac.jp

2 2. GENERAL RCEDURE An engineering calculation method, by which an A-weighted sound pressure level at a prediction point is directly calculated, is based on the distance attenuation (inverse squared law) on a hemifree field, considering sound attenuation due to diffraction, ground effect and meteorological effect by adding their correction terms. A. Basic Equation For an omni-directional point source located on a road, A-weighted sound pressure level L A at a prediction point is given by the following equation. L = LW 8 20lgr, (1) A A cor where, L WA is the A-weighted sound power level of a running vehicle [db], r is the direct distance [m], cor is a correction term [db]. The correction is given as follows. Δ L =, (2) cor dif grnd air where, dif is the correction term of diffraction [db], grnd is the correction term of ground effect [db], air is the correction term of air absorption [db]. B. Correction Terms a. Correction for diffraction effect uch shielding objects as various kinds of noise barriers, embankment, and so on, provide noise reduction due to diffraction effects. In the AJ RTN-Model 2008, several kinds of barriers and shielding objects and a factor which affect sound diffraction effect are listed up as shown in Table 1 and the calculation methods for their corrections are provided. Each correction term is calculated based on the fundamental correction term d which is determined with the path length difference. Table 1: Definition of correction terms for diffraction effect Fundamental correction for diffraction effect d ingle diffraction over a barrier dif,sb Diffraction over a barrier with its finite length dif,fb Embankment / building dif,dd Multiple barriers (installed with sufficient distance) dif,db, dif,tb Edge-overhang barrier dif,hb Edge-modified barrier dif,emb Low-height barrier (its height is around 1 m) dif,low Transmitted sound through a barrier dif,trans aa. Calculation of fundamental correction for diffraction effect d d is given by the following numerical expression as, 20 10lg( cspec ) cspec d = sinh ( cspec ) 0 cspec < 1. (3) min[ 0, sinh ( ) ] spec < 0 + c spec c Here, the sign of is made to be minus when the source can be seen from the prediction point, as shown in Fig.1. The value of c spec is given as is shown in Table 2. Relationship between d and is shown in Fig. 2.

3 Direct path l=, Diffraction path r=+ is invisible from is visible from =l r>0 = (l r) <0 Fig. 1: Definition of path length difference over a barrier d [db] 密粒舗装 Dense asphalt concrete 排水性舗装 Drainage asphalt concrete 排水性舗装 Drainage ( asphalt 一年未満 concrete ) (within 1 year after pavement) invisible 見えない場合 case (>0) ( > 0) -5 visible 見える場合 case (<0) ( < 0) Diffraction path difference [m] d [db] invisible 見えない場合 case ( (>0) > > 0) 0) -5 visible 見える場合 case (<0) ( < ( 0) < 0) Diffraction 回折経路差 path path difference [m] [m] [m] (a) Road traffic noise (b) tructure borne noise Fig. 2: Correction chart for d Note 1: Values of the correction for structure borne noise are valid for all types of the structures. Note 2: When considering a directivity of sound radiation from a vehicle, sound power level is corrected with the directivity in a direction connecting the source and diffraction points. ab. Correction for single barrier dif,sb The correction term for single diffraction dif,sb, which is applied to single straight barriers and road shoulders, is given as the same value of d. Δ L = (4) dif, sb d Table 2: Values of c spec Category of noise c spec Road Dense asphalt concrete 0.85 traffic Drainage asphalt concrete 0.75 noise within 1 year 0.65 tructure borne noise 0.50 Curbs, guardrails and guard cables on flat roads shall be neglected. Note 1: In the case where the correction for the diffraction exceeds -30 db, transmitting sound through the barrier may not be negligible. In such cases, careful attention should be paid for designing of a noise barrier. Γ1 Γ2 Γ3 A B Calculate propagation without a barrier Finite length barrier Calculate correction for diffraction over the top Γ4 Γ0 Γ5 Γ6 Γ7 Γ8 Fig. 3: one-path method Fig. 4: Field separation for calculating the diffraction in the method synthesizing contributions of top and side diffraction ac. Correction for barrier with finite length dif,fb As calculation methods of the correction for a barrier with finite length, a simple one-path method and a method synthesizing contributions of top and side diffraction are proposed. In the one-path method, only the diffraction effect over the top of the barrier is considered. For C D

4 calculating L Aeq when a source moves along a road as shown in Fig. 3, the correction is determined being dependent on the relationship of the positions between the source and prediction point. dif,sb is considered when the shortest path of passes over the finite length barrier, whereas such a diffraction effect is neglected when the does not pass over the barrier. n the other hand, by the method synthesizing contributions of top and side diffraction, the correction term diff,fb is calculated as follows. Viaduct, bank and cut roads Flat road dif,fb dif, fb = = 10 lg { ( ) ( )} , (5) =, (6) where, ijk... means the correction for diffraction of a hemi-infinite barrier where areas of Γ i, Γ j, Γ k, in Fig. 4 are simultaneously opening state. ad. Correction of double diffraction dif,dd for bank and building Correction of double diffraction dif,dd by a thick obstacles as embankments and buildings, as shown in Fig. 5, is given regardless of their surface impedance and opening angle of the wedge, as follows. Δ L dif,dd = + 5 Ⅲ,, (7) + 5 ⅠⅡ, Ⅲ, where, ABC and ABC means a correction for diffraction d and path length difference, respectively, when the propagating path is ABC. Ⅰ Ⅱ Ⅲ < (a) (b) < Fig. 5: Diffraction over an embankment Fig. 6: Diffraction path over double barriers ae. Correction of multiple diffraction dif,db, dif,tb Calculation method of a correction for double diffraction by two barriers which are installed with a sufficient distance for neglecting the influence of reflections between the barriers (around 5 m or more) is provided as, dif,db =. (8) < As an extension of the above method, calculation method of correction for triple diffraction by three barriers is also provided in the AJ RTN-Model af. Correction for edge-overhang barrier dif,hb Noise barriers with their top edges are bent are generally referred as the edge-overhang barriers. Correction of diffraction for the edge-overhang barriers shall be calculated as a dif,sb for an imaginary straight barrier shown in Fig. 7. Note 1: ufficient attention is required when the height of the imaginary straight barrier may become extremely high. Edge-overhang barriers with their lengths of overhangs being 1 m or less can be substituted by thick barriers as shown in Fig. 8.

5 Imaginary Edge-overhang barrier straight barrier Fig. 7: Imaginary barrier for an edge-overhang barrier Fig. 8: Approximation of edge-overhang barrier ag. Correction for edge-modified barrier dif,hb Well developed noise barriers having some acoustical devices as sound absorbers on their top edges in order to reduce diffraction sound are generally referred as the edge-modified barriers. The correction for diffraction of the edge-modified barrier shall be calculated as, Δ L =, (9) dif, emb dif,hb c where, dif,hb is a correction for diffraction for an imaginary straight barrier, c is an additional correction related the attenuation effect at the edge of barriers. c should be obtained by experiments or numerical analysis 1. ah. Correction for low-height barrier dif,low For the low-height barrier (its height is around 1 m) on a flat road, the correction for diffraction dif,low shall be calculated by applying the concept of insertion loss as, Δ L =, (10) dif, low d,1 d,0 where, d,1, d,0 are d for imaginary barriers with their top being 1 and 0 in Fig. 9, respectively. ai. Correction for diffraction considering transmitted sound through the barrier dif,trans When the contribution of transmitted sound through a barrier is taken into consideration, the following correction for diffraction dif,trans is used. dif,trans d,1 /10 ( dif,slit RA,RTN ) /10 { + 10 } Δ L = 10lg 10, (11) where, d,1 is d for a barrier with its top being 1 in Fig. 10, dif,slit is the correction for the slit diffraction, R A,RTN is the sound transmission loss of the barrier in which the A-weighted spectrum of the road traffic noise is taken into consideration. b. Correction for ground effect When sound propagates from a road to a prediction point, sound attenuates due to various ground effects of road surfaces, road slope and roadside ground surface. The correction for the excess attenuation due to the ground effect grnd is calculated as follows. n grnd = grnd, i, (12) 0 grnd, i 1 i = 1 K = 0 i lg ( r r ) i c, i Fig. 9: Calculation of correction for diffraction of low height barrier ri r r < r i c, i c, i 1 Barrier 0 Fig. 10: Transmitted sound through a barrier Aperture, (13) 1 0 Fig. 11: A slit diffraction through a barrier

6 where, grnd,i is a correction for ground effect on the i-th ground surface [db], K i is a coefficient that characterizes the attenuation rate per doubling of distance, r i is a distance, r c,i is distance where excess attenuation on the i-th ground effect starts increasing. K i and r c,i are given by expressions for three types of ground with finite impedance 2. c. Correction for air absorption air Correction due to air absorption air is specified on the basis of the standard atmospheric condition of 20 C temperature and of 60 % relative humidity and it is given as follows. 2 r r r air = , (14) where, r is the distance [m] between a source point and a prediction point. The correction is obtained based on I d. Calculation method of sound reflection For prediction of road traffic noise at roadside areas of depressed or semi-underground roads and overhead/flat road juxtaposition sections, sound reflection should be taken into consideration. For the treatment of sound reflection, two kinds of calculation methods are prepared in this model. ne is specular reflection applied to flat surface with sufficiently large size in comparison with the wavelength and the other is scattered reflection employed to uneven surface. da. pecular reflection method uppose a source, prediction point and a flat hemi-infinite reflection surface with its edge being as shown in Fig. 12 (a). A reflection sound from the surface is regarded as diffraction sound which reaches from a mirror image source for via a diffraction edge for an image barrier as shown in Fig. 12 (b). The reflection sound L A,refl is calculated as follows. LA, refl = LW A 8 20lgr refl abs, (15) where refl, abs are corrections for reflection and absorption by the surface, respectively. The correction for reflection refl is calculated from the following r, which is based on Babinet s principle for energy field and calculated as follows (see Fig. 13) lg( cspec ) cspec 1 r = , (16) sinh {( cspec ) } 0 cspec < 1 where c spec is the same values as shown in Table. 2. For a hemi-infinite reflection surface, refl is calculated as follows. 3 Δ Lrefl = r [ is invisible from ] (17) r 10 Δ L = 10lg 1 10 [ is visible from ] (18) refl ( ) hemi-infinite surface Fig.12: Reflection from a hemi-infinite surface r imaginary barrier r [db] -40 Dense asphalt concrete -35 Drainage asphalt concrete Drainage asphalt concrete -30 (within 1 year after pavement) ath length difference [m] Fig.13: Relationship between r and

7 For a flat reflection surface with finite width, the slit method 3 shall be adopted. The correction refl,slit due to the diffraction of slit opened between the edge 1 and 2 shown in Fig.14 is specified as follows. refl,slit refl,1 10 refl, Δ L = 10lg10, (19) where, refl,1 and refl,2 are corrections for reflection for the edges 1 and 2, respectively. Based on the same concept, in the AJ RTN-Model 2008, the calculation method of the reflection sound from a rectangular surface such as a building façade is also shown Fig.14: Barrier edges considered in the slit method db. cattered reflection method The assumption of this method is that a wall does not reflect sound specularly, but in a completely diffuse manner, i.e., according to Lambert s law. For the arrangement in Fig.15, total A-weighted sound pressure level of reflected sounds L Arefl is given as follows. cosθ cosθ L = W 13 σ 1 2 A, refl L A + 10lg d 2 2 r1 r2 abs. (20) dc. Correction for surface absorption For the calculation of reflection sound, absorption of the surface can be also considered. A correction for absorption of a surface abs shall be calculated as follows. = lg(1 ), (21) abs 10 α A, RTN where, α A,RTN is an absorption coefficient which is calculated under consideration of spectral characteristic of road traffic noise. In the AJ RTN-Model 2008, values of α A,RTN are given as Table 3. Table 3: Absorption coefficient for materials Δ σ Material r 1 θ1 n θ 2 r 2 Fig.15: cattered reflection α A,RTN Backing sound absorption panel for overhead road 0.90 ide panel of sound absorption for depressed road 0.85 Absorptive noise barrier (Unified metal panel) 0.75 Absorptive material for exterior of building 0.75 Absorptive material for a pier 0.70 Concrete and asphalt concrete e. Meteorological effect Meteorological effect is generally difficult to be included in an engineering model, because it is a complicated phenomenon caused by wind profile and temperature profile above ground. As is the same consideration in AJ RTN-Model 2003, wind effect is provided as an expected deviation of L Aeq due to vector wind REDICTIN METHD FR ECIAL RAD CAE AJ RTN-Model 2008 provides prediction methods for special road cases such as an interchange, a signalized intersection, a depressed or semi-underground road, an overhead road and double deck viaduct. The methods are fundamentally based on the general calculation procedure

8 described above, but some special treatments may be required. Here is some more information needed in the prediction. A. Interchange and Intersection The model provides acceleration and deceleration of speed of vehicles as shown in Table 4 to calculate speed profile in computer programming. The service time for paying highway charge is specified for noise exposure time and it is shown in Table 5. Table 4: Acceleration and deceleration of vehicles running on an interchange [m/s 2 ] mall vehicle Heavy vehicle Category of vehicle asseng Light Middle Heavy er car truck truck truck Acceleration Deceleration Table 5: ervice time at tollgate Entrance (Receiving a card) 6 s Exit (Toll collection by cash) 14 s Toll collection by fixed charge 8 s B. ignalized Intersection 4 There exist many signalized intersections along general roads in urban areas, and individual vehicle moves with frequent starting, acceleration, steady running, deceleration and stopping on the roads. The behavior is complicated to be described in detail, but it can be roughly considered to be non-steady flow. Based on such a simplification, noise level at a signalized intersection can be simply calculated as a sum of L Aeq s which are calculated for the two crossing roads by applying sound power level for non-steady flow. NTE: In reality, sound power level of individual vehicle changes to considerable extent according to the signal schedules. In order to make detailed investigation on the change of noise level due to signal schedules, more detailed calculation methods are necessary. Aroad Fig.16: Two crossing roads at a signalized intersection B road C. Road Tunnel In the model, two hypothetical sources are assumed. ne is a point source that represents a direct contribution of sound from a vehicle in tunnel. The other is a surface source that represents residual sound with multiple reflections on the walls inside the tunnel. The model is developed on the basis of sound energy balance inside the tunnel 5. D. Depressed and emi-underground Road The problems in the prediction are the treatment of multiple sound reflections between the retained walls. To cope with the problem, (1) Image sources method, (2) Hypothetical point source method 6,7 and (3) Wave-based numerical analysis such as two-dimensional BEM or FDTD are provided in the model. E. verhead Road and Double Deck Viaduct Noise reflection from the underside of an overhead roadway and a double deck viaduct is provided in the AJ model. The reflection is treated by slit method or scattered reflection method as described in 2.B.d, the selection of which depends on the roughness of the surface. In a special case where multiple reflections affect, 2D-BEM or 2D-FDTD is to be used.

9 4. RAD TRAFFIC NIE IN BUILD-U AREA Building is an obstacle that shields and reflects noise. To calculate the effect of building, both sound reflection and diffraction should be taken into account. The AJ model provides two kinds of calculation methods: one is a deductive model based on the method described in the section 2 for a single building, and the other is an empirical model for relatively high density build-up area. A. Noise behind a ingle Building The L Aeq behind a single building shall be calculated as sum of contributions of a direct sound, diffraction sounds and reflection sounds by applying the calculation methods of correction for diffraction and reflection by a barrier with finite length. Here, the building is modeled as a rectangle object without sound absorption. This method shall be also applied to calculation of L Aeq for build-up area where the buildings are located at sufficient intervals that the influence of multiple reflections can be ignored. B. Noise in Build-up Areas For a build-up area with high density, it is much difficult to calculate sound propagation theoretically. In the previous version of the AJ RTN-Model, a method for calculating averaged L Aeq in an assessment section 8. In the revised version of the Model, a calculation method for L Aeq at a specific position in a build-up area is newly provided. L Aeq at a specific position in a build-up area shall be calculated as sum of A-weighted equivalent continuous sound pressure level in case without any buildings, L Aeq,0, and a correction for attenuation by buildings, bldgs. L = L (22) Aeq Aeq,0 bldgs The numerical expressions of the correction bldgs are empirically deduced based on experimental results and are calculated with several parameters characterizing a relationship between a build-up area and a prediction point - a height of a prediction point, total viewing angle of an objective road, shortest distance between a prediction point and the road and a height of buildings 9. The detailed procedure is described in the literature 9. REFERENCE 1 T. kubo, T. Matsumoto, K. amamoto,. Funahashi, T. kura, K. Nakasaki and M. amamoto, Noise barriers with diffraction-reducing devices on top edge: ropagation prediction applying intrinsic efficiencies determination by impulse-response measurement, roc. of Inter-noise 2009 (2009). 2 K. amamoto, M. amashita and T. Mukai Revised expression of vehicle noise propagation over ground, J. Acoust. oc. Jpn. (E), 15, (1994). 3 K. amamoto, K. oshihisa, T. Miyake, T. Tajika and H. Tachibana, Road traffic noise prediction model AJ RTN-Model 2003 proposed by the Acoustical ociety of Japan art 3: Calculation model of sound propagation, roc. of 18 th ICA, IV (2004) 4. Namikawa, H. oshinaga, T. Tajika,. shino, K. oshihisa and K. amamoto, imple method for predicting noise in the vicinity of signalized intersections, roc. of Inter-noise 2009 (2009). 5 T. Miyake, K. Takagi, K. amamoto, H. Tachibana, rediction of road traffic noise around tunnel mouth, roc. of Inter-noise 2000, , (2000) 6. akamoto and H. Tachibana, Experimental study on calculation model of road traffic noise radiated from semiunderground roads, roc. of 18 th ICA, IV , (2004). 7. akamoto, A. Fukushima and K. amamoto, Numerical investigation on radiation characteristics of road traffic noise from semi-underground structure, roc. of Inter-noise 2009 (2009). 8 K. Uesaka, H. hnishi, T. Chiba and K. Takagi, rediction and evaluation method for road traffic noise in builtup areas, roc. of Inter-noise 2000, (2000). 9 K. Fujimoto, rediction of insertion loss of road traffic noise caused by detached houses at the area facing road, roc. of Inter-noise 2009 (2009).