Sound absorption mechanism of porous asphalt pavement

Transcription

1 J. Acoust. Soc. Jpn. (E) 20, 1 (1999) Sound absorption mechanism of porous asphalt pavement Michiyuki Yamaguchi,* Hiroshi Nakagawa,** and Takuya Mizuno*** * Bridgestone Corporation, 1, Kashio-cho, Totsuka-ku, Yokohama, Japan ** Nittobo Acoustic Engineering Co., Ltd., Midori, Sumida-ku, Tokyo, Japan *** Fukuda Road Construction Co., Ltd., 2031, Nakanoshima-ogata, Nishikawa-machi, Nishikanbara-gun, Niigata, Japan (Received 30 May 1998) The aim of this study is to clarify the sound absorption mechanism of porous asphalt pavement by comparing it with those of the glass wool and urethane foam etc., which are well-known porous sound absorbing materials. In order to elucidate the sound absorption mechanism, we measured the propagation constant and characteristic impedance of a sound wave traveling inside the material under the plane wave incident condition using an acoustic tube, and calculated the behavior of the sound waves in the material based on the measurement results. We concluded that the sound absorption of the porous asphalt pavement is caused by the following mechanism. Because the sound waves in the porous asphalt pavement material generally used in Japan exhibit less attenuation than those in glass wool or flexible urethane foam, the multi-reflected waves remain inside the material, and interfere with the wave reflected from the front surface of the material. In particular, in the frequency range below 1 khz where the sound waves exhibit less attenuation inside the material, the sound absorption coefficient peaks at a frequency at which the antiphase condition is satisfied between the multi-reflective waves in the material and the sound wave reflected from the front surface of the material. Furthermore, the frequency range above 1 khz is characterized in that since the attenuation gradually increases while the interference decreases, the sound absorption coefficient of the porous asphalt pavement is determined by its surface reflective wave. Keywords : Porous asphalt, Sound absorption mechanism, Propagation constant, Characteristic impedance, Interference of sound wave PACS number : Ev 1. INTRODUCTION Although porous asphalt pavement was developed primarily with the aim of preventing traffic accidents caused by slippery roads, its continuous porous structure was also found to have a sound absorbing effect, which makes porous asphalt pavement useful for the reduction of traffic noise. However, many aspects of the sound absorbing mechanism remain to be clarified. Although porous asphalt pavement is effective in reducing traffic noise, it is generally considered that the noise reduction does not depend only on the noise absorbing action of the road surface substructure. It appears that the decrease in tire noise due to the interaction between the tread of a tire and the road surface also contributes much to the noise reduction effect. Accordingly, it is important from the standpoint of noise reduction to clearly distinguish the role of

2 J. Acoust. Soc. Jpn. (E) 20, 1 (1999) the substructure from the role of the interaction between the tread of a tire and the road surface. The author and others have conducted a series of studies on porous asphalt pavement material, focusing on the sound absorption property of the material. In recent years, the sound absorption property of porous asphalt pavement has been the subject of many investigations, and the Porous Asphalt Study Group, sponsored by technological development center, Nagaoka university of technology, has held two conferences and reported the results of related studies.1,2) In addition, studies by Meiarashi, et al.,3-5) a study by Hatanaka, et al.,6) a study by Iwase, et al.,7) etc. have been reported. The present report describes the sound absorption mechanism of porous asphalt pavement to clarify its role as sound absorption material, and also to search for the possibility of enhancing its sound absorptive function. 2. METHOD FOR INVESTIGATING THE SOUND ABSORPTION MECHANISM 2.1 Test Samples Porous asphalt pavement consists of a mixture of Table 1 Test samples.

3 M. YAMAGUCHI et al. : SOUND ABSORPTION MECHANISM OF POROUS ASPHALT PAVEMENT crushed aggregate, sand, and limestone powder, which account for about 95 % of the whole, and modified asphalt binder which accounts for about 5% of the whole. The pavement material is reinforced by making the sand and limestone powder adhere to the surface of the crushed aggregate in order to thicken the film layer of the binder. The porous asphalt material typically used in Japan has a void ratio of about 20 %, and a thickness ranging from 40 mm to 50 mm for general roads. Samples used in this study were prepared in the laboratory using aggregate with a quite commonly used diameter ranging from 13 mm to 5 mm. Various values of void ratio and thickness were used. A number of samples (3 to 6 units) were prepared for each target void ratio and thickness, since we expected that a certain dispersion would occur during preparation. The properties of prepared samples are listed in Table 1. The apparent densities of the samples shown in, the table were obtained in the following manner. The dried samples were weighed with an accuracy of 0.1 g, and their diameter and thickness were measured with an accuracy of 0.1 mm using calipers. For each sample two mutually orthogonal 'arbitrary diameters were measured, and the thickness at two points on each diameter. The average apparent density of the samples was derived by respectively substituting the average cross-section and thickness for A and L in expression (1). Average apparent density of the samples where WS : The average weight of the samples (kg) A : The average cross-section of the samples (m2) L : The average thickness of the samples (m) In addition, the average apparent void ratio was derived from expression (2). Average apparent void ratio of the samples (1) (2) where Dm : The average apparent density of the samples (kg/m3) The theoretical maximum density* (kg/m3) * The virtual density at which the void ratio of a sample consisting of aggregate and asphalt at a certain mixing ratio becomes 0 %. (3) where Wa: The mixing ratio of asphalt (%) Da: The density of asphalt (kg/m3) The density of water at room temperature (103 kg/m3) Wi : The mixing ratio of each aggregate (%) Gi : The specific gravity of each aggregate Here, The first two digits of each test number used in the table, for example 20 of represent the target void ratio, the middle digit represents the target thickness, and the final digit represents the serial number. 2.2 Acoustic Test In order to clarify the acoustic effect of the material, use of the sound absorption coefficient alone is not sufficient to determine the internal structure of the pavement material. It is also necessary to know the state of sound wave propagation in the material. Measurement of the propagation constant and characteristic impedance enables us to determine the state of the reflection of the incident sound waves from the front surface and the attenuation of the sound waves transmitted in the material. The propagation constant and characteristic impedance are representative acoustic properties of a material. They are complex values determined on the assumption that the material is of infinite thickness. The propagation constant represents the state of attenuation and sound wave velocity when a sound wave propagates through the material, while the characteristic impedance corresponds to the ratio of sound pressure to particle velocity at any given point in the material. These characteristic values can be obtained easily in an impedance tube by using two microphones and changing the thickness of the air layer behind the sample to measure the acoustic impedance. An impedance tube method using two microphones was applied to measure the sound absorption coefficient, propagation constant, and characteristic impedance of a sound wave under the condition that a plane wave impinged perpendicularly on the front surface of the sample material. In addition, the measurement was carried out accord-

4 J. Acoust. Soc. Jpn. (E) 20, 1 (1999) respectively. (7) (8) Fig. 1 and Block the diagram sample of the impedance where k : The atmospheric wavelength constant Z0: The atmospheric characteristic impedance As is obvious from the above, the propagation constant and characteristic impedance can be derived from expressions (5) through (8) by replacing one air layer with the other provided behind the sample. Furthermore, the sound absorption coefficient can be derived from the acoustic impedance of the surface of the sample using expression (9). tube adapter. ing to the system using a system introduced by Utsuno, et al.,8) as is shown in Fig Measurement principle The acoustic impedance Z1 at the front surface of a test sample with thickness L can be represented using the acoustic impedance Z2 at the opposite surface of the sample with expression (4). (4) where Zc: The characteristicimpedance γ: Zc The and propagation γ can be constant represented of the sample of the sample. by expressions (5) and (6). (5) (9) Measurement method As described in Paragraph above, in order to obtain the propagation constant and characteristic impedance, it is necessary to measure two types of acoustic impedance of the sample by replacing one air layer with the other. In this study, as shown in Fig. 1, we used an acoustic tube having a movable stiff wall (piston) behind the air layer and a loud speaker toward the front surface of the sample. Then, a pseudo-random sound signal emitted from the loud speaker is received by microphones 1 and 2 so that the transfer function H between the microphones 1 and 2 can be measured using a 2-channel FFT analyzer. Thus, the acoustic impedance Z1 of the sample at the front surface in the acoustic tube using air layer L0 could be derived from expression (10). (6) (10) where Z1 or Z1' : The acoustic impedance of a sample with thickness L plus air layer L0 or L0', which is sandwiched between the sample and the movable piston, as viewed from the front surface of the sample. Further, Z2 or Z2' is the acoustic impedance of a closed tube of air layer L0 or L0' sandwiched between the sample and the movable piston, as viewed from the opposite surface of the sample. They are represented by expressions (7) and (8), 32 where DX : The spacing between microphones LX : The distance between microphone front surface of the sample 1 and 2 1 and the Next, the acoustic impedance of the surface of the sample due to the preparation of air layer L0' behind the sample was obtained in a similar manner, and Zc and crushed tube, tube γ were calculated. aggregate placing may cause Since is not the sample sound well fitted directly leakage asample made of to the impedance in the impedance so that it is difficult to

5 M. YAMAGUCHI et al. : SOUND ABSORPTION MECHANISM OF POROUS ASPHALT PAVEMENT obtain a correct measured value. We, therefore, prepared an adapter as shown in Fig. 1, and placed the sample in the adapter. In order to enhance the fit between the sample and the inner wall of the impedance tube, the sample was wrapped with adhesive fabric tape to eliminate any gap between the inner wall of the tube and the sample. Furthermore, the outer diameter of the sample was reduced to 100 mm. The measurements were made for two different frequency bands. The first frequency band covered the range from 80 to 400 Hz with a sound receiving interval DX of 300 mm and an FFT frequency resolution f of 0.5 Hz, and the second frequency band covered the range from 200 to 2 khz peaks prominently in the frequency range below 1 khz. The sound absorption characteristic in the frequency range above 1 khz differs from that in the frequency range below 1 khz. This result suggests that the sound absorption mechanism differs between the frequencies below and above 1 khz as long as the void ratio is greater than 14 % Relationship between sample thickness and sound absorption coefficient Figures 8, 5, and 9 show the results of measuring the sound absorption coefficient of material with a fixed void ratio (target value : 20 %) and a target material thickness of 30 mm, 60 mm and 90 mm, with a sound receiving interval Dx of 70 mm, and an FFT frequency resolution f of 4 Hz. The sound receiving interval was set in such a way that the first microphone was fixed, while the second microphone was movable. 3. MEASUREMENT RESULTS 3.1 Sound absorption coefficient Relationship between void ratio and sound absorption coefficient Figures 2 through 7 show the measurement results of the sound absorption coefficient of samples of dense asphalt and porous asphalt with a fixed target thickness of 60 mm and with a target void ratio of 14 %, 17 %, 20 %, 23 %, and 26 %, respectively. The curves in the figures indicate that the sound absorption characteristic appears at a,void ratio of 17 % and greater, while the sound absorption coefficient Fig. 3 Sound absorption characteristics of porous asphalt samples (Target void ratio : 14%). Fig. 2 Sound absorption characteristics of dense asphalt samples. Fig. 4 Sound absorption characteristics of porous asphalt samples (Target void ratio : 17%).

6 J. Acoust. Soc. Jpn. (E) 20, 1 (1999) Fig. 5 Sound absorption characteristics of porous asphalt samples (Target void ratio : 20%). Fig. 7 Sound absorption characteristics of porous asphalt samples (Target void ratio : 26%). Fig. 6 Sound absorption characteristics of porous asphalt samples (Target void ratio : 23%). Fig. 8 Sound absorption characteristics of porous asphalt samples (Target thickness : 30 mm). respectively. These figures show that when the thickness is doubled or tripled from 30 mm to 60 mm or 90 mm, the sound absorption peak in the frequency range below 1 khz is shifted down to nearly 1/2 or 1/3 of the original frequency, respectively. This suggests that there is a certain relationship between the sound absorption and the thickness of the sample in the frequency range below 1 khz. 3.2 Acoustic Characteristics of the Material The above-mentioned sound absorption characteristics indicates that there is a difference in the sound absorption patterns of usual porous asphalt pavement material in frequencies below and above 1 khz. In order to investigate possible causes of such a difference, we measured the propagation constant and characteristic impedance of a porous asphalt pavement sample, and for each void ratio shown in Figs. 2 through 7. Figures 10 through 12 show the measurement results for the propagation constant and characteristic impedance. The real part of the propagation constant is the attenuation constant ƒ, which is the attenuation per unit length in the sound wave propagation. Figure 10 shows the attenua-

7 M. YAMAGUCHI et al.: SOUND ABSORPTION MECHANISM OF POROUS ASPHALT PAVEMENT Fig. 11 Phase velocity of sound wave in porous asphalt samples. Fig. 9 Sound absorption characteristics of porous asphalt samples (Target thickness : 90 mm). Fig. 12 Characteristic impedance of porous asphalt samples. Fig. 10 Sound attenuation characteristics in porous asphalt samples. tion per centimeter in units of db. The imaginary part of the propagation constant is the phase constant Ĉ, which can be represented by expression 2 Ĕf / Cm, where Cm is the propagation velocity (phase velocity) of the sound wave in the material, and f is the frequency. Figure 11 shows the phase velocity calculated using this expression. The characteristic impedance Zc is shown with the atmospheric characteristic impedance Z0 used as the reference value Attenuation constant From Fig. 10 and Figs. 2 through 7, it can be seen that the attenuation of sound waves inside the sample is not necessarily marked in the frequency range below 1 khz where the sound absorption coefficient peaks. Although the attenuation increases as the void ratio decreases, it can be inferred that the increase in sound absorption in this frequency range is not due to the attenuation inside the sample. In the frequency range above 1 khz, the attenuation inside the sample gradually increases, and this tendency becomes conspicuous as the void ratio decreases. It can be inferred that the sound absorption in this range is due to the attenuation inside the material Phase velocity As shown in Fig. 11, the phase velocity in the sample drops to about 100 m/s, or less than 1/3 of the atmospheric phase velocity. The phase velocity decreases further as void ratio decreases Characteristic impedance As is obvious from Fig. 12, the characteristic

8 J. Acoust. Soc. Jpn. (E) 20, 1 (1999) impedance is fairly high compared with the atmospheric characteristic impedance. Since the sample material has a stiff skeletal structure with a void ratio as low as less than 26 %, only the air inside the material is considered to be subject to the elastic deformation caused by the sound wave. Accordingly, it can be inferred that the sound particle motion is considerably obstructed by the rigid structure of the sample. 3.3 The Future Problems to Solve The data of the sound absorption coefficient shown in Fig. 2 through 9 exhibits a certain dispersion compared to nominal values. This dispersion cannot be explained by differences in the void ratio and thickness of the sample alone. Therefore, it is necessary to determine the relationship between the internal structure of the sample and the acoustic characteristics. A possible clue to the resolution of a cause of such dispersion is to compare the properties of samples used in our test with the chart prepared by Delany and Bazley9) who experimentally demonstrated, using fabric sound absorbing material, the existence of a certain relationship between the flow resistance, characteristic impedance, and propagation constant. We intend to investigate a possible cause of the dispersion in the future. 4. SOUND WAVE BEHAVIOR IN RELATION TO THE MATERIAL 4.1 Sound Reflection from a Sample with Infinite Thickness The behavior of an incident sound wave on the front surface of the sample in relation to the properties of the sample material, based on experimental values such as the propagation constant, characteristic impedance, etc. Assuming that a sound wave is incident on a sample of infinite thickness, the incident sound pressure pi, the sound pressure Pr reflected from the front surface of the sample, and the sound pressure pt transmitted into the sample can be represented by expressions (11), (12), and (13), respectively.m) The sound pressure amplitude of the incident wave is assumed to be a unit value, whet (13) The distance (depth) of a measured point from the front surface of the sample (m) The atmospheric wavelength constant (radian/m) The atmospheric and material characteristic impedances (N s/ m3) The propagation constant of the material : The attenuation constant of the material (napers/m) (1 naper/m = db/m) The atmospheric and material sound velocities (m/s) Measured values of the propagation constant and characteristic impedance were substituted into expressions (11) through (13) to determine the behaviors of the sound waves. The behaviors of the sound waves of representative samples numbered and , which previously showed the acoustic characteristics described in Section 3.2 are shown in Figs. 13 through 16, the behaviors of the sound wave in the frequency range below 1 khz in which the sound absorption coefficient peaks are shown in Figs. 13 and 15, and the behaviors of the sound waves at a frequency of 1.5 khz are shown in Figs. 14 and 16. Similar results were obtained for the other samples. The following conclusions may be drawn: (1) At the frequency within the frequency range (11) (12) Fig. 13 Sound propagation at most absorbing frequency (568 Hz) of the sample

9 M. YAMAGUCHI et al.: SOUND ABSORPTION MECHANISM OF POROUS ASPHALT PAVEMENT Fig. 14 Sound propagation at 1.5 khz of the sample Fig. 15 Sound propagation at most absorbing frequency (392 Hz) of the sample Fig. 16 Sound propagation at 1.5 khz of the sample below 1 khz at which the sound absorption coefficient peaks, nearly the same quantity of the reflected wave as that of the incident sound wave occur on the front surface of the sample. This reflected wave is somewhat reduced at a frequency of 1.5 khz, and the reflected wave with a greater void ratio generates less reflected wave. (2) At the frequency within the frequency range below 1 khz at which the sound absorption coefficient peaks, the sound wave transmitted through the sample exhibits little attenuation over a distance as small as the thickness of the sample. This tendency is prominent for samples with higher void ratio. (3) At a frequency of 1.5 khz, all the waves transmitted through inside the samples attenuate rapidly. 4.2 Multiple Sound Reflection from a Sample with Finite Thickness As shown in Figs. 13 and 15, at the frequency below 1 khz at which the sound absorption coefficient peaks, the sound waves are propagated in the sample without attenuation. However, since the sample has a finite thickness, the waves arriving at the opposite surface of the sample reflected from that surface, change their directions and return to the front surface of the sample. Moreover, since the opposite surface of the sample is in contact with a stiff wall, which is actually the base layer for the porous asphalt pavement, complete reflection occurs on the opposite surface. Since the samples are nearly 6 cm thick, the pressure of the sound waves that were reflected from the opposite surface of the samples and returned to the front surface corresponds to the sound pressure of the transmitted waves that traveled a distance of 12 cm. As the figures show, because the phase of the reflected waves is opposite to that of the incident wave, the sound waves that are reflected from the opposite surface, returned to the front surface, and are then emitted from the front surface into the air cause destructive antiphase interference with the wave reflected directly from the front surface. Therefore, we attempted to ascertain the effects of such interference through further calculation. When a transmitted wave represented by expression (13) is transmitted to the sample with thickness L, is totally reflected from a stiff wall, and is then returned to the front surface of the sample, the sound pressure by pt0 and particle velocity vt0 of the transmitted wave can be represented by expressions (14) and (15), respectively.

10 J. Acoust. Soc. Jpn. (E) 20, 1 (1999) (14) (15) When this transmitted wave is reflected from the stiff wall and returned to the front surface of the sample, the returned wave is partly reflected from the front surface of the sample back into the sample and the rest is transmitted into the atmosphere. If the sound pressure and particle velocity of the former wave reflected back into the sample and those of the latter wave transmitted into the atmosphere are denoted by pt1, vt1, Pr1, and vr1, they are represented by expressions (16) through (19), respectively, where Pt1 and Pr1 are the sound pressure amplitudes of the reflected and transmitted waves. (16) (17) (18) (19) At x = 0, since the sound pressures and particle velocities of the reflected and transmitted waves must be equal on both sides of the boundary surface, the amplitudes of the sound pressures and those of the particle velocities are represented by expressions (20) and (21), using the preceding expressions (14) through (19). (20) (21) Therefore, the sound pressure amplitude of the reflected wave and that of the transmitted wave on the front surface of the sample are represented by expressions (22) and (23), respectively. (22) (23) Accordingly, when this reflection is repeated N Fig. 17 Sound propagation at most absorbing frequency (880 Hz) of the sample times in the sample sandwiched between the air and the stiff wall, the amplitude of the sound wave ptn that again returns from the front surface to the sample material and that of the sound wave prn that is emitted to the air can be represented by expressions (24) and (25), respectively. (24) (25) Expressions (24) and (25) were used to plot the behaviors of the sound waves at the frequency below 1 khz at which the sound absorption coefficient peaks for the thinnest sample, numbered (void ratio 21.4 %, and thickness 30 mm). The behaviors of the sound waves reflected a number of times (N =1 to 5) in the sample at the abovementioned frequency (880 Hz) are plotted in Fig. 17. The multi-reflected waves ((4)) are partly emitted into the air in the phase opposite to the incident wave ((5)), and destructively interfere with the wave ((2)) directly reflected from the the sample, resulting in the decrease in the total sound pressure at the front surface of the sample ((6)), or resulting in the increase in the sound absorption coefficient. 4.3 Calculation of the Sound Absorption Coefficient The apparent sound absorption coefficient of the porous asphalt sample was derived, based on the above concept, from expression (26) using the sound pressure amplitude obtained on the front surface

11 M. YAMAGUCHI et al.: SOUND ABSORPTION MECHANISM OF POROUS ASPHALT PAVEMENT (x=0) of the sample. (26) The sound absorption coefficient was calculated for three test samples , and under three conditions of sound reflection ; (1) only the direct reflection from the front surface of the sample was considered (i.e. PrN=0), (2) one reflection and (3) five reflections from the opposite surface of the sample material was considered. The results of calculation are shown in Figs. 18 through 20, together with those obtained from expression (9), which are expressed as 'measured' in the figures. sample is taken into consideration, the calculated value approaches the value of the sound absorption coefficient obtained from expression (9). In contrast, if the effects of the waves reflected from the opposite surface on the sound absorption coefficient at frequencies other than the peak frequency are taken into account, the sound absorption coefficient decreases further. It is clear that the reflective wave from the front surface of the sample and those from the opposite surface interfere with each other in this frequency range. On the other hand, in the frequencies higher than the frequency at which the Since the porous asphalt samples have high impedance, the amplitude of the waves reflected from the front surface is large. The sound absorption coefficient calculated from these reflected waves is nearly constant at around % until the frequency reaches a certain value, and then it increases. This phenomenon indicates that the amplitude of the transmitted waves increased in the higher frequency range. Next, by considering the aforementioned prominent peak of the sound absorption coefficient in the frequency range below 1 khz, it is clarified that although the sound absorption coefficient ranges only from about 20 to 30 % if the waves reflected from the opposite surface are not considered as described above, but if these reflected waves are taken into consideration, the aforementioned peak of the sound absorption coefficient appear. Furthermore, if the multi-reflection in the Fig. 19 Comparison of measured absorption coefficient with calculated absorption coefficient of the sample Fig. 18 Comparison of measured absorption coefficient with calculated absorption coefficient of the sample Fig. 20 Comparison of measured absorption coefficient with calculated absorption coefficient of the sample

12 J. Acoust. Soc. Jpn. (E) 20, 1 (1999) sound absorption coefficients of these samples peak and further higher than the frequency at which the sound absorption coefficients of these samples dip, the interference is not so high as that in those lower frequencies although the interference still remains, and the attenuation inside the samples is considerable. In summary, the sound absorption property of the porous asphalt pavement material is divided into two frequency ranges. In the former frequency range, the sound absorption coefficient of the porous asphalt material is determined by the interference between the sound wave reflected from the front surface of the material and that from the opposite surface of the material. In the latter frequency range, the sound absorption coefficient of the material is determined by the attenuation of the sound wave inside the material, proving that the porous asphalt pavement material has such a absorption mechanism as mentioned above. 5. COMPARISON WITH OTHER POROUS MATERIALS Porous asphalt material was compared with various other porous sound absorbing materials including glass wool, flexible urethane foam and another type of porous sound absorbing material made of thin sheets of cloth (apparent density : 220 kg/m3, thickness : 1.6 mm) with an air space (9.5 cm thick) between them (See Fig. 21). In addition, the cloth of the sample consisting of cloth/air-layer/cloth shown in Fig. 21 was prepared integrally so as to entirely cover both the front and back surfaces of the sample. The acoustic characteristics of these porous sound absorbing materials were measured in the same manner as those of the porous asphalt samples. The difference in the sound absorption characteristics between the porous asphalt pavement material and the conventional porous materials is described in the following sections. 5.1 Glass Wool and Flexible Urethane Foam The acoustic characteristics of glass wool samples GW-1 and GW-2, which have apparent densities of 38 kg/m3 and 97 kg/m3 and thicknesses of 50.6 mm and 25.7 mm, are shown in Fig. 22 (measured propagation constant), and Fig. 23 (measured characteristic impedance). The acoustic characteristics of flexible urethane foam samples U-1 and U-2, which have apparent densities of 36 kg/m3 and 35 kg/m3 and thicknesses of 19.4 mm and 19.8 mm are shown Fig. 22 Sound propagation characteristics in the glass wool samples. Fig. 21 Arrangement of the thin cloth/airlayer/thin cloth sample. Fig. 23 Characteristic impedance of the glass wool samples.

13 M. YAMAGUCHI et al.: SOUND ABSORPTION MECHANISM OF POROUS ASPHALT PAVEMENT Fig. 24 Sound propagation characteristics in the flexible urethane foam samples. Fig. 26 Comparison of measured absorption coefficient with calculated absorption coefficient of the glass wool samples. Fig. 25 Characteristic impedance of the flexible urethane foam samples. in Fig. 24 (measured propagation constant), and Fig. 25 (measured characteristic impedance). Comparison of the results for our porous asphalt drain sample with those for the glass wool samples and flexible urethane foam samples shows that the internal sound attenuation characteristic of our porous asphalt sample is similar to those of the latter samples when the void ratio is less than 17 %. From these acoustic characteristics of the glass wool and flexible urethane foam samples, their sound absorption coefficients were calculated for N= 1 and N= 1 to 2 using expressions (24) through (26) in the same manner as for our porous asphalt sample. The results for the glass wool samples are shown in Fig. 26, and those for the flexible urethane foam samples in Figs. 27 and 28, respectively. Each of Fig. 27 Comparison of measured absorption coefficient with calculated absorption coefficient of the flexible urethane foam sample (U-1). these figures includes the case in which the waves reflected from the opposite surface of the sample are not considered, i.e., the result of calculation in the case of PrN=0 using expression (26). Since the glass wool and flexible urethane foam have low

14 J. Acoust. Soc. Jpn. (E) 20, 1 (1999) impedance, there is less reflection from the front surfaces of these materials. Also, due to the high degree of attenuation inside the material, these samples exhibit weaker interference than the porous asphalt samples. In the glass wool, the sound absorption characteristic is clearly observed over the entire frequency range. In this respect, the flexible urethane foam shows weaker interference than that of the porous asphalt sample, but a certain degree of destructive interference appears just above 1 khz. 5.2 Cloth/Air-Layer/Cloth This material is known to exhibit a peak in the sound absorption coefficient at the frequency at which the thickness of the air layer corresponds to one-quarter of the wavelength of the sound wave (a sample with such a thickness is hereinafter referred to as a 1/4-wavelength sample). Such a sample was tested for comparison because it shows a peak similar to that of the porous asphalt sample. Figure 29 shows the propagation constant of the sample Fig. 30 Characteristic impedance of the thin cloth/air-layer/thin cloth sample. Fig. 28 Comparison of measured absorption coefficient with calculated absorption coefficient of the flexible urethane foam sample (U-2). Fig. 29 Sound propagation characteristics in the thin cloth/air-layer/thin cloth sample. Fig. 31 Comparison of measured absorption coefficient with calculated absorption coefficient of the thin cloth/air-layer/thin cloth sample.

15 M. YAMAGUCHI et al.: SOUND ABSORPTION MECHANISM OF POROUS ASPHALT PAVEMENT material, Fig. 30 the measured result of the characteristic impedance of the material, and Fig. 31 the result of calculation and measurement arranged in a manner similar to those in Section 5.1. Since there is almost no reflection from the front surface of the sample over the entire frequency range, the sound absorption characteristic is determined by the reflective wave from the opposite surface of the sample. The sound absorption mechanism is clearly different from that of the porous asphalt sample. 6. CONCLUSIONS This investigation has clarified the sound absorption mechanism of porous asphalt pavement material. Our conclusions are summarized as follows.. (1) Although the thickness of glass wool or flexible urethane foam for use in a typical architectural space is in the range from 20 to 50 mm, while the usual thickness of porous asphalt pavement is in the range from 40 to 50 mm, since the sound absorption property of these types of material contains the interference which mutually acts between the wave reflected from the front surface of the material and the waves reflected from the opposite surface, the wave inside the porous asphalt material is less attenuated than that in glass wool or flexible urethane foam, and the multi-reflective waves remain inside the porous asphalt material and interfere with the wave reflected from the front surface. In the frequency band below 1 khz, where the internal wave attenuation is particularly,small, the sound absorption coefficient peaks at a frequency at which the antiphase condition is satisfied between the reflected multi-reflective waves and the wave reflected from the front surface of the material. Moreover, since the attenuation gradually increases and the interference decreases in the frequency band above 1 khz, the sound absorption coefficient of the porous asphalt material is determined by the wave reflected from the front surface of the material. (2) As described in Paragraph (1) above, the frequency at which the sound absorption coefficient peaks is determined by the thickness of the material and its internal void structure, and when the thickness is doubled or tripled, the frequency at which the sound absorption coefficient peaks is shifted down to 1/2 or 1/3. (3) The sound absorption peak of the porous asphalt sample mentioned in Paragraph (1) is caused by a completely different mechanism from that in a 1/4-wavelength sample. (4) The sound absorption coefficient of porous asphalt pavement material can be predicted using expressions (12), (25), and (26) taking into consideration the multi-reflection inside the material, the propagation constant, and the characteristic impedance. Since these mathematical expressions yield accurate results for glass wool and others, it appears that they are also applicable to other porous materials. (5) The characteristics of the sound adsorption coefficient of the present porous asphalt pavement material are primarily determined by the structure of the material. It is, therefore, a problem to be solved in the future to enhance the internal sound wave attenuation as long as the material is used for sound absorption. REFERENCES 1) The First Proceedings, Issued from the Porous Asphalt Study Group, Sponsored by Technological Development Center, Nagaoka University of Technology (1992) (in Japanese). 2) The Second Proceedings, Issued from the Porous Asphalt Study Group, Sponsored by Technological Development Center, Nagaoka University of Technology (1996) (in Japanese). 3) S. Meiarashi, T. Miyagawa, and M. Ishida, "Absorption characteristics of drainage asphalt pavement," J. Acoust. Soc. Jpn. (J) 49, (1993) (in Japanese). 4) S. Meiarashi, M. Ishida, and T. Kaku, "Consideration on noise reduction factors of drainage asphalt pavement and its appreciation," J. Acoust. Soc. Jpn. (J) 49, (1993) (in Japanese). 5) S. Meiarashi and T. Fujiwara, "Sound absorption characteristics of porous elastic road surface," Tech. Rep. Noise Vib. Acoust. Soc. Jpn. N (1995) (in Japanese). 6) H. Hatanaka, K. Yamamoto, and Y. Terakado, "An acoustic characteristics of the drainage asphalt," Tech. Rep. Noise Vib. Acoust. Soc. Jpn. N (1997) (in Japanese). 7) T. Iwase and R. Kawabata, "Some acoustic characteristics of porous asphalt," Tech. Rep. Noise Vib. Acoust. Soc. Jpn. N (1997) (in Japanese). 8) H. Utsuno, T. Tanaka, and T. Fujikawa, "Transfer function method for measuring characteristic impedance and propagation constant of porous materials," J. Acoust. Soc. Am. 86, (1989). 9) M. E. Delany and E. N. Bazley, "Acoustical properties of fibrous absorbent materials," Appl. Acoust. 3, (1970). 10) Y. Kohashi, Sound and Sound Wave (Shokabou, Tokyo,1969), p. 94 (in Japanese). 43