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Eindhoven University of Technology

BACHELOR

Effect of moisture content on sound attenuation over vegetated roofs an experimental set-up for long-term measurements

van Pruissen, E.G.

Award date:

2017

Link to publication

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Effect of moisture content on sound attenuation over vegetated roofs An experimental set-up for long-term measurements

Bachelor End Project of

Elisabeth van Pruissen, Eindhoven University of Technology

Supervisors: drs. Chang Liu, dr. ir. Maarten Hornikx, prof. dr. Herman Clercx January 2017, Eindhoven

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Abstract

In this paper, the sound attenuation between two microphone positions over a vegetated roof (in Eindhoven, The Netherlands) is predicted and measured as a function of the water content of the roof, to determine the sound absorption by the vegetated roof. Different flow resistivity and porosity are found (Beekman, 2012) for various volumetric water content (VWC) levels and used to predict the attenuation for various water content percentages. Test measurements were done to determine the optimal place on the roof for the experimental set-up. After that, measurements were conducted with one microphone placed alternately on two positions while the vegetation was artificially watered. The theoretical prediction showed an interference pattern caused by the phase shift that occurs when the sound interacts with the ground. It also showed that the SPL difference decreases for higher VWC, so the absorption is lower for higher VWC. The height of the SPL difference peaks in the model is in good agreement with the test measurements, although the frequency of the peaks is shifted by 1000 Hz. However, the artificial watering experiments didn’t show a clear relationship between the sound absorption and the water content. The uncertainty in the calibration of the moisture meter, the inhomogeneity of the watering and the fact that the soil was already very dank may be responsible for this result.

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Table of Contents

1. Introduction ... 4

2. Theory... 4

2.1. The vegetated roofs ... 4

2.2 Parameters of interest ... 5

2.2.1. Parameters of the air ... 6

2.2.2. Parameters of the vegetation ... 6

2.3 Water Content ... 7

2.4. Prediction model ... 7

2.4.1. Model for surface impedance ... 8

2.4.2. Model for SPL difference ... 9

3. Experimental set-up ... 10

3.1. Optimal position ... 11

3.2. Equipment ... 13

3.2.1. Calibration ... 13

3.2.2. Power supply ... 14

3.3. Sweep signal ... 14

4. Result and Discussion ... 15

4.1. Prediction ... 15

4.2. Test measurements ... 17

4.3.Artificial Watering ... 18

5. Conclusion ... 20

6. Further Research ... 20

7. Bibliography ... 21

8. Appendix ... 22

8.1 Derivation of the 68% interval for VWC ... 22

8.2 Matlab Scripts ... 22

8.3 Set-up test measurements ... 26

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1. Introduction

Green roofs are gaining popularity in Europe because of their positive effect on the environment.

With scientists predicting more extreme weather, green roofs can retain the water and thus unburden the sewer. In the city of Copenhagen it is even mandatory for new flat roofs to be vegetated so the urban heat island effect is reduced, buildings are insulated by the roof and the architectural variation is increased (Proefrock, 2012). Beyond these advantages multiple

experiments have shown that green roofs reduce sound pressure levels of the surroundings (van Renterghem, 2014). In this paper the attenuation of sound over a green roof is examined by measuring the sound pressure level difference between two points on a vegetated roof at Eindhoven, the Netherlands. Sound over roofs can be attenuated by vegetation resulting in less noise. To quantify this attenuation, the sound pressure level difference is measured as a function of the moisture content measured by a moisture meter. A sweep signal is generated using a Matlab script and test measurements were done to find the optimal position on the roof for a long term set- up. After the calibration of the moisture meter, a short measurement with artificially watered vegetation was conducted. All these measurements are compared to predictions from a theoretical model implemented in Matlab.

The theory behind the theoretical model and the absorption of sound by vegetation are listed in chapter 2. After that, the experimental set-up is elaborated on and graphs of the test measurements are shown in chapter 3. The result of the artificial watering measurement and the test

measurements are discussed in chapter 4 followed by the conclusion in chapter 5 and

recommendation for further research in chapter 6. The bibliography and appendix with the Matlab scripts are listed in respectively chapter 7 and 8.

2. Theory

2.1. The vegetated roofs

There are three categories of green roofs: intensive, semi-intensive and extensive. The extensive green roofs, such as the one used in this experiment, are self-sustaining which means they need little or no maintenance. An extensive green roof consists of multiple layers, all with their own function. These layers are shown in figure 1. From top to bottom, the first layer is the vegetation in the growing medium. The depth and the type of vegetation can vary between different brands, ranging from herbs, small grasses and flowering plants. These plants have their roots in the growing medium that consists mostly of three components; sand, compost and lightweight inorganic

aggregate (Sailor, Hutchinson, & Bokovoy, 2008). The plants can attract small animals which benefits the ecosystem (Currie, B.A., Bass, B., 2010). The filter layer’s function is to separate the earth and other organic material from the layer beneath, which is the drainage layer. Without the filter layer, the drainage layer can get clogged with small particles and slit, resulting in the stop of surplus water drainage. These filter layers are made of geotextiles or other woven materials.

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Figure 1, overview of the different layers of an extensive green roof (‘’Building a green roof’’ , 2014).

Green roofs have various advantages compared to normal roofs. As stated above, the vegetation can have a positive effect on the ecosystem surrounding it. Another advantage is the retaining of water:

during long periods of heavy rainfall a green roof will gradually release the water, and thus unburden the sewer. These water retaining capabilities depend strongly on the depth of the soil and the type of vegetation. Another advantage is insulation. Because of the insulation by the roof, less heating and cooling is necessary for the building and the green roof reduces the heat island effect (Zhao et al, 2014). The roof where this experiment is done consists mostly of sedum. Sedum and other crassulacean acid metabolism (CAM) plants are very drought tolerant. Research done by Liu et al.

showed that sedum can do without water for 113 days (Liu, Shyu, & Fang, 2012).

Despite all these advantages, the installation of a green roof is a weak point. A leak made during the installation is hard to find and results in taking most of the vegetation off to detect the leak. This can be time-consuming and costly.

2.2 Parameters of interest

The propagation of sound over vegetation depends on multiple parameters. These are parameters of the air (temperature gradient, wind direction, humidity) and, when sound waves interact with the vegetation, parameters of the vegetation. Parameters that are important are the porosity of the vegetation and the shape of the pores in the soil and connection between them (called the tortuosity), the flow resistivity, the (mean) thickness of the layer and the surface roughness (K.

Attenborough, n.d.).

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2.2.1. Parameters of the air

As stated above, parameters of the air may be important for the attenuation of sound. The sound is attenuated in the air itself by interaction with the air molecules. This attenuation depends on parameters such as temperature, humidity of the air and frequency. In 1845 ‘Stokes law of sound attenuation’ was published. This formula says the amplitude of a wave decreases exponentially with the distance. The rate of the decrease is determined by the factor 𝛼

𝛼 = 2𝜂𝜔2

3𝜌𝑉3 (1) Where 𝜂 is the dynamic viscosity, 𝜔 the frequency of the sound, V the speed of sound in the medium and 𝜌 the density of the medium. The amplitude of a wave through a Newtonian fluid at a distance d is then given by

𝐴(𝑑) = 𝐴(0) ∙ 𝑒−𝛼𝑑 (2) For air at a pressure of 1 atmosphere and 383.16 Kelvin the value for 𝛼 ≈ 1.75 ∙ 10−11. The

difference in attenuation at 1 Hz and 2.5 kHz for a distance of 5.6 meter is 0.08 dB. This is not significant for this experiment and air absorption is therefore not included in the results (Angelus, 2012).

2.2.2. Parameters of the vegetation

The porosity is defined as the fraction of the volume of interconnected pores and the total volume.

Pores that are closed and therefore not connected with the outer air don’t contribute to the porosity of a medium. The porosity is given by

ℎ = 𝑉0

𝑉𝑡𝑜𝑡𝑎𝑙 (3) Where 𝑉0 is the volume of the connected pores and 𝑉𝑡𝑜𝑡𝑎𝑙 the total volume.

The tortuosity gives information about the connection between the pores, when the connections are curved, sound waves will experience more resistance (Cox & D’Antonio, 2009).

The flow resistivity is a measure for the pressure needed to drive a unit (particle) flow through the vegetation. The unit of flow resistivity is 𝑁 ∙ 𝑠 𝑚⁄ 2 and the formula is

𝜎 = ∆𝑃

𝑈 ∙ 𝑑 (4) where ∆𝑃 is the static pressure drop, d is the thickness of the material in meters and U is the volume flow (Cox & D’Antonio, 2009).

When the surface has no roughness there will be specular reflection (angle of incidence is equal to the angle of reflection) and there will be interference due to the path length difference between the direct and reflected sound. This is called the ground effect. When the surface is rough, the incident wave will reflect more diffusely and the interference will decrease especially for the high

frequencies, because the wavelengths are small relative to the roughness. The same holds for the pore size: the higher frequency range will attenuate more, because small wavelengths easily

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penetrate the pores where they lose energy due to friction and the phase of the wave changes. The attenuation on top of the air attenuation is linear with the distance traveled.

When sound waves are reflected on a surface, the phase and magnitude change. The amount of change depends strongly on the difference in acoustic impedance of the ground and the air, both the imaginary part and the real part are important. The real part is called the resistive part and is associated with energy loss due to sound radiation and friction. The imaginary part, also called the reactant part, is associated with the stiffness and mass of the material (Møller, 1964). The

impedance is a function of the frequency and the angle of incidence and is defined as the ratio of the complex sound pressure on a given surface to the sound flux through that surface. Impedance can be measured in an impedance tube, but then the angle of incidence is fixed at 𝜋

2. This normal impedance is inaccurate for experiments with grazing angles.

2.3 Water Content

Water content in a porous medium will change the porosity, the flow resistivity and the effective thickness of the medium and therefore the surface impedance. With higher water content, the hard backing layer will be higher and therefore the effective depth of the soil will decrease (Horoshenkov, 2006). Experiments done on different ground types without roots show that the addition of moisture causes a decrease of the flow resistivity towards a minimum at around 10% (mass) water content.

When further increasing the mass water content, the flow resistivity increases too. The used

measure for water content in this paper is the volumetric water content (VWC) percentage, which is defined as

𝑉𝑊𝐶 (%) =𝑉𝑤𝑎𝑡𝑒𝑟

𝑉𝑡𝑜𝑡𝑎𝑙 ∙ 100 (5) Where V stands for volume. For ground with roots the minimum is at 0% water content (Dickinson &

Doak, 1970). Both the impedance and the flow resistivity change more rapidly in the low VWC range (0% up to 10%) than for high VWC (Horoshenkov & Mohamed, 2006).

More water in the vegetation of the roof will have a negative effect on the thermal insulation (Castleton et al, 2010). Furthermore, the difference in impedance is less uniform across the soil for high VWC (Cramond & Don, 1987).

2.4. Prediction model

To compare the measured data with theory, a script written by Chang Liu in Matlab is adapted for this experiment. The script uses a Slit Pore Model to calculate the propagation constant and the impedance for different porosity and flow resistance. The calculated values are used as an input for the equations of Kai Ming Li (Li, Waters-Fuller, & Attenborough, 1998). These equations approximate the sound pressure profile of a source close to porous ground and are used in the script. The output of the script is the difference in sound pressure level between the two microphones for different VWC.

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2.4.1. Model for surface impedance

The Slit Pore model is a model to calculate the impedance and the propagation constant of a porous medium. There are a few assumptions made in the model; the tortuosity of the pores is constant, the pores are slit-like, the porous material is rigid and the last layer is hard backing so it reflects all the incoming acoustic energy. The output of the model depends on the porosity, the flow resistivity, the frequency and the thickness of the layer.

Nicolas et al. (Nicolas, 1985) introduced a surface impedance for porous layers in a motionless frame that is a function of the refraction angle. The surface impedance is given by

𝑍𝑠=𝑖𝑍 ∙ cot ( 𝑘1∙ 𝑑 ∙ 𝑐𝑜𝑠𝜃1)

𝑐𝑜𝑠𝜃1 (6) where d is the thickness of the layer, 𝑘1 is the wavenumber in the medium, Z the characteristic impedance and 𝜃1 the refraction angle that is related to the angle of incidence by

𝑠𝑖𝑛𝜃1= 𝑘0

𝑘1𝑠𝑖𝑛𝜃 (7) with 𝜃 the angle of incidence and 𝑘0 the wavenumber in air (Allard, 2009). The characteristic

impedance is the impedance at a certain point, sometimes also called the specific impedance, and equals the speed of sound in the medium times the density.

The equation for the characteristic impedance is

𝑍𝑐 = 1

𝑐0𝜌0√𝑇 ∙ 𝜌(𝜆)

2∙ 𝐶(𝜆) (8)

T is again the tortuosity, h is the porosity, 𝑐0 the speed of sound in air and 𝜌0 the density of air.

𝜌(𝜆) = 𝜌0

𝐺𝑠(𝜆) (9)

𝐶(𝜆) = 𝛾 − (𝛾 − 1)𝐺𝑠∙ 𝜆√𝑁𝑃𝑅

𝛾𝑃0 (10)

The equation for the bulk modulus 𝐶(𝜆) of the air in the pores comes from Stinson; he relates the viscous effect and the thermal effects. (He assumes that the air in the pores is an ideal gas) (Callaway

& Ramer, 1952). 𝛾 is the specific heat capacity per unit mass at constant pressure divided by the specific heat capacity per unit mass at constant volume and 𝑁𝑃𝑅 is the Prandtl number, which gives the ratio between momentum diffusivity and thermal diffusivity.

For a circular cross-section of the pores, 𝐺𝑠 is given by

𝐺𝑠(𝜆) = 1 − tanh (𝜆√−𝑖

𝜆√−𝑖) (11)

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Biot (Attenborough, Bashir, & Taherzadeh, 2011) suggested to implement a frequency independent pore shape parameter 𝑠𝐵. With this parameter the formula for 𝜆 becomes

𝜆 = 𝑠𝐵(3𝜌0𝜔𝑇

ℎ ∙ 𝑅𝑠 )1/2 (12) were 𝑅𝑠 is the first input variable of the model, the flow resistivity.

The tortuosity can be expressed as a function of the porosity, The Bruggeman relation is a good approximation for various porous materials in which the pores are connected (Agar, 1963) (Meredith and Tobias, 1962). This relation between tortuosity and porosity is given below

𝑇 = √1

ℎ (13)

2.4.2. Model for SPL difference

Kai Min Li et al (Li, Waters-Fuller, & Attenborough, 1998) have made an extension of the classical Weyl-van der Pol theory for electromagnetic waves to model the propagation of sound over ground with extended reaction, which means the SPL at one point is influenced by the SPL around it, over multiple layers that are semi-infinite or have a hard-backed layer.

The Weyl-van der Pol theory approximates the sound field over a surface. It was the first to represent the spherical wave front interacting with the ground as a sum of plane wave fronts. The sound field is a sum of the direct field, reflected field and the ground waves that are present in the lower frequencies. The low frequencies undergo a phase shift when interacting with the vegetation, this phase shift is almost 180 degrees and results in destructive interference. If it wasn’t for the low ground waves, the low frequencies would be largely attenuated.

Figure 2, prediction of the attenuation (Huisman, 1990) due to the vegetation with at ‘F’ a peak from the ground waves, at ‘d’ a drop caused by the phase shift due to the interaction with the vegetation and at ‘I’ an interference pattern caused by the geometry of the set up.

The interference pattern of the attenuation due to the vegetation is shown in figure 2 (Huisman, 1990). The first peak is caused by the low frequency ground waves, the drop at ‘d’ is caused by the phase shift and is called the ground dip because the shape of the dip and first peak depend strongly on the impedance of the soil which determines the phase change and the degree of permeation. The pattern at ‘I’ is the interference pattern caused by the geometry (Huisman, 1990).

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The spherical wave can be represented as a two-dimensional Fourier integral in the dimensions x and y where 𝜉1 and 𝜉2 are the complex wavenumbers in those directions (Brekhovskikh & Godin, 1999).

exp (𝑖𝑘𝑟)

𝑟 = ∬ 𝐴(𝜉1, 𝜉2) ∙ e𝑖(𝜉1𝑥+𝜉2𝑦)𝑑𝜉1𝑑𝜉2 (14)

+∞

−∞

Where A can be written as

𝐴(𝜉1, 𝜉2) = 𝑖

2𝜋√𝑘2− 𝜉12− 𝜉22 (15) The sound pressure of the reflected wave can then be written as

𝑝𝑟 = 𝑖

2∫ 𝜉𝑑𝜉

𝜇 𝑉(𝜉) ∙ 𝐽0(𝜉𝑟) ∙ exp[𝑖𝜇(𝑧 + 𝑧0)] (16)

+∞

−∞

With 𝜉 = √𝜉12+ 𝜉22 and 𝜇 = √𝑘2− 𝜉2 , 𝑉(𝜉) the reflection coefficient, 𝐽0(𝜉𝑟) the zeroth Bessel function, r the distance between source and receiver. By changing the integration over 𝜉 to 𝜇 the integral can be numerically solved. This formula is numerically solved for the experimental set-up of this paper and converted to SPL (difference) for different values of porosity and flow resistivity. The results are listed in chapter 4.

3. Experimental set-up

In this experiment the absorption of sound over vegetated roofs is measured for different volumetric water content. The roof is located on the campus of Eindhoven University of Technology, located in Eindhoven, the Netherlands. The green roof is on the first floor and is surrounded by the higher floors of the rest of the building as can be seen in figure 3. This figure is an old photo found on Google Earth and the building behind the roof is replaced by the new building Flux.

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3.1. Optimal position

Figure 3, screenshot of Google Earth image of the green roof of Cascade with the old building that is no longer there.

Several test measurements were done on the roof to determine the place with a low background noise and no disturbing reflections. The equipment used for the test measurements is listed in appendix 3. To ensure enough interaction of the sound with the vegetation, the microphones and the speaker are placed low above the vegetation, which has a thickness varying from 3 up to 10 cm.

The microphones have a height of 4.0 cm above the surface and the cone of the speaker is placed in a Perspex box at height of 2.5 cm. Therefore the sound beams will have grazing incidence with the roof. The speaker is first placed near the edge of the east side of the roof. While keeping the distance between the speaker and the first microphone fixes at 0.6 meter, the second microphone was moved further away with steps of one meter. With the increase of the distance between the two microphones, the longest distance with an acceptable signal to noise ratio (SNR) is determined.

With a longer distance between the microphones the effect of the Volumetric Water Content (VWC) will be greater.

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In figure 4 the Signal to Noise Ratio, extracted from the used Dirac program, is plotted as a function of inter-microphone distance. The plotted SNR is a mean value for the frequencies between 500 Hz and 4000 Hz. For a good signal the SNR should not be lower than 15 dB. When the distance to the second microphone is increased, the signal itself needs to be louder to achieve the same SNR, which is bothersome for the people inside the building or passing by the building.

Figure 4, Signal to Noise ratio calculated from the test measurements for different distances between the source and the microphone

After changing the inter-microphone distance, the optimal placement on the roof is determined by shifting the whole set up towards the Flux building. The best place (highest SNR) for the set up was found to be as far away from the Flux building as possible with the speaker directed to the west. A plan of the roof with the measurements of the accessible area (22 x 34 m) is visualized in figure 5.

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Figure 5, plan of the first floor roof of the Cascade building, with the position of the source and microphones.

3.2. Equipment

The moisture meter is of the type EC-5 and measures the dielectric permittivity of the soil, which changes with water content. The microphones for the long term measurement are from the

University of Gent and send the data to Gent using a cellular router. These microphones were made by people of the university of Gent and were used in a project for the Intelligent Distributed

Environmental Assessment (IDEA). Attached to the microphone is a printed circuit board that can be seen as a small computer. This computer processes the data: instead of the sound pressure, the data sent is the spectrum of every 1/8 of a second in 1/3 frequency bands. This data is loaded in the Matlab script ‘Analyzing_sweeps_VWC_VanPruissen’. This script reads the number of samples for every recorded sweep sound, because the sample rate is not constant. In the same script the data of the moisture meter is loaded. With this data a plot is made of the SPL difference between the two microphones (in dB), for every frequency band, versus the volumetric water content (in %).

3.2.1. Calibration

To measure the moisture content of the soil an EC-5 moisture meter is used. To improve the precision, a calibration is done using a soil sample of the vegetation with known moisture content.

The parameter of interest is the volumetric water content (VWC) and is defined as follows 𝑉𝑊𝐶(%) = 𝑉𝑤𝑎𝑡𝑒𝑟

𝑉𝑤𝑒𝑡 ∙ 100 (17) where 𝑉𝑤𝑎𝑡𝑒𝑟 is the volume of the water and 𝑉𝑤𝑒𝑡 is the total volume of the wet material, including air holes. A piece of the green roof vegetation was weighed at saturation and then oven-dried till the mass hardly changed anymore. With this final mass assumed to be the mass at VWC=0, the moisture

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meter was calibrated. Three measurements were done with the EC-5 for each VWC at different positions, because the soil is not completely homogeneous. The mean value of the three points is used for the calibration. The linear relation and the calibration graph are listed below. The linear calibration that was found is

𝑉𝑊𝐶 (%) = (222 ± 21) ∙ 𝑉𝑜𝑙𝑡𝑎𝑔𝑒(𝑉) − (58.5 ± 6.5) (18)

Figure 6, linear fit of the calibration points of the EC-5 moisture meter with a slope of 222 and an intercept 0f -58.

3.2.2. Power supply

There are various parts of the experimental set-up that need a power supply when placed on the roof for a long term. The first is the laptop running the script for the sweep sound, the second is the ibox datalogger that is connected to the moisture meter and the last are the microphones that are connected to a cellular router. They can’t be directly connected to the network of Eindhoven University of Technology because the data of the microphones is sent to a server in Gent, which is protected by a firewall. The distance from the power supply to the green roof is 50 meters. The cable lies in the open air and because of safety it can only be on a low voltage. The ibox and the cellular router are on the roof connected to this power supply in a waterproof box. Because of the low voltage the amplifier and the laptop are placed in the room of the power supply. A better (lower impedance) and longer cable was attached to the speaker because it now needs to bridge 50 meters.

3.3. Sweep signal

The signal that is analyzed is a linear sweep sound from 50 to 5000 Hz made with a Matlab script.

The script is listed in appendix 2. The used sweep sound lasts four seconds, but this is easily altered in the script. In the script of the sweep sound there is also a timer. This timer has multiple variables that can be altered by the user; the interval between the sweeps, the start time and the end time.

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For this experiment a begin time of 22:00 and end time of 7:00 was taken with an interval of half an hour. By playing the sweep sound after working hours the inconvenience for the people in Flux and Cascade is brought to a minimum.

4. Results and Discussion

4.1. Prediction

The paper of T. Van Renterghem and D. Botteldooren (van Renterghem & Botteldooren, 2014), gives an idea of what to expect from the experiment. There are some differences, such as the shielding that is present in the experiment of van Renterghem, but not in this experiment. A model is used to predict the propagation of sound over layered porous media with extended reaction by a point source from the paper by Kai Ming Li, Tim Waters-Fuller, and Keith Attenborough (1998, United Kingdom). The input of this model is the number of layers, the depth, the impedance of the layers and the propagation constant.

The Slit Pore model is used to calculate the impedance- and the propagation constant of the vegetation. The necessary input for this model (porosity and flow resistance at various water content levels) was taken from (Beekman, 2012). The parameters are listed in table 1.

In the paper of Beekman (2012) the parameter ‘percentage of saturation’ is used. This parameter can be converted to VWC (for this soil) by setting 22,4% VWC, which is the measured saturation during the calibration, to 100% saturation. The rest of the values can then be altered with the equation below.

𝑉𝑊𝐶 (%) = % 𝑜𝑓 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 ∙ 0.224 (19) In the same paper, the impedance of a green substrate is measured in an impedance tube. The depth of the substrate (7.56 cm), is close to that of the substrate on the roof of Cascade. By implementing these values in a Slit Pore model, the impedance and propagation constant are calculated for different Volumetric Water Content. The impedance and propagation constant are used to give a prediction of the sound pressure level difference between the two microphones for different Volumetric Water Content.

Table 1, flow resistivity and porosity for different values of volumetric water content, converted from saturation percentage as found in the paper of Beekman, 2012.

VWC (%) Porosity Flow resistivity (pa*s/m2)

0 0.43 25000

11.5 0.44 25000

17.0 0.43 23000

17.9 0.31 22000

22.4 0.23 24000

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Figure 7, prediction of the sound level difference in decibel between the two microphones for different percentage of volumetric water content for one layer. The two microphones are placed 5.1 meter apart with a thickness of 4 cm. The source is located at a height of 2.5 cm and 60 cm from the first microphone. The depth of the substrate is 7.65 cm.

The model predicts a decreasing SPL difference for increasing Volumetric Water Content, as expected. The bigger the difference, the more sound absorption there is between the two

microphones. The decrease is steeper for the frequencies above 1 kHz. This is in accordance with the paper of Gent which shows no dependence between absorption and VWC from 0 to 250 Hz and little dependency up to 400 Hz. However, the graphs for 11.5% and 17.0% are very similar. This can be explained by looking at the values for the flow resistivity and porosity. For all the VWC above, these values are very close to each other and therefore the Matlab model gives more or less the same result. More accurate values of the impedance and propagation constant as function of the VWC may give better results.

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4.2. Test measurements

The prediction is in good agreement with the SPL difference calculated from the test measurements.

Although the peak is shifted approximately 1000 Hz to the right when compared to figure 7.

Figure 8, sound pressure level difference in decibel calculated from the test measurement with the microphone positions 5.1 meter apart.

The result looks as if interference is going on. But at first it seems the ground effect can’t be the explanation, because the speaker and the microphones are placed close to the ground resulting in a very small path length difference for the direct and indirect sound (Δ𝐿 ≈ 4.4 ∙ 10−4 𝑚). But as stated in chapter 4 a phase shift of almost 180 degrees occurs in the low frequency range when the sound interacts with the vegetation, resulting in destructive interference (C. Howorth, 1991). Another way to represent the absorption of sound is to normalize the SPL of the second microphone by the SPL of the first microphone, this is shown in figure 9 for the same data as used for figure 8..

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Figure 9, fraction of the magnitude that is recorded by the second microphone by normalizing the second microphone with the first microphone, calculated from the test measurements. With the same set up as inserted in the model prediction.

Figure 9 shows that between the 30% and 60% of the decibels arrived at the second microphone.

Interference is now more visibly in the higher frequency range which is not caused by the phase change, but due to the geometry of the set-up.

4.3.Artificial Watering

Because the waterproof microphones couldn’t be used, experiments were done with the same microphone as the test measurements. To change the moisture content of the roof, water is poured over the roof that was divided into square meters. Each time, 900 ml was distributed as uniformly as possible over the square meter and after twenty minutes, a measurement is done. In order to determine the VWC, four measurements were made at different points in the vegetation (between the two receiver positions) and the average was taken.

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Figure 10, sound pressure at the second microphone, normalized by dividing it by the sound pressure at the first microphone, for different VWC (in %) after artificial watering of the green roof. The uncertainty in the VWC is approximately 7% for values around 30%. Both microphones are 5.1 meters apart at a height of 4 cm.

The normalized magnitude in figure 9 is significantly larger than during the test measurements, which means less sound is absorbed. This is especially the case at the low frequencies where only 20% is absorbed. An explanation may be the high VWC during the artificially watered measurements (the vegetation was visibly less dank during the test measurements), additionally the SPL at the first microphone was higher during the watered experiment, which may have led to some reflections.

The black line represents the first measurement. This is strange because it should have the lowest VWC. Another thing that stands out is the little difference between the measurements. The

vegetation was already very dank at the beginning of the experiment, probably close to saturation.

When the vegetation is saturated, all the extra water will be collected in the black cups under the filter layer. When the cups are filled, the water won’t be retained anymore and will flow towards the sewer. The differences between the VWC is not significant, because the uncertainty in the VWC is 21 ∙ 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 which is around 7% for 30% VWC. The derivation of this uncertainty is listed in appendix 1. The VWC percentage is above the measured saturation value during the calibration measurements. An explanation for this can be the fact that the calibration piece had less moss and was perhaps already sear and could therefore absorb less moisture.

The big uncertainty in the VWC can be caused by the inhomogeneity of the vegetation on the roof . Furthermore the compactness of the soil, which also influences the voltage of the moisture meter, differs over the roof. Lastly the moisture meter needs to be inserted under an angle, because the vegetation isn’t deep enough to insert the meter vertically. According to the manufacturer, it was no problem, but the manual said it would influence the uncertainty.

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The high VWC measured (higher than the calibrated saturation value) has effect on the conversion of

% of saturation to VWC(%) that was used for the prediction of figure 7. The VWC listed in table 1 will be lower for a higher saturation value.

5. Conclusion

The green roof on the building of Cascade at Eindhoven University of Technology is suitable for a long term experiment with the two microphones from Gent and the EC-5 moisture meter. The optimal position is with the microphone 4.7 meters from the edge of the roof on the east side. The two microphones should be 5.1 meters apart in order to obtain a good signal for a SPL around 70 dB at the first microphone. The best way to represent the absorption is by normalizing the SPL of the second microphone by that of the first.

The model predicts a decreasing absorption with increasing water content, which is confirmed by comparing the test measurement to the artificially watered measurement. The absorption increases with the frequency, although there is an interference pattern visible due to the phase change of almost 180 degrees when the sound waves interact with the vegetation.

6. Further Research

If the microphone from Gent is repaired, the experiment can be conducted for a long time with natural rainfall. The moisture meter should be held in one place, that way the effect of

increasing/decreasing VWC will be visible. The question is whether to invest in an extra moisture meter, to account for the inhomogeneous water content in the vegetation. The uncertainty of the calibration remains constant, but for high VWC the inhomogeneity increases which also influences the uncertainty. An extra moisture meter would therefore be especially beneficial for higher VWC.

Another thing that could be interesting to investigate is the drainage layer. This layer can be filled with water or not resulting in an air layer or approximately a hard backing layer of water. The script that is used for the predictions can be further altered for two layers to investigate the effect of this.

Another thing that could be included is a normalized prediction for different VWC.

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7. Bibliography

Agar, J. N. (1963). Advances in Electrochemistry and Electrochemical engineering; volume 2, Electrochemical engineering. Journal of Electroanalytical Chemistry (1959), 6(6), 497.

doi:10.1016/0022-0728(63)80183-7

Allard, J. F. (2009). Prediction of the acoustic field due to a point source over a porous layer. The Journal of the Acoustical Society of America, 125(4), 1864–1867. doi:10.1121/1.3081500

Angelus, J. (Ed.). (2012). Stokes’ Law (Sound Attenuation). Duct Publishing.

Attenborough, K. (no date). A review of ground impedance models for propagation modelling, Department of Engineering, The University of Hull.

Attenborough, K., Bashir, I., & Taherzadeh, S. (2011). Outdoor ground impedance models. The Journal of the Acoustical Society of America, 129(5), 2806–2819. doi:10.1121/1.3569740

Brekhovskikh, L. M., & Godin, O. A. (1999). Acoustics of layered media II. doi:10.1007/978-3-662- 03889-5

Callaway, D. B., & Ramer, L. G. (1952). The use of perforated facings in designing low frequency resonant absorbers. The Journal of the Acoustical Society of America, 24(3), 309–312.

doi:10.1121/1.1906897

Castleton, H. F., Stovin, V., Beck, S. B. M., & Davison, J. B. (2010). Green roofs; building energy savings and the potential for retrofit. Energy and Buildings, 42(10), 1582–1591.

doi:10.1016/j.enbuild.2010.05.004

Cox, T. J., & D’Antonio, P. (2009). Acoustic absorbers and diffusers: Theory, design and application (2nd ed.). New York: Taylor & Francis.

Cramond, A. J., & Don, C. G. (1987). Effects of moisture content on soil impedance. The Journal of the Acoustical Society of America, 82(1), 293–301. doi:10.1121/1.395565

Currie, B.A., Bass, B., 2010. Using Green Roofs to Enhance Biodiversity in the City of Toronto.

Dickinson, P. J., & Doak, P. E. (1970). Measurements of the normal acoustic impedance of ground surfaces. Journal of Sound and Vibration, 13(3), 309–322. doi:10.1016/s0022-460x(70)80021-9 Horoshenkov, K. V., & Mohamed, M. H. A. (2006). Experimental investigation of the effects of water saturation on the acoustic admittance of sandy soils. The Journal of the Acoustical Society of

America, 120(4), 1910–1921. doi:10.1121/1.2338288

Howorth, C. (1991). Sound propagation over rigid porous layers Ph.D. thesis, the open university.

Huisman, W. (1990). Sound propagation over vegetation-covered ground. Nijmegen IDEA, Retrieved January 7, 2017, from Intelligent Distributed Environmental Assessment http://users.ugent.be/~tvrenter/publicaties/poster_IDEA.pdf

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Li, K. M., Waters-Fuller, T., & Attenborough, K. (1998). Sound propagation from a point source over extended-reaction ground. The Journal of the Acoustical Society of America, 104(2), 679–685.

doi:10.1121/1.423307

Liu, T. ., Shyu, G. ., & Fang, W. . (2012). Drought tolerance and thermal effect measurements for plants suitable for extensive green roof planting in humid subtropical climates. Energy and Buildings, 47, 180–188. doi:10.1016/j.enbuild.2011.11.043

Møller, A. R. (1964). The acoustic Impedance in experimental studies on the middle ear.

International Audiology, 3(2), 123–135. doi:10.3109/05384916409074077

Proefrock, P. (2012, October 10). Copenhagen adopts a mandatory green roof policy. Retrieved December 23, 2016, from http://inhabitat.com/copenhagen-adopts-a-mandatory-green-roof-policy/

Renterghem, T., & Botteldooren, D. (2014). Influence of rainfall on the noise shielding by a green roof. Building and Environment

Sailor, D. J., Hutchinson, D., & Bokovoy, L. (2008). Thermal property measurements for ecoroof soils common in the western U.S. Energy and Buildings, 40(7), 1246–1251.

doi:10.1016/j.enbuild.2007.11.004

Zhao, M., Tabares-Velasco, P. C., Srebric, J., Komarneni, S., & Berghage, R. (2014). Effects of plant and substrate selection on thermal performance of green roofs during the summer. Building and Environment, 78, 199–211. doi:10.1016/j.buildenv.2014.02.011

(2014, January 22). Building a green roof or rooftop garden. Retrieved January 7, 2017, from Tools Technology & Methods, http://conststudy.com/building-green-roof-rooftop-garden/

.

8. Appendix

8.1 Derivation of the 68% interval for VWC

𝑆𝑉𝑊𝐶 = √∑ (𝜕𝑉𝑊𝐶

𝜕𝑥𝑖 )

2

∙ 𝑆𝑥(𝑖)2

𝑁 𝑖=1

𝑆𝑉𝑊𝐶 = √(𝜕𝑉𝑊𝐶

𝜕𝑠𝑙𝑜𝑝𝑒)

2

𝑆𝑠𝑙𝑜𝑝𝑒2+ ( 𝜕𝑉𝑊𝐶

𝜕𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡)

2

𝑆𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡2= 21 ∙ 𝑉𝑜𝑙𝑡𝑎𝑔𝑒

8.2 Matlab Scripts

Matlab script for the generation of the sweep sound and the timer

close all clear all

%% signal generation

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fs = 48000; % sample frequency (how many samples per second) sl = 1; % signal length

N = 4*sl.*fs;

dt = linspace(0,1/fs,N); % time sample (how many second per sample)

tv = zeros(1,N);

tv(1)=0;

for i=2:N;

tv(i)=tv(i-1)+dt(i); % time vector %vector is sum of earlier elements end

flow = 50; % lower frequency fup = 4000; % upper frequency

%

fc = (logspace(log10(flow),log10(fup),4*fs));

% vector from flow to fup logaritmical of 4*48000 parts omega = 2.*pi.*fc;

sinwaves = sin(omega.*tv);

p3 = sinwaves;

[value,index] = find(p3 == max(p3));

p3 = p3.*1./p3(index);

%the function soundsc automaticaly scales in range 0 to 1.

%% Timer for playing the sound during the night

begintijd = 22;

eindtijd = 7;

c = clock;

tic

% check time of day time_to_play_sound = 30;

while toc < 2000 % can be while 1 to let it play infinitely long

current_time_hours = toc/3600 + c(4)+ c(3)/60;

current_time_minutes = toc/60 + c(5)+ c(6)/60;

if current_time_hours > 24

current_time_hours = toc/3600 + c(4)+ c(3)/60 - 24;

if current_time_hours >= begintijd || current_time_hours <= eindtijd disp(toc/60 + c(5)+ c(6)/60)

if floor(current_time_minutes) == time_to_play_sound

disp('Sound is being played') soundsc(p3,fs)

time_to_play_sound = time_to_play_sound + 30;

end end end end

The Matlab script for analyzing the data of the microphones from Gent and the EC-5 moisture meter.

close all clear all

%% inlezen van de data

filename_410 = 'Foi410_Eindhoven_30-11-2015.txt';

filename_411 = 'Foi411_Eindhoven_30-11-2015.txt';

newdata_410=importdata(filename_410);

newdata_411=importdata(filename_411);

%% microphone 1

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A1 = newdata_410(:,5) == 30;

B1 = newdata_410(:,5) == 0;

C1 = newdata_410(:,6) == 0;

D1 = newdata_410(:,6) == 1;

E1 = newdata_410(:,6) == 2;

F1 = newdata_410(:,6) == 3;

G1 = newdata_410(:,6) == 4;

K1 = find(A1+B1+C1+D1+E1+F1+G1 == 2);

Sweeps1 = newdata_410(K1,:);

length_sweeps1 = find(diff(K1)>10);% index of the beginning of every new sweep

%% microphone 2

A2 = newdata_411(:,5) == 30;

B2 = newdata_411(:,5) == 0;

C2 = newdata_411(:,6) == 0;

D2 = newdata_411(:,6) == 1;

E2 = newdata_411(:,6) == 2;

F2 = newdata_411(:,6) == 3;

G2 = newdata_411(:,6) == 4;

K2 = find(A2+B2+C2+D2+E2+F2+G2 == 2);

Sweeps2 = newdata_411(K2,:);

length_sweeps2 = find(diff(K2)>10);% index of the beginning of every new sweep

%% sommeren over de lengte van de opnamens

Averages410 = zeros(length(length_sweeps1)-1,31);% 31 = number of frequencybands Averages411 = zeros(length(length_sweeps2)-1,31);

for i = 1:length(length_sweeps1)-1;

Averages410(1,:) = sum(Sweeps1(1:length_sweeps1(1),8:end),1)/length_sweeps1(1);

Averages410(i+1,:) =

sum(Sweeps1(length_sweeps1(i)+1:length_sweeps1(i+1),8:end),1)/(length_sweeps1(i+1)- length_sweeps1(i));

end

for i = 1:length(length_sweeps2)-1;

Averages411(1,:) = sum(Sweeps2(1:length_sweeps2(1),8:end),1)/length_sweeps2(1);

Averages411(i+1,:) =

sum(Sweeps2(length_sweeps2(i)+1:length_sweeps2(i+1),8:end),1)/(length_sweeps2(i+1)- length_sweeps2(i));

end

% The matrix Averages has the spectrum of a sweep on every row

Difference = Averages411 - Averages410(1:23,:);%can be changed to Averages410(:,:)

%% Data of the moisture meter

startjaar = newdata_410(K1(1),1);%startyear startmaand = newdata_410(K1(1),2);%startmonth startdag = newdata_410(K1(1),3);%startday startuur = newdata_410(K1(1),4);%starthour startminuut = newdata_410(K1(1),5);%startminute startseconde = newdata_410(K1(1),6);%startseconde

newdata = importdata ('i029-140519-140728.txt');

datum_vector = newdata.textdata(:,1);

tijd_vector = newdata.textdata(:,2);

index_startdatum = find(cellfun(@(x) isequal(x,'19-5-14'),datum_vector));% data and time of first sweep have to be filled in here

inedx_starttijd = find(cellfun(@(x) isequal(x,'20:17:16'),tijd_vector));

index_start = find(index_startdatum == inedx_starttijd);

%% Taking the rigth data from moisture data

interval = 10; % time between measurepoints of the moisture meter in minutes interval_sweeps = 30; %time between sweeps in minutes

Voltage = zeros((length(newdata.data)-index_start)/(interval_sweeps/interval)+1,1);

for i = 0:(length(newdata.data)-index_start)/(interval_sweeps/interval)

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Voltage(i+1,1) = newdata.data(index_start+i*interval_sweeps/interval,2);%

Getting data from indexstart end

VWC = 222.1.*Voltage-57.5;%calibration line of the moisture meter

%% Plotting attenuation versus VWC for every frequency band

plot(VWC(1:length(Difference)), Difference)% can be changed to VWC(:,Difference)

Matlab script used for the predictions

close all clear all

fc = round(logspace(log10(200),log10(4000),500));

T = 18.7;%20.4;

c1 = 331.3+0.606*T;

% speed of sound during measurement [m/s]

lamda = c1./fc; % wave length

rho1 = 1.2; % density of air [kg/m^3]

omega = 2*pi*fc;

k1 = omega/c1; %wavevector

fcenter = [200 250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000]; % 1/3 octave bands

flower = round(2^(-1/6).*fcenter); % lowest frequency clear T

hhs = [0.025 0.025];%hoogte van de bron

hhr = [0.04 0.04];% hoogte van de 1ste en 2de microfoon rr = [0.6 5.7]; %afstand source - mic1 en source - mic2

Rindirec = sqrt(rr.^2+(hhs+hhr).^2);

Rdirec = sqrt(rr.^2+(hhs-hhr).^2);

ttheta = atan(rr./(hhs+hhr));

%% Parameters for SP model;

sigma = [25000 0.43 0.0756]; %flow resistivity/porosity/thickness

%% impedance model (Slit-pore) K = 1.42e5; % adiabatic bulk modulus Pr = 0.713; % Prandtl number

gamma = 1.4;

% Slit pore impedance model

T2 = sigma(2)^(-0.5); % tortuosity

lambda2 = sqrt(3*rho1*omega*T2./(sigma(1)*sigma(2)));

lambdaNpr2 = lambda2.*sqrt(Pr);

Gs2 = 1-tanh(lambda2.*sqrt(-1i))./(lambda2.*sqrt(-1i));

GsNpr2 = 1-tanh(lambdaNpr2.*sqrt(-1i))./(lambdaNpr2.*sqrt(-1i));

rho22 = rho1./Gs2;

C2 = K.^(-1).*(gamma-(gamma-1).*GsNpr2);

Zc = sqrt(T2./(sigma(2).^2)*rho22./C2)./(rho1*c1);

kc = omega.*sqrt(T2.*rho22.*C2);

% wavenumber

N = length(fc);

ppe = zeros(2, N);

L = zeros(2, N);

Lp = zeros(2,length(flower)-1);

for mmm=1:2;

Rdirect = Rdirec(mmm);

Rindirect = Rindirec(mmm);

theta = ttheta(mmm);

hs = hhs(mmm);

hr = hhr(mmm);

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r = rr(mmm);

n2_1 = kc./k1;

s2_1 = 1./(Zc.*n2_1);

% density ratio

costh = sqrt(1-1./(n2_1.^2)+cos(theta).^2./(n2_1.^2));

Zmodel_p = 1i.*Zc./(sigma(2)*costh).*cot(kc.*sigma(3).*costh);

%% Sommerfeld integral % Define Matrices first pe_1 = zeros(1,N);

pe_2 = zeros(1,N);

pe = zeros(1,N);

for mn=1:length(fc)

umax_1 = k1(mn);

du_1 = 0.001;

u_1 = du_1/2:du_1:umax_1-du_1/2;

costh2_1 = sqrt(kc(mn).^2-k1(mn).^2+u_1.^2)./kc(mn);

V_1 = (1i.*Zc(mn).*u_1.*cot(costh2_1.*kc(mn).*sigma(3))./k1(mn)-

(sigma(2).*costh2_1))./((1i.*Zc(mn).*u_1.*cot(costh2_1.*kc(mn).*sigma(3)))./k1(mn)+

(sigma(2).*costh2_1));

pe_1(:,mn) = 1i.*sum(V_1.*besselj(0,sqrt(k1(mn).^2-

u_1.^2).*r).*exp(1i.*u_1.*(hs+hr)).*du_1);%hier een - voorzetten?

umax_2 = 200;

du_2 = 0.001;

uu_2 = du_2/2:du_2:umax_2-du_2/2;

u_2=1i.*uu_2;

costh2_2=sqrt(kc(mn).^2-k1(mn).^2+u_2.^2)./kc(mn);

V_2=((1i.*Zc(mn).*u_2.*cot(costh2_2.*kc(mn).*sigma(3)))./k1(mn)-

(sigma(2).*costh2_2))./((1i.*Zc(mn).*u_2.*cot(costh2_2.*kc(mn)*sigma(3)))./k1(mn)+(

sigma(2).*costh2_2));

pe_2(:,mn)=-1i.*sum(V_2.*besselj(0,sqrt(k1(mn).^2- u_2.^2).*r).*exp(1i.*u_2.*(hs+hr)).*du_2.*i);

pe(:,mn)=pe_1(:,mn)+pe_2(:,mn)+exp(1i.*k1(mn).*Rdirect)./Rdirect;

end

ppe(mmm,:)=pe;

L(mmm,:)=20*log10(real(pe));

DiffL = L(1,:) - L(2,:);

plot(fc,DiffL) grid on

xlabel('Frequency') ylabel('SPL difference')

end

8.3 Set-up test measurements

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