# Study on Air Void Characteristics and Hydraulic Characteristics of Porous Asphalt Concrete Based on Image Processing Technology

Authors: Zhanqi Wang; Jianguang Xie; Lei Gao; Yanping Liu; Kuan Li
Journal: Geofluids
 (2021)

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## Abstract

The appearance of porous asphalt (PA) pavement is to solve the problem of road ponding in rainy days. The internal air voids in PA pavement are the main functional structure that determines its drainage performance. It is of great practical significance to find out the relationship between void drainage capacity and air voids. This paper is aimed at researching the relationship between three-dimensional (3D) pore structures and drainage performance of PA concrete. Four samples were formed and scanned by CT equipment to obtain the internal cross-sectional CT images. Image dodging algorithm and OTSU method were conducted to deal with these CT images for segmenting them into three subimages (void image, asphalt mortar image, and aggregate image) according to the three components of PA concrete. The voids on void images were identified and classified into three groups according to the three kind of pores (interconnected pore, semi-interconnected pore, and closed pore) and reshaped them into 3D pore structures according to the overlapping principle. Then, the volume and size distribution of the pores was analyzed. Besides, this research mainly focused on the influence of several parameters obtained from interconnected pores on the drainage performance of PA concrete at last. The permeability coefficient of PA concrete samples was tested, and equations between permeability coefficient and void content were fitted linearly. The distribution of hydraulic radius and cross-sectional area ratio was calculated and researched by statistical methods. A new parameter, perimeter variation coefficient, is proposed to study the influence of boundary wall roughness on the drainage performance. At last, equivalent drainage channel was drawn to reflect the drainage capacity of PA concrete.


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## Body

## 1. Introduction

In the engineering field, water stability and drainage problems have always been perplexing engineers and scholars [1–4]. Porous asphalt (PA) pavement is known as a kind of environmental friendly pavement due to its drainage, noise reduction, and antiskid properties [5–7]. PA pavement was originally designed for rapidly draining the rainwater to improve driving safety on rainy days. The drainage performance is closely linked with its interconnected pore structures [8, 9]. However, pore structures usually exist in PA concrete in extremely complex geometry, which poses a great challenge to study the relationship between drainage performance and characteristic parameters of pore structures.Void parameters (such as void content and size) are commonly used indicators instead of characteristic parameters of pore structures for researching its influence on drainage performance or other properties by most researchers [10–14]. Void parameters are usually obtained from two-dimensional cross-sectional images by using computed tomography (CT) technology combined with image processing technology. Although it is relatively easy to obtain void parameters, more efforts are needed to develop and propose pore characteristic parameters of pore structures, so as to study its influence on drainage performance more accurately. Three-dimensional (3D) reconstruction of pore structures is an important step to research its influence on drainage performance or other properties. Due to the complexity of pore geometry, there is still a lack of effective methods to reconstruct the 3D geometry and obtain characteristic parameters of pore structures at present, and only a few researchers have done some work in this field [15–17]. Gruber et al. [15] reconstructed the 3D model of pores and simulated the fluid flow in PA concrete sample by Avizo and ANSYS 12.0. Zhao et al. [16] proposed a method to separate the valid and invalid interconnected pores in PA concrete. Besides, in terms of drainage performance, most researches generally regarded PA concrete as permeable medium to study its macro drainage performance, but not to study the impact of its structure properties on drainage performance from the micro structure perspective [18–20]. Garcia et al. [18] analyzed the permeability reduction in drainage asphalt mixtures through a self-developed device and using the coefficient of permeability as the indicator to reflect the drainage performance of drainage asphalt mixtures. Aboufoul et al. [19] investigated the effects of air void topology on hydraulic conductivity in asphalt mixtures by using 3D printing technology, and permeability coefficient was also used for predicting the hydraulic conductivity.In this paper, the authors tried to find the key parameters affecting hydraulic characteristics based on image processing technology, which paves the way for further revealing the drainage characteristics of PA concrete. First, 3D pore structures were successfully reconstructed by overlapping principle. Second, the volume and size distribution of pores was analyzed. Third, the permeability coefficient of PA concrete samples was tested and equations between permeability coefficient and void content were fitted linearly. At last, several key hydraulic parameters affecting hydraulic characteristics were studied.


## 2. Materials and Mix Design

Four PA concrete (PAC-13) specimens were taken as the research object in this paper whose target void content was set to be 16%, 18%, 20%, and 22%, respectively. Due to mold size, the specimens were formed with the same size of300mm×300mm×40mm, in which the coarse aggregate was basalt, the fine aggregate was basalt machine-made sand, and appropriate amount of limestone powder was used as mineral powder filler. In addition, SBS-modified asphalt mixed high-viscosity additives (HVA) were used as binder to increase the adhesion between asphalt mortar and aggregates. The aggregate gradation is shown in Figure 1.Figure 1
Aggregate gradation.


## 3. CT Image Processing

CT scanning technology was used to scan the specimens to observe the internal structure, mainly observing the pore structures in PA concrete. Due to the allowed sample size of CT equipment, the four specimens were, respectively, cut into nine pieces with the same size of100mm×100mm×40mm, and the central piece was taken as target sample I~IV to be scanned. Besides, the samples were scanned along the thickness direction with an interval of 0.14 mm. In the process, 275, 272, 270, and 273 CT images were generated from the sample I~IV, respectively.Image processing is an important step to obtain and evaluate the characteristic of pore structures. A reliable image segmentation algorithm is indispensable and essential to segment these CT images. Image processing generally involves four steps: image graying (RGB to gray), median filtering, contrast enhancement, and image segmentation [6, 16]. Image segmentation is the most important step in the whole process; the segmentation algorithm directly determines the accuracy of subimages after segmentation. As we know, the OTSU algorithm [21] is a commonly used method to segment gray images due to its advantages such as simplicity, efficiency, and accuracy. The OTSU algorithm describes a method to separate target object and background in a digital image by finding out the key thresholds for classifying all the pixels into different groups. In this paper, the OTSU algorithm was also used in image segmentation. All the CT images were separated into three subimages by the OTSU algorithm according to the three components (void, asphalt mortar, and aggregate) of PA concrete, as shown in Figure 2. However, the quality of subimages was always disappointing while CT images without further improved process. For example, Figures 2(a1), 2(a2), and 2(a3) are subimages of CT image Figure 2(a), whose white areas stand for void, asphalt mortar, and aggregate, respectively. It is obvious in the figures that a part of aggregate was missing and wrongly classified as asphalt mortar or void. In most cases, CT images need to be preprocessed by specific methods before segmentation to eliminate some specific defects that affect the accuracy of segmentation. In this research, a universal phenomenon was found in most CT images that the aggregate in the center shows brighter (with larger intensity) while the aggregate at four corners shows darker (with smaller intensity), as shown in Figure 2(a). So it can be inferred that the uneven illumination may be the main defect that affects the accuracy of segmentation which needs to be preprocessed. Subsequently, a series of image dodging algorithms were conducted to unify the illuminance component of CT images before segmentation.Figure 2
CT image segmentation: (a) without dodging; (b) MASK dodging; (c) Retinex dodging; (d) homomorphic filter dodging; (e) 2D gamma dodging; (∗1) void; (∗2) asphalt mortar; (∗3) aggregate. The range of “∗” is (a)–(e).
(a)(b)(c)(d)(e)To meet different image processing demands in different fields, a variety of image dodging algorithms have been developed by researchers, such as MASK dodging [22], homomorphic filter dodging [23], Retinex dodging [24], and 2D gamma dodging [25]. In this paper, they were all conducted on the CT images to unify the illuminance component and then separated into three subimages, respectively, as shown in Figure 2. It is easy to find that CT image preprocessed by 2D gamma dodging shows the best segmentation effect: less aggregate missing and asphalt mortar and void being closest to actual situation. It should be noted, however, that this research mainly focused on the pore structures in PA concrete. A novel method to identify and reconstruct pore structures was introduced in Section 4, and the proportion of pore structures that connected with the outside space was calculated by MATLAB. The results are shown in Table 1.Table 1
Proportion of pore structures that connected with the outside space (%).
SampleIIIIIIIVWithout dodgingVc13.1014.8821.6725.12E34.897.157.303.262D gammaVc12.9314.4221.0324.47E33.183.854.125.77MASKVc13.0515.1122.2725.89E34.448.8010.230.27RetinexVc18.2521.5329.1330.21E87.9955.0444.2116.33HomomorphicVc13.2815.0821.9125.35E36.828.608.472.37Vp9.7113.8920.2025.97Furthermore, the four samples were placed into a measuring cup with proper amount of distilled water to measure the proportion of pore structures that connected with the outside space according to Equation (1). The measuring cup is shown in Figure 3, and measuring results are listed in Table 1. In addition, the errors between measured values and calculated values were obtained by Equation (2) and also listed in Table 1.(1)Vp=Va−VWVs,(2)E=∣Vp−Vc∣Vp,where Vp is the measured proportion of pore structures that connected with the outside space, Va is the volume of distilled water, Vw is the volume of distilled water with sample, Vs is the volume of sample, Vc is the calculated proportion of pore structures that connected with the outside space, and E is the error between Vp and Vc.Figure 3
Measuring device.
(a)(b)From Table1, it can be concluded that image dodging could improve the visual and sensory effects, but limited help for image segmentation. Compared with the measured values and errors, values calculated from the CT images that are preprocessed by 2D gamma image dodging are more accurate and reliable than the others. Values calculated from images preprocessed by Retinex image dodging show the maximum error. Considering the image segmentation effect and calculation accuracy, 2D gamma dodging algorithm was chosen to unify illumination of CT images for further research, eventually.


## 4. Identification and Reconstruction of Pore Structures

### 4.1. Identification of Pore Structures

As mentioned above, a series of CT images was obtained and separated into three subimages, including void image, asphalt mortar image, and aggregate image. Pore structures in PA concrete could be reconstructed through an appropriate algorithm by using air voids in void images. Actually, such an algorithm is available: overlapping principle. It is easy to imagine that air voids in two adjacent void images that share a common overlapping area, from the top view, must belong to the same pore structure if the interval of the two void images is close enough along the thickness direction. According to the overlapping principle, all the air voids in different CT images can be identified and classified into independent groups that belong to different pore structures. Thus, all the air void groups can be reshaped into pore structures by MATLAB, respectively.


### 4.2. Reconstruction of Pore Structures

Pore structures in PA concrete mainly can be classified into three types: interconnected pore (IP), semi-interconnected pore (SP), and closed pore (CP). Interconnected pore refers to the pore with two open ends that connected with the outside space at the top and bottom of samples. Semi-interconnected pore refers to the pore with an open end and a dead end. Closed pore refers to the pore with two dead ends that isolated from the outside space. According to the overlapping principle, a MATLAB program was properly edited and executed to reconstruct all the pore structures. Figure4 shows all the interconnected pore structures in the four samples. It can be seen that samples I~IV contain 3, 3, 1, and 1 interconnected pore, respectively. Pore structures in image (a)~(c) were reconstructed from sample I, images (d)~(f) were reconstructed from sample II, images (g) and (h) were reconstructed from samples III and IV, respectively. However, it is discouraged that all the pores have a complex and disorderly structure which turned out to be a challenge for further research. Besides, the samples also contain thousands of closed pores and dozens of semi-interconnected pores, which are not listed in Figure 4 due to the space limitation of the paper. In addition, it also can be inferred that the sample formed by the aggregate gradation with smaller target void content is more likely to form multiple independent interconnected pores, while the sample formed by the aggregate gradation with larger target void content is more likely to form single overall interconnected pore.Figure 4
Interconnected pore structures.
(a)
I-1(b)
I-2(c)
I-3(d)
II-1(e)
II-2(f)
II-3(g)
III(h)
IV


## 4.1. Identification of Pore Structures

As mentioned above, a series of CT images was obtained and separated into three subimages, including void image, asphalt mortar image, and aggregate image. Pore structures in PA concrete could be reconstructed through an appropriate algorithm by using air voids in void images. Actually, such an algorithm is available: overlapping principle. It is easy to imagine that air voids in two adjacent void images that share a common overlapping area, from the top view, must belong to the same pore structure if the interval of the two void images is close enough along the thickness direction. According to the overlapping principle, all the air voids in different CT images can be identified and classified into independent groups that belong to different pore structures. Thus, all the air void groups can be reshaped into pore structures by MATLAB, respectively.


## 4.2. Reconstruction of Pore Structures

Pore structures in PA concrete mainly can be classified into three types: interconnected pore (IP), semi-interconnected pore (SP), and closed pore (CP). Interconnected pore refers to the pore with two open ends that connected with the outside space at the top and bottom of samples. Semi-interconnected pore refers to the pore with an open end and a dead end. Closed pore refers to the pore with two dead ends that isolated from the outside space. According to the overlapping principle, a MATLAB program was properly edited and executed to reconstruct all the pore structures. Figure4 shows all the interconnected pore structures in the four samples. It can be seen that samples I~IV contain 3, 3, 1, and 1 interconnected pore, respectively. Pore structures in image (a)~(c) were reconstructed from sample I, images (d)~(f) were reconstructed from sample II, images (g) and (h) were reconstructed from samples III and IV, respectively. However, it is discouraged that all the pores have a complex and disorderly structure which turned out to be a challenge for further research. Besides, the samples also contain thousands of closed pores and dozens of semi-interconnected pores, which are not listed in Figure 4 due to the space limitation of the paper. In addition, it also can be inferred that the sample formed by the aggregate gradation with smaller target void content is more likely to form multiple independent interconnected pores, while the sample formed by the aggregate gradation with larger target void content is more likely to form single overall interconnected pore.Figure 4
Interconnected pore structures.
(a)
I-1(b)
I-2(c)
I-3(d)
II-1(e)
II-2(f)
II-3(g)
III(h)
IV


## 5. Distribution of Pore Structures

### 5.1. Volume Distribution

There are generally thousands of pore structures in PA concrete, most of which are micro closed pores. The number and volume of pore structures in the four samples were calculated and listed in Table2 after 3D reconstruction process. It can be seen that the number of closed pores with volume less than 1 mm3 accounts for more than 70% of the total number; however, their cumulative volume accounts for a very small proportion of the total volume of all the pores in the samples, which is less than 0.5%. In specimens I-V, the cumulative volume of all closed pores accounts for 8.53%, 7.62%, 1.97%, and 0.28% of the total pore volume, respectively. And the cumulative volume of all semi-interconnected pores accounts for 3.64%, 1.57%, 0.13%, and 0.05% of the total pore volume, respectively. The volume of interconnected pore is the absolutely dominant part of the total pore volume in samples I~IV, accounting for 87.83%, 90.81%, 97.90%, and 99.67%, respectively. It should be noted that each sample contains only one interconnected pore in the table. Actually, PA concrete with lower void content may contain several independent interconnected pores. It was found that the surface texture of samples has an important influence on 3D reconstruction process. The surface texture is an open boundary with a certain depth. All the independent interconnected pores will intersect with the surface texture at the top or bottom to form a whole. Therefore, the CT image within the texture depth must be deducted in the 3D reconstruction process to achieve the purpose of separating independent interconnected pores. For instance, three independent interconnected pores are separated from samples I and II when deducting CT images covering the texture depth in the 3D reconstruction process.Table 2
Number and volume distribution of pore structures.
Volume range (mm3)IIIIIIIVNum.Vol.Num.Vol.Num.Vol.Num.Vol.0~1IP00.0000.0000.0000.00SP319.94299.51387.96388.56CP945158.941101193.641378120.2937838.531~10IP00.0000.0000.0000.00SP1976.932164.22519.03611.13CP212675.86263838.51111358.6842136.7810~100IP00.0000.0000.0000.00SP6179.238377.49370.19221.75CP682060.12682182.7628574.10569.49100~500IP00.0000.0000.0000.00SP5927.522374.0900.0000.00CP71141.295782.713401.3400.00>500IP141566.90147654.50172185.50187136.70SP1530.8000.0000.0000.00CP00.0000.0000.0000.00Total129547327.53149852477.43156773737.0947287422.94


### 5.2. Size Distribution

As we know, the size of pore structures is definitely a significant factor that directly determines the drainage performance of PA concrete. However, due to the complex geometry of pore structures, it is difficult to find a reasonable parameter to characterize its size. In this research, equivalent diameter of voids on each CT images was calculated to reflect the size of pore structures from the perspective of statistics, as shown in Figure5. Equivalent diameter refers to the diameter of a circle whose area equal to the void. It can be seen that the void size is mainly distributed below 2.61 mm, most of which belongs to interconnected pores. The size of voids belonging to closed pores and semi-interconnected pores is mainly distributed below 5.21 mm. In terms of interconnected pores, void size is mainly below 5.21, but the distribution range is relatively wide, and the maximum value is greater than 20.86 mm. With the increase of void content, the proportion of void with large size gradually increases.Figure 5
Size distribution of voids.
(a)
I(b)
II(c)
III(d)
IV


## 5.1. Volume Distribution

There are generally thousands of pore structures in PA concrete, most of which are micro closed pores. The number and volume of pore structures in the four samples were calculated and listed in Table2 after 3D reconstruction process. It can be seen that the number of closed pores with volume less than 1 mm3 accounts for more than 70% of the total number; however, their cumulative volume accounts for a very small proportion of the total volume of all the pores in the samples, which is less than 0.5%. In specimens I-V, the cumulative volume of all closed pores accounts for 8.53%, 7.62%, 1.97%, and 0.28% of the total pore volume, respectively. And the cumulative volume of all semi-interconnected pores accounts for 3.64%, 1.57%, 0.13%, and 0.05% of the total pore volume, respectively. The volume of interconnected pore is the absolutely dominant part of the total pore volume in samples I~IV, accounting for 87.83%, 90.81%, 97.90%, and 99.67%, respectively. It should be noted that each sample contains only one interconnected pore in the table. Actually, PA concrete with lower void content may contain several independent interconnected pores. It was found that the surface texture of samples has an important influence on 3D reconstruction process. The surface texture is an open boundary with a certain depth. All the independent interconnected pores will intersect with the surface texture at the top or bottom to form a whole. Therefore, the CT image within the texture depth must be deducted in the 3D reconstruction process to achieve the purpose of separating independent interconnected pores. For instance, three independent interconnected pores are separated from samples I and II when deducting CT images covering the texture depth in the 3D reconstruction process.Table 2
Number and volume distribution of pore structures.
Volume range (mm3)IIIIIIIVNum.Vol.Num.Vol.Num.Vol.Num.Vol.0~1IP00.0000.0000.0000.00SP319.94299.51387.96388.56CP945158.941101193.641378120.2937838.531~10IP00.0000.0000.0000.00SP1976.932164.22519.03611.13CP212675.86263838.51111358.6842136.7810~100IP00.0000.0000.0000.00SP6179.238377.49370.19221.75CP682060.12682182.7628574.10569.49100~500IP00.0000.0000.0000.00SP5927.522374.0900.0000.00CP71141.295782.713401.3400.00>500IP141566.90147654.50172185.50187136.70SP1530.8000.0000.0000.00CP00.0000.0000.0000.00Total129547327.53149852477.43156773737.0947287422.94


## 5.2. Size Distribution

As we know, the size of pore structures is definitely a significant factor that directly determines the drainage performance of PA concrete. However, due to the complex geometry of pore structures, it is difficult to find a reasonable parameter to characterize its size. In this research, equivalent diameter of voids on each CT images was calculated to reflect the size of pore structures from the perspective of statistics, as shown in Figure5. Equivalent diameter refers to the diameter of a circle whose area equal to the void. It can be seen that the void size is mainly distributed below 2.61 mm, most of which belongs to interconnected pores. The size of voids belonging to closed pores and semi-interconnected pores is mainly distributed below 5.21 mm. In terms of interconnected pores, void size is mainly below 5.21, but the distribution range is relatively wide, and the maximum value is greater than 20.86 mm. With the increase of void content, the proportion of void with large size gradually increases.Figure 5
Size distribution of voids.
(a)
I(b)
II(c)
III(d)
IV


## 6. Hydraulic Characteristics

PA pavement is aimed at quickly removing the rain water, increasing the skid resistance of pavement to improve the driving safety when it was born in the world. Pore structures act as a drainage pipe to drain rain water from pavement surface. The drainage performance of PA pavement depends on the size and geometry of pores. Due to the complex geometry of pores, it is hard to find a representative parameter to evaluate its drainage performance. Some researchers [18, 19] considered PA concrete sample as a whole to test its permeability coefficient for evaluating its drainage performance according to Darcy’s law [26] (Equation (3)) which was first proposed and used to test the permeability of soils. Although permeability coefficient may be a good choice for evaluating drainage performance in a sense, it is still a challenge to reveal the internal relationship between drainage performance and geometry of pores.(3)Q=kA∆HL,where Q is the seepage water volume per unit time, cm3/s; k is the permeability coefficient, cm/s; A is the top surface area of sample to be tested, cm2; ΔH is the water head difference between top and bottom of sample to be tested, cm; and L is the thickness of sample to be tested, cm.


### 6.1. Permeability Coefficient

According to Darcy’s law, permeability coefficient of samples I-IV was tested by constant water head method [26] in this research and the results are shown in Figure 6. Figure 6(a) shows the relationship between permeability coefficient and void content which was calculated from CT images. It can be seen that there is a highly linear positive correlation between permeability coefficient and void content. The correlation coefficient reaches 0.998. Figure 6(b) shows the relationship between permeability coefficient and measured void content Vp. It should be noticed that measured void content only involves the proportion of pore structures that connected with the outside space. Likewise, it can be found that the permeability coefficient also shows a high linear correlation with the measured void content, and the correlation coefficient reaches 0.987.Figure 6
Relationship between permeability coefficient and void content.
(a)(b)


### 6.2. Hydraulic Parameters

In Equation (3), ΔH refers to the mean value of water head loss, and L refers to the sample thickness rather than the seepage path. Actually, the flow pattern of water in the pore structures is extremely complex; due to the complex geometry of pores, it is hard to find an effective method for revealing the relationship between water head loss and flow pattern of water. This research mainly focused on some key parameters and analyzed their variation law, which lays a foundation for further study of hydraulic characteristics.As a kind of Newtonian fluid, flow resistance will be produced in the process of water flow due to its viscosity. To overcome the resistance, a part of mechanical energy will be consumed, resulting in head loss. There are two main reasons for the water head loss. One is the influence of viscosity. The interaction between water and solid wall boundary causes uneven velocity distribution on the cross section, which leads to friction resistance in the water flow. The liquid needs to consume a part of energy to overcome the friction resistance. The other is the influence of solid wall boundary. The sharp change of boundary shape will change the internal structure of water flow and produce vortex flow. The particles in the flow will collide with each other to convert kinetic energy and potential energy. In this process, a part of mechanical energy is converted into heat energy, resulting in energy loss. Besides, the head loss is also related to the microscopic motion of the liquid. Due to the microscopic motion, flow patterns of water can be divided into two types: laminar flow and turbulent flow. Osborne Reynolds [27, 28] has revealed the different nature of the two flow patterns through experiments in the 1880s and studied the relationship between head loss and pipe diameter, wall roughness, and velocity. According to the different reasons causing the water head loss, it can be generally divided into two parts, namely, the water head loss along flow path and the local water head loss. The general calculation equations are as follows [27]:(4)hf=λl4Rv22g,(5)λ=fRe,ΔR,(6)hj=ζv22g,(7)ζ=fA1A2,where hf is the water head loss along flow path, λ is the resistance coefficient along flow path, l is the flow path, R is the hydraulic radius, Δ is the boundary wall roughness, Re is the Reynolds number, v is the flow velocity, g is the acceleration of gravity, hj is the local water head loss, ζ is the local resistance coefficient, and A1/A2 is the cross-sectional area ratio at cross section change.In Equations (4)–(7), there are many unknown parameters that need to be determined. Only R and A1/A2 can be directly calculated from the CT images while the others are hard to obtain. Figure 7 shows the distribution of R and A1/A2 of interconnected pores in samples I~IV. Hydraulic radius is an important parameter that can comprehensively reflect the influence of cross-sectional shape and size on average velocity. A1/A2 can reflect the size change on each cross section of pores. It can be concluded from Figure 7(a) that hydraulic radius is mainly distributed in the range of [0.18, 0.88) mm, accounting for 83.54%, 85.90%, 77.54%, and 69.94% of the total number, respectively, in samples I~V, and the curves gradually flatten with the increase of specimen number, indicating that with the increase of void content, the number of larger voids increases gradually, and the drainage capacity increases in a sense. Besides, it can be seen from Figure 7(b) that the area ratio of adjacent cross sections of interconnected pores is mainly below 0.1, accounting for 99.43%, 99.71%, 99.38%, and 99.24% of the total number, respectively, in samples I~IV, indicating that the geometry of pore structures in PA concrete is extremely complex, which poses a very difficult challenge to the study of its drainage performance or other performances. Meanwhile, it can be found that almost all the values of A1/A2 are less than 1, indicating that the size of voids near the top is larger than that near the bottom.Figure 7
Distribution of hydraulic radius andA1/A2.
(a)(b)In Equation (5), λ is the function of Re, R, and Δ. Δ, called boundary wall roughness, refers to the average value of bulge height of boundary wall, which is an important factor that cannot be ignored. For pipe with regular shape, the roughness can be easily obtained, but for the pore structure in porous asphalt concrete, it is almost impossible to define and obtain the boundary wall roughness due to its complex shape. In this research, another similar parameter, called perimeter variation coefficient, was defined to reflect the boundary wall roughness. The perimeter variation coefficient is defined as follows:(8)CR=Po−PcPc,where CR is the perimeter variation coefficient, Po is the perimeter of void, and Pc is the perimeter of a circle equal to the area of the void.Figure8 shows the distribution of perimeter variation coefficient in samples I~IV.Figure 8
Distribution of perimeter variation coefficient.It can be seen that the values less than 1.06 account for 93.98%, 92.5%, 88.00%, and 85.01%, respectively, in samples I~V; likewise, the values larger than 1.06 account for 6.07%, 7.50%, 12.00%, and 14.99%, respectively. It can be concluded that the perimeter variation coefficient of samples with more void content is generally larger than that with less void content. The larger perimeter variation coefficient means that the perimeter contacting with the water flow becomes larger, which produces greater resistance to the water flow and is not conducive to the pavement drainage.It is easy to imagine that larger area for water passing on a cross section will show greater drainage capacity. Considering the interconnected pores as a whole pipe with only one water passing channel, take the centroid of all the voids on each CT images as the center of the pipe, and take the accumulated area value of each void on an image as the area of the channel; then, draw a circle on each cross section, respectively, as shown in Figure9. It can be seen that the size of the channel near the top is larger than that near the middle and lower part. The size of channels with larger sample number is generally larger than that with smaller sample number, indicating that sample with larger void content tends to show better drainage performance.Figure 9
Equivalent drainage channel.
(a)
I(b)
II(c)
III(d)
IV


## 6.1. Permeability Coefficient

According to Darcy’s law, permeability coefficient of samples I-IV was tested by constant water head method [26] in this research and the results are shown in Figure 6. Figure 6(a) shows the relationship between permeability coefficient and void content which was calculated from CT images. It can be seen that there is a highly linear positive correlation between permeability coefficient and void content. The correlation coefficient reaches 0.998. Figure 6(b) shows the relationship between permeability coefficient and measured void content Vp. It should be noticed that measured void content only involves the proportion of pore structures that connected with the outside space. Likewise, it can be found that the permeability coefficient also shows a high linear correlation with the measured void content, and the correlation coefficient reaches 0.987.Figure 6
Relationship between permeability coefficient and void content.
(a)(b)


## 6.2. Hydraulic Parameters

In Equation (3), ΔH refers to the mean value of water head loss, and L refers to the sample thickness rather than the seepage path. Actually, the flow pattern of water in the pore structures is extremely complex; due to the complex geometry of pores, it is hard to find an effective method for revealing the relationship between water head loss and flow pattern of water. This research mainly focused on some key parameters and analyzed their variation law, which lays a foundation for further study of hydraulic characteristics.As a kind of Newtonian fluid, flow resistance will be produced in the process of water flow due to its viscosity. To overcome the resistance, a part of mechanical energy will be consumed, resulting in head loss. There are two main reasons for the water head loss. One is the influence of viscosity. The interaction between water and solid wall boundary causes uneven velocity distribution on the cross section, which leads to friction resistance in the water flow. The liquid needs to consume a part of energy to overcome the friction resistance. The other is the influence of solid wall boundary. The sharp change of boundary shape will change the internal structure of water flow and produce vortex flow. The particles in the flow will collide with each other to convert kinetic energy and potential energy. In this process, a part of mechanical energy is converted into heat energy, resulting in energy loss. Besides, the head loss is also related to the microscopic motion of the liquid. Due to the microscopic motion, flow patterns of water can be divided into two types: laminar flow and turbulent flow. Osborne Reynolds [27, 28] has revealed the different nature of the two flow patterns through experiments in the 1880s and studied the relationship between head loss and pipe diameter, wall roughness, and velocity. According to the different reasons causing the water head loss, it can be generally divided into two parts, namely, the water head loss along flow path and the local water head loss. The general calculation equations are as follows [27]:(4)hf=λl4Rv22g,(5)λ=fRe,ΔR,(6)hj=ζv22g,(7)ζ=fA1A2,where hf is the water head loss along flow path, λ is the resistance coefficient along flow path, l is the flow path, R is the hydraulic radius, Δ is the boundary wall roughness, Re is the Reynolds number, v is the flow velocity, g is the acceleration of gravity, hj is the local water head loss, ζ is the local resistance coefficient, and A1/A2 is the cross-sectional area ratio at cross section change.In Equations (4)–(7), there are many unknown parameters that need to be determined. Only R and A1/A2 can be directly calculated from the CT images while the others are hard to obtain. Figure 7 shows the distribution of R and A1/A2 of interconnected pores in samples I~IV. Hydraulic radius is an important parameter that can comprehensively reflect the influence of cross-sectional shape and size on average velocity. A1/A2 can reflect the size change on each cross section of pores. It can be concluded from Figure 7(a) that hydraulic radius is mainly distributed in the range of [0.18, 0.88) mm, accounting for 83.54%, 85.90%, 77.54%, and 69.94% of the total number, respectively, in samples I~V, and the curves gradually flatten with the increase of specimen number, indicating that with the increase of void content, the number of larger voids increases gradually, and the drainage capacity increases in a sense. Besides, it can be seen from Figure 7(b) that the area ratio of adjacent cross sections of interconnected pores is mainly below 0.1, accounting for 99.43%, 99.71%, 99.38%, and 99.24% of the total number, respectively, in samples I~IV, indicating that the geometry of pore structures in PA concrete is extremely complex, which poses a very difficult challenge to the study of its drainage performance or other performances. Meanwhile, it can be found that almost all the values of A1/A2 are less than 1, indicating that the size of voids near the top is larger than that near the bottom.Figure 7
Distribution of hydraulic radius andA1/A2.
(a)(b)In Equation (5), λ is the function of Re, R, and Δ. Δ, called boundary wall roughness, refers to the average value of bulge height of boundary wall, which is an important factor that cannot be ignored. For pipe with regular shape, the roughness can be easily obtained, but for the pore structure in porous asphalt concrete, it is almost impossible to define and obtain the boundary wall roughness due to its complex shape. In this research, another similar parameter, called perimeter variation coefficient, was defined to reflect the boundary wall roughness. The perimeter variation coefficient is defined as follows:(8)CR=Po−PcPc,where CR is the perimeter variation coefficient, Po is the perimeter of void, and Pc is the perimeter of a circle equal to the area of the void.Figure8 shows the distribution of perimeter variation coefficient in samples I~IV.Figure 8
Distribution of perimeter variation coefficient.It can be seen that the values less than 1.06 account for 93.98%, 92.5%, 88.00%, and 85.01%, respectively, in samples I~V; likewise, the values larger than 1.06 account for 6.07%, 7.50%, 12.00%, and 14.99%, respectively. It can be concluded that the perimeter variation coefficient of samples with more void content is generally larger than that with less void content. The larger perimeter variation coefficient means that the perimeter contacting with the water flow becomes larger, which produces greater resistance to the water flow and is not conducive to the pavement drainage.It is easy to imagine that larger area for water passing on a cross section will show greater drainage capacity. Considering the interconnected pores as a whole pipe with only one water passing channel, take the centroid of all the voids on each CT images as the center of the pipe, and take the accumulated area value of each void on an image as the area of the channel; then, draw a circle on each cross section, respectively, as shown in Figure9. It can be seen that the size of the channel near the top is larger than that near the middle and lower part. The size of channels with larger sample number is generally larger than that with smaller sample number, indicating that sample with larger void content tends to show better drainage performance.Figure 9
Equivalent drainage channel.
(a)
I(b)
II(c)
III(d)
IV


## 7. Further Research

Although the 3D geometry of pore structures in PA concrete has been successfully reconstructed, it still remains a challenge to propose several key parameters for describing the geometry characteristics. Besides, there is no doubt that the drainage performance of pavement is related to the shape, size, roughness, and other related parameters of interconnected pores, but there is still a lack of effective way to obtain these parameters to evaluate its drainage performance, which needs further research.


## 8. Conclusions

This paper is aimed at researching the relationship between 3D pore structures and drainage performance of PA concrete. Four samples were formed and scanned by CT equipment to obtain the internal cross-sectional CT images. Image processing technology and OTSU method were conducted to deal with these CT images for segmenting them into three subimages (void image, asphalt mortar image, and aggregate image) according to the three components of PA concrete. The voids on void images were identified and classified into three groups according to the three kind of pores (interconnected pore, semi-interconnected pore, and closed pore) and reshaped them into 3D pore structures. Then, the volume and size distribution of the pores was analyzed. Besides, this research mainly focused on the influence of several parameters obtained from interconnected pores on the drainage performance of PA concrete at last. The conclusions are as follows:(1)
Image dodging plays an important role in CT image segmentation process. 2D gamma dodging shows an excellent performance in unifying the illumination component of CT images to improve the image segmentation effect(2)
Pore structures in PA concrete can be classified into three types according to the interconnectivity, including interconnected pore, semi-interconnected pore, and closed pore. Pore structures in the PA concrete can be reconstructed according to the overlapping principle(3)
PA concrete generally contains a lot of pores, most of which are closed pores, but their cumulative volume only accounts for about 0.5% of the total pore volume. The other small parts are semi-interconnected pores and interconnected pores; however, their cumulative volume accounts for more than 99% of the total pore volume(4)
The void size is mainly distributed below 2.61 mm, most of which belongs to interconnected pores. The size of voids belonging to closed pores and semi-interconnected pores is mainly distributed below 5.21 mm. With the increase of void content, the proportion of void with large size gradually increases(5)
There is a highly linear positive correlation between permeability coefficient and void content. The correlation coefficient reaches 0.998. The permeability coefficient also shows a high linear correlation with the measured void content, and the correlation coefficient reaches 0.987(6)
Hydraulic radius is mainly distributed below 0.88 mm. With the increase of void content, the number of larger voids increases gradually, indicating that the drainage capacity increases in a sense. The geometry of pore structures in PA concrete is extremely complex. Meanwhile, almost all the values ofA1/A2 are less than 1, indicating that the size of voids near the top is larger than that near the bottom(7)
The perimeter variation coefficient of samples with more void content is generally larger than that with less void content. The larger perimeter variation coefficient means that the perimeter contacting with the water flow becomes larger, which produces greater resistance to the water flow and is not conducive to the pavement drainage. PA concrete with larger void content is more likely containing larger water passing channel, which tends to show a better drainage performance



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*Source: 9432323-2021-10-14.xml*