Relationship between percolation mechanism and pore characteristics of recycled permeable bricks based on X-ray computed tomography

The relationship between percolationmechanism and pore characteristics for recycled permeable bricks with different porosities is investigated in this study based on X-ray computed tomography (X-CT). Permeability coefficients are measured and some characteristics including size, amount, and distribution of the pore are analysed. The results show that the effective porosity and permeability coefficient of the recycled permeable bricks exhibit a linear relationship first and then a quadratic curve relationship, where the critical effective porosity is 12%.Meanwhile, we discovered that nonlinear channels in permeable bricks are larger and fewer comparedwith linear percolation channels, regardless of whether the percolation stage is linear or nonlinear. Additionally, when the area and number ratios of the linear and nonlinear percolation channels reached 80% and 10%, respectively, the overall percolation state of the permeable bricks changed from linear to nonlinear percolation. This research is helpful to improve themechanical and percolation properties of recycled concrete bricks and promote the application of porous permeable material.


Introduction
Rapid urbanisation greatly meets the needs of people's lives while leading to several problems such as environmental pollution, urban waterlogging, and the urban heat island effect. The use of construction waste to prepare permeable bricks not only enables the recycling of construction waste, but also helps alleviate urban waterlogging. Owing to the effective mitigation of urban problems, studies regarding recycled permeable bricks have received widespread attention.
Currently, some engineering applications of recycled permeable concrete exist; however, research related to them is still in the initial stage, and pertain primarily to the mix ratio and basic properties, such as flexural strength, compressive strength, porosity, and permeability coefficient [1][2][3][4][5][6][7][8]. Some scholars studied the relationship between the pore structure and permeability coefficient of permeable concrete and provided some interesting researching results. Kuang et al. studied permeable pavement porestructure parameters using a modified Kozeny-Carman model and discovered that the relationship between permeability coefficient (k) and porosity exhibited a power law model [9]; Sumanasooriya et al. [10], Sumanasooriya and Neithalath [11], Neithalath et al. [12] employed a computational procedure to predict the permeability of 12 different pervious concrete mixtures. Zhong et al. [13] used the linear path function proposed by Lu et al. [14] to calculate the pore size distribution of permeable concrete and verified it through image analysis. These studies mainly analysed the relationship between the internal pore structure and permeability, but did not reveal the internal percolation mechanism of permeable concrete and the key parameters governing the percolation state.
Hence, to reveal the percolation mechanism, an indepth investigation regarding the relationship between the permeability and pore characteristics of recycled permeable bricks based on the existing porous media percolation theory was performed in this study. Regarding porous medium percolation theory, Darcy's law is the most extensively used empirical formula for calculating flow in porous media. Subsequently, Reynolds identified two different fluid morphologies, i.e. laminar and turbulent, and reported that a critical velocity (v) existed between the two, which was related to the equivalent diameter (d), viscosity (µ), and density (ρ) of the fluid, hence, the Reynolds number In addition, Bachmat et al. discovered that Darcy's law in porous media percolation is applicable only at low Reynolds numbers (Re <1~10) [15]. Many scholars studied the deviation from Darcy's law. For example, Hubbert [16] and Scheidegger [17], reported that the deviation from Darcy's law was caused by inertial forces, and that the fluid was in a nonlinear laminar flow stage. The characterisation of internal pore structure is critical to study the percolation problem in porous media. Currently, the main methods for characterising pores include image analysis as well as intrusive and nonintrusive methods. Among them, the intrusive method mainly includes the mercury injection method and nitrogen adsorption methods [18], whereas the nonintrusive method mainly include nuclear magnetic resonance, sound absorption coefficient [19], small-angle scattering, and X-ray computed tomography (X-CT). X-CT offers outstanding advantages in the analysis of pore structure in porous media owing to its nondestructive and high accuracy. In recent years, many re-searchers have applied X-CT to concrete materials. Results show that X-CT is not only used to identify the internal components of concrete based on image grayscale [20], but also used to characterise changes in pores and cracks in concrete and the interface between aggregates and cement at different time periods [21][22][23][24][25]. At the same time, X-CT is often used to characterize the dynamic changes of the internal structure of concrete under external loads [26][27][28].
Therefore, the pore structure in permeable bricks was studied based on X-CT images, and the percolation state of recycled permeable bricks was analysed based on porous media percolation theory in this study. Furthermore, the effects of the distribution, number, and pore size of linear and nonlinear channels on the permeability of recycled permeable bricks were studied to ascertain the relationship between the percolation mechanism and pore characteristics of recycled permeable bricks.

Materials
P.O 42.5 cement in accordance with the requirements of the GB175-2007 Chinese standard [29] produced by Zhejiang Qianchao Co., Ltd. and fly ash in accordance with the requirements of the GB/T 1596-2017 Chinese standard [30]      were used, and their properties are listed in Table 1 and Table 2 respectively. The superplasticiser used in the test was polycarboxylic superplasticiser produced by Qingdao Hongxia Company, and its properties are listed in Table 3. The recycled aggregates produced by Haining Hongxiang Building Materials Co., Ltd. were used, and its basic properties are listed in Table 4. PVA fibre with a bulk density of 0.45 g/cm 3 and hydroxypropyl methyl cellulose (HPMC) were used as admixtures in the test. The properties of PVA fibre are presented in Table 5.

Preparation of recycled permeable bricks
After being stirred in an LHB-III asphalt mixer, cement mixture with recycled aggregate was poured into a steel mould measuring 40 mm × 120 mm × 160 mm and subjected to a certain pressure (3.0 MPa) using a pressure testing machine. A photograph of the experimental setup is shown in Figure 1. Moulded samples were cured indoors at 20 ∘ C for 24 h and then cured at the standard curing temperature of 20 ∘ C and a humidity above 95%. The mix ratio design of the recycled permeable brick was based on the volume method of the target porosity. Specifically, the amount of each material was calculated according to the volume formula after determining the empirical water-cement ratio and setting the target porosity. The amount of fly ash was 10% of the binding materials, and the amount of superplasticiser was adjusted to ensure that the same fluidity for each test group. The mix proportions of the specimens are shown in Table 6. Groups C are recycled permeable bricks with different target porosities, whereas groups M are recycled permeable bricks modified with PVA fibre and HPMC.

Determination of water permeability coeflcient
At the age of 28 days, a 75-mm-diameter cylinder was removed from the recycled permeable brick using a coring machine, and the water permeability coefficient was measured in accordance with the requirements of the GB / T 25993-2010 Chinese standard [31]. The formula to calculate the water permeability coefficient is shown in (2).
Where Q is the seepage flow (cm 3 ); L is the thickness of the permeable brick (cm); A is the cross-sectional area of the permeable brick (cm 2 ); H is the head difference (cm); t is the seepage time (s); Kτ is the water permeability coefficient (cm/s).

Determination of effective porosity by Archimedes
The effective porosities of recycled permeable bricks by Archimedes were measured in accordance with the requirements of the DB11/T775-2010 Chinese standard [32]. After the specimen was dried to a constant weight in an oven at (105±5) ∘ C, the size of the specimen was measured, and the volume V (cm 3 ) was calculated. Subsequently, the specimens was immersed in water and the weight, m1 (g) of the specimen in water was measured. The weight m 2 (g) of the specimen was measured after the specimen was removed from the water and dried in an oven at 60 ∘ C for 24 h. The formula to calculate the effective porosity P by Archimedes is shown in (3).

X-CT
An XHT320 X-ray computed tomography scanner with a resolution less than 10 µm from Zhejiang University was used. The permeable brick was dried in an oven at 60 ∘ C for 48 h, and then a computed tomography scan was performed to obtain a three-dimensional (3D) image of the permeable brick, as shown in Figure 2. The 3D image of the permeable brick was cut horizontally into 200 layers, and the porosity was calculated using a Matlab program. First, the pixel threshold was determined for binarisation; then, the 'bwareaopen' function was used to denoise and the 'bwlabel' function to obtain the pore area; finally, the 'tabulate' function was used to count the distribution frequency of the pores. The binary process is shown in Figure 3, from which we can count the effective porosity of each sample as well as the area and number of pores of different sizes.

.1 Effective porosity of recycled permeable bricks by X-CT and Archimedes
The effective porosity of the recycled permeable bricks obtained from Archimedes and X-CT are shown in Figure 4. As shown, the effective porosities obtained by the two test methods were close, and the overall trend was consistent. When the effective porosity was small, the effective porosity by Archimedes was smaller than the effective porosity by X-CT. As the effective porosity increased, the effective porosity by Archimedes increased faster and exceeded the effective porosity by X-CT. This occurred because Archimedes' method could not incorporate closed pores, whereas X-CT When the effective porosity was small, more closed pores appeared inside the permeable brick, rendering the porosity by Archimedes smaller than the porosity by X-CT; when the effective porosity increased, the decrease in cement slurry reduced the proportion of closed pores and the effect of closed pores was less prominent than that of the pores on the surface error layer, rendering the porosity by Archimedes greater than that by X-CT. Figure 5 shows the relationship between the effective porosity and permeability coefficient by Archimedes and X-CT. The fitting function is shown in the figure, where K A is the permeability coefficient obtained by Archimedes, K C is the permeability coefficient obtained by X-CT, and Pe is the effective porosity. As shown in the figure, the relationships between effective porosity and permeability coefficient obtained using the two methods were similar. As the effective porosity increased, both K A and K C increased linearly first and then increased in a curve. The critical effective porosities obtained by Archimedes and X-CT were both approximately 12%. When the effective porosity was less than 12%, a linear relationship was exhibited between the effective porosity and permeability coefficient; however, when the effective porosity was greater than 12%, a quadratic function relationship was exhibited between the effective porosity and permeability coefficient, indicating that the larger the effective porosity, the faster the permeability coefficient increased. Meanwhile, at the linear stage, the fitting slopes obtained by X-CT and Archimedes were similar, i.e. approximately 0.4; at the quadratic function stage, the increase

Percolation mechanism of recycled permeable bricks based on porous medium percolation theory
According to porous media percolation theory [33][34][35][36], a functional relationship is exhibited between the effective porosity and permeability coefficient because as the effective porosity increased, the number and size of pores inside the permeable brick increased, causing the Reynolds number to increase gradually; hence, the laminar flow transformed into a turbulent flow. Therefore, we propose to divide the percolation channels inside the recycled permeable brick into linear and nonlinear channels. A linear channel refers to a type of percolation channel where the Reynolds number is small and the viscous force of the channel is dominant, thereby presenting a linear laminar flow. A nonlinear channel is a type of percolation channel where the dominance of channel percolation changes from viscous force to inertial force as the Reynolds number increases, thereby presenting a nonlinear laminar flow. The effective porosity increased gradually with the Reynolds number of the channels. When the Reynolds number was less than the critical Reynolds number, the percolation of the linear channel was dominant such that the overall percolation state inside the permeable bricks was reflected as a linear laminar flow; when the Reynolds number exceeded the critical Reynolds number, the nonlinear laminar flow percolation was dominant such that the overall percolation state inside the permeable brick was reflected as a nonlinear laminar flow.
According to the relationship between effective porosity and permeability coefficient, the critical effective porosity of the percolation state inside the recycled permeable brick was 12%. When the effective porosity was less than 12%, the linear channels dominated, and the overall percolation state of the permeable bricks was reflected as a linear laminar flow; when the effective porosity was greater than 12%, the nonlinear channels dominated, and the overall percolation state inside the permeable bricks was reflected as a nonlinear laminar flow.

Distribution of pores inside recycled permeable bricks
The 3D image of the recycled permeable bricks obtained by X-CT were sliced horizontally into 200 layers to obtain the pore structure of each layer of the recycled permeable bricks, as shown in Figure 6. The effective porosity of each slice of the recycled permeable bricks can be calculated using Matlab. The distribution of effective porosity with different layers is shown in Figure 7.  permeable bricks were relatively large, indicating that the pressure formed caused the porosity of the surface and bottom to increase, and that the effect of the pressing passive surface was greater than that of the pressing active surface. By contrast, the effective porosities of the middle layers were relatively small.
It is clear that the deviation in the effective porosity distribution should be monitored when preparing permeable bricks. If moulding methods such as double-sided or double pressing can be adopted, then the longitudinal distribution of pores in the permeable bricks will be more uniform and the overall permeability will improve.

Linear channels and nonlinear channels of recycled permeable bricks
Based on the relationship between effective porosity and permeability coefficient, the critical effective porosity was approximately 12%. The C4 group was closest to this critical state; therefore, it was regarded as the critical point for the change in the percolation state, where the effective porosity was 12.3%, and the permeability coefficient was 4.3×10 −2 cm/s. Meanwhile, the kinematic viscosity of water was 1.006×10 −6 m 2 /s at 20 ∘ C, and Re = 1 was defined as the boundary between linear laminar and nonlinear laminar. Therefore, the critical pore diameter (dcr) was 0.233 cm according to Reynolds formula (1). As such, channels with equivalent pore diameters larger than 0.233 cm were considered as nonlinear channels in this study.
To study the distribution of nonlinear and linear channels in recycled permeable bricks and ascertain its relationship with the overall percolation state of permeable bricks, the total area, total number, and average area of the linear and nonlinear channels of the recycled permeable bricks in 200 layers were calculated in a Matlab program. Their relationships with effective porosity are shown in Figure 8-10.
As shown in Figures 8-10, the total areas of the nonlinear channels are always larger than those of the linear channels, and the total numbers of nonlinear channels are always smaller than that of linear channels. For the nonlinear channels, the total and average areas increased linearly, and the total numbers increased slightly between 13 and 30 with the increase in effective porosity. Meanwhile, the total areas, total numbers, and average areas of the linear channels did not change significantly with the increase in effective porosity. For the linear channels, the total area declined slightly between 0.7 and 1.1 cm 2 , the total numbers  Therefore, both linear and nonlinear channels existed inside the permeable bricks regardless of whether the linear percolation stage was linear or nonlinear. In addition, the areas of the linear channels were always smaller than those of the nonlinear channels, and the numbers of linear channels were always greater than those of the nonlinear channels. We believe that the change in the overall percolation state of the permeable bricks was due to the different development laws of the area and the numbers of linear and nonlinear channels. The decisive factor for the overall percolation state of the permeable brick may be the proportion of the area and the number of linear and nonlinear channels, rather than their specific values. Hence, the areas and numbers of nonlinear channels were calculated based on those parameters, and the results are shown in Figure 11. Figure 11 shows that the proportion of the area and the number of nonlinear channels of the permeable bricks increased linearly with the effective porosity. In addition, the threshold of the percolation state requires the proportion of area of the nonlinear channel to be approximately 80% and the proportion of number of nonlinear channels to be approximately 10%. When the two proportions reached the threshold, the percolation state of the permeable bricks changed from linear to nonlinear percolation with a network-like nonlinear laminar flow system forming inside the permeable brick.

Conclusion
In this study, pore structure characteristics including pore size, number, and distribution inside a permeable brick was investigated through X-CT and a Matlab program, and the relationship between percolation mechanism and pore characteristics of recycled permeable bricks was ascertained. The main conclusions are as follows: 1. With the increase in the effective porosity obtained by Archimedes and X-CT, the permeability coefficients of recycled permeable bricks increased linearly first and then increased in a quadratic function. In the linear stage, the fitting slopes of the graphics obtained by X-CT and Archimedes were similar, i.e. approximately 0.4. In the quadratic stage, the increase rate of the permeability coefficient obtained by X-CT was greater with the increase in the effective porosity. 2. The critical effective porosity of the percolation state inside the recycled permeable bricks was 12%. When the effective porosity was less than 12%, the linear channels dominated the percolation flow, and the overall percolation state of the permeable brick presented a linear laminar flow; when the effective porosity was greater than 12%, the nonlinear channels dominated the percolation flow, and the overall percolation state of the permeable brick presented a nonlinear laminar flow. 3. Regardless of whether the percolation stage was linear or nonlinear, the total areas of the nonlinear channels were always larger than those of the linear channels, and the total numbers of nonlinear channels were always smaller than those of the linear channels. With the increase in the effective porosity, the total and average areas of the nonlinear channels increased linearly and the number of nonlinear channels increased slightly; however, the total area, number, and average area of the linear channels did not change significantly. Additionally, when the area and number of nonlinear channels reached approximately 80% and 10%, respectively, the overall percolation state of the permeable bricks changed from a linear percolation flow to a nonlinear percolation flow.
This research is helpful to improve the mechanical and percolation properties of recycled concrete bricks and promote the application of porous permeable material.

Conflict of interest:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability statement:
The data that support the findings of this study are available on request from the corresponding author.