# A Comparative Study on Water and Gas Permeability of Pervious Concrete

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{−8}to 10

^{−4}m

^{2}. However, the difference between the gas and water permeability of pervious concrete remains unknown. There is no reason that the gas and water permeability of pervious concrete would correlate similarly to those of normal concrete. For instance, for normal concrete, gas permeability has been found to be greater than water permeability due to the gas slippage effect [13,14,15]. This effect is substantial on fluid transport within normal concrete, but it is not necessarily notable on fluid transmission inside pervious concrete because the pores of the two kinds of concrete are several orders of magnitude different [16]. Thus, it is worth measuring the gas permeability of pervious concrete and examining how this permeability is different from water permeability.

## 2. Experiments

#### 2.1. Sample Preparation

^{3}and a crushing index of 8.0%. The cement/aggregate ratio was 1:4. In addition, to enhance the workability of the fresh mixture, a water reducing agent of 2% relative to the cement mass was supplemented to fabricate all pervious samples. The mixture proportions of the pervious concrete samples are shown in Table 1.

^{3}. All mixtures were layered and inserted layer by layer to ensure the uniformity of the specimens and produce good continuous pores. Without any vibratory compaction, the mixture in the mold was leveled with a scraper. All samples were de-molded after 48 h and then cured in a standard room at 20 °C and with a relative humidity of more than 95%. To avoid the impact of vibration inhomogeneity, cylinders with a diameter of 100 mm and a height of 100 mm were drilled from the pervious samples after they had cured for 28 days using a core drilling machine and 25 mm was cut off the top and bottom surfaces of the cylinder samples for treatment. Every cured block was drilled for six cores with a diameter of Φ100 mm × 100 mm (Figure 1).

_{1}is the weight of the sample with underwater buoyancy (kg), m

_{2}is the weight of the dried sample (kg), ρ is the water density (1.0 g/cm

^{3}) and V is the sample volume (m

^{3}).

#### 2.2. Water Permeability Test

_{l}(m

^{3}) was collected during the time interval ∆t, the permeability coefficient k

_{l}(m

^{2}) of the pervious concrete could be calculated using Equation (2):

_{l}is the water viscosity (Pa.s), ρ is the water density (kg/m

^{3}), g is the gravitational force (m/s

^{2}), h is the difference between the water head inlet and outlet (h = 0.1 m), L is the sample length (m) and A is the cross-sectional area of the pervious concrete sample (m

^{2}).

#### 2.3. Gas Permeability Test

#### 2.3.1. Gas Permeameter for Normal Concrete

_{g}(m

^{3}/s) is collected during the time interval t (s), the apparent gas permeability k

_{g}(m

^{2}) of pervious concrete is calculated using:

_{g}represents the dynamic viscosity of the gas (Pa.s), P

_{i}represents the gas pressure at the inlet (Pa) and P

_{0}represents the gas pressure at the outlet, which is normally set as the atmospheric pressure (1.03 × 10

^{−5}Pa).

^{−18}m

^{2}, a length of 10 cm, a diameter of 10 cm and an assumed gas pressure at the inlet of 2 P

_{atm}(~0.2 Mpa) [21], collecting 10 cm

^{3}of gas would require 15,420 s (4.3 h). In reality, more time is required to complete a testing cycle because the test cannot commence until a steady flow is attained. The testing time could range from 5–7 days [22]. If a sample is to be tested under different pressure gradients, it would require several months. Precautions must be taken to prevent evaporation losses from the soap bubble volumetric gas flowmeter during these long testing times.

_{i}− P

_{atm}needed to be set as low as possible because the gas flow rate through pervious concrete is orders of magnitude faster than that through normal concrete. The minimum difference was set as 100 Pa because digital pressure gauges have an accuracy of 100 Pa. Assuming the same sample geometry and a gas permeability of 10

^{−10}m

^{2}, the gas collected by the gas flowmeter would have been 42 cm

^{3}/s. This rate would be too fast to be recorded correctly by the soap bubble volumetric gas flowmeter. Actual gas flow rates tend to be higher than this value (42 cm

^{3}/s) because greater relative pressures (>100 Pa) are expected during the test and gas permeability tends to be greater than 10

^{−10}m

^{2}. Therefore, the steady flow method indicated in Figure 3 is widely used to calculate the permeability of normal concrete but is unsuitable to measure the permeability of pervious concrete.

#### 2.3.2. A Novel Device for Testing the Gas Permeability of Pervious Concrete

_{1}and noting that P

_{1}− P

_{2}= ρ

_{l}g∆h, we obtained:

_{l}and ρ

_{g}are the densities of water and gas (kg/m

^{3}), respectively, ∆h is the head difference read from the venturi tube (m), A

_{1}and A

_{2}are the cross-sectional areas of the larger and smaller sections of the venturi tube (m

^{2}), respectively, and C

_{D}is the coefficient of the longitudinal friction loss that was induced by the gas compressing in the tube’s narrow section [23].

_{g}(m

^{2}) could be computed as:

_{F}is a drag constant of dimensionless form, which is approximately equal to 0.55 according to Ward’s work [24]. The gas that flowed from the side with a large pressure is signified by the negative sign on the right hand side. In Equation (9), all variables could be measured except the gas permeability k

_{g}, which could be solved using the iterative numerical method.

#### 2.4. Testing Information

_{D}= 0.97) was estimated according to [23].

## 3. Results

^{−10}to 10

^{−9}m

^{2}, which represented the predicted permeability of pervious concrete. Considering that there is seldom water pooling on pervious pavement surfaces, the water head difference across the sample was set to be relatively small. The pressure gradient used during the gas permeability test was set to be relatively large to maintain the measurable head difference in the capillary tube. Although the applied pressures were different, the extrapolation of the gas permeability and water permeability could draw the same conclusion, i.e., the water permeability was several times greater than the gas permeability.

_{v}represents the inherent permeability of the material (which can be calculated when the applied pressure approaches infinity (m

^{2})) and p

_{m}is the average pressure. In these permeability tests, p

_{m}was:

_{0}represents the atmospheric pressure (1.03 × 10

^{5}Pa). Substituting Equation (11) into Equation (10) and noting that $\rho \mathit{gh}/2\ll {p}_{0}$, Equation (12) can be obtained:

_{v}, b) and compares the porosity and density. The permeability of the pervious concrete samples accorded with Equation (13), as vindicated by Figure 7 and R

^{2}in Table 2. The intrinsic permeability k

_{v}was the permeability when the pressure difference reached infinity. Taking into consideration the fact that an infinite mean pressure is identical to an infinite pressure difference (i.e., ${p}_{1}+{p}_{0}\to \infty $ is equal to ${p}_{1}-{p}_{0}\to \infty $), the permeability k

_{v}in Equation (10) had the same meaning and magnitude as the permeability k

_{v}in Equation (13); both were the intrinsic permeability.

_{v}increased with porosity, which was completely consistent with the research results in the literature [25,26,27]. A linear correlation is shown in Figure 7, which also shows good agreement. However, in this study, the porosity of the pervious concrete samples was limited to a narrow range (25~32%) while the typical permeability of pervious concrete can be around 15~35%, so there was not a good correlation between the intrinsic permeability and porosity. The water permeability of the samples was found to be approximately 4–5 times greater than the gas permeability.

## 4. Discussion

#### 4.1. Difference between Water and Gas Permeability

#### 4.2. Standardizing the Permeability Test for Pervious Concrete

_{v}and the correlation coefficient b, according to Equation (13) [21,33]. Both of these values can be used as reference parameters to compare the permeability of different pervious concrete samples. The water heads should be kept at low magnitudes, such as < 20 cm. This is because there is very seldom water pooling on in situ pervious concrete surfaces. The purpose of using a low pressure gradient is also to encourage a laminar flow through the sample.

## 5. Conclusions

^{−10}to 10

^{−9}m

^{2}, depending on the applied pressure. The measured gas permeability was found to be lower than the water permeability. This difference could be due to the wetting of internal pores by water, which reduced the surface tension between the fluid and the medium. Because of this reduction in surface tension, the seeping water needed to overcome lower viscous forces than the percolating gas. This phenomenon was contrary to the observations for normal concrete, for which the gas permeability is greater than the water permeability due to the gas slippage effect.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The prepared pervious concrete samples (

**a**) cylindrical sample is drilled from the specimen; (

**b**) Drilled samples.

**Figure 2.**The instrument for measuring the permeability of the pervious concrete samples: (

**a**) schematic outline; (

**b**) laboratory setup.

**Figure 4.**The developed apparatus to measure the gas permeability of pervious concrete: (

**a**) schematic outline; (

**b**) laboratory setup.

**Figure 7.**The measured values of the permeability of the pervious concrete samples and the reciprocals of the pressure differences.

Sample | Cement | Water | Aggregate | Water Reducer |
---|---|---|---|---|

w/c = 0.25 | 523.16 | 130.79 | 1509.00 | 1.40 |

w/c = 0.28 | 486.35 | 136.18 | 1509.00 | 1.40 |

Sample | k_{v} (m^{2}) | b (KPa) | R^{2} | Porosity | Density | ||||
---|---|---|---|---|---|---|---|---|---|

Water | Gas | Water | Gas | Water | Gas | (%) | (kg/m^{3}) | ||

Mix1 | No.1 | 12.43 | 3.77 | 0.22 | 1.08 | 0.931 | 0.986 | 31.59 | 1731 |

No.2 | 8.06 | 2.00 | 0.25 | 1.98 | 0.916 | 0.997 | 28.19 | 1767 | |

Mix2 | No.1 | 7.56 | 1.74 | 0.31 | 2.56 | 0.930 | 0.956 | 26.59 | 1802 |

No.2 | 4.96 | 1.09 | 0.35 | 3.01 | 0.929 | 0.998 | 25.64 | 1828 |

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**MDPI and ACS Style**

Wei, G.; Tan, K.; Liang, T.; Qin, Y.
A Comparative Study on Water and Gas Permeability of Pervious Concrete. *Water* **2022**, *14*, 2846.
https://doi.org/10.3390/w14182846

**AMA Style**

Wei G, Tan K, Liang T, Qin Y.
A Comparative Study on Water and Gas Permeability of Pervious Concrete. *Water*. 2022; 14(18):2846.
https://doi.org/10.3390/w14182846

**Chicago/Turabian Style**

Wei, Gang, Kanghao Tan, Tenglong Liang, and Yinghong Qin.
2022. "A Comparative Study on Water and Gas Permeability of Pervious Concrete" *Water* 14, no. 18: 2846.
https://doi.org/10.3390/w14182846