# Experimental Study on the Mechanical Properties of Reinforced Pervious Concrete

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Raw Material

_{3}A) content of 5.78%, tricalcium silicate (C

_{3}S) content of 62.00%, dicalcium silicate (C

_{2}S) content of 10.80% and tetracalcium aluminum ferrite (C

_{4}AF) content of 8.70%.

^{3}of cement, 1530 kg/m

^{3}of coarse aggregate, 130 kg/m

^{3}of water, and 2.2 kg/m

^{3}of superplasticizer.

#### 2.2. Test Specimens and Methods

#### 2.2.1. Compressive Strength Test

#### 2.2.2. Flexural Strength Test

#### 2.2.3. Elastic Modulus Test

#### 2.2.4. Measurement of Water Permeability Coefficient

^{−2}cm/s) and refers to the test instrument measured in the literature of Hong et al. [39]. The inner diameter of the upper end of the water pipe is a 95 mm acrylic pipe and is connected to a pervious concrete PVC pipe. The pipes are connected with rubber sleeves and iron rings are used to pressurize them to prevent leakage. The permeability coefficient Equation (2) is as follows:

_{1}is the cross-sectional area of the upper acrylic tube (cm

^{2}), A

_{2}is the measure of the cross-sectional area of the test object (cm

^{2}), h1 is the initial water head height (cm), h

_{2}is the final water head position (cm), L is the height of specimen (cm), and t is the the time it takes for water to flow from h

_{1}to h

_{2}(sec).

#### 2.2.5. Porosity Measurement Test

_{1}) is calculated, as shown in Equation (3).

_{1}is the connected porosity (%), W

_{1}is the specimen immersed in water and weighed after being saturated with water, W

_{2}is the dry internally saturated weight of the specimen soaked in water for 24 h, and V

_{1}is the volume of the specimen measured and calculated with a caliper.

#### 2.2.6. Repeated Load Test

## 3. Results and Discussion

#### 3.1. Results of Material Testing of Pervious Concrete and Reinforcing Material

#### 3.2. Repeated Load Test Results of Pervious Concrete Cylindrical Specimen

_{c}) of pervious concrete.

#### 3.3. Results of Stress and Strain Model of Pervious Concrete

#### 3.3.1. Single Compressive Stress–Strain Curve

_{c}′ is the ultimate peak stress of the cylindrical specimen, ε

_{c}′ is the strain value when the compressive strength reaches the ultimate peak stress,$nisthe\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{f}\mathrm{i}\mathrm{t}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}=\frac{{E}_{c}}{({E}_{c}-{E}_{c}^{\prime})}$, where ${E}_{c}^{\prime}=\frac{{f}_{c}^{\prime}}{{\epsilon}_{c}^{\prime}}$, and $\mathrm{k}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{y}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}k=0.67+\frac{{f}_{c}^{\prime}}{62}$(MPa).

_{c}′, ε

_{c}′ and E

_{c}are the average values of the experimental data of each ratio, and E

_{c}′, n and k are obtained from the empirical formula. The stress–strain curve obtained by bringing the above parameters into Popovics Equation (5) is the red curve in Figure 10 and is compared with other experimental values. It is evident that the experimental values closely resemble the Popovics parameter curve. Therefore, it can be inferred that the stress–strain curve of pervious concrete can also be predicted directly using Equation (5) proposed by Popovics.

#### 3.3.2. Compressive and Single Compressive Stress–Strain Curves after Repeated Loading

#### 3.4. Results of Mechanical Behavior of Beams under Repeated Loading and Single Loading

#### 3.4.1. Beam Bending Strength

^{b}× 80

^{h}× 500

^{L}mm. Figure 12 shows the flexural strength of pervious concrete beam specimens with and without the glass fiber mesh and steel wire mesh. In the figure, the beam specimens are numbered 1 and 2, such as NB-O1 or NB-O2, which are direct single-load failure tests. Each number has two beam specimens. The specimens numbered 3 and 4, such as NB-O3 or NB-O4, are subjected to single-load failure after 50,000 cycles of repeated loading. Among them, NB-O3 and NB-O4 were damaged during 35,000 and 42,500 repeated loads, respectively, so their single compression strength after repeated loading cannot be measured. The results showed that the glass fiber mesh had no significant effect on the bending strength, but the steel mesh had a double increase in the flexural strength. The flexural rupture strength test of pervious concrete beams includes specimens with and without wire mesh and fiber-free pervious concrete by Lee et al. [7]. A total of 13 specimens were used to analyze the cracking moment coefficient. The results are shown in Table 7. It can be obtained that the average cracking coefficient of permeable concrete is 0.86. Equation (6) will be used as the subsequent design calculation of the cracking modulus (f

_{r}) of pervious concrete.

#### 3.4.2. Force Behavior of Beams during Repeated Loading

_{c}I

_{e}) at each repeated stage.

_{c}I

_{e}values for each repeated cycle show a substantial decrease at 10,000 cycles, followed by a relatively stable pattern.

## 4. Conclusions

- Variations in the compressive strength and elastic modulus were observed between single and repeated loading conditions. Repeated loading led to a slight increase in both compressive strength (8%) and elastic modulus (16%) due to a compaction effect.
- The compressive strength (fc′) was determined to be around 15 MPa. Empirical formulas for elastic modulus and cracking modulus, as derived in Equations (4) and (6), are useful for pervious concrete component design.
- This study applied the Popovics stress–strain curve theory, finding that the compressive behavior aligns with typical pervious concrete behavior (Equation (5)).
- Popovics stress–strain curves after single compression and repeated loading exhibited similar trends (correspondence only reaching strain values of 0.25%), with data after 10,000 and 50,000 loading cycles slightly exceeding the recommended single compression curve.
- Pervious concrete initially displayed greater stiffness and section rigidity in single loading but showed a reduction in stiffness and section rigidity with an increased number of repeated loading cycles.
- The addition of steel wire mesh to pervious concrete significantly improved flexural strength, approximately doubling that of ordinary pervious concrete, and enhanced ductility in the reinforced specimens.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Repeated load test plan (

**a**) compressive cylindrical specimen and (

**b**) bending beam specimen.

**Figure 8.**Repeated load test: (

**a**) compressive strength and (

**b**) elastic modulus of pervious concrete corresponding to load cycles.

**Figure 11.**Comparison of Popovics stress–strain curves after single compression and repeated loading.

**Figure 12.**Flexural strength of pervious concrete beam with and without glass fiber mesh and steel mesh.

**Figure 13.**Changes in (

**a**) stiffness and (

**b**) section rigidity of beam specimens with and without wire mesh during repeated loading cycles.

**Figure 14.**Comparison of repeated load–displacement diagrams of beam specimens with and without wire mesh (NB-O, NB-G and NB-S).

Sieve Size | Individual Fraction Retained by Mass (%) | Passing by Mass (%) | Cumulative Retained by Mass (%) |
---|---|---|---|

9.5 mm | 0 | 100 | 0 |

#4 (4.75 mm) | 72.3 | 27.7 | 72.3 |

#8 (2.36 mm) | 22.5 | 5.2 | 94.8 |

#16 | 2.0 | 3.2 | 96.8 |

#30 | 1.2 | 2.0 | 98.0 |

#50 | 2.0 | 0 | 100 |

#100 | 0 | 0 | 100 |

Pan | 0 | 0 | 100 |

Fineness modulus = 5.62 |

Grid Type | R108 | G96 | G120 |
---|---|---|---|

Grid size (mm) | 9 × 9 | 25 × 25 | 40 × 40 |

Grid weight (g/m^{2}) | 140 | 130 | 145 |

Chemical coating | Alkali resistant |

Pervious Concrete | Mean | Standard Deviation | Coefficient of Variation (%) | ACI 522R-10 Standard |
---|---|---|---|---|

Water permeability coefficient (cm/s) | 2.39 | 0.20 | 8.17 | ≥0.1 |

Porosity (%) | 20.35 | 1.82 | 8.96 | 18~35 |

Mesh | Code | Width | Diameter/ Thickness (mm) | A_{S} *(mm ^{2}) | f_{u} * (MPa) | Δ * (%) | E_{C}(MPa) |
---|---|---|---|---|---|---|---|

Glass fiber | R108 | 0.39 | 0.91 | 0.35 | 764 | 2.26 | 33,825 |

G96 | 0.51 | 1.99 | 1.02 | 627 | 1.82 | 34,461 | |

G120 | 0.61 | 3.26 | 1.98 | 655 | 1.87 | 35,059 | |

Steel wire | D5 | - | 5 | 19.63 | 621 | 15 | 200,000 |

_{S}: cross-sectional area, f

_{u}: tensile breaking strength, Δ: elongation).

Specimen# | ${\mathit{f}}_{\mathit{c}}^{\prime}$(MPa) | ${\mathit{\epsilon}}_{\mathit{c}}^{\prime}$ | ${\mathit{E}}_{\mathit{c}}$(MPa) |
---|---|---|---|

NC-O1(0)-1 | 15.59 | 0.0019 | 9438 |

NC-O1(0)-2 | 15.62 | 0.0020 | 11,125 |

NC-O1(0)-3 | 15.10 | 0.0024 | 9608 |

N-O-1 [7] | 13.32 | 0.0018 | 8605 |

N-O-2 [7] | 12.51 | 0.0012 | 13,650 |

N-O-3 [7] | 16.79 | 0.0017 | 14,985 |

N-O-4 [7] | 14.95 | 0.0013 | 13,984 |

N-O-5 [7] | 16.87 | 0.0021 | 10,306 |

N-O-6 [7] | 14.83 | 0.0031 | 9816 |

Mean | 15.06 | 0.002 | 11,280 |

Standard deviation | 1.43 | 0.0006 | 2322 |

CV (%) | 9.5 | 29.4 | 20.6 |

Parameter | fc′ (MPa) | εc′ (%) | Ec′ (MPa) | Ec (MPa) | n | k | k, _{suggest} |
---|---|---|---|---|---|---|---|

Mean | 15.06 | 0.002 | 7530 | 11,280 | 3.01 | 0.91 | 1 |

Specimen# | f_{r} | f_{c}′ | $\sqrt{{\mathit{f}}_{\mathit{c}}\prime}$ | k |
---|---|---|---|---|

NB-O1 | 2.16 | 15.44 | 3.93 | 0.55 |

NB-O2 | 2.16 | 15.44 | 3.93 | 0.55 |

NB-G1 | 2.36 | 15.44 | 3.93 | 0.60 |

NB-G2 | 1.90 | 15.44 | 3.93 | 0.48 |

NB-G3 | 2.90 | 15.44 | 3.93 | 0.74 |

NB-G4 | 2.72 | 15.44 | 3.93 | 0.69 |

NB-S1 | 5.32 | 15.44 | 3.93 | 1.35 |

NB-S2 | 5.23 | 15.44 | 3.93 | 1.33 |

NB-S3 | 5.71 | 15.44 | 3.93 | 1.45 |

NB-S4 | 5.52 | 15.44 | 3.93 | 1.40 |

N-O-1 [7] | 3.01 | 14.88 | 3.86 | 0.78 |

N-O-2 [7] | 3.33 | 15.19 | 3.90 | 0.85 |

N-O-3 [7] | 2.71 | 15.35 | 3.92 | 0.69 |

Mean | 3.47 | 15.37 | 3.92 | 0.86 |

Specimen# | Cycles | (a) $\mathbf{P}$ $\left(\mathbf{k}\mathbf{N}\right)$ | (b) ${\u2206}_{\mathit{i}}$ $\left(\mathbf{m}\mathbf{m}\right)$ | (c) = (a)/(b) ${\mathbf{K}}_{\mathit{i}}$ $(\mathbf{k}\mathbf{N}/\mathbf{m}\mathbf{m})$ | ${\mathbf{E}}_{\mathbf{c}}{\mathbf{I}}_{\mathbf{e},\mathit{i}}$ $\mathbf{k}\mathbf{N}$$-{\mathbf{m}\mathbf{m}}^{2}$ $\times {10}^{7}$ | $\frac{{\mathbf{E}}_{\mathbf{c}}{\mathbf{I}}_{\mathbf{e},\mathit{i}}}{{\mathbf{E}}_{\mathbf{c}}{\mathbf{I}}_{\mathbf{e},1}}$ |
---|---|---|---|---|---|---|

NB-O (no wire mesh) | 1 | 1.5 | 0.1869 | 8.03 | 3.23 | 1.00 |

10,000 | 1.5 | 0.2708 | 5.54 | 2.37 | 0.73 | |

20,000 | 1.5 | 0.3513 | 4.27 | 2.39 | 0.74 | |

30,000 | 1.5 | 0.4253 | 3.53 | 2.28 | 0.71 | |

40,000 | 1.5 | 0.4933 | 3.04 | 2.55 | 0.79 | |

50,000 | - | - | - | - | - | |

NB-G (glass fiber mesh) | 1 | 1.5 | 0.1564 | 9.59 | 6.36 | 1.00 |

10,000 | 1.5 | 0.2613 | 5.74 | 5.55 | 0.87 | |

20,000 | 1.5 | 0.3356 | 4.47 | 5.51 | 0.87 | |

30,000 | 1.5 | 0.4247 | 3.53 | 5.38 | 0.85 | |

40,000 | 1.5 | 0.5169 | 2.90 | 5.33 | 0.84 | |

50,000 | 1.5 | 0.6137 | 2.44 | 4.73 | 0.74 | |

NB-S (steel mesh) | 1 | 1.8 | 0.1837 | 9.80 | 4.28 | 1.00 |

10,000 | 1.8 | 0.3097 | 5.81 | 2.97 | 0.69 | |

20,000 | 1.8 | 0.4259 | 4.23 | 2.78 | 0.65 | |

30,000 | 1.8 | 0.5440 | 3.31 | 2.81 | 0.66 | |

40,000 | 1.8 | 0.6611 | 2.72 | 2.72 | 0.63 | |

50,000 | 1.8 | 0.7753 | 2.32 | 2.81 | 0.66 |

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## Share and Cite

**MDPI and ACS Style**

Lee, M.-G.; Wang, Y.-C.; Wang, W.-C.; Chien, H.-J.; Cheng, L.-C.
Experimental Study on the Mechanical Properties of Reinforced Pervious Concrete. *Buildings* **2023**, *13*, 2880.
https://doi.org/10.3390/buildings13112880

**AMA Style**

Lee M-G, Wang Y-C, Wang W-C, Chien H-J, Cheng L-C.
Experimental Study on the Mechanical Properties of Reinforced Pervious Concrete. *Buildings*. 2023; 13(11):2880.
https://doi.org/10.3390/buildings13112880

**Chicago/Turabian Style**

Lee, Ming-Gin, Yung-Chih Wang, Wei-Chien Wang, Hung-Jen Chien, and Li-Chi Cheng.
2023. "Experimental Study on the Mechanical Properties of Reinforced Pervious Concrete" *Buildings* 13, no. 11: 2880.
https://doi.org/10.3390/buildings13112880