^{#}Fan Li and Xin Cai contributed equally to this work

In this paper, the effects of different influencing factors and factor interaction on the compressive strength and permeability of recycled aggregate pervious concrete (RAPC) were studied based on the response surface method (RSM). By selecting the maximum aggregate size, water cement ratio and target porosity as design variables, combined with laboratory tests and numerical analysis, the influences of three factors on the compressive strength and permeability coefficient of RAPC were revealed. The regression equation of compressive strength and permeability coefficient of recycled aggregate pervious concrete were established based on RSM, and the response surface model was optimized to determine the optimal ratio of RAPC under the conditions of meeting the mechanical and permeability properties. The results show that the mismatch item of the model is not significant, the model is credible, and the accuracy and reliability of the test are high, but the degree of uncorrelation between the test data and the model is not obvious. The sensitivity of the three factors to the compressive strength is water cement ratio > maximum coarse aggregate particle size > target porosity, and the sensitivity to the permeability coefficient is target porosity > maximum coarse aggregate particle size > water cement ratio. The absolute errors of the model prediction results and the model optimization results are 1.28 MPa and 0.19 mm/s, and the relative errors are 5.06% and 4.19%, respectively. With high accuracy, RSM can match the measured results of compressive strength and permeability coefficient of RAPC.

In recent years, urban rainstorm and floods have occurred frequently in cities. Experts have pointed out that impermeability and water logging of urban pavements and easy accumulation of water are some of the main causes of this situation. In this context, pervious concrete, as an important material basis for realizing the ‘sponge city’, has become the focus of researchers’ attention [

For conventional bearing concrete, people tend to pursue its small porosity in order to meet the strength requirements. However, for pervious concrete, due to the need to meet the requirements of water permeability, its porosity must be maintained within a certain range, and its strength and structural stability must also be ensured. From the perspective of pore structure, closed pores, semi-connected pores and connected pores are three types of pervious concrete pores [

The mix proportion design methods of pervious concrete mainly include specific surface area method, mass method, calculation formula method and volume method. Nguyen et al. [

In general, the current research on RAPC is mostly about the influence of single variable on its performance, while the influence of multi-factor interaction on its performance is rarely studied, and the research focus is more on the influence of coupling effect on its performance. Therefore, the response surface methodology (RSM) [

The raw materials for the test: (1) Mixing water: tap water; (2) Recycled coarse aggregate: the removal components of the concrete frame structure are artificially broken to remove steel bars. After crushing by jaw crusher and artificial screening, the basic performance indicators of coarse aggregate are shown in

Aggregate type | Size/mm | Performance density/( |
Stacking density/( |
Moisture content/% | 15 min water absorption/% | Crush index/% |
---|---|---|---|---|---|---|

Recycled aggregate | 5∼10 | 2559 | 1230 | 2.53 | 5.13 | 9.53 |

10∼15 | 2527 | 1212 | 4.21 | 5.97 | 18.31 | |

15∼20 | 2408 | 1185 | 5.90 | 6.96 | 29.30 |

Due to the difference in structure and composition, pervious concrete and ordinary concrete have very different proportions and design processes. From the design results, porosity and strength are the two main indicators that need to be considered for both ordinary concrete and porous concrete. For ordinary concrete, the principle of porosity is that the smaller the better. However, for permeable concrete, due to the need to meet the requirements of water permeability, its porosity must be maintained within a certain range, and its strength and structural stability must be ensured [

In the

The amount of coarse aggregate per unit volume.

Group | Aggregate size (mm) | W/C | Porosity (%) | Coarse aggregate |
Cement |
Water |
Water reducer |
---|---|---|---|---|---|---|---|

1 | 5∼10 | 0.20 | 15 | 1382 | 590 | 147 | 5.90 |

2 | 5∼10 | 0.25 | 20 | 1382 | 465 | 140 | 4.65 |

3 | 5∼10 | 0.30 | 25 | 1382 | 359 | 126 | 3.59 |

4 | 10∼15 | 0.20 | 15 | 1435 | 475 | 119 | 4.75 |

5 | 10∼15 | 0.25 | 20 | 1435 | 359 | 108 | 3.59 |

6 | 10∼15 | 0.30 | 25 | 1435 | 478 | 167 | 4.78 |

7 | 15∼20 | 0.20 | 15 | 1473 | 358 | 90 | 3.58 |

8 | 15∼20 | 0.25 | 20 | 1473 | 487 | 146 | 4.87 |

9 | 15∼20 | 0.30 | 25 | 1473 | 379 | 133 | 3.79 |

In the formula, α is the correction coefficient of coarse aggregate dosage, which is 0.98.

Cement paste volume.

In the formula,

Water-cement ratio

Cement consumption per unit volume.

Water consumption per unit volume.

The amount of additive per unit volume.

In the formula a is the dosage of additive (%).

The manufacture and maintenance of specimens are carried out indoors. Artificial mixing concrete was used in the test, and the size of specimens was 150 mm × 150 mm × 150 mm. The specimen production process is shown in the figure. After the specimen was formed for 1 d, it was put into the standard curing room for 28 d. The specific process is shown in

The bearing area of the pervious concrete specimen is different from that of ordinary concrete. The bearing area of ordinary concrete is the size of the specimen, and pervious concrete indicates that there are many pores, and the pore part does not bear pressure. Therefore, the bearing area of pervious concrete should be the area occupied by removing the pore part [

The permeability coefficient is one of the most important indicators of permeable concrete. At present, the determination method of permeability coefficient is roughly divided into two categories: fixed head method and falling head method. The difference between the two methods is shown in

In this paper, the maximum aggregate particle size, water cement ratio and target porosity are set as response factors, and three factors and three levels are set. The 28 d compressive strength and permeability coefficient are taken as response values. The response surface design analysis is carried out by Design-Expert software. The specific test factors and level values are shown in

Factor | −1 | 0 | 1 |
---|---|---|---|

Maximum coarse aggregate size (mm): A | 10 | 15 | 20 |

Water cement ratio: B | 0.20 | 0.25 | 0.30 |

Target porosity (%): C | 15% | 20% | 25% |

Number | Maximum coarse aggregate size A | Water cement ratio B | Target porosity (%) C | 28 d compressive strength (MPa) | Permeability coefficient (mm/s) |
---|---|---|---|---|---|

1 | 10 | 0.2 | 20 | 26.4 | 2.4 |

2 | 20 | 0.2 | 20 | 12.8 | 3.2 |

3 | 10 | 0.3 | 20 | 18.2 | 2.2 |

4 | 20 | 0.3 | 20 | 9.8 | 4.7 |

5 | 10 | 0.25 | 15 | 25.2 | 1.5 |

6 | 20 | 0.25 | 15 | 12.5 | 1.9 |

7 | 10 | 0.25 | 25 | 14.6 | 2.8 |

8 | 20 | 0.25 | 25 | 14.5 | 2.8 |

9 | 15 | 0.2 | 15 | 24.3 | 1.7 |

10 | 15 | 0.3 | 15 | 14.9 | 2.1 |

11 | 15 | 0.2 | 25 | 23.8 | 2.9 |

12 | 15 | 0.3 | 25 | 10.1 | 3.5 |

13 | 15 | 0.25 | 20 | 18.2 | 2.2 |

14 | 15 | 0.25 | 20 | 18.9 | 2 |

15 | 15 | 0.25 | 20 | 18.5 | 2.2 |

16 | 15 | 0.25 | 20 | 18.5 | 2.3 |

17 | 15 | 0.25 | 20 | 18.2 | 2.2 |

According to the best approximation theorem of Weierstrass polynomial, most functions can be approximated by polynomials. Therefore, in practical applications, regardless of the relationship between the influencing factors and the response target value, the polynomial approximation model can be studied and discussed [

The compressive strength and permeability coefficient of RAPC were analyzed by multiple regression fitting, and the multiple regression equations of the coded value and the actual value were obtained as shown in

In formula:

Analysis of variance and significance test were performed on the above regression equations, as shown in

Source | Sum of squares | df | Mean square | Model performance | ||
---|---|---|---|---|---|---|

Model | 414.54 | 11 | 37.69 | 451.32 | <0.0001 | significant |

A-Maximum coarse aggregate size | 40.96 | 1 | 40.96 | 490.54 | <0.0001 | |

B-Water cement ratio | 133.40 | 1 | 133.40 | 1597.63 | <0.0001 | |

C-Target porosity | 7.02 | 1 | 7.02 | 84.10 | 0.0003 | |

AB | 6.76 | 1 | 6.76 | 80.96 | 0.0003 | |

AC | 39.69 | 1 | 39.69 | 475.33 | <0.0001 | |

BC | 4.62 | 1 | 4.62 | 55.36 | 0.0007 | |

A² | 11.15 | 1 | 11.15 | 133.52 | <0.0001 | |

B² | 0.0106 | 1 | 0.0106 | 0.1264 | 0.7367 | |

A²B | 17.70 | 1 | 17.70 | 211.99 | <0.0001 | |

A²C | 1.36 | 1 | 1.36 | 16.30 | 0.0099 | |

AB² | 10.58 | 1 | 10.58 | 126.71 | <0.0001 | |

Residual | 0.4175 | 5 | 0.0835 | |||

Lack of fit | 0.0855 | 1 | 0.0855 | 1.03 | 0.3675 | Not significant |

Pure error | 0.3320 | 4 | 0.0830 | |||

Cor total | 414.96 | 16 |

Source | Sum of squares | df | Mean square | Model performance | ||
---|---|---|---|---|---|---|

Model | 9.40 | 9 | 1.04 | 81.92 | <0.0001 | significant |

A-Maximum coarse aggregate size | 2.72 | 1 | 2.72 | 213.53 | <0.0001 | |

B-Water cement ratio | 0.6613 | 1 | 0.6613 | 51.86 | 0.0002 | |

C-Target porosity | 2.88 | 1 | 2.88 | 225.88 | <0.0001 | |

AB | 0.7225 | 1 | 0.7225 | 56.67 | 0.0001 | |

AC | 0.0400 | 1 | 0.0400 | 3.14 | 0.1198 | |

A² | 0.4379 | 1 | 0.4379 | 34.35 | 0.0006 | |

B² | 1.63 | 1 | 1.63 | 127.97 | <0.0001 | |

C² | 0.2684 | 1 | 0.2684 | 21.05 | 0.0025 | |

AC² | 1.05 | 1 | 1.05 | 82.45 | <0.0001 | |

Residual | 0.0893 | 7 | 0.0128 | |||

Lack of fit | 0.0413 | 3 | 0.0138 | 1.15 | 0.4323 | Not significant |

Pure error | 0.0480 | 4 | 0.0120 | |||

Cor total | 9.49 | 16 |

The

The statistical analysis results of the RAPC compressive strength and water permeability regression equation errors are shown in ^{2} of the model were 0.9990 and 0.9906, respectively, indicating that the predicted values of the model were in good agreement with the measured values. The model calibration coefficient of determination ^{2} were 0.9968 and 0.9785, that is, the model regression equation can simulate the response value changes of 99.68% and 97.85%, respectively. The absolute values of the difference between the model calibration coefficient of determination ^{2} and the model prediction coefficient of determination ^{2} were 0.0356 and 0.1026, respectively, which were less than 0.2, indicating that the regression model can fully explain the process problems. The precisions (

Statistical project | Compressive strength/permeability coefficient | Statistical project | Compressive strength/permeability coefficient |
---|---|---|---|

0.289/0.1129 | 0.9990/0.9906 | ||

17.61/2.51 | 0.9968/0.9785 | ||

1.64/4.51 | 0.9612/0.8759 | ||

16.09/1.18 | 68.3752/37.0948 |

Therefore, the regression equation of the model can replace the true value of the test and analyze the test results. From

The three-dimensional response surface and contour map established by the response surface analysis method can intuitively reflect the influence of the interaction between experimental factors on the response target (compressive strength and permeability coefficient), that is, when a certain factor is a certain value, the influence of the interaction between the other two factors on the response value. The contour shape can reflect the strength of the interaction effect. The elliptic shape indicates that the interaction between the two factors is obvious, while the circular shape is the opposite. The level selection of the third factor in this paper is determined by the optimal condition of the response target.

Therefore, in the comprehensive selection of RAPC mix proportion, according to its demand for physical performance indicators, that is, to meet the strength and permeability requirements of RAPC application scenarios, the region where the required performance is determined according to the response surface, and the fine test can be carried out, so as to avoid blind test without understanding the change of law, and reduce unnecessary material, financial and human losses.

With the use of the optimization options in Design-Expert software, the input conditions (maximum coarse aggregate particle size, water cement ratio, target porosity) are set in the range of low value to high value of the factor level, and the response target value is solved to obtain the target response results and their suitability. The error between the model optimization prediction results and the measured results is shown in

Response index | Response condition | Response results | Appropriateness | ||
---|---|---|---|---|---|

Maximum coarse aggregate size/mm | W/C | Target porosity /% | |||

Compressive strength/MPa | 10.02 | 0.23 | 15.13 | 26.57 | 1 |

Permeation coefficient/mm⋅s^{−1} |
19.99 | 0.29 | 21.43 | 4.72 | 1 |

Make RAPC under the following test conditions and obtain performance indicators: Compressive strength: the maximum coarse aggregate particle size is10 mm, water cement ratio is 0.2, the target porosity is 15%; permeability coefficient: the maximum coarse aggregate particle size is 20 mm, water cement ratio is 0.3, the target porosity is 20%. The conditions in the above optimization results are used for experimental verification, and the results are shown in

Test metric | Response condition | Measured results | Absolute error | Relative error | ||
---|---|---|---|---|---|---|

Maximum coarse aggregate size/mm | W/C | Target porosity /% | ||||

Compressive strength/MPa | 10 | 0.2 | 15 | 25.29 | 1.28 | 5.06% |

Permeation coefficient/mm⋅s^{−1} |
20 | 0.3 | 20 | 4.53 | 0.19 | 4.19% |

In the optimization results, the optimization results of compressive strength and permeability coefficient of RAPC are 26.57 MPa and 4.72 mm/s, respectively, and the corresponding measured compressive strength and permeability coefficient are 25.29 MPa and 4.53 mm/s, respectively. The absolute errors with the model optimization results are 1.28 MPa and 0.19 mm/s, and the relative errors are 5.06% and 4.19%, respectively, with high accuracy. The experimental results are close to the prediction results of model optimization, indicating that the response surface analysis method is of practical significance for experimental design, analysis and target prediction.

Based on RSM, an optimization model with RAC compressive strength and permeability coefficient as response values and maximum aggregate particle size, water cement ratio and target porosity as corresponding factors was established. The model was considered to have a certain degree of credibility fitted by multiple regression approximation equations, variance analysis and error statistical analysis. On this basis, the corresponding surface and contour plots were drawn and it was found that the influence of water cement ratio on the compressive strength of RAC exceeds the maximum coarse aggregate particle size and target porosity, while the significance of porosity on the permeability coefficient of RAC exceeds the maximum coarse aggregate particle size and water cement ratio. In addition, under the multi-factor interaction of RAC, the optimal result of the strength model was obtained when the maximum aggregate size was 10 mm, the water-cement ratio was 0.2, and the target porosity was 15%, at which time the 28 d compressive strength of RAC was 25.29 MPa. It is the optimal result of the permeability model when the maximum aggregate size was 20 mm, the water-cement ratio was 0.3, and the target porosity was 20%. at which time the permeability coefficient of RAC was 4.53 mm/s, and the relative errors were 5.06% and 4.19% respectively compared with the measured data.

Thanks to the help provided by Teacher Cai Xin of the College of Mechanics and Materials from Hohai University.