# Study on Strength Variation of Permeable Concrete Based on Differential Calorimetry Method and Multi-Index Test

Authors: Sanqiang Yang; Meng Guo; Shichao Duan; Na Liu; Haonan Wu; Erxia Du; Meichen Liang
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

With the implementation of the Xiongan New Area and the urbanization construction plan surrounding the Beijing-Tianjin satellite, it is urgent to study and apply the sponge-permeable paving materials to solve the “urban waterlogging and heat island effect.” In this paper, the hydration microscopic characteristics of cementitious materials are analyzed by means of the differential scanning calorimetry (DSC) test. The test of water-cement ratio, porosity, and gradation structure on the strength and permeability coefficient is emphasized, and the strength change rule of porous permeable concrete is obtained. The research results are shown as follows: (1) The DSC test shows that the effect of temperature on the hydration process of cement is obvious. With the increase of temperature, the two exothermic peaks of cement hydration increase significantly and tend to overlap and the exothermic process is shortened. At 85°C, only one exothermic peak appeared, indicating that C3S hydration and ettringite formation process were completed at the same time in a relatively short time. (2) The optimal water-binder ratio of pervious concrete ranges from 0.24 to 0.30, and the optimal porosity ranges should be controlled within the range of 15%–25%. Moreover, the open gradation of pervious concrete mix ratio design is selected, and the cement content should be within the range of 20%–25%. (3) The mathematical model of permeability coefficient and porosity ratio of permeable concrete is established:k=−0.0003n2+0.0057n−0.0044; the mathematical model of permeability coefficient and compressive strength of open-graded pervious concrete: k=0.99006−0.05389c+8.02×10−4c2. The research results can provide theoretical support and technical guidance for the design and construction of permeable materials of sponge cities in Xiongan New Area and surrounding ring new area, which are of great engineering value.


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## Body

## 1. Introduction

In recent years, with the establishment and implementation of the Xiongan New Area construction and the national top-level planning plan for the satellite cities around Beijing and Tianjin, the construction of the sponge city in Xiongan New Area has accelerated [1]. Aiming at the sharp increase in hardened areas such as parks, plazas, and carriageways in the surrounding areas of the Xiongan New Area, the water circulation is worsened and the green area is reduced, which indirectly or directly affects the entire regional ecological environment [2]. The specific phenomena include the local high temperature, urban water logging, land subsidence, and severe dust and haze [3]. Under this background, it is urgent to study and apply sponge permeable concrete.The performance problem of permeable concrete materials has been the main focus of domestic and overseas scholar researches, mainly investigating the influence of water glue ratio, aggregate size, porosity and gradation structure on mechanical performance and water permeability of permeable concrete [4]. Kevern et al. from the State University of Iowa studied the influence of aggregate particle size on pervious concrete and found that the use of a single particle size aggregate can significantly improve the porosity of permeable concrete but the strength is relatively low. The workability and strength of concrete can be significantly improved by adding fine sand to the aggregate and latex to the mixing process [5]. Jiang et al. from Tongji University found that aggregate particle size and gradation are the key factors affecting porosity, permeability coefficient, and compressive strength of permeable concrete. The additives such as water-reducing agent, silica fume, and polymer emulsion can effectively improve the compressive strength and workability of the permeable concrete, but has less influence on the water permeability [6]. However, the main research is focused on the type and size of the aggregates, the structure, and the additive, and it does not have a systematic understanding of the material.As an important factor affecting the performance of concrete, porosity has been extensively studied by scholars at home and abroad. Deo and Neithalath, from Clarkson University, USA, studied the influence of pore structure on compressive behavior of permeable concrete. It is concluded that the compressive strength of pervious concrete decreases by about 50% for every 10% increase in porosity [7]. Sriravindrarajah et al. from the Sydney University of Technology, Australia, studied the mix ratio of permeable concrete. It is found that the compressive strength of pervious concrete mainly depends on the porosity, age, and binder of the aggregate. In case of a fixed porosity, the shape and size of the test piece also affect the compressive strength of the permeable concrete [8]. These studies may well support our next study, but lack of specificity, if we can study a linear relationship plot, will be a good representation of the relationship between them.Ibrahim et al. has been studying the effects of different water glue on the performance of water concrete, through practical experiments. The researchers give a linear model of compressive strength and water permeability: compressive strength = constant +a∗ unit cement consumption + b∗ water glue ratio + c∗ water consumption + d∗ aggregate (4.5 mm) + e∗ aggregate (9.5 mm) + f∗ aggregates (19.5 mm); permeability coefficient = constant + a∗ unit cement dosage + b∗ water-binder ratio + c∗ water consumption + d∗ aggregate (4.5 mm) + e∗ aggregate (9.5 mm) + f∗ aggregate (19.5 mm). Compressive strength and permeability coefficient are linear with the influencing factors, but the coefficients are not consistent [9]. There are not many studies on water-cement ratio, but the size of water-cement ratio affects the rheological property of slurry and is also the main parameter that determines the difference in strength and permeability of pervious concrete, which needs to be studied in detail [10].Based on the analysis of foreign and domestic research status, most of the permeable paving materials are concentrated in the field of grading structure design, lacking systematic and comprehensive material cognition; Secondly, the testing method is not advanced enough to change the material principle; moreover, the analysis of concrete indicators is single, lacking theoretical models, and it is difficult to reveal the intrinsic relevance of multi-index technical parameters [11]. Therefore, it is necessary to conduct multi-index experimental research on the strength and permeability coefficient of pervious concrete materials and analyze the hydration characteristics of cement from the microscopic perspective. Based on this, this paper relies on the construction project “Key Technology Research of Urban Road and Green Space Sponge Construction” and the Basic Research Fund of Materials in Hebei Province and analyzes the variation law of the strength of permeable concrete materials by means of differential heat and multi-index test methods [12]. Finally, the microscopic characteristics of cement hydration of permeable concrete are obtained, and the internal correlation law of multi-index technical parameters of permeable concrete is revealed, and various theoretical parameter models based on strength are constructed [13]. The research results fill the gap in the research on the influence strength of the multi-index test on permeable concrete, fit the mathematical model between different parameters by analyzing the experimental data, and formalize the relationship, providing strong support for the subsequent related research. The research results can provide theoretical support and technical guidance for the design and construction of permeable materials of sponge cities in Xiongan New Area and surrounding ring new area, which are of great engineering value.


## 2. Test Plan Design

The main factors affecting the strength of porous permeable concrete are the hydration characteristics of cementitious materials and the technical parameters of concrete [14]. In this study, the differential scanning calorimetry (DSC) test was used to analyze the hydration characteristics of cementitious materials; The parameter analysis of porous permeable concrete mainly relies on the test of the influence of water-binder ratio, porosity, and grading structure on strength and permeability coefficient.


### 2.1. Experimental Design of Hydration Characteristics of Cementitious Materials

This test uses PO.42.5 cement-based cementitious materials. In terms of the conventional cement hydration, the developing analysis of ettringite and the hydration test of C3S cannot show the effect of temperature on the microproperties of cement hydration [15]. In this study, differential scanning calorimetry (DSC) is used to determine the thermal analysis of the relationship between heat and temperature of PO.42.5 cement under temperature control procedures (temperature rise, constant temperature, and temperature drop). The principle is that according to the thermal effect of the PO.42.5 cement sample, a heat flow difference proportional to the temperature difference is generated between the sample end and the reference end, the temperature difference can be continuously measured by the thermocouple, the DSC spectrum is obtained after being corrected to the heat flow difference, and then the hydration characteristics of the cementitious material are analyzed [16]. The test equipment and program interface of differential scanning calorimetry (DSC) are shown in Figures 1 and 2.Figure 1
DSC200F3-type instrument.Figure 2
DSC software program interface.PO.42.5 cement-based cementitious material differential scanning calorimetry (DSC) test program design is as follows: The test sample is controlled at 5 mg ± 1 mg. The test temperature control program is to increase the cement to 80°C at a rate of 20 K/min at room temperature of 25°C.Then, the temperature is lowered for 5 min, the temperature is lowered to −60°C at a rate of 20 K/min, and then the temperature is raised to room temperature of 25°C at a rate of 10 K/min. At the end of the test, the Tg was directly obtained by a program or manually adjusted to obtain a Tg. The DSC test sample is shown in Figure3.Figure 3
DSC test sample.


### 2.2. Design of Technical Parameter Test Scheme for Pervious Concrete

The design of the test scheme for porous permeable concrete is mainly divided into the test scheme of water-binder ratio and strength, the test scheme of porosity and strength, and the test scheme of grading structure and strength. This is shown in Table1.Table 1
Test plan design.
Program
Water-cement ratio
Ratio of set
Cement dosage (kg/m3)
Dosage of water-reducing agent (kg/m3)
Dosage of reinforcing agent (kg/m3)
Aggregate dosage (kg)
Permeable coefficient (cm/s)
7 d compressive strength (MPa)
28 d compressive strength (MPa)
2.36–4.75
4.75–9.5
Program A
WBR1
CR1
C1
WR1
F1
—
CA1
PC1
7-CS1
28-CS1
WR1
F2
FA1
CA2
PC2
7-CS2
28-CS2
C2
WR2
F3
—
CA3
PC3
7-CS3
28-CS3
WR2
F4
FA2
CA4
PC4
7-CS4
28-CS4
C3
WR3
F5
FA3
—
PC5
7-CS5
28-CS5
WR3
F6
FA4
CA5
PC6
7-CS6
28-CS6
Program B
WBR2
CR2
C1
WR4
F1
—
CA1
PC7
7-CS7
28-CS7
WR4
F2
FA1
CA2
PC8
7-CS8
28-CS8
C2
WR5
F3
—
CA3
PC9
7-CS9
28-CS9
WR5
F4
FA2
CA4
PC10
7-CS10
28-CS10
C3
WR6
F5
FA3
—
PC11
7-CS11
28-CS11
WR6
F6
FA4
CA5
PC12
7-CS12
28-CS12
Program C
WBR3
CR3
C1
WR7
F1
—
CA1
PC13
7-CS13
28-CS13
WR7
F2
FA1
CA2
PC14
7-CS14
28-CS14
C2
WR8
F3
—
CA3
PC15
7-CS15
28-CS15
WR8
F4
FA2
CA4
PC16
7-CS16
28-CS16
C3
WR9
F5
FA3
—
PC17
7-CS17
28-CS17
WR9
F6
FA4
CA5
PC18
7-CS18
28-CS18


## 2.1. Experimental Design of Hydration Characteristics of Cementitious Materials

This test uses PO.42.5 cement-based cementitious materials. In terms of the conventional cement hydration, the developing analysis of ettringite and the hydration test of C3S cannot show the effect of temperature on the microproperties of cement hydration [15]. In this study, differential scanning calorimetry (DSC) is used to determine the thermal analysis of the relationship between heat and temperature of PO.42.5 cement under temperature control procedures (temperature rise, constant temperature, and temperature drop). The principle is that according to the thermal effect of the PO.42.5 cement sample, a heat flow difference proportional to the temperature difference is generated between the sample end and the reference end, the temperature difference can be continuously measured by the thermocouple, the DSC spectrum is obtained after being corrected to the heat flow difference, and then the hydration characteristics of the cementitious material are analyzed [16]. The test equipment and program interface of differential scanning calorimetry (DSC) are shown in Figures 1 and 2.Figure 1
DSC200F3-type instrument.Figure 2
DSC software program interface.PO.42.5 cement-based cementitious material differential scanning calorimetry (DSC) test program design is as follows: The test sample is controlled at 5 mg ± 1 mg. The test temperature control program is to increase the cement to 80°C at a rate of 20 K/min at room temperature of 25°C.Then, the temperature is lowered for 5 min, the temperature is lowered to −60°C at a rate of 20 K/min, and then the temperature is raised to room temperature of 25°C at a rate of 10 K/min. At the end of the test, the Tg was directly obtained by a program or manually adjusted to obtain a Tg. The DSC test sample is shown in Figure3.Figure 3
DSC test sample.


## 2.2. Design of Technical Parameter Test Scheme for Pervious Concrete

The design of the test scheme for porous permeable concrete is mainly divided into the test scheme of water-binder ratio and strength, the test scheme of porosity and strength, and the test scheme of grading structure and strength. This is shown in Table1.Table 1
Test plan design.
Program
Water-cement ratio
Ratio of set
Cement dosage (kg/m3)
Dosage of water-reducing agent (kg/m3)
Dosage of reinforcing agent (kg/m3)
Aggregate dosage (kg)
Permeable coefficient (cm/s)
7 d compressive strength (MPa)
28 d compressive strength (MPa)
2.36–4.75
4.75–9.5
Program A
WBR1
CR1
C1
WR1
F1
—
CA1
PC1
7-CS1
28-CS1
WR1
F2
FA1
CA2
PC2
7-CS2
28-CS2
C2
WR2
F3
—
CA3
PC3
7-CS3
28-CS3
WR2
F4
FA2
CA4
PC4
7-CS4
28-CS4
C3
WR3
F5
FA3
—
PC5
7-CS5
28-CS5
WR3
F6
FA4
CA5
PC6
7-CS6
28-CS6
Program B
WBR2
CR2
C1
WR4
F1
—
CA1
PC7
7-CS7
28-CS7
WR4
F2
FA1
CA2
PC8
7-CS8
28-CS8
C2
WR5
F3
—
CA3
PC9
7-CS9
28-CS9
WR5
F4
FA2
CA4
PC10
7-CS10
28-CS10
C3
WR6
F5
FA3
—
PC11
7-CS11
28-CS11
WR6
F6
FA4
CA5
PC12
7-CS12
28-CS12
Program C
WBR3
CR3
C1
WR7
F1
—
CA1
PC13
7-CS13
28-CS13
WR7
F2
FA1
CA2
PC14
7-CS14
28-CS14
C2
WR8
F3
—
CA3
PC15
7-CS15
28-CS15
WR8
F4
FA2
CA4
PC16
7-CS16
28-CS16
C3
WR9
F5
FA3
—
PC17
7-CS17
28-CS17
WR9
F6
FA4
CA5
PC18
7-CS18
28-CS18


## 3. Test Data Analysis

### 3.1. Analysis of Differential Scanning Calorimetry Test Data

Figures4 and 5 show the hydration process curves of cement over time at different temperatures. By comparing and analyzing the exothermic characteristics of the hydration process, it can be seen that at 15°C, the hydration reaction exotherm of the cement starts from about 200 minutes, reaches a peak at 533 minutes, and lasts for about 800 minutes. At higher temperatures, only 1-2 minutes is required for the cement-water mix to start releasing heat, reaching a peak in about 8 minutes, only lasting for about 20 minutes.Figure 4
Cement protoplasmic DSC curve under the condition of 25°C.Figure 5
Cement protoplasmic DSC curve under the condition of 35°C.Figure6 shows a 15°C–85°C temperature range, the influence of temperature on the hydration process of cement. With the increase of temperature, the second stage of cement hydration is continuously advanced and it is close to the exothermic peak of the first stage. The two exothermic peaks tend to overlap each other, and with the increase of temperature, the exothermic peak is greatly improved. The exothermic process is rapidly shortened. When the temperature reaches 85°C, the C3S hydration and ettringite formation process are completed simultaneously in a short period of time, and only an exothermic peak is exhibited on the exothermic curve.Figure 6
Influence of temperature on hydration process.It can be seen from Figure7 that the cement hydration curing temperature is increased. During the hydration process of the cement, the reaction activation degree of the reactants increases, the probability of collision and action increases and the hydration speed increases remarkably.Figure 7
Cement protoplasmic DSC curve under the condition of 85°C.


### 3.2. Effect of Water-to-Gel Ratio on Strength and Permeability Coefficient

The size of the water-to-binder ratio affects the rheological properties of the slurry and is also the main parameter determining the difference in strength and water permeability of the permeable concrete [17]. The water-binder ratio is changed, and the strength and water permeability coefficient of the permeable concrete are tested and analyzed. The results are shown in Figures 8 and 9.Figure 8
Relationship between water-binder ratio and compressive strength.Figure 9
Relationship between water-binder ratio and water permeability coefficient.It can be seen from Figures8–10 that with the increase of water-binder ratio, the strength of the permeable concrete gradually increases and the permeability coefficient of the permeable concrete gradually decreases. When the water-binder ratio is greater than 0.22, the strength growth trend is significant; when the water-binder ratio is greater than 0.32, the permeability coefficient of the permeable concrete is significantly reduced. The analysis shows that when the water-binder ratio is too large, the fluidity of the cement slurry is enhanced, causing the gelled slurry to permeate, and the strength and the water permeability coefficient are both deteriorated. Considering the performance of both strength and permeability coefficient, it is recommended that the optimal water-binder ratio of pervious concrete should be within the range of 0.24–0.30 within w/c, and the strength can meet the requirements of CJJ/T135-2009 that the strength of pervious concrete should be greater than or equal to 20.0 MPa.Figure 10
Comprehensive relationship between water-binder ratio residual strength and water permeability coefficient.Some researchers studied the influence of water-binder ratio on compressive strength and permeability coefficient and the effect of interfacial behavior on composites performance [18]. The trend of compressive strength change of pervious concrete from 7 d to 28 d under the four water-binder ratios of 0.23, 0.25, 0.27, and 0.3 was tested and analyzed. The research results showed that the compressive strength of pervious concrete with a water-binder ratio of 0.25 was the best in the test, and its compressive strength increased by 35.2% from 7 d to 28 d, and its maximum compressive strength reached 30 MPa [19]. At the same time, the paper also points out that, with the same number of vibration times, the plastic-bone ratio increases with the increase of the water-binder ratio, which is likely to lead to excessive cementing materials at the bottom of the specimen, thus plugging up the bottom gaps, and the water permeability decreases correspondingly, and the water permeability coefficient decreases. In the case of 10 times of vibration consolidation, the permeability coefficient of permeable concrete with water-binder ratio of 0.25 is 0.4.By comparing the experimental data analysis with the experimental data of Jiao, it can be concluded that the optimal water-binder ratio w/c range of 0.24–0.30 for pervious concrete is reliable when both strength and permeability are taken into account [20, 21].


### 3.3. Effect of Porosity on Strength and Permeability Coefficient

Porosity plays a decisive role in the strength of permeable concrete. Concrete materials are not uniform linear materials, so the strength and porosity of concrete is also difficult to characterize as a simple linear relationship. The study analyzed the effect of porosity on the strength and permeability coefficient through experiments, as shown in Figures11–13.Figure 11
Relationship between porosity and compressive strength.Figure 12
Relationship between porosity and permeability.Figure 13
Comprehensive relationship between porosity, strength, and permeability.It can be seen from Figures11–13 that with the increase of porosity, the strength of pervious concrete decreases gradually and the permeability coefficient of pervious concrete increases gradually. When the porosity is more than 25%, its strength does not meet the specifications; when the porosity is more than 11.3%, the permeability coefficient of pervious concrete increases significantly. The analysis shows that when the porosity is too large, the space accumulation structure of pervious concrete becomes worse, the function of granular material embedding becomes weaker, and increasing pore distribution significantly affects the effective formation of aggregate skeleton strength. Considering both strength and permeability coefficient, it is suggested that the optimum porosity range of pervious concrete should be controlled in the range of 15%–25%. The scatter plots of permeability coefficient and porosity of pervious concrete are constructed, and by fitting analysis, the functional relation can be obtained: k=−0.0003n2+0.0057n−0.0044.


### 3.4. Effect of Grading Type on Strength and Permeability Coefficient

Using the fractal dimension mathematical theory model, the grading design of the permeable concrete is carried out, and the three schemes of typical open-graded, semiopen-graded, and dense-graded are, respectively, formulated. In the laboratory test, the mixture test pieces of the three schemes are prepared and the strength test and the water permeability coefficient test are carried out. The test data are shown in Figure14–16.Figure 14
Relationship between grading type and strength.Figure 15
Relationship between grading type and permeability coefficient.Figure 16
Comprehensive relationship between grading type, strength and permeability coefficient.It can be seen from Figures14–16 that the three grading designs selected in this test can meet the requirements of the specification, and the open gradation has the best water permeability coefficient and the semiopen gradation is second. Under the same compressive strength, the thickness of the mixture has a significant influence on the water permeability coefficient. Under the same water permeability coefficient, the amount of cement has a significant influence on the compressive strength.Sonebi and Bassuoni’s research demonstrated that under the same porosity of the test group, the volume method is adopted to design the mix ratio of different aggregate-gradation pervious concrete [22]. The 28 d compressive strength of pervious concrete was tested, and the failure characteristics of the specimens were combined. The analysis shows that the compressive strength increases with the increase of small particle size aggregate content and the compressive strength of 5∼10 mm aggregate content of 75% is 34.06% higher than that of 25%. With the increase of fine aggregate content, the stress concentration at the end or corner of pervious concrete decreases when it is compressed, and the area of the bearing surface of the test block tends to be stable and increase, so that the compressive strength of pervious concrete can be improved.Considering the permeability coefficient of pervious concrete, it is suggested to choose the mix ratio design of open-graded pervious concrete through comprehensive analysis, and the cement content should be within the range of 20%–25%.


### 3.5. Relationship between Compressive Strength and Permeability Coefficient of Open-Graded Structure

According to the excellent characteristics of the open-graded obtained from the previous section test, the test of the compressive strength and permeability coefficient of the permeable concrete based on the open-graded type is studied. The data are shown in Figure17.Figure 17
Relationship between permeability and strength of open-graded structures.It can be seen from Figure17, with the increase of compressive strength of pervious concrete, the water permeability coefficient decreases gradually. When the compressive strength increases from 18 MPa to 25 MPa, the water permeability coefficient decreases remarkably; when the compressive strength increases further, the decreasing trend of permeation coefficient slows down. The scatter plot of the permeability coefficient and compressive strength of the permeable concrete is constructed, and the fitting function of the permeability coefficient and the compressive strength is obtained as follows: k=0.99006−0.05389c+8.02×10−4c2.


## 3.1. Analysis of Differential Scanning Calorimetry Test Data

Figures4 and 5 show the hydration process curves of cement over time at different temperatures. By comparing and analyzing the exothermic characteristics of the hydration process, it can be seen that at 15°C, the hydration reaction exotherm of the cement starts from about 200 minutes, reaches a peak at 533 minutes, and lasts for about 800 minutes. At higher temperatures, only 1-2 minutes is required for the cement-water mix to start releasing heat, reaching a peak in about 8 minutes, only lasting for about 20 minutes.Figure 4
Cement protoplasmic DSC curve under the condition of 25°C.Figure 5
Cement protoplasmic DSC curve under the condition of 35°C.Figure6 shows a 15°C–85°C temperature range, the influence of temperature on the hydration process of cement. With the increase of temperature, the second stage of cement hydration is continuously advanced and it is close to the exothermic peak of the first stage. The two exothermic peaks tend to overlap each other, and with the increase of temperature, the exothermic peak is greatly improved. The exothermic process is rapidly shortened. When the temperature reaches 85°C, the C3S hydration and ettringite formation process are completed simultaneously in a short period of time, and only an exothermic peak is exhibited on the exothermic curve.Figure 6
Influence of temperature on hydration process.It can be seen from Figure7 that the cement hydration curing temperature is increased. During the hydration process of the cement, the reaction activation degree of the reactants increases, the probability of collision and action increases and the hydration speed increases remarkably.Figure 7
Cement protoplasmic DSC curve under the condition of 85°C.


## 3.2. Effect of Water-to-Gel Ratio on Strength and Permeability Coefficient

The size of the water-to-binder ratio affects the rheological properties of the slurry and is also the main parameter determining the difference in strength and water permeability of the permeable concrete [17]. The water-binder ratio is changed, and the strength and water permeability coefficient of the permeable concrete are tested and analyzed. The results are shown in Figures 8 and 9.Figure 8
Relationship between water-binder ratio and compressive strength.Figure 9
Relationship between water-binder ratio and water permeability coefficient.It can be seen from Figures8–10 that with the increase of water-binder ratio, the strength of the permeable concrete gradually increases and the permeability coefficient of the permeable concrete gradually decreases. When the water-binder ratio is greater than 0.22, the strength growth trend is significant; when the water-binder ratio is greater than 0.32, the permeability coefficient of the permeable concrete is significantly reduced. The analysis shows that when the water-binder ratio is too large, the fluidity of the cement slurry is enhanced, causing the gelled slurry to permeate, and the strength and the water permeability coefficient are both deteriorated. Considering the performance of both strength and permeability coefficient, it is recommended that the optimal water-binder ratio of pervious concrete should be within the range of 0.24–0.30 within w/c, and the strength can meet the requirements of CJJ/T135-2009 that the strength of pervious concrete should be greater than or equal to 20.0 MPa.Figure 10
Comprehensive relationship between water-binder ratio residual strength and water permeability coefficient.Some researchers studied the influence of water-binder ratio on compressive strength and permeability coefficient and the effect of interfacial behavior on composites performance [18]. The trend of compressive strength change of pervious concrete from 7 d to 28 d under the four water-binder ratios of 0.23, 0.25, 0.27, and 0.3 was tested and analyzed. The research results showed that the compressive strength of pervious concrete with a water-binder ratio of 0.25 was the best in the test, and its compressive strength increased by 35.2% from 7 d to 28 d, and its maximum compressive strength reached 30 MPa [19]. At the same time, the paper also points out that, with the same number of vibration times, the plastic-bone ratio increases with the increase of the water-binder ratio, which is likely to lead to excessive cementing materials at the bottom of the specimen, thus plugging up the bottom gaps, and the water permeability decreases correspondingly, and the water permeability coefficient decreases. In the case of 10 times of vibration consolidation, the permeability coefficient of permeable concrete with water-binder ratio of 0.25 is 0.4.By comparing the experimental data analysis with the experimental data of Jiao, it can be concluded that the optimal water-binder ratio w/c range of 0.24–0.30 for pervious concrete is reliable when both strength and permeability are taken into account [20, 21].


## 3.3. Effect of Porosity on Strength and Permeability Coefficient

Porosity plays a decisive role in the strength of permeable concrete. Concrete materials are not uniform linear materials, so the strength and porosity of concrete is also difficult to characterize as a simple linear relationship. The study analyzed the effect of porosity on the strength and permeability coefficient through experiments, as shown in Figures11–13.Figure 11
Relationship between porosity and compressive strength.Figure 12
Relationship between porosity and permeability.Figure 13
Comprehensive relationship between porosity, strength, and permeability.It can be seen from Figures11–13 that with the increase of porosity, the strength of pervious concrete decreases gradually and the permeability coefficient of pervious concrete increases gradually. When the porosity is more than 25%, its strength does not meet the specifications; when the porosity is more than 11.3%, the permeability coefficient of pervious concrete increases significantly. The analysis shows that when the porosity is too large, the space accumulation structure of pervious concrete becomes worse, the function of granular material embedding becomes weaker, and increasing pore distribution significantly affects the effective formation of aggregate skeleton strength. Considering both strength and permeability coefficient, it is suggested that the optimum porosity range of pervious concrete should be controlled in the range of 15%–25%. The scatter plots of permeability coefficient and porosity of pervious concrete are constructed, and by fitting analysis, the functional relation can be obtained: k=−0.0003n2+0.0057n−0.0044.


## 3.4. Effect of Grading Type on Strength and Permeability Coefficient

Using the fractal dimension mathematical theory model, the grading design of the permeable concrete is carried out, and the three schemes of typical open-graded, semiopen-graded, and dense-graded are, respectively, formulated. In the laboratory test, the mixture test pieces of the three schemes are prepared and the strength test and the water permeability coefficient test are carried out. The test data are shown in Figure14–16.Figure 14
Relationship between grading type and strength.Figure 15
Relationship between grading type and permeability coefficient.Figure 16
Comprehensive relationship between grading type, strength and permeability coefficient.It can be seen from Figures14–16 that the three grading designs selected in this test can meet the requirements of the specification, and the open gradation has the best water permeability coefficient and the semiopen gradation is second. Under the same compressive strength, the thickness of the mixture has a significant influence on the water permeability coefficient. Under the same water permeability coefficient, the amount of cement has a significant influence on the compressive strength.Sonebi and Bassuoni’s research demonstrated that under the same porosity of the test group, the volume method is adopted to design the mix ratio of different aggregate-gradation pervious concrete [22]. The 28 d compressive strength of pervious concrete was tested, and the failure characteristics of the specimens were combined. The analysis shows that the compressive strength increases with the increase of small particle size aggregate content and the compressive strength of 5∼10 mm aggregate content of 75% is 34.06% higher than that of 25%. With the increase of fine aggregate content, the stress concentration at the end or corner of pervious concrete decreases when it is compressed, and the area of the bearing surface of the test block tends to be stable and increase, so that the compressive strength of pervious concrete can be improved.Considering the permeability coefficient of pervious concrete, it is suggested to choose the mix ratio design of open-graded pervious concrete through comprehensive analysis, and the cement content should be within the range of 20%–25%.


## 3.5. Relationship between Compressive Strength and Permeability Coefficient of Open-Graded Structure

According to the excellent characteristics of the open-graded obtained from the previous section test, the test of the compressive strength and permeability coefficient of the permeable concrete based on the open-graded type is studied. The data are shown in Figure17.Figure 17
Relationship between permeability and strength of open-graded structures.It can be seen from Figure17, with the increase of compressive strength of pervious concrete, the water permeability coefficient decreases gradually. When the compressive strength increases from 18 MPa to 25 MPa, the water permeability coefficient decreases remarkably; when the compressive strength increases further, the decreasing trend of permeation coefficient slows down. The scatter plot of the permeability coefficient and compressive strength of the permeable concrete is constructed, and the fitting function of the permeability coefficient and the compressive strength is obtained as follows: k=0.99006−0.05389c+8.02×10−4c2.


## 4. Conclusions

By means of the differential scanning calorimetry (DSC) test, the hydration microscopic characteristics of cementitious materials are analyzed. By testing the influence of water-binder ratio, porosity, and grading structure on the strength and permeability coefficient, the strength change rule of porous permeable concrete is obtained.Finally, the microscopic characteristics of porous permeable concrete hydration are revealed, and the internal correlation mechanism of multi-index technical parameters of permeable concrete is proposed, and various theoretical parameter models based on strength are constructed. The following research conclusions are obtained:(i)
By means of differential scanning calorimetry (DSC) test analysis, the effect of temperature on the hydration process of cement is obvious. With the increase of temperature, the two exothermic peaks of cement hydration increase significantly and tend to overlap and the exothermic process is shortened. At 85°C, only one exothermic peak appeared, indicating that C3S hydration and ettringite formation process were completed at the same time in a relatively short time.(ii)
According to the research, the optimal water-binder ratio of pervious concrete ranges from 0.24 to 0.30 and the optimal porosity ranges should be controlled within the range of 15%–25%. Moreover, the open gradation of pervious concrete mix ratio design is selected, and the cement content should be within the range of 20%–25%.(iii)
A mathematical model of the permeability coefficient and porosity of permeable concrete materials is constructed:k=−0.0003n2+0.0057n−0.0044; the mathematical model of permeability coefficient and compressive strength of open-graded permeable concrete materials: k=0.99006−0.05389c+8.02×10−4c2.



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*Source: 7918924-2019-08-20.xml*