*2.5. Freeze-Thaw Cycle and Water-Stability Test*

Most road-base materials are macroporous, and strength loss frequently occurs during the freeze–thaw cycle. The specimens' mass and strength loss needed to be investigated through a freeze–thaw test in the seasonally frozen ground region. The 28-day and 90-day specimens were selected for the freeze–thaw test, and 10 cycles were used (frozen for 16 h at −18 ◦C and thawed for 8 h in 20 ◦C = one cycle), as shown in Figure 6a.

(**a**) (**b**)

**Figure 6.** Freeze–thaw cycle and water-stability test: (**a**) freeze–thaw test; (**b**) water immersion.

The water-stability test examined the waterproof performance or water resistance of the road sub-base layer. For example, one water-stability cycle included initial immersion in water for 1 d and air-drying for 2 d, and then soaking in water for 1 d and air-drying for 2 d, as shown in Figure 6b. After five cycles, the compressive strength of the specimen was measured and compared with the specimen without immersion, and the calculation formula is shown in Equation (2):

$$\text{S} = \frac{\text{R}\_{\text{sc}}}{\text{R}\_{\text{c}}} \times 100 \tag{2}$$

where S is the coefficient of water stability; Rsc is the specimen strength after five cycles; and Rc is specimen strength without cyclic immersion.

#### **3. Experimental Test Results**

#### *3.1. Sieve Analysis*

Based on the centrifugal separation method in the Highway Engineering Asphalt and Asphalt Mixture code (JTG E20-2011), a centrifugal extraction apparatus was used to extract the waste–asphalt mixture. The 7- and 10-year RAP samples were selected, and softening point and penetration were tested to analyze the aging effects. With the increase of service life, penetration showed a decreasing trend, but the softening point showed the opposite (penetration: 65.1% for 7 years vs. 38.3% for 10 years, and softening point: 11.6% vs. 41.0%). It was observed that the coarse aggregate occupied a high portion of the waste–asphalt mixture, and a particle size below 2.36 mm accounted for about 10% of the total mass. This can be attributed to the fine aggregate bonding with asphalt to form larger particles, as shown in Figure 7a. The performance of asphalt deteriorated with time, and the sieve results of the extracted mixture are shown in Figure 7b. Compared with the untreated asphalt mixture, the fine aggregate particle-size distribution showed an apparent improvement between the upper and lower limits. It can be concluded that the untreated RAP aggregate required the extraction process before casting concrete to meet the gradation composition requirement.

**Figure 7.** Reclaimed asphalt sieve analysis: (**a**) untreated RAP mixture; (**b**) extracted RAP mixture.

### *3.2. Axial Compressive-Strength Tests*

Figures 8–10 show the RAP axial compressive-strength variation when subjected to cement dosages from 3.5% to 5.5%. It was observed that the cement dosage had a positive effect on axial strength, and the optimal cement dosage was 5.5%. Similarly, the optimal RAP substitute ratio was determined to be 40%.

**Figure 8.** Analysis of the 7-day axial compressive-strength test with variation of cement dosage and RAP.

**Figure 9.** Analysis of the 28-day axial compressive-strength test with variation of cement dosage and RAP.

**Figure 10.** Analysis of the 90-day axial compressive-strength test with variation of cement dosage and RAP.

The relationship between axial compressive strength and curing time is shown in Figure 11. When the RAP replacement ratio was increased from 30% to 40%, the axial compressive strength increased by 1.22% to 14.37% as the cement dosage remained constant. On the contrary, the axial compressive strength decreased by 2.68% to 16.50% when the RAP replacement ratio reached 50%. Therefore, it can be concluded that the axial strength increases initially and decreases afterward with the increase of the RAP replacement ratio. However, the axial compressive strength exerted a continuous positive effect (4.19~17.91% for 4.5% and 5.82~12.06% for 5.5%) with the increase of cement dosage when the RAP content remained constant. All these observations show that a critical RAP substitute ratio and cement dosage exist to achieve the maximum RAP axial strength. The cost efficiency and environmental friendliness also need to be balanced.

**Figure 11.** The relationship between axial compressive strength and curing time for various specimens.

Similarly, the compressive strength showed an increasing trend with curing time no matter the amount of cement dosage and RAP (24.79~40.99% from 7 to 28 days, and 4.28~7.73% from 28 to 90 days). The increasing trend turning flat can be explained by the hydration reaction gradually finishing.

#### *3.3. Splitting Tensile-Strength Tests*

The 28-day specimen's splitting-strength relationship between RAP and cement dosage is shown in Figure 12. It can be observed that the RAP specimen's splitting strength showed an upward trend with the increase of cement dosage. For the different RAP replacement ratios, an increasing trend was observed for all cement dosage cases, but the growth rate and maximum splitting strength varied. The maximum growth rate was 21.4% when subjected to the 5.5% cement dosage and 50% RAP replacement ratio. For the 30% RAP replacement ratio and 5.5% cement dosage, the maximum splitting strength reached 0.65 MPa. Similarly, the splitting strength showed a slowly decreasing trend with an increase of the reclaimed asphalt mixture replacement ratio. The higher cement dosage showed a better splitting resistance (16.21% for 3.5% vs. 9.1% for 5.5%). The lower RAP replacement ratio showed a higher splitting strength. It can be concluded that the RAP aggregate substitute NA had a negative influence on concrete's splitting tensile strength, and the increasing of cement dosage effectively relieved this strength degradation.

For 90 days of curing time, the splitting strength relationship between cement dosage and reclaimed asphalt replacement ratio is shown in Figure 13. The 90-day splitting strength had a similar increasing trend to that of 28 days, but a higher splitting strength and growth rate were observed. For the 30% reclaimed asphalt mixture, the highest growth rate of 39.1% was observed when compared with cement dosage from 3.5% to 4.5%. Therefore, the maximum splitting strength was 0.95 MPa for the 30% reclaimed asphalt mixture and 5.5% cement dosage.

Figure 14 shows the 90-day splitting strength concerning the variation of reclaimed asphalt mixture and cement dosage. The splitting strength showed a descending trend with the increase of reclaimed asphalt. The 4.5% cement dosage and 50% reclaimed asphalt exerted the highest strength-loss rate (8.8%). Compared with 28 days, specimens' splitting strength growth rate showed an increasing trend, up to 44.7% for 90 days curing time.

**Figure 13.** Analysis of the 90-day reclaimed asphalt splitting tensile-strength test with variation of cement dosage and RAP.

**Figure 14.** Reclaimed asphalt splitting tensile strength with respect to curing time.

It can be concluded that the cement dosage had a positive effect on splitting strength when the reclaimed asphalt mixture remained constant. However, reclaimed asphalt had a negative effect as the cement dosage was constant. Therefore, the splitting strength was a positively correlated function of curing time if the cement dosage and reclaimed asphalt remained constant.

The compressive resilience modulus of reclaimed asphalt with various cement dosages is shown in Figures 15–17. The compressive resilience modulus was positively correlated with cement dosage while negatively affecting the RAP replacement ratio, no matter the curing-time variation. For 28 days of curing time, the minimum compressive resilience modulus was 721.8 MPa (3.5% cement dosage and 50% reclaimed asphalt), and the maximum value was 1394.7 MPa (5.5% cement dosage and 30% reclaimed asphalt). For 3.5% cement dosage, the maximum compressive resilience modulus loss was 20.2% when the RAP content was increased from 30% to 40%. With an increased curing time of up to 90 days, the compressive resilience modulus showed an increasing trend, and the maximum value

reached 1771.2 MPa. It was concluded that the increase of compressive resilience modulus mainly depended on the concrete curing time and cement dosage. However, the RAP had a significant negative effect when compared with NA.

**Figure 15.** Results for the 28-day compressive-resilience modulus test: (**a**) cement dosage variation; (**b**) RAP replacement ratio.

**Figure 16.** Analysis of the 90-day compressive-resilience modulus test: (**a**) cement dosage variation; (**b**) RAP replacement ratio.

**Figure 17.** Compressive-resilience modulus test results with respect to curing time.

#### *3.4. Dry- and Temperature-Shrinkage Tests*

Figure 18 shows the relationship between the dry-shrinkage coefficient and water-loss rate. With the increase of water-loss rate, the drying-shrinkage coefficient showed a similar increasing trend when the cement dosage was increased from 3.5% to 5.5%. Three increase stages were observed, which included the slowly ascending stage (0–3.4% for 3.5%, 0–3.2% for 4.5%, and 0–2.6% for 5.5%), rapid-growth stage (3.4–4.5% for 3.5%, 3.2–4% for 4.5%, and 2.6–3.4% for 5.5%), and steady stage. Compared with other cases, the 5.5% cement dosage had the maximum shrinkage coefficient and minimum water-loss rate. With the increase of curing time, the drying-shrinkage strain showed a fast and then slow increasing trend. The drying-shrinkage coefficient gradually increased with the decrease of cement dosage—1.15 times for 4.5% and 1.25 times for 5.5%. The drying-shrinkage strain gradually increased with the increase of water-loss rate, and it also had a positive effect with cement dosage on constant water-loss rate. Two increase zones were observed, which included a slowly ascending zone (0–3.4% for 3.5%, 0–3.2% for 4.5%, and 0–2.6% for 5.5%) and a rapid growth zone (larger than 3.4% for 3.5%, larger than 3.2% for 4.5%, and larger than 2.6% for 5.5%). All these observations showed that the higher cement dosage facilitated an adequate cement hydration reaction, leading to higher shrinkage. Beyond that, more cement particles filled the RAP aggregate void and occupied the space that originally belonged to water.

**Figure 18.** Analysis of the dry-shrinkage test: (**a**) dry-shrinkage coefficient related to water-loss rate; (**b**) dry-shrinkage strain related to time.

The temperature shrinkage data related to 40% reclaimed asphalt and cement dosages from 3.5% to 5.5% are summarized in Figure 19. The temperature-shrinkage coefficient showed a gradually decreasing trend with an increase of cement dosage, and all shrinkage values were located between 6.41 × <sup>10</sup>−<sup>6</sup> and 19.9 × <sup>10</sup><sup>−</sup>6. The 3.5% cement dosage exerted the maximum temperature shrinkage coefficient, and the sharply ascend zone occurred between 0 ◦C and −10 ◦C. All the observations can be attributed to the pore water in specimens causing a freezing volume expansion between 0 ◦C and −10 ◦C, and a slight shrinkage coefficient was seen in other temperature zones.

#### *3.5. Freeze-Thaw Cycle and Water-Stability Tests*

With the increase of curing time from 28 to 90 days, both the mass and strength loss rate gradually decreased the exact cement dosage, as shown in Figure 20. For the same curing time, the increased cement dosage had a positive effect on maintaining the strength and mass of the RAP specimen. All these observations imply that the increased curing time and cement dosage effectively reduced the RAP specimen's internal porosity, which mainly depended on the degree of cement hydration reaction. It can be concluded that the higher cement dosage and longer curing time effectively improved the RAP frost resistance.

**Figure 19.** Analysis of the temperature shrinkage coefficient.

**Figure 20.** Analysis of the freeze–thaw-cycle test: (**a**) mass loss rate; (**b**) strength loss rate.

For specimens with 40% reclaimed asphalt and various cement dosages from 3.5% to 5.5%, the compressive strength related to dry–wet cycles (with and without) is summarized in Figure 21. It can be observed that the dry–wet cycles reduced the specimens' compressive strength, and the water-stability coefficient exerted a good water resistance with an increase of cement dosage.

#### *3.6. Microcosmic Analysis*

Unlike cement stone and aggregate direct adsorption, an asphalt layer exists between cement stone and aggregate in reclaimed asphalt specimens. In order to observe the interface between cement and asphalt, the scanning electron microscope (SEM) method is used to investigate the influence of existing asphalt. The asphalt sample was in a solid state in a reclaimed asphalt mixture and was not heated during recycling.

Figure 22a shows the morphology diagram of cement stone in the reclaimed asphalt mixture, and the observation area is not in contact with reclaimed asphalt. Compared with traditional cement stabilized materials, the RAP surface was uneven and angular, validated by higher void content as shown in Table 1. Figure 22b shows the interface between cement stone and asphalt in the reclaimed asphalt mixture. It can be observed that the asphalt was effectively filled with the porosity within the cement mixture, forming embedded connection strength. Due to the crushing process of RAP aggregate, the cement stone and asphalt were bonded with an irregular dividing line, and a concave and convex shape was observed. Adhesion partially retarded the hydration reaction between the cement mortar and aggregate, which caused the lower strength generation. Figure 22c shows the asphalt particle embedded in cement stone, and some small particles are also absorbed on cement stone due to crushing and mixing. Many microholes appeared on the surface of bituminous mixture particles. This can be explained by the higher water absorption than for the NA aggregate (Table 1).

**Figure 21.** Analysis of the water-stability test.

(**c**)

**Figure 22.** Scanning electron microscope (SEM) method: (**a**) cement stone; (**b**) interface between cement stone and asphalt; (**c**) bituminous mixture particles bond to cement.

#### **4. Numerical Simulation Analysis**

The 7-day compressive-strength test data (Figure 8) was selected to establish a numerical analysis model, which was mainly used to predict the variation law of the reclaimed asphalt mixture's compressive strength with respect to the influence of multiple factors. Two independent variables were considered in the presented numerical analysis model: reclaimed asphalt replacement ratio (30%, 40%, and 50%) and cement dosage (3.5%, 4.5%, and 5.5%). Due to the limited test data, the Monte Carlo simulation method was used to expand the sample number to a sizeable, reasonable size (4500 samples). The simulation data distribution was assumed to be a normal distribution, and the data boundary was selected for mean value ± standard deviation, as shown in Figure 23a. Compared with the relative errors, the predicted points had good agreement with the tested values (R<sup>2</sup> = 0.908), which met the accuracy requirements of the model prediction analysis. A bivariate nonlinear strength-fitting equation is presented based on the nonlinear regression analysis method, as shown in Equation (3):

$$\begin{aligned} Z &= -6.384 + 0.475X + 0.604Y - 0.0059X^2 - 0.0176Y^2\\ &\text{(20\%} \le X \le 60\%, 3\% \le Y \le 6\%) \end{aligned} \tag{3}$$

where X is the reclaimed asphalt mixture content (%); Y is cement dosage (%); and Z is the 7-day compressive strength (MPa).

**Figure 23.** Numerical simulation of compressive strength: (**a**) Monte Carlo simulation; (**b**) 3D diagram of the nonlinear strength-fitting equation.

In order to exhibit the relationship among variables in the bivariate nonlinear strength equations, a three-dimensional effect diagram was constructed in MATLAB. Figure 23b shows the three-dimensional surface related to X (content of reclaimed asphalt mixture), Y (cement dosage), and Z (7-day compressive strength). For example, a point in the figure (X 26.8; Y 4.5; Z 4.473) represents a predicted 7-day compressive strength of 4.473 MPa when subjected to the reclaimed asphalt mixture content of 26.8% and a cement dosage of 4.5%. It can be concluded that the 7-day compressive strength can be predicted in the presented numerical model when subjected to various cement dosages and reclaimed asphalt mixture, and vice versa.

Similarly, considering the effect of freeze–thaw cycles, a revised numerical analysis model was established to predict the strength reduction of the reclaimed asphalt mixture. For example, two variables were considered for the 40% reclaimed asphalt mixture content: curing time (28 and 90 days) and cement dosage (3.5%, 4.5%, and 5.5%). Due to test data being limited, the Monte Carlo method was used to simulate 3000 samples, and the data-distribution type was assumed to be a normal distribution. Figure 24a shows that

the simulated data points were in good agreement with the test values (R2 = 0.915), which met the accuracy requirements of the model prediction analysis. The nonlinear regression analysis method was used to create a bivariate nonlinear strength-fitting equation, as shown in Equation (4):

$$\begin{aligned} Z &= 28.5561 - 0.0398275 \text{X} - 3.25298 \text{Y} \\ &\text{(20 } \le \text{X} \le 100, \text{0\%} < \text{Y} \le 6\text{\%)} \end{aligned} \tag{4}$$

where X is the curing time of reclaimed asphalt mixture; Y is cement dosage (%); and Z is the compressive strength loss rate (%) of reclaimed asphalt mixture.

**Figure 24.** Numerical simulation of compressive-strength-loss rate: (**a**) Monte Carlo simulation; (**b**) 3D diagram of nonlinear strength-loss fitting equation.

Figure 24b shows the relationship among X (curing time), Y (cement dosage), and Z (compressive strength loss rate) in the 3D model. For example, a point was randomly selected in the figure (X 91.3; Y 3.35; Z 14.02), representing the predicted value of compressive strength loss rate of 14.02% for 91.3 days curing time and 3.35% cement dosage. It can be concluded that the presented numerical model could effectively predict the reclaimed asphalt mixture strength reduction when subjected to the freeze–thaw effect.

A simplified numerical model was created for practical engineering applications when considering the relationship between cement dosage and 28-day strength-loss rate. The nonlinear regression method was used to build the strength-degradation equation (Equation (5)), which included 1500 data points by Monte Carlo simulation:

$$\text{Y} = 40.558 - 8.210\text{X} + 0.439\text{X}^2 \text{ (\ $\%$ } \le \text{X} \le 6\text{\%)}\tag{5}$$

where X is the cement dosage (%), and Y is the 28-day compressive-strength-loss rate (%) under the freeze–thaw effect. Compared with the relative error between the predicted value and the tested value, the 1500 simulated data points showed a good consistency with the measured value (R<sup>2</sup> = 0.998), which could meet the accuracy requirements of the model-prediction analysis, as shown in Figure 25.

In order to facilitate data selection for the construction technicians, the maximum replacement ratio of reclaimed asphalt is presented for various cement dosages, considering both with and without the freeze–thaw effect. Figure 26 shows the maximum replacement ratio of reclaimed asphalt with respect to various cement dosages. There was an apparent descending trend when considering the freeze–thaw effect, and the increasing cement dosage effectively improved the replacement ratio. It can be concluded that the maximum replacement ratio of the reclaimed asphalt mixture can be selected with different cement dosages. For specific cement dosages, the linear interpolation method can be used to obtain the maximum replacement ratio.

**Figure 25.** Nonlinear strength-loss-rate fitting equation with respect to freezing-damage effects.

**Figure 26.** The maximum replacement ratio of reclaimed asphalt with respect to various cement dosage: (**a**) with the freeze–thaw effect; (**b**) without the freeze–thaw effect.

#### **5. Conclusions**

This paper investigated the mechanical performance of reclaimed asphalt mixtures. More specifically, mechanical properties such as compressive strength, splitting strength, compressive modulus of resilience, were examined, as well as the results of freeze–thaw cycling tests. The main conclusions were as follows:

According to the axial compressive and splitting tensile-strength tests, critical RAP substitute ratios (30%) and cement dosage (5.5%) exist to achieve the maximum mechanical performance. However, the cost efficiency and environmental friendliness also need to be balanced. It can be concluded that the RAP aggregate substitute NA had a negative influence on concrete compression and splitting tensile strength, and the increasing of cement dosage effectively relieved this strength degradation.

It seems that the higher cement dosage represented an adequate cement hydration reaction through dry- and temperature-shrinkage tests, which led to higher shrinkage occurring. Beyond that, a noticeable temperature-shrinkage-increase zone (between 0 ◦C and −10 ◦C) was observed due to the pore water freezing and causing a volume-expansion effect.

The 5.5% cement dosage and 90 days of curing time exerted the most robust RAP frost resistance in the freeze–thaw-cycle and water-stability tests. Therefore, it can be concluded that the increased curing time and cement dosage effectively reduced the RAP specimen's internal porosity, and mainly depended on the degree of the cement hydration reaction.

In the scanning electron microscope (SEM) analysis, an irregular dividing line between the cement stone and asphalt was observed for the RAP aggregate. The concave and convex surfaces partially retarded the hydration reaction between the cement mortar and aggregate, which caused lower strength generation and higher water absorption than NA.

A nonlinear compression-strength regression equation was presented using RAP content and cement dosage through a Monte Carlo numerical-simulation method. Considered with different highway-grade requirements, the corresponding RAP replacement ratio and cement dosage limits were determined.

**Author Contributions:** Conceptualization and methodology, W.X.; software and data curation, W.L. and Y.J.; validation, W.X., W.L. and Y.J.; writing—original draft preparation, W.L. and Y.J.; writing review and editing, W.X.; funding acquisition, W.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Transportation Department of Heilongjiang Province in China, grant number 2019HLJ0012.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Wenjie Zhang \*, Yuqiang Zhao, Fengcheng Huang, Yongheng Zhong and Jianwei Zhou**

School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; zhao1599484022@163.com (Y.Z.); hfc\_free@163.com (F.H.); 13965913060@163.com (Y.Z.); zhjwhvac@njust.edu.cn (J.Z.)

**\*** Correspondence: zhangwenjie001@139.com

**Abstract:** In recent years, with the rapid development of China's economy, China's energy demand has also been growing rapidly. Promoting the use of renewable energy in China has become an urgent need. This study evaluates the potential of solar photovoltaic (PV) power generation on the roofs of residential buildings in rural areas of mainland China and calculates the area that can used for generating energy, the installed capacity, and the power generation, and conducts a comprehensive analysis of the economic benefits of investing in the construction of distributed PV systems in various provinces. The findings unveiled in this study indicate that China still has more than 6.4 billion m<sup>2</sup> of rural construction area available for the installation of PV modules. If this is all used for solar power generation, the annual power generation can reach up to 1.55 times the electricity consumption of urban and rural residents for the whole society. Through a comprehensive evaluation of energy efficiency and economic benefits, the Chinese mainland can be divided into three types of resource areas. The three types of resource areas have their own advantages and disadvantages. According to their own characteristics and advantages, we can reasonably formulate relevant policies to accelerate the development of PV system application in rural areas.

**Keywords:** solar energy; distributed PV system; energy-saving benefits; economic benefit; rural areas of China; forecasting
