*3.7. Comparison Analysis Based on Radar Chart Evaluation Method*

The radar chart evaluation method is conducted to quantitatively compare the effect of steel slag and basalt on the performance of RAM. The nine evaluation indicators, including residual Marshall stability, tensile strength ratio, spatter loss, dynamic stability, tensile strain, texture depth, British Pendulum Number, intercept K of fatigue equation, absolute value of creep slope in HWT test, were used in radar chart. They were denoted as RMS, TSR, SL, DS, TS, TD, BPN, Intercept K, CS, respectively. Table 6 provides the nine indicators of twelve groups in matrix A. Then the indicators are standardized and non-linear transformed referring to Equations (1) and (2), as shown in Table 7.

**Table 6.** Evaluation indicators of RAM with different RAP content.




Figure 11 summaries the radar charts for RAM with different RAP content. The discrepancies in the enhancement effect of steel slag are presented clearly. Incorporating steel slag reveals a significant improvement on RMS, TSR, DS, TS, TD, BPN and Intercept K in contrast to SL and CS. The appropriate RAP content in steel slag RAM can be identified from the charts considering the improvement of a certain performance indicator.

**Figure 11.** Radar charts for RAM with different RAP content: (**a**) 0 RAP; (**b**) 10% RAP; (**c**) 20% RAP; (**d**) 30% RAP; (**e**) 40% RAP; (**f**) 50% RAP.

According to Equations (3)–(7), the characteristic vectors (*u<sup>i</sup>* ) and evaluation vectors (*νi* ) in matrices can be calculated, as listed in Table 8. Calculation results of comprehensive evaluation function (f) for twelve groups are elaborated in Figure 12. It is indicated that steel slag virgin asphalt mixture reveals the largest f value of 0.9710. The addition of RAP decreases f value of RAM with steel slag. When RAP dosage elevates from 0 to 50% with an interval of 10%, the f value of steel slag RAM are 0.9119, 0.8694, 0.7801, 0.6872 and 0.6456 with a decrement of 6.1%, 10.5%, 19.7%, 29.2% and 33.5%. Distinct from steel slag RAM, basalt RAM exhibits an upward and then downward trend as the increasing RAP dosage. This is due to the greater enhancement effect of RAP content on DS of basalt RAM than

steel slag RAM. The f value of basalt RAM with 50% RAP content reduces by 28.1% and reaches to 0.5928. While RAM incorporated with steel slag possesses the larger f value than basalt under the same RAP content.


**Table 8.** The characteristic vectors and evaluation vectors of matrices.

**Figure 12.** Comprehensive evaluation index of steel slag and basalt RAM.

#### **4. Conclusions**

In this study, the pavement performances of recycled asphalt mixtures (RAM) with steel slag and basalt were examined using volume performance, moisture susceptibility, high temperature stability performance, low temperature performance, skid resistance and durability. Then, an improved radar chart evaluation method was applied to quantitatively assess their comprehensive performance. The following conclusions can be summarized.

• The incorporation of steel slag elevates the residual Marshall stability (RMS), tensile strength ratio (TSR) and diminishes the Cantabro spatter loss of RAM, endowing its superior moisture susceptibility than basalt RAM. Steel slag RAM involving 50% RAP dosage demonstrates a RMS of 90.5%, TSR of 89.3% and spatter loss of 5.5%, which remains at a high level;


The above conclusions have verified that incorporating steel slag reinforces comprehensive road performance of recycled asphalt mixtures, which is conducive to promoting environmental sustainability. Further study is essential to investigate the engineering implementation and energy consumption of recycled asphalt mixtures involving steel slag.

**Author Contributions:** Conceptualization, S.W. and C.Y.; Data curation, Z.W. and C.Y.; Funding acquisition, S.W. and J.X.; Investigation, Z.W., C.Y. and Z.Z; Methodology, Z.W., F.W. and C.Y.; Project administration, S.W. and Y.X.; Supervision, S.W.; Validation, Z.Z., Y.X. and L.Z.; Writing—original draft, Z.W.; Writing—review & editing, J.X., F.W. and L.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was sponsored by National Key R&D Program of China (No. 2018YFB1600200), Key R&D Program of Guangxi Province (No. 2021AB26023), Key R&D Program of Hubei Province (No. 2020BCB064) and Hebei Provincial Communication Department project (No. YC-201926).

**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.
