Comprehensive Laboratory Evaluation of Crack Resistance for an Asphalt Rubber Stress-Absorbing Membrane Interlayer (AR-SAMI)

: Reﬂective cracking is a common distress of semi-rigid base asphalt pavements and overlay pavement projects. An asphalt rubber stress-absorbing membrane interlayer (AR-SAMI) prepared by waste tires is an effective engineering solution for treating reﬂective cracking. This method can also reduce black pollution. However, there is no uniﬁed test method and index for crack resistance evaluation. In this work, AR-SAMIs with different air voids and gradations were investigated. A small beam bending test (BBT) at − 10 ◦ C and 15 ◦ C, crack expansion SCB (CE-SCB) test, low-temperature SCB (LT-SCB) test, and Overlay Test (OT) were performed to evaluate the crack resistance of AR-SAMI comprehensively. Statistical analysis was also performed. Results showed that the crack resistance of AR-SAMI improved as the air voids decreased. The crack resistance of 10-A gradation with more ﬁne aggregate was excellent. However, the AR-SAMI with more coarse aggregate had better crack extension resistance under the condition of pre-existing cracks. There are differences in the evaluation results of different test methods due to the various evaluation focus. The − 10 ◦ C BBT, CE-SCB, and OT were recommended to evaluate the crack resistance comprehensively. Research results can guide the evaluation method or index selection of crack resistance and the optimization of AR-SAMI mixture design under different working conditions.


Introduction
Reflective cracking is a common type of distress in asphalt pavement caused by existing cracks in the underlying layer [1,2]. Semi-rigid base asphalt pavements, composite road (or bridge) pavements, and pavement maintenance of overlay projects have potential risks of reflective cracking. Reflective cracking can cause fissuration, loosening, and other distress under the coupling effect of multiple factors, such as water, loading, and temperature. It can significantly reduce pavement performance and directly affect the service life of the pavement [3,4]. Therefore, how to effectively mitigate the occurrence of reflective cracking and improve the quality of pavement engineering has become one of the urgent technical problems for pavement construction and maintenance [5,6].
The commonly used techniques for treating reflective cracking include the following three types: laying geosynthetic materials, adding an unbound aggregate layer between the surface layer and the base layer, and adding a stress-absorbing membrane interlayer (SAMI) [7][8][9][10][11]. Among them, the SAMI has been widely used as an effective method to slow the expansion of reflective cracking [12][13][14]. Due to its special functional requirements, a SAMI generally uses polymer modified asphalt, crumb rubber modified asphalt (CRMA), example, the construction temperature of the crumb rubber asphalt mixture was high due to its high viscosity. Pan et al. [21] used warm mix technology to reduce the compaction temperature by 30 • C. It still had good low-temperature performance, which could be suitable for pavement cracking disposal in cold areas. Zeng et al. [12] used fibers for AR-SAMI modification, which improved its crack resistance and fatigue life on the semi-rigid base. Wang et al. [22] used amorphous poly alpha-olefin (APAO) to modify AR-SAMI. The Overlay Test (OT) results showed that the adhesion performance and crack resistance of the mixture were improved.
Unlike conventional asphalt mixtures, SAMI should have good crack resistance in addition to the traditional pavement performance requirements such as high temperature, low temperature, and water stability. Crack resistance includes the ability to resist crack formation and crack expansion [3]. Numerical simulation techniques have been used to investigate it. Among them, finite element (FE) and discrete element method (DEM) were most commonly used. For example, Thives et al. [23] used Ansys calculations to show that pavement fatigue life could be improved up to eight times using AR-SAMI compared to a regular asphalt mixture under Brazilian climatic conditions. Zeng et al. [12] used FE to verify that AR-SAMI with fibers could significantly reduce the stress concentration in cracks. Pei et al. [24] used DEM to analyze the destructive properties of asphalt pavement overlay on cement pavement, which guided the application of the paving technology under different working conditions. However, due to the complexity of the effects of cracking, it was not easy to accurately construct an analytical model that matched the actual material composition and application conditions. As a result, the numerical simulation had a significant deficiency in material selection and mixture composition optimization design. Therefore, the experimental evaluation methods still had the most direct guidance value for the mixture design of SAMI.
However, there was no unified standard for crack resistance test evaluation. Therefore, scholars have proposed a variety of test evaluation methods. For example, the small beam bending test (BBT) was utilized in China [25]. The semicircular bending (SCB) tests with pre-cut cracks have been set as the standard test by AASHTO, including the crack extension SCB (CE-SCB) test [26] and low-temperature SCB (LT-SCB) test [27]. There are also Overlay Tests (OT) in Texas [22,28] and wheel fatigue tests [29]. Depending on the generation mechanism, the causes of cracks vary significantly under different working conditions. Four major modes of asphalt pavement cracking exist, including thermal, reflection, bottomup fatigue, and top-down [30]. Due to the different testing principles, the crack resistance performance reflected by each index varies greatly. For example, the low-temperature flexural-tensile strain in BBT is the control index of the Chinese specification, which focuses on characterizing the resistance to crack formation [31]. The SCB tests with pre-cut cracks focus on characterizing the resistance to crack expansion in the presence of cracks [9,32]. The OT test is similar to the fatigue test and characterizes the crack resistance degradation of the specimen under fixed deformation [9,33].
To sum up, existing studies have investigated the effect of AR-SAMI on traditional road performance but less on crack resistance. Meanwhile, numerical simulation techniques were generally used in existing studies to evaluate the crack resistance of SAMI. There is a lack of systematic standards for different working conditions when using test methods, as the standards are not unified across countries. Meanwhile, the existing studies generally used a single evaluation technique, which could not comprehensively characterize the comprehensive crack resistance performance of the SAMI. As a result, they could not guide the optimal design of the SAMI. Although AR-SAMI has been initially promoted in the treatment of reflective cracking, the evaluation of its comprehensive anti-cracking performance needs to be further strengthened. The evaluation method and index applicability research especially still need to be deepened.
In this work, three gradation types of AR-SAMI mixtures with two air voids (AV, 2.5% and 4.0%) were designed. The anti-cracking performances of AR-SAMI were evaluated through different temperatures (−10 • C, 15 • C) of BBT, CE-SCB test, LT-SCB test, and OT. Meanwhile, the test results were compared by statistical methods to select the appropriate comprehensive evaluation test methods and indices. This work can provide a reference for the crack resistance evaluation of similar SAMI and can guide the mixture design of AR-SAMI under different working conditions.

Materials and Methods
The research flowchart of this study can be depicted in Figure 1. cracks [9,32]. The OT test is similar to the fatigue test and characterizes the crack resistance degradation of the specimen under fixed deformation [9,33]. To sum up, existing studies have investigated the effect of AR-SAMI on traditional road performance but less on crack resistance. Meanwhile, numerical simulation techniques were generally used in existing studies to evaluate the crack resistance of SAMI. There is a lack of systematic standards for different working conditions when using test methods, as the standards are not unified across countries. Meanwhile, the existing studies generally used a single evaluation technique, which could not comprehensively characterize the comprehensive crack resistance performance of the SAMI. As a result, they could not guide the optimal design of the SAMI. Although AR-SAMI has been initially promoted in the treatment of reflective cracking, the evaluation of its comprehensive anticracking performance needs to be further strengthened. The evaluation method and index applicability research especially still need to be deepened.
In this work, three gradation types of AR-SAMI mixtures with two air voids (AV, 2.5% and 4.0%) were designed. The anti-cracking performances of AR-SAMI were evaluated through different temperatures (−10 °C, 15 °C) of BBT, CE-SCB test, LT-SCB test, and OT. Meanwhile, the test results were compared by statistical methods to select the appropriate comprehensive evaluation test methods and indices. This work can provide a reference for the crack resistance evaluation of similar SAMI and can guide the mixture design of AR-SAMI under different working conditions.

Materials and Methods
The research flowchart of this study can be depicted in Figure 1.

Crumb Rubber Modified Asphalt
The crumb rubber modified asphalt was prepared with 70 # A base asphalt, crumb rubber, and stabilizer (as shown in Figure 2). The dosage of crumb rubber was 20 wt%. The stabilizer is shown in Figure 2, produced by Guangxi Transportation Science and Technology Group Co., Ltd. (Nanning, China).

Crumb Rubber Modified Asphalt
The crumb rubber modified asphalt was prepared with 70 # A base asphalt, crumb rubber, and stabilizer (as shown in Figure 2). The dosage of crumb rubber was 20 wt%. The stabilizer is shown in Figure 2, produced by Guangxi Transportation Science and Technology Group Co., Ltd. (Nanning, China). The technical indices of crumb rubber modified asphalt are shown in Table 1.

Aggregate
The limestone crushed stone was used as coarse and fine aggregate. The main technical indices of aggregate are shown in Table 2. The technical indices meet the performance requirements of highway aggregate [31].  The technical indices of crumb rubber modified asphalt are shown in Table 1.

Aggregate
The limestone crushed stone was used as coarse and fine aggregate. The main technical indices of aggregate are shown in Table 2. The technical indices meet the performance requirements of highway aggregate [31].

Mixture Design
There was no national standard for the design of AR-SAMI. Considering AC-10 type was mostly used in the highway project, the AC-10 gradations in JTG F40-2004 [31], DB45/T 1098-2014 [35], and DG/TJ08-2109-2012 [36] were analyzed. Three gradations were determined based on summary results, as shown in Table 3. Two air voids of 2.5% and 4.0% were selected. The mixture design was based on the combination of gradation and air voids. The Marshall design method was used to determine the optimal asphalt-aggregate ratio and volume parameters. The test results are shown in Table 4. Among them, voids in the mineral aggregate (VMA) and voids filled with asphalt binder (VFA) comply with the relevant requirements of JTG F40-2004 [31].

Gradation Evaluation by Bailey Method
The Bailey method was used to quantify and analyze the differences between the three gradations.
The following three indicators were used according to the theory of the Bailey method [37]: Coarse Aggregate Ratio (CA), Fine Aggregate Coarse Ratio (FA C ), and Fine Aggregate Fine Ratio (FA f ). The formulae for calculating each index are as follows: The BBTs at −10 • C and 15 • C were conducted with reference to JTG E20-2011 (T 0715-2011) [34]. The specimen size was 250 mm × 30 mm × 35 mm, and the span diameter was 200 mm. The three-point loading tests were carried out by using the universal material testing machine (Shanghai Hualong WDW-100C). The loading rate was 50 mm/min. Three parallel specimens were tested in each group. The mean and standard deviation were calculated separately.
The maximum flexural-tensile strain (S ft ) and strain energy density (D se ) were calculated. The maximum flexural-tensile strain indicates the maximum strain value of the small beam specimen during the test. The strain energy density means the energy consumed by the specimen during the whole process of loading damage. Among them, the strain energy density is the strain energy per unit volume, which can be calculated by using the envelope area of the σ (stress)-ε (strain) curve during the damage process [38]. The calculation formula is as follows: where ε B is the corresponding strain to the stress peak of the specimen (mm).

Crack Extension Semicircular Bending (CE-SCB) Test
The CE-SCB test was performed at room temperature (25 ± 0.5 • C) using pre-cut crack semicircular specimens in accordance with AASHTO TP 124-16 [26]. The specimen dimensions are shown in Figure 3. The notches were 15 ± 1 mm deep and 2.0 ± 1.0 mm wide. Each group of tests has four parallel specimens. The mean and standard deviation were calculated separately.

Small Beam Bending Test (BBT)
The BBTs at −10 °C and 15 °C were conducted with reference to JTG E20-2011 (T 0715-2011) [34]. The specimen size was 250 mm × 30 mm × 35 mm, and the span diameter was 200 mm. The three-point loading tests were carried out by using the universal material testing machine (Shanghai Hualong WDW-100C). The loading rate was 50 mm/min. Three parallel specimens were tested in each group. The mean and standard deviation were calculated separately.
The maximum flexural-tensile strain (Sft) and strain energy density (Dse) were calculated. The maximum flexural-tensile strain indicates the maximum strain value of the small beam specimen during the test. The strain energy density means the energy consumed by the specimen during the whole process of loading damage. Among them, the strain energy density is the strain energy per unit volume, which can be calculated by using the envelope area of the σ (stress)-ε (strain) curve during the damage process [38]. The calculation formula is as follows: where εB is the corresponding strain to the stress peak of the specimen (mm).

Crack Extension Semicircular Bending (CE-SCB) Test
The CE-SCB test was performed at room temperature (25 ± 0.5 °C) using pre-cut crack semicircular specimens in accordance with AASHTO TP 124-16 [26]. The specimen dimensions are shown in Figure 3. The notches were 15 ± 1 mm deep and 2.0 ± 1.0 mm wide. Each group of tests has four parallel specimens. The mean and standard deviation were calculated separately.  The fracture energy (Gf) and the flexibility index (FI) could be calculated from the load-displacement curve (as shown in Figure 4). Gf denotes the energy required to create a unit surface area of a crack, and FI is an index intended to characterize the damage resistance of asphalt mixtures. The larger the value of the two indicates the stronger the crack resistance of asphalt mixtures under normal temperature conditions. Among them, The fracture energy (G f ) and the flexibility index (FI) could be calculated from the load-displacement curve (as shown in Figure 4). G f denotes the energy required to create a unit surface area of a crack, and FI is an index intended to characterize the damage resistance of asphalt mixtures. The larger the value of the two indicates the stronger the crack resistance of asphalt mixtures under normal temperature conditions. Among them, FI takes into account the slope of the force-displacement curve m at the later stage of crack expansion ( Figure 4). It could indicate the resistance to crack expansion after the formation of cracks in the mixture.

Low-Temperature Semicircular Bending (LT-SCB) Test
LT-SCB test used semicircular pre-cut specimens to evaluate the ability of the m to resist damage under low-temperature conditions referring to the AASHTO TP test method [27]. The specimen preparation of the LT-SCB test was roughly the s the CE-SCB test. The difference was that the thickness of the cut specimen was a to 24.7 ± 2 mm. The test temperature was −10 °C. Each group of tests had four p specimens. The mean and standard deviation were calculated separately.
The fracture energy Gf and fracture toughness KIC (also known as mode I critica intensity factor) of the asphalt mixture under low-temperature conditions were cal with reference to the specification. The higher the index value, the better the resist the compound to crack expansion at low temperatures.

Overlay Test (OT)
The OT was performed with reference to the TEX-248-F [39]. The Marshall c tion method (T 0702-2011) [34] was used to form specimens (152.4 mm × 95.3 m cylindrical specimen with a 38.1 ± 0.5 mm thickness was obtained by cutting off and bottom parts. Then, both ends of the specimen were cut, and the specimen with a width of 76.2 ± 0.5 mm was obtained. The specimen-cutting process and procedure are shown in Figure 5. The test temperature was 25 ± 0.5 °C. A relaxation period of at least 10 min sh maintained before the test. The test would stop when the maximum load was redu 93%. When loading cycles reached 1200, it would also terminate the test. The init

Low-Temperature Semicircular Bending (LT-SCB) Test
LT-SCB test used semicircular pre-cut specimens to evaluate the ability of the mixture to resist damage under low-temperature conditions referring to the AASHTO TP 105-13 test method [27]. The specimen preparation of the LT-SCB test was roughly the same as the CE-SCB test. The difference was that the thickness of the cut specimen was adjusted to 24.7 ± 2 mm. The test temperature was −10 • C. Each group of tests had four parallel specimens. The mean and standard deviation were calculated separately.
The fracture energy G f and fracture toughness K IC (also known as mode I critical stress intensity factor) of the asphalt mixture under low-temperature conditions were calculated with reference to the specification. The higher the index value, the better the resistance of the compound to crack expansion at low temperatures.

Overlay Test (OT)
The OT was performed with reference to the TEX-248-F [39]. The Marshall compaction method (T 0702-2011) [34] was used to form specimens (152.4 mm × 95.3 mm) The cylindrical specimen with a 38.1 ± 0.5 mm thickness was obtained by cutting off the top and bottom parts. Then, both ends of the specimen were cut, and the specimen sample with a width of 76.2 ± 0.5 mm was obtained. The specimen-cutting process and the test procedure are shown in Figure 5. FI takes into account the slope of the force-displacement curve m at the later stage of crack expansion ( Figure 4). It could indicate the resistance to crack expansion after the formation of cracks in the mixture.

Low-Temperature Semicircular Bending (LT-SCB) Test
LT-SCB test used semicircular pre-cut specimens to evaluate the ability of the mixture to resist damage under low-temperature conditions referring to the AASHTO TP 105-13 test method [27]. The specimen preparation of the LT-SCB test was roughly the same as the CE-SCB test. The difference was that the thickness of the cut specimen was adjusted to 24.7 ± 2 mm. The test temperature was −10 °C. Each group of tests had four parallel specimens. The mean and standard deviation were calculated separately.
The fracture energy Gf and fracture toughness KIC (also known as mode I critical stress intensity factor) of the asphalt mixture under low-temperature conditions were calculated with reference to the specification. The higher the index value, the better the resistance of the compound to crack expansion at low temperatures.

Overlay Test (OT)
The OT was performed with reference to the TEX-248-F [39]. The Marshall compaction method (T 0702-2011) [34] was used to form specimens (152.4 mm × 95.3 mm) The cylindrical specimen with a 38.1 ± 0.5 mm thickness was obtained by cutting off the top and bottom parts. Then, both ends of the specimen were cut, and the specimen sample with a width of 76.2 ± 0.5 mm was obtained. The specimen-cutting process and the test procedure are shown in Figure 5. The test temperature was 25 ± 0.5 °C. A relaxation period of at least 10 min should be maintained before the test. The test would stop when the maximum load was reduced by 93%. When loading cycles reached 1200, it would also terminate the test. The initial load and final load were recorded. Then, the load loss rate (LLR) and crack resistance index The test temperature was 25 ± 0.5 • C. A relaxation period of at least 10 min should be maintained before the test. The test would stop when the maximum load was reduced by 93%. When loading cycles reached 1200, it would also terminate the test. The initial load and final load were recorded. Then, the load loss rate (LLR) and crack resistance index (CRI) were calculated according to the specification. There were three parallel specimens in each group. The mean and standard deviation were calculated separately. The OT is a tensile fatigue test. LLR indicates the reduction rate of the final load compared with the initial loading. The smaller the value, the better the resistance to damage. CRI is an inherent property of the specimen, which is obtained by fitting the power equation of the curve of the load and the number of loading cycles during the loading process. The higher the value, the better the crack resistance of the mixture.

Small Beam Bending Test
The BBTs were conducted at −10 • C and 15 • C, respectively. Test results are shown in Figures 6 and 7. (CRI) were calculated according to the specification. There were three parallel specimens in each group. The mean and standard deviation were calculated separately. The OT is a tensile fatigue test. LLR indicates the reduction rate of the final load compared with the initial loading. The smaller the value, the better the resistance to damage. CRI is an inherent property of the specimen, which is obtained by fitting the power equation of the curve of the load and the number of loading cycles during the loading process. The higher the value, the better the crack resistance of the mixture.

Small Beam Bending Test
The BBTs were conducted at −10 °C and 15 °C, respectively. Test results are shown in Figures 6 and 7.   (CRI) were calculated according to the specification. There were three parallel specimens in each group. The mean and standard deviation were calculated separately. The OT is a tensile fatigue test. LLR indicates the reduction rate of the final load compared with the initial loading. The smaller the value, the better the resistance to damage. CRI is an inherent property of the specimen, which is obtained by fitting the power equation of the curve of the load and the number of loading cycles during the loading process. The higher the value, the better the crack resistance of the mixture.

Small Beam Bending Test
The BBTs were conducted at −10 °C and 15 °C, respectively. Test results are shown in Figures 6 and 7.   (a) There were differences in the variation patterns between S ft and D se with air voids and gradation. Considering the different characterization meanings of the two indices, S ft and D se , should be selected for comprehensive evaluation of the crack resistance. Although S ft and D se at different temperatures showed the variation law of increasing with decreasing air voids, there are differences in the variation law of S ft and D se with different gradations (Figure 8). For example, for the 10-B-1 and 10-B-2 gradations, S ft and D se showed opposite patterns with the gradation change. According to the meaning, S ft is the maximum strain when the specimen is damaged, indicating the deformation resistance of the mixture. However, this index is a single evaluation index, which cannot comprehensively evaluate the BBT results [38]. According to the principle of D se calculation, the calculation of this index involves the whole process from loading to damage of the mixture, which can better reflect the comprehensive influence of multiple factors [40]. It can effectively evaluate the fracture resistance of the mixture under the test temperature conditions. Therefore, S ft and D se were recommended to evaluate the crack resistance comprehensively.
opposite patterns with the gradation change. According to the meaning, Sft is th mum strain when the specimen is damaged, indicating the deformation resistanc mixture. However, this index is a single evaluation index, which cannot comprehe evaluate the BBT results [38]. According to the principle of Dse calculation, the calc of this index involves the whole process from loading to damage of the mixture can better reflect the comprehensive influence of multiple factors [40]. It can effe evaluate the fracture resistance of the mixture under the test temperature con Therefore, Sft and Dse were recommended to evaluate the crack resistance comp sively. (b) As the air voids decreased, the crack resistance of the mixture improved. T provement of crack resistance indices was more significant at −10 °C when the ai decreased to 2.5%. It was because when air voids were reduced, the internal com of the mixture was closer. Contact stress between the constituent particles was enh which was conducive to resistance to external loads. Meanwhile, the asphalt film th increased at low air voids (Table 5), which strengthened the cohesion of the particl improved the resistance to deformation. The improvement of each index at differe peratures by reducing air voids is shown in Figure 8. The improvement range w 2.1~6.7% at 15 °C. In comparison, it was 19.0~46.6% at −10 °C. (c) The crack resistance of the 10-A gradation mixture was better than that of th two groups. As shown in Figure 6, the Sft and Dse values of the 10-A gradation m were higher than the other two groups at different air voids and test temperatu cording to the calculation results of the key sieve and Bailey method [37] parame shown in Table 6), the 2.36 mm passing rate, 2.36-4.75 mm particle size content, and aggregate ratio (CA) of 10-A gradation were significantly higher than the other two According to the calculation principle, the CA value indicates the proportion of 2. mm aggregate to 4.75-9.5 mm aggregate. Larger CA values indicate higher content aggregates in the coarse aggregate. The higher fine aggregate content could effe promote crack healing at the early loading stage. Thus, it might exhibit relative (b) As the air voids decreased, the crack resistance of the mixture improved. The improvement of crack resistance indices was more significant at −10 • C when the air voids decreased to 2.5%. It was because when air voids were reduced, the internal compaction of the mixture was closer. Contact stress between the constituent particles was enhanced, which was conducive to resistance to external loads. Meanwhile, the asphalt film thickness increased at low air voids (Table 5), which strengthened the cohesion of the particles. This improved the resistance to deformation. The improvement of each index at different temperatures by reducing air voids is shown in Figure 8. The improvement range was only 2.1~6.7% at 15 • C. In comparison, it was 19.0~46.6% at −10 • C. (c) The crack resistance of the 10-A gradation mixture was better than that of the other two groups. As shown in Figure 6, the S ft and D se values of the 10-A gradation mixture were higher than the other two groups at different air voids and test temperatures. According to the calculation results of the key sieve and Bailey method [37] parameters (as shown in Table 6), the 2.36 mm passing rate, 2.36-4.75 mm particle size content, and coarse aggregate ratio (CA) of 10-A gradation were significantly higher than the other two types. According to the calculation principle, the CA value indicates the proportion of 2.36-4.75 mm aggregate to 4.75-9.5 mm aggregate. Larger CA values indicate higher content of finer aggregates in the coarse aggregate. The higher fine aggregate content could effectively promote crack healing at the early loading stage. Thus, it might exhibit relatively high crack resistance performance.  [37], CA is the coarse aggregate ratio; FA c is the ratio of the coarse aggregate to the fine in the fine aggregate; FA f is the ratio of the coarser aggregate to the finer aggregate in the finest aggregate.

Crack Extension Semicircular Bending Test
Each mixture was tested according to the CE-SCB test method mentioned above. The measured G f and FI test results are shown in Figure 9.  [37], CA is the coarse aggrega FAc is the ratio of the coarse aggregate to the fine in the fine aggregate; FAf is the ratio of the aggregate to the finer aggregate in the finest aggregate.

Crack Extension Semicircular Bending Test
Each mixture was tested according to the CE-SCB test method mentioned abov measured Gf and FI test results are shown in Figure 9. (a) The variation of Gf and FI were consistent with the change of air voids and tion (Figure 9), indicating that both indices can be used to evaluate the crack exp resistance of AR-SAMI. According to the meaning, Gf reflects the energy required crack expansion of the asphalt mixture. FI is the inherent property of the mixture m and characterizes the crack expansion resistance rate. The value of |m| was small FI was high. The slope of the force-displacement curve after the peak of the curve w indicates the better crack expansion resistance of AR-SAMI. In terms of the above tes the two had good consistency.
(b) When the air voids were reduced, the crack extension resistance of AR-SA creased, and 10-A gradation had the maximum enhancement. With the reduction voids, the Gf and FI of each mixture increased, and the two indices increased by 11.0%, and 13.6%, and 40.0%, 4.4%, and 23.2%, respectively, indicating that reduci air voids could enhance the crack expansion resistance of AR-SAMI. The mixtu compact due to the reduction of air voids. The decrease in inter-particle voids effe inhibited the rapid development of cracks. It was demonstrated by the need for fracture energy to reach a fully extended crack. In addition, the two indices of th gradation mixture increased significantly higher than that of 10-B, indicating th crack expansion resistance of AR-SAMI with more fine aggregate was more sensi the change of air voids.
(c) Among the three gradations, the crack expansion resistance of the 10-B ty (a) The variation of G f and FI were consistent with the change of air voids and gradation (Figure 9), indicating that both indices can be used to evaluate the crack expansion resistance of AR-SAMI. According to the meaning, G f reflects the energy required for the crack expansion of the asphalt mixture. FI is the inherent property of the mixture material and characterizes the crack expansion resistance rate. The value of |m| was small when FI was high. The slope of the force-displacement curve after the peak of the curve was flat indicates the better crack expansion resistance of AR-SAMI. In terms of the above test data, the two had good consistency.
(b) When the air voids were reduced, the crack extension resistance of AR-SAMI increased, and 10-A gradation had the maximum enhancement. With the reduction of air voids, the G f and FI of each mixture increased, and the two indices increased by 17.8%, 11.0%, and 13.6%, and 40.0%, 4.4%, and 23.2%, respectively, indicating that reducing the air voids could enhance the crack expansion resistance of AR-SAMI. The mixture was compact due to the reduction of air voids. The decrease in inter-particle voids effectively inhibited the rapid development of cracks. It was demonstrated by the need for higher fracture energy to reach a fully extended crack. In addition, the two indices of the 10-A gradation mixture increased significantly higher than that of 10-B, indicating that the crack expansion resistance of AR-SAMI with more fine aggregate was more sensitive to the change of air voids.
(c) Among the three gradations, the crack expansion resistance of the 10-B type (including 10-B-1 and 10-B-2) mixture was significantly better than 10-A. As shown in Figure 9, the G f and FI of 10-A were significantly lower than those of 10-B types. The indices of the 10-A at 2.5% air voids were still lower than the 10-B types with 4.0% air voids. It was because the passing rate of the 2.36 mm key sieve and CA value of 10-B types were smaller, indicating they had less fine aggregate content and coarse aggregate content of the finer aggregate. In contrast, the coarser aggregate was relatively more. In the presence of cracks, the more coarse aggregate facilitated the strain release at the cracks, which exhibited better resistance to crack expansion.

Low-Temperature Semicircular Bending Test
Each mixture was tested according to the LT-SCB test method mentioned above. G f and K IC results are shown in Figure 10.
Sustainability 2023, 15, x FOR PEER REVIEW 9, the Gf and FI of 10-A were significantly lower than those of 10-B types. The ind the 10-A at 2.5% air voids were still lower than the 10-B types with 4.0% air voids because the passing rate of the 2.36 mm key sieve and CA value of 10-B types were s indicating they had less fine aggregate content and coarse aggregate content of th aggregate. In contrast, the coarser aggregate was relatively more. In the presence of the more coarse aggregate facilitated the strain release at the cracks, which exhibited resistance to crack expansion.

Low-Temperature Semicircular Bending Test
Each mixture was tested according to the LT-SCB test method mentioned ab and KIC results are shown in Figure 10. (a) The variation of Gf and KIC was consistent with the change of air voids, whil were some differences with gradations. Considering the different focus of the two i Gf and KIC were recommended to characterize the low-temperature crack expans sistance of the AR-SAMI. As the air voids decreased, both indices increased. Ho there was no significant correspondence with the change of gradation. For example the air voids were 4.0%, the Gf of the 10-A was the lowest, but its KIC was the highe Gf reflects the energy required to resist deformation. It takes into account the whole ing process. In comparison, KIC demonstrates the ability to absorb energy in the f process. It takes into account the impact of the specimen load and size. So, there ferences between Gf and KIC.
(b) Gf and KIC increased as the air voids decreased. The 10-A gradation increase significantly. When the design air voids were reduced from 4.0% to 2.5%, Gf and three gradations increased. There were 23.7%, 2.7%, and 10.0% and 12.5%, 4.2%, an respectively. It showed that the mixture compactness increased with the air vo creased. It was beneficial to improve the crack expansion resistance of AR-SAMI. while, for the finer gradation (10-A), reducing the air voids could enhance the lo perature crack resistance.
(c) The coupling influence of air voids complicated the influence of gradation SCB test results. When the air voids were 4%, Gf of 10-A was the lowest, and 10-B the highest. The indices showed an opposite magnitude relationship when the ai decreased to 2.5%. Gf of 10-A was the highest and 10-B-1 was the lowest. It show the coarse aggregate content was higher at larger air voids (4%), thus with higher G ever, the improvement of Gf was more significant with the gradation with more fi (a) The variation of G f and K IC was consistent with the change of air voids, while there were some differences with gradations. Considering the different focus of the two indices, G f and K IC were recommended to characterize the low-temperature crack expansion resistance of the AR-SAMI. As the air voids decreased, both indices increased. However, there was no significant correspondence with the change of gradation. For example, when the air voids were 4.0%, the G f of the 10-A was the lowest, but its K IC was the highest. The G f reflects the energy required to resist deformation. It takes into account the whole cracking process. In comparison, K IC demonstrates the ability to absorb energy in the fracture process. It takes into account the impact of the specimen load and size. So, there are differences between G f and K IC .
(b) G f and K IC increased as the air voids decreased. The 10-A gradation increased most significantly. When the design air voids were reduced from 4.0% to 2.5%, G f and K IC of three gradations increased. There were 23.7%, 2.7%, and 10.0% and 12.5%, 4.2%, and 3.2%, respectively. It showed that the mixture compactness increased with the air voids decreased. It was beneficial to improve the crack expansion resistance of AR-SAMI. Meanwhile, for the finer gradation (10-A), reducing the air voids could enhance the low-temperature crack resistance.
(c) The coupling influence of air voids complicated the influence of gradation on LT-SCB test results. When the air voids were 4%, G f of 10-A was the lowest, and 10-B-1 was the highest. The indices showed an opposite magnitude relationship when the air voids decreased to 2.5%. G f of 10-A was the highest and 10-B-1 was the lowest. It showed that the coarse aggregate content was higher at larger air voids (4%), thus with higher G f . However, the improvement of G f was more significant with the gradation with more fine aggregate after decreasing the air voids to 2.5%. In addition, the FI varied with gradation at different air voids in the same pattern, all of which were 10-A maximum.

Overlay Test
OT test was conducted at 25 • C with 1200 loadings. Then, LLR and CRI were calculated, respectively. The test results are shown in Figure 11.
Sustainability 2023, 15, x FOR PEER REVIEW

Overlay Test
OT test was conducted at 25 °C with 1200 loadings. Then, LLR and CRI were lated, respectively. The test results are shown in Figure 11. (a) The LLR and CRI showed good consistency with the change of air voids an dation. As air voids decreased, the LLR of each specimen decreased, and the C creased. Among the three gradations, the index values of 10-A and 10-B-1 were th and better than that of 10-B-2. According to the meaning, the LLR indicates the lo duction ratio at cyclic tensile with fixed displacement. The CRI indicates the decr rate of loading. Although the evaluation of the two indices had differences, as far data are concerned, both indices could show the crack resistance of the AR-SAMI the loading process.
(b) As the air voids decreased, the LLR decreased, and the CRI increased, ind that the fatigue cracking resistance of the AR-SAMI was enhanced. The 10-B-2 test were the worst among three gradations at two air voids. In addition, the LLR of all mens was larger than 93% after 1200 cycles of loading, indicating that the AR-SAM the test requirements of the OT.

Correlation Analysis of Evaluation Indices
Among the above crack resistance evaluation tests and indices, there were diffe in the evaluation focus. The Pearson Test was conducted using statistical analysis ther investigate the correlation between the above test methods and indices. Analy sults are shown in Figure 12. (a) The LLR and CRI showed good consistency with the change of air voids and gradation. As air voids decreased, the LLR of each specimen decreased, and the CRI increased. Among the three gradations, the index values of 10-A and 10-B-1 were the same and better than that of 10-B-2. According to the meaning, the LLR indicates the load reduction ratio at cyclic tensile with fixed displacement. The CRI indicates the decreasing rate of loading. Although the evaluation of the two indices had differences, as far as the data are concerned, both indices could show the crack resistance of the AR-SAMI under the loading process.
(b) As the air voids decreased, the LLR decreased, and the CRI increased, indicating that the fatigue cracking resistance of the AR-SAMI was enhanced. The 10-B-2 test results were the worst among three gradations at two air voids. In addition, the LLR of all specimens was larger than 93% after 1200 cycles of loading, indicating that the AR-SAMI met the test requirements of the OT.

Correlation Analysis of Evaluation Indices
Among the above crack resistance evaluation tests and indices, there were differences in the evaluation focus. The Pearson Test was conducted using statistical analysis to further investigate the correlation between the above test methods and indices. Analysis results are shown in Figure 12.
(a) Among the five test methods, there were differences in the evaluation consistency of the respective two indices for each test. Among them, there was a significant correlation between the different evaluation indices of three test methods (−10 • C BBT, CE-SCB test, and OT). A single index could be used for alternative evaluation of the crack resistance of AR-SAMI. In the remaining two test methods (15 • C BBT and the LT-SCB test), their two indices did not have a significant correlation, indicating that their two indices of test methods had large differences. There did not exist simple substitution or conversion relationships. Therefore, both indices of the above two tests should be used to evaluate AR-SAMI comprehensively. Sustainability 2023, 15, x FOR PEER REVIEW 13 (a) Among the five test methods, there were differences in the evaluation consis of the respective two indices for each test. Among them, there was a significant correl between the different evaluation indices of three test methods (−10 °C BBT, CE-SCB and OT). A single index could be used for alternative evaluation of the crack resistan AR-SAMI. In the remaining two test methods (15 °C BBT and the LT-SCB test), thei indices did not have a significant correlation, indicating that their two indices of test m ods had large differences. There did not exist simple substitution or conversion rela ships. Therefore, both indices of the above two tests should be used to evaluate AR-S comprehensively.
(b) Among the five test methods, there were good correlations between the indi some test methods, and mutual substitution could be considered in the correspon performance evaluation. The specific analyses are as follows:  (b) Among the five test methods, there were good correlations between the indices of some test methods, and mutual substitution could be considered in the corresponding performance evaluation. The specific analyses are as follows:

•
Evaluation of crack resistance: The two indices of the LT-SCB test were significantly correlated with the D se of −10 • C BBT. So, the D se of −10 • C BBT could be a substitute to evaluate the results of the LT-SCB test. However, indices of the LT-SCB test were not significantly related to the S ft of the −10 • C BBT. Considering only S ft was used in China [31], it is necessary to add D se to evaluate crack resistance. In addition, studies have shown that asphalt mixtures are more likely to form cracks at low temperatures [33]. Therefore, instead of 15 • C BBT, −10 • C BBT results can be used to evaluate crack resistance. • Evaluation of crack expansion resistance: Indices of the CE-SCB test were not significantly related to other test indices. However, there was a significant correlation between the two indices of this test. Since FI considered the post-peak load characteristics, it could better reflect the resistance of crack expansion. Therefore, the FI could be used to evaluate the crack expansion resistance of AR-SAMI. • Evaluation of fatigue crack resistance: There was a significant correlation between the two indicators in the OT. The two OT indices were significantly correlated with the −10 • C S ft . However, considering the significant differences between the two test conditions and crack types, a more general correlation still needs further verification. Therefore, using CRI to evaluate the fatigue crack resistance performance of AR-SAMI is still recommended.
Considering the validity and comprehensiveness of the evaluation indices and the simplicity of the test methods and indices, the following test methods and indices (as shown in Table 7) are recommended for the comprehensive evaluation of the crack resistance of AR-SAMI. The recommended test methods and indices were adopted. Test results of crack resistance at different gradations and air voids were processed using the Min-Max normalization method. The normalized heat map of crack resistance is shown in Figure 13.
sistance of AR-SAMI. The recommended test methods and indices were adopted. Test results of cr sistance at different gradations and air voids were processed using the Min-Max n ization method. The normalized heat map of crack resistance is shown in Figure 13  In summary, the crack resistance indices of the three gradations were better wh air voids were small. But, there were differences in the performance indices of di gradations. Comparing the four indices of the ARSAMI under two air voids, the of all gradations with 2.5% air voids were significantly higher than those of 4.0% air Among all gradations, 10-A had the three highest indices (−10 °C Sft, −10 °C Dse, an at two air voids. However, the FI of 10-A was the worst. It indicates that the cr sistance of AR-SMAI varies in different evaluation focus and even existed the op phenomenon. Different test methods focus differently on evaluating crack resistance. The B single damage test that focuses on evaluating the strength characteristics of the AR The two SCB tests focus on evaluating crack expansion resistance under pre-crack tions. The LT-SCB test focuses on low-temperature resistance to crack expansion mance. The OT focuses on performance decay under cyclic loading. It is similar In summary, the crack resistance indices of the three gradations were better when the air voids were small. But, there were differences in the performance indices of different gradations. Comparing the four indices of the ARSAMI under two air voids, the indices of all gradations with 2.5% air voids were significantly higher than those of 4.0% air voids. Among all gradations, 10-A had the three highest indices (−10 • C S ft , −10 • C D se , and CRI) at two air voids. However, the FI of 10-A was the worst. It indicates that the crack resistance of AR-SMAI varies in different evaluation focus and even existed the opposite phenomenon.
Different test methods focus differently on evaluating crack resistance. The BBT is a single damage test that focuses on evaluating the strength characteristics of the AR-SAMI. The two SCB tests focus on evaluating crack expansion resistance under pre-crack conditions. The LT-SCB test focuses on low-temperature resistance to crack expansion performance. The OT focuses on performance decay under cyclic loading. It is similar to the fatigue performance test. Therefore, the design of the AR-SAMI needs to consider the evaluation results of the crack resistance under different tests. AR-SAMI should be a comprehensive balance design. For example, the BBT of AR-SAMI should be adopted for the new pavement construction because the sublayer cracks have not been formed. Suppose the AR-SAMI is added to the existing pavement. The CE-SCB test should be considered as the cracks already exist on the existing pavement with potential problems. Considering the OT can evaluate the tensile fatigue crack resistance performance, the OT should be a priority selection if the traffic volume is high. In addition, the inconsistency of evaluation results further indicated the necessity of using different test methods to comprehensively evaluate the crack resistance performance in various aspects of performance requirements.

Conclusions
AR-SAMI with two air voids and three gradations was selected. The BBT at different temperatures and CE-SCB, LT-SCB, and OT tests were conducted to evaluate the crack resistance. Statistical analysis of the test indices was performed. The main findings are as follows: • All test methods showed that the crack resistance indices of AR-SAMI were significantly improved when the air voids were reduced from 4.0% to 2.5%. Therefore, the comprehensive crack resistance of AR-SAMI may perform better when the design air voids are decreased.

•
The gradation 10-A, which contains more fine aggregate, performed better on most crack resistance indices. However, its crack extension resistance was poor. The CE-SCB and the LT-SCB tests showed that the 10-B type (including 10-B-1 and 10-B-2) with more coarse aggregate had better crack extension resistance under pre-existing cracks. • There are differences in the evaluation results of different test methods and indices due to the differences in the evaluation mechanism. The test evaluation methods and corresponding indices should be selected according to the engineering characteristics of applications. The crack resistance should be designed in a targeted and comprehensive balance method. Considering the validity, comprehensiveness, and simplicity of the evaluation tests and indices, the test methods and indices in Table 7 were recommended for the comprehensive evaluation of the crack resistance of AR-SAMI.
In this work, the conclusions are based on three ten-type gradations. The type and number of test gradations are small, which has some limitations. Therefore, other mixture types and a wider range of gradations still need to be thoroughly analyzed for more universal research conclusions. In addition, the pavement performances (including hightemperature performance, low temperature performance, and water stability) and bonding properties of AR-SAMI should be combined for a comprehensive evaluation of the engineering application.
Author Contributions: Conceptualization, P.L. and Z.L.; methodology, W.P.; validation, S.T. and J.L.; formal analysis, W.P. and J.L.; investigation, J.L. and S.L.; resources, P.L. and Z.L.; data curation, W.P. and J.L.; writing-original draft preparation, S.T. and J.L.; writing-review and editing, W.P. and P.L.; supervision, P.L.; project administration, P.L.; funding acquisition, P.L. All authors have read and agreed to the published version of the manuscript. Data Availability Statement: All data, models, and code generated or used during the study appear in the published article.

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