# Experimental Study on the High-Temperature Shear Performance of Asphalt Mixtures

Authors: Jia’ning Huang; Ruiduo Li; Song Yin; Pengfei Liu
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

The influence of temperature on the shear performance of asphalt mixtures and the feasibility of using the deformation strength as an index of the high-temperature shear performance of these mixtures were explored in this study. Taking AC-13C and AC-20C asphalt mixtures as the research objects, uniaxial compression, rutting, deformation strength, and uniaxial static load creep tests were carried out at temperatures 40°C, 45°C, 50°C, 55°C, and 60°C. The correlations between the deformation strength and modulus of resilience, compressive strength, dynamic stability, and stiffness of the asphalt mixtures were studied. The test results show that the influence of temperature on the compressive strength, resilience modulus, and deformation strength of the asphalt mixtures decreases significantly as the temperature increased, and the rutting deformation of the two kinds of asphalt mixtures increased as the temperature increased. Strong correlations exist between the deformation strength and the modulus of resilience, the compressive strength, and the dynamic stability of asphalt mixtures, so the deformation strength can be used as an evaluation index of the high-temperature shear performance of asphalt mixtures.


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## Body

## 1. Introduction

Asphalt pavement diseases mainly include cracks, ruts, and pits. The rut disease also includes fluid ruts and structural ruts. The former refers to the repeated action of wheel rolling under high-temperature conditions when the load stress exceeds the stability limit of the asphalt mixture. The latter refers to the permanent deformation of each structural layer under the asphalt surface, including the roadbed, due to the load exceeding the strength of the pavement layer. The rutting of asphalt pavement is mainly related to the permanent deformation of asphalt mixtures at high temperatures. Therefore, it is essential to reduce the rutting rate of asphalt pavement by studying the permanent deformation characteristics of asphalt mixtures at high temperatures.At present, creep tests are mainly used to study the high-temperature permanent deformation characteristics of asphalt mixtures [1]. Through creep tests, the constitutive relationship of asphalt mixtures under loading can be obtained, and then leaching can reflect the stress state and deformation behavior of green mixtures.Molenaar et al. [2] and Hafez [3] studied the performance of asphalt mixtures through unconfined creep tests. Jiang et al. [4] examined the permanent deformation characteristics of asphalt mixtures under multiple repeated loads. Moriyoshi et al. [5] investigated the strain distribution law inside asphalt mixtures at high temperatures through rutting tests. Karami et al. [6] analyzed the permanent deformation of asphalt pavement mixtures through dynamic creep tests.The uniaxial static penetration test method has been extensively used to study the high-temperature permanent deformation characteristics of asphalt mixtures due to its advantages of simple instrumentation and convenient operation [7, 8]. Golsefidi and Sahaf [9] studied the influence of different loading methods on the shear performance of asphalt mixtures. Lijun et al. [10–12] proposed the use of a uniaxial penetration test to evaluate the shear performance of asphalt mixtures and further used a uniaxial penetration repeated shear test to study the permanent deformation characteristics of asphalt mixtures under different stress levels [13, 14]. The principle of the uniaxial penetration test is the application of a load at a loading rate of 1 mm/min on a cylindrical specimen to simulate the wheel load on the actual road surface, as shown in Figure 1(a). The test specimen is a cylinder with dimensions of Φ100 mm × 100 mm or Φ150 mm × 100 mm. The round, flat steel indenters have a diameter of 28.5 mm or 42.0 mm (Figure 1(b)). Huang et al. [15] obtained the corresponding test parameters through numerical simulation of the uniaxial penetration creep test of a rutting board by using the finite element method. Then, the rutting deformation of flexible base asphalt pavement was estimated and analyzed by using the finite element method. Cai [16] identified a linear relationship between the shear strength and the temperature by using a uniaxial penetration test of asphalt mixtures at different temperatures.Figure 1
Single-axis penetration test device. (a) Diagram of the uniaxial penetration test head. (b) Uniaxial penetration test.
(a)(b)The above research results demonstrate that the uniaxial penetration test can better simulate the actual pavement stress state under wheel loading. However, this test also has some defects. The loading rate of the uniaxial penetration test is 1 mm/min, which can be approximately simplified to a static load. This situation is quite different from the dynamic load action of wheels running at high speed. Thus, the stress distribution of an asphalt mixture specimen is very different from that of the actual asphalt pavement. Second, the uniaxial static load creep test is advantageous because it uses simple equipment and is convenient and practical. However, in uniaxial static load creep tests under the condition of high-temperature, the sample will undergo accelerated creep and damage occurs. Third, the uniaxial static load creep test cannot reflect the lateral restraint of asphalt mixtures under vehicle loads. Finally, in a uniaxial penetration test, cylindrical steel indenters with flat bottoms cause stress concentrations in asphalt mixtures at the indenter edges.Based on the aforementioned research, a cylindrical uniaxial compression test and a rutting test were carried out for AC-13C and AC-20C asphalt mixtures. The pressure head of the single-axle static load penetration test was improved to more closely simulate the load action form of vehicle tires on asphalt pavement. Then, the deformation strength test and the uniaxial penetration creep test were carried out with the improved circular indenter. The correlations between the deformation strength and the compressive rebound modulus, the compressive strength, and the dynamic stability of asphalt mixtures were studied. The feasibility of using the deformation strength as an evaluation index of the high-temperature shear performance of asphalt mixtures was discussed.


## 2. Test Materials

### 2.1. Preparation of Asphalt Mortar

#### 2.1.1. Asphalt

The asphalt was No. 70 grade A road petroleum asphalt. The basic physical properties of asphalt were determined according to “Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering” (JTG E20–2011) [17] standard test methods. The results are shown in Table 1.Table 1
Basic technical characteristics of asphalt.
ProjectUnitMeasured valuePenetration (100 g, 5 s)5°C0.1 mm6.715°C0.1 mm17.925°C0.1 mm60.6PI—−1.04Equivalent softening point (T800)°C49.7Equivalent breaking point T1. 2°C−10.4Ductility5°Ccm1.415°Ccm35.6Softening point°C48.3


#### 2.1.2. Physical Properties of Aggregates

The mineral materials used in the test were coarse aggregates (limestone, from Jiaxian, Henan, China), fine aggregates (sand and detritus, sand from LuShan, Henan, China; detritus is the lower part of the 2.36 mm sieve when the quarry breaks the stone), and ore powder. The coarse aggregates included the following three grades: 5–10 mm, 10–15 mm, and 15–20 mm. The fine aggregates included sand and gravel. According to the “Test Methods of Aggregate for Highway Engineering” (JTG E42-2005) [18], the net basket method was used to measure the relative density of the gross volume of the coarse aggregate. The apparent relative density and the gross relative density of the fine aggregates were measured using the volumetric flask method and the slump cylinder method. The performance indices of the coarse aggregate and fine aggregates obtained through the tests are listed in Tables 2 and 3.Table 2
Performance indices of the coarse aggregates.
Nominal diameter (mm)Los Angeles attrition loss (%)Apparent relative density (t/m3)Water absorption (%)Needle-flake particle content (%)5–1021.22.771.5018.910–1517.32.860.4311.310–2014.82.840.4512.5Table 3
Performance indices of the fine aggregates.
NameApparent relative density (t/m3)Silt content (%)Sand2.654.4


### 2.2. Preparation of Asphalt Mixture Specimens

According to the median gradation of AC-13C and AC-20C asphalt mixtures specified in “Technical specifications for construction of highway asphalt pavements” (JTG F40-2004) [19], the mineral aggregate gradation composition is designed, which can ensure the stability of the mineral aggregate gradation of the specimen and reduce the test error caused by the heterogeneity of raw materials. Mineral gradation composition of AC-13C and AC-20C asphalt mixtures according to the median gradation composition of asphalt mixtures designed for crude dense-gradation asphalt mixture is shown in Table 4.Table 4
Mineral aggregate gradation ranges of the AC-13 and AC-20C asphalt mixtures.
AC-13CAC-20CScreen-aperture (mm)Upper limit (%)Lower limit (%)Midvalue (%)Screen-aperture (mm)Upper limit (%)Lower limit (%)Midvalue (%)————26.5100100100————191009095161001001001692788513.2100909513.28062719.5856876.59.57250614.756838534.755626412.365024372.364416301.18381526.51.18331222.50.62810190.6248160.320713.50.3175110.15155100.151348.50.0758460.075735According to the Marshall test, the optimal asphalt contents of the AC-13C and AC-20C asphalt mixtures are 4.76% and 4.03%, respectively. The preparation of the raw minerals and bitumen was in accordance with the requirements of the “Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering” (JTG E20–2011) [17] and the “Test Methods of Aggregate for Highway Engineering” (JTG E42–2005) [18]. Figure 2 shows the preparation of the cylindrical specimens with diameters and heights of 100 mm by static pressing molding.Figure 2
Sample making. (a) Molds used for testing the molded specimens. (b) Molded parts of the specimens.
(a)(b)


## 2.1. Preparation of Asphalt Mortar

### 2.1.1. Asphalt

The asphalt was No. 70 grade A road petroleum asphalt. The basic physical properties of asphalt were determined according to “Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering” (JTG E20–2011) [17] standard test methods. The results are shown in Table 1.Table 1
Basic technical characteristics of asphalt.
ProjectUnitMeasured valuePenetration (100 g, 5 s)5°C0.1 mm6.715°C0.1 mm17.925°C0.1 mm60.6PI—−1.04Equivalent softening point (T800)°C49.7Equivalent breaking point T1. 2°C−10.4Ductility5°Ccm1.415°Ccm35.6Softening point°C48.3


### 2.1.2. Physical Properties of Aggregates

The mineral materials used in the test were coarse aggregates (limestone, from Jiaxian, Henan, China), fine aggregates (sand and detritus, sand from LuShan, Henan, China; detritus is the lower part of the 2.36 mm sieve when the quarry breaks the stone), and ore powder. The coarse aggregates included the following three grades: 5–10 mm, 10–15 mm, and 15–20 mm. The fine aggregates included sand and gravel. According to the “Test Methods of Aggregate for Highway Engineering” (JTG E42-2005) [18], the net basket method was used to measure the relative density of the gross volume of the coarse aggregate. The apparent relative density and the gross relative density of the fine aggregates were measured using the volumetric flask method and the slump cylinder method. The performance indices of the coarse aggregate and fine aggregates obtained through the tests are listed in Tables 2 and 3.Table 2
Performance indices of the coarse aggregates.
Nominal diameter (mm)Los Angeles attrition loss (%)Apparent relative density (t/m3)Water absorption (%)Needle-flake particle content (%)5–1021.22.771.5018.910–1517.32.860.4311.310–2014.82.840.4512.5Table 3
Performance indices of the fine aggregates.
NameApparent relative density (t/m3)Silt content (%)Sand2.654.4


## 2.1.1. Asphalt

The asphalt was No. 70 grade A road petroleum asphalt. The basic physical properties of asphalt were determined according to “Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering” (JTG E20–2011) [17] standard test methods. The results are shown in Table 1.Table 1
Basic technical characteristics of asphalt.
ProjectUnitMeasured valuePenetration (100 g, 5 s)5°C0.1 mm6.715°C0.1 mm17.925°C0.1 mm60.6PI—−1.04Equivalent softening point (T800)°C49.7Equivalent breaking point T1. 2°C−10.4Ductility5°Ccm1.415°Ccm35.6Softening point°C48.3


## 2.1.2. Physical Properties of Aggregates

The mineral materials used in the test were coarse aggregates (limestone, from Jiaxian, Henan, China), fine aggregates (sand and detritus, sand from LuShan, Henan, China; detritus is the lower part of the 2.36 mm sieve when the quarry breaks the stone), and ore powder. The coarse aggregates included the following three grades: 5–10 mm, 10–15 mm, and 15–20 mm. The fine aggregates included sand and gravel. According to the “Test Methods of Aggregate for Highway Engineering” (JTG E42-2005) [18], the net basket method was used to measure the relative density of the gross volume of the coarse aggregate. The apparent relative density and the gross relative density of the fine aggregates were measured using the volumetric flask method and the slump cylinder method. The performance indices of the coarse aggregate and fine aggregates obtained through the tests are listed in Tables 2 and 3.Table 2
Performance indices of the coarse aggregates.
Nominal diameter (mm)Los Angeles attrition loss (%)Apparent relative density (t/m3)Water absorption (%)Needle-flake particle content (%)5–1021.22.771.5018.910–1517.32.860.4311.310–2014.82.840.4512.5Table 3
Performance indices of the fine aggregates.
NameApparent relative density (t/m3)Silt content (%)Sand2.654.4


## 2.2. Preparation of Asphalt Mixture Specimens

According to the median gradation of AC-13C and AC-20C asphalt mixtures specified in “Technical specifications for construction of highway asphalt pavements” (JTG F40-2004) [19], the mineral aggregate gradation composition is designed, which can ensure the stability of the mineral aggregate gradation of the specimen and reduce the test error caused by the heterogeneity of raw materials. Mineral gradation composition of AC-13C and AC-20C asphalt mixtures according to the median gradation composition of asphalt mixtures designed for crude dense-gradation asphalt mixture is shown in Table 4.Table 4
Mineral aggregate gradation ranges of the AC-13 and AC-20C asphalt mixtures.
AC-13CAC-20CScreen-aperture (mm)Upper limit (%)Lower limit (%)Midvalue (%)Screen-aperture (mm)Upper limit (%)Lower limit (%)Midvalue (%)————26.5100100100————191009095161001001001692788513.2100909513.28062719.5856876.59.57250614.756838534.755626412.365024372.364416301.18381526.51.18331222.50.62810190.6248160.320713.50.3175110.15155100.151348.50.0758460.075735According to the Marshall test, the optimal asphalt contents of the AC-13C and AC-20C asphalt mixtures are 4.76% and 4.03%, respectively. The preparation of the raw minerals and bitumen was in accordance with the requirements of the “Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering” (JTG E20–2011) [17] and the “Test Methods of Aggregate for Highway Engineering” (JTG E42–2005) [18]. Figure 2 shows the preparation of the cylindrical specimens with diameters and heights of 100 mm by static pressing molding.Figure 2
Sample making. (a) Molds used for testing the molded specimens. (b) Molded parts of the specimens.
(a)(b)


## 3. Test Experiment

### 3.1. Test of Uniaxial Compression

Figure3 shows the electronic universal testing machine, which can automatically load and unload, collect data, and generate displacement curves and other curves for test specimens. The completed AC-13C and AC-20C specimens were subjected to uniaxial compression tests at 40°C, 45°C, 50°C, 55°C, and 60°C using the electronic universal testing machine. The compressive strength and compressive rebound modulus of both specimens were obtained.Figure 3
CMT5105 microcomputer-controlled electronic universal testing machine.


### 3.2. Rutting Test

Figure4 shows the rut specimen with length × width × height dimensions of 300 mm ×300 mm × 5 mm made in accordance with “Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering” (JTG E20–2011) [17].Figure 4
Rut specimen.Figure5 shows the rutting test instrument produced by Italian Controls and a photo of an experiment with it.Figure 5
Rut tester.The dynamic stability of the AC-13C and AC-20C asphalt mixtures was calculated according to the following equation:(1)DS=t1−t2×Nd2−d1×C1×C2.In this equation, DS is the dynamic stability of the asphalt mixture (times/mm),d1 is the deformation corresponding to time t1 (mm), d2 is the deformation corresponding to time t2 (mm), C1 is the type coefficient of the test instrument (1.0), C2 is the specimen coefficient, and N is the test rolling frequency, which is usually 42 times/min. The width of the specimen was 300 mm.


### 3.3. Test of Deformation Strength

Figure6 shows a schematic diagram of the rutting damage caused by vehicles on asphalt pavement. The research shows that the shear performance of an asphalt mixture is one of the most important factors affecting the rutting of the asphalt pavement. Figure 7 presents how Doh et al. [20] adopted the deformation strength method (SD method) to simulate a vehicle load. In the test process, the loading rate of 50.8 mm/min better simulates the vibration load generated by tires when a vehicle is running at high speeds.Figure 6
Schematic diagram of rutting disease.Figure 7
Schematic diagram of the SD method.Based on the uniaxial penetration test, the bottom of the original indenter was rounded by the SD method. Therefore, the indenter was more similar to the load action mode of an actual vehicle tire on a road surface. Figure8 shows an illustration of the improved indenter. At the beginning of the loading stage, the asphalt specimen was consolidated and then allowed to sag. Figure 9 shows the specimen with cracks appearing and expanding until failure caused by continuous loading.Figure 8
Improved indenter (D = 40 mm, r = 10 mm).Figure 9
Failure mode of the failure specimen (AC-13C).The deformation strength calculated by the SD method is influenced by both the shear strength and the plastic deformation (see equation (2) for the deformation strength calculation formula of the SD method). Compared with the uniaxial penetration test based on elastic mechanics, this method can better simulate the real situation of the asphalt pavement under a vehicle load,(2)SD=4PπD−2r−2ry−y22.In this equation,SD is the deformation strength (MPa), P is the largest load (N), D is the diameter of the indenter (mm), r is the indenter bottom arc radius (Figure 8) (mm), and y is the maximum vertical deformation that occurs when the specimen is damaged (mm).The electronic universal testing machine shown in Figure3 was employed for the loading test (with the improved indenter). The test loading rate was 50.8 mm/min. The pressure of the specimen failure was taken as the maximum load. Formula (2) was applied to compute the deformation strength of the asphalt mixture. Three parallel tests were performed for each sample, and the average value was taken as the result.


### 3.4. Test of Uniaxial Penetration Creep

The improved uniaxial penetration creep test can avoid the stress concentration around the pressure head caused by the traditional penetration test and better reflect the vehicle tire load form. Therefore, the penetration head used for the deformation strength test mentioned above was used in the uniaxial penetration creep test for asphalt mixtures in this study. The test temperatures were 40°C, 45°C, 50°C, 55°C, and 60°C, and the pressure was 220 N.


## 3.1. Test of Uniaxial Compression

Figure3 shows the electronic universal testing machine, which can automatically load and unload, collect data, and generate displacement curves and other curves for test specimens. The completed AC-13C and AC-20C specimens were subjected to uniaxial compression tests at 40°C, 45°C, 50°C, 55°C, and 60°C using the electronic universal testing machine. The compressive strength and compressive rebound modulus of both specimens were obtained.Figure 3
CMT5105 microcomputer-controlled electronic universal testing machine.


## 3.2. Rutting Test

Figure4 shows the rut specimen with length × width × height dimensions of 300 mm ×300 mm × 5 mm made in accordance with “Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering” (JTG E20–2011) [17].Figure 4
Rut specimen.Figure5 shows the rutting test instrument produced by Italian Controls and a photo of an experiment with it.Figure 5
Rut tester.The dynamic stability of the AC-13C and AC-20C asphalt mixtures was calculated according to the following equation:(1)DS=t1−t2×Nd2−d1×C1×C2.In this equation, DS is the dynamic stability of the asphalt mixture (times/mm),d1 is the deformation corresponding to time t1 (mm), d2 is the deformation corresponding to time t2 (mm), C1 is the type coefficient of the test instrument (1.0), C2 is the specimen coefficient, and N is the test rolling frequency, which is usually 42 times/min. The width of the specimen was 300 mm.


## 3.3. Test of Deformation Strength

Figure6 shows a schematic diagram of the rutting damage caused by vehicles on asphalt pavement. The research shows that the shear performance of an asphalt mixture is one of the most important factors affecting the rutting of the asphalt pavement. Figure 7 presents how Doh et al. [20] adopted the deformation strength method (SD method) to simulate a vehicle load. In the test process, the loading rate of 50.8 mm/min better simulates the vibration load generated by tires when a vehicle is running at high speeds.Figure 6
Schematic diagram of rutting disease.Figure 7
Schematic diagram of the SD method.Based on the uniaxial penetration test, the bottom of the original indenter was rounded by the SD method. Therefore, the indenter was more similar to the load action mode of an actual vehicle tire on a road surface. Figure8 shows an illustration of the improved indenter. At the beginning of the loading stage, the asphalt specimen was consolidated and then allowed to sag. Figure 9 shows the specimen with cracks appearing and expanding until failure caused by continuous loading.Figure 8
Improved indenter (D = 40 mm, r = 10 mm).Figure 9
Failure mode of the failure specimen (AC-13C).The deformation strength calculated by the SD method is influenced by both the shear strength and the plastic deformation (see equation (2) for the deformation strength calculation formula of the SD method). Compared with the uniaxial penetration test based on elastic mechanics, this method can better simulate the real situation of the asphalt pavement under a vehicle load,(2)SD=4PπD−2r−2ry−y22.In this equation,SD is the deformation strength (MPa), P is the largest load (N), D is the diameter of the indenter (mm), r is the indenter bottom arc radius (Figure 8) (mm), and y is the maximum vertical deformation that occurs when the specimen is damaged (mm).The electronic universal testing machine shown in Figure3 was employed for the loading test (with the improved indenter). The test loading rate was 50.8 mm/min. The pressure of the specimen failure was taken as the maximum load. Formula (2) was applied to compute the deformation strength of the asphalt mixture. Three parallel tests were performed for each sample, and the average value was taken as the result.


## 3.4. Test of Uniaxial Penetration Creep

The improved uniaxial penetration creep test can avoid the stress concentration around the pressure head caused by the traditional penetration test and better reflect the vehicle tire load form. Therefore, the penetration head used for the deformation strength test mentioned above was used in the uniaxial penetration creep test for asphalt mixtures in this study. The test temperatures were 40°C, 45°C, 50°C, 55°C, and 60°C, and the pressure was 220 N.


## 4. Interpretations of the Experimental Results

### 4.1. Relationships between the Compressive Strength, the Compressive Resilience Modulus, and the Temperature of the Asphalt Mixtures

Figure10 is the correlation analysis diagram of the compressive strength and the temperature of the AC-13C and AC-20C asphalt mixtures. As the temperature increased, the compressive strength of the two asphalt mixtures decreased gradually. At 40°C, the compressive strength of the AC-13C asphalt mixture was greater than that of the AC-20C mixture. As the temperature increased, this advantage gradually disappeared and became a disadvantage. When the temperature increased to 60°C, the compressive strength of the AC-13C asphalt mixture was slightly lower than that of the AC-20C mixture. As the temperature increased from 40°C to 60°C, the compressive strength of the AC-13C asphalt mixture decreased by 51.82% and that of the AC-20C asphalt mixture decreased by 43.83%. The compressive strength of the AC-13C asphalt mixture was greatly affected by the temperature increase. Moreover, the compressive strength of the AC-13C and AC-20C asphalt mixtures exhibits a linear exponential decrease as the temperature increased, and the coefficients of determination of the two asphalt mixtures were 0.9587 and 0.9630, respectively. Interestingly, in the case of very high temperature (60°C), two asphalt mixtures were observed to possess a strength that was lower than the predicted value of the exponential curve. Because, at this temperature, the contribution of the cohesion between the aggregates to the strength was almost zero, and the strength of the asphalt mixture was probably completely provided by the strength of the aggregate itself and the friction between the aggregates.Figure 10
Correlation analysis of the compressive strength and the temperature of the AC-13C and AC-20C asphalt mixtures.Figure11 presents the correlation analysis diagram of the compressive resilience modulus and the temperature of the asphalt mixture. As the temperature increased, the compressive resilience modulus of the two asphalt mixtures decreased gradually. The compressive resilience modulus of the AC-13C asphalt mixture was lower than that of the AC-20C mixture. As the temperature increased to 60°C, the compressive strength of the AC-13C asphalt mixture decreased by 64.64%, and that of the AC-20C asphalt mixture decreased by 58.42%. The compressive resilience modulus of the two asphalt mixtures exhibited a linear exponential decrease as the temperature increased, and the determination coefficients were 0.99887 and 0.99652, respectively.Figure 11
Correlation analysis between the compressive resilience modulus and the temperature of the AC-13C and AC-20C asphalt mixtures.


### 4.2. Relationships between the Rutting Deformation, Dynamic Stability, and Temperature of the Asphalt Mixtures

Figures12 and 13 show the logarithmic correlation analysis diagrams of the rutting deformation and time for the AC-13C and AC-20C asphalt mixtures, respectively. The rutting deformation of the two asphalt mixtures increased gradually with time. Simultaneously, the higher the temperature was, the greater the rutting deformation of the two asphalt mixtures was. The final rutting deformation of the AC-13C asphalt mixture at 60°C was 2.264 times that at 40°C, and that of the AC-20C mixture at 60°C was 2.160 times that at 40°C. Therefore, the temperature has a great influence on the rutting deformation of the asphalt mixtures. The rutting deformation of the two asphalt mixtures showed a first-order linear exponential growth relationship with the logarithm of time.Figure 12
Correlation analysis of the AC-13C asphalt mixtures rutting deformation and the logarithm of time.Figure 13
Correlation analysis of the AC-20C asphalt mixtures rutting deformation and the logarithm of time.Figure14 exhibits the correlation analysis diagram of the dynamic stability and temperature of the two asphalt mixtures. As the temperature increased, the dynamic stability of the two asphalt mixtures decreased gradually. The dynamic stability of the AC-13C asphalt mixture was lower than that of the AC-20C mixture. When the temperature increased from 40°C to 60°C, the compressive strength of the AC-13C asphalt mixture decreased by 74.14% and that of the AC-20C asphalt mixture decreased by 70.61%. The dynamic stability of the two asphalt mixtures exhibited a first-order linear exponential decrease as the temperature increased. The determinative coefficients of the two asphalt mixtures were 0.98180 and 0.99278.Figure 14
Correlation analysis of the dynamic stability and temperature of the AC-13C and AC-20C asphalt mixtures.


### 4.3. Relationship between the Uniaxial Penetration Creep of the Asphalt Mixtures and Temperature

It can be seen from the data in Figures15 and 16 that the creep curve of asphalt mixtures can be divided into two stages: at Stage 1, the creep rates decreased with time, and at Stage 2, the creep tends to be steady, the steady creep rates to be constant, and the creep curves were similar to straight lines. The creep rates of the two asphalt mixtures at different temperatures are presented in Figures 15 and 16. It can be seen from the figures that the transient strains of AC-13C and AC-20C asphalt mixtures increase as the test temperature increased, and at the same time, the higher the temperature, the greater the creep. At the same temperature, the transient strain of the AC-20C asphalt mixture was smaller than that of the AC-13C asphalt mixture. In stage 2, the creep rates of both asphalt mixtures increase as the temperature increased; however, at the same temperature, the creep rate of the AC-13C asphalt mixture was smaller than that of the AC-20C asphalt mixture.Figure 15
Creep curve of the AC-13C asphalt mixture at different temperatures.Figure 16
Creep curve of the AC-20C asphalt mixture at different temperatures.The stiffness modulus parameters were extracted from the creep curves, and Figure17 presents the variation in the stiffness modulus with temperature. As the temperature increased, the stiffness modulus of the two asphalt mixtures decreased gradually, signifying that as the temperature increased, the cementitious material in the asphalt mixture softened, and the friction between aggregates decreased, thus reducing the deformation resistance of the asphalt mixture. The stiffness modulus of the asphalt mixture showed a good regularity with the temperature. The determination coefficients of the AC-13C and AC-20C mixtures were 0.9961 and 0.9985, respectively.Figure 17
Correlation analysis diagram of the stiffness modulus and the temperature of the AC-13C and AC-20C asphalt mixtures.


### 4.4. Correlation Analysis of the Deformation Strength, Compressive Strength, Compressive Resilience Modulus, and Dynamic Stability of the Asphalt Mixtures

Figure18 shows the correlation analysis diagram between the deformation strength and temperature of the AC-13C and AC-20C asphalt mixtures. As the temperature increased, the deformation strength of both asphalt mixtures decreased gradually. At the same temperature, the deformation strength of the AC-13C asphalt mixture was lower than that of the AC-20C mixture, meaning that the shear strength of the AC-13C asphalt mixture was lower than that of the AC-20C mixture. However, as the temperature increased, the gap gradually decreased. As the temperature increased from 40°C to 60°C, the deformation strength of the AC-13C asphalt mixture decreased by 56.12%, and that of the AC-20C asphalt mixture decreased by 63.67%. The decrease in the deformation strength of the AC-20C asphalt mixture was greatly affected by the temperature increase. The deformation strength of the AC-13C and AC-20C asphalt mixtures exhibited a linear exponential decrease as the temperature increased. The determination coefficients of the AC-13C and AC-20C mixtures were 0.99858 and 0.99837, respectively.Figure 18
Correlation analysis of the deformation strength and temperature of the AC-13C and AC-20C asphalt mixtures.The deformation strength of the two asphalt mixtures was fitted with the compressive strength, the compressive resilience modulus, and the dynamic stability, respectively, and the obtained parameters are shown in Table5.Table 5
Parameters obtained by fitting the deformation strength with the compressive strength, compressive resilient modulus, and dynamic stability.
Model and parametersY=aZ+babR2Deformation strength (Z) and compressive strength (Y)AC-13C0.08500.23540.9292AC-20C0.04260.35290.9528Deformation strength (Z) and compressive resilience modulus (Y)AC-13C45.2581−50.34160.9999AC-20C30.051620.39580.9969Deformation strength (Z) and dynamic stability (Y)AC-13C1045.9359−1929.47190.9756AC-20C703.9401−43.80970.9521The correlation analysis diagram of the compressive strength and deformation strength of the two asphalt mixtures at different temperatures are presented in Figure19. Furthermore, Figure 20 shows the correlation analysis diagram of the compressive rebound modulus and the deformation strength of the two asphalt mixtures at different temperatures. The comparison of Figures 19 and 20 reveals a strong linear correlation between the resilience modulus of the asphalt mixture and the deformation strength. The linear correlation coefficients of the two asphalt mixtures were 0.9999 and 0.9969. The linear correlation between the compressive strength and deformation strength was acceptable, and the linear correlation coefficients of the two asphalt mixtures were 0.9292 and 0.9528. It can be concluded that the compressive performance of an asphalt mixture is approximately reflected by its deformation strength.Figure 19
Correlation analysis chart of the deformation strength and compressive strength of the two asphalt mixtures at different temperatures.Figure 20
Correlation analysis chart of the deformation strength and compressive resilient modulus of the two asphalt mixtures at different temperatures.Figure21 presents the linear correlation analysis diagram of the deformation strength and dynamic stability of the two asphalt mixtures at different temperatures. The linear correlation coefficients of the AC-13C and AC-20C asphalt mixtures were 0.9756 and 0.9521, respectively. A strong linear correlation between the deformation strength and the dynamic stability of the two asphalt mixtures was observed at different temperatures. The high-temperature shear performance of asphalt mixtures can be reflected by the deformation strength.Figure 21
Correlation analysis chart of the deformation strength and dynamic stability of the two asphalt mixtures at different temperatures.


### 4.5. Correlation Analysis of the Dynamic Stability, Deformation Strength, and Stiffness Modulus of the Asphalt Mixtures

Figure22 shows the correlation analysis diagram of the dynamic stability and stiffness modulus of the two asphalt mixtures at different temperatures. Figure 23 shows the correlation analysis diagram of the deformation strength and stiffness modulus of the two asphalt mixtures at the same temperature. The parameters obtained by fitting the dynamic stability, deformation strength, and stiffness modulus of the two asphalt mixtures are shown in Table 6. A good correlation between the dynamic stability and the stiffness modulus of the asphalt mixture was observed, and the coefficients of determination of the two asphalt mixtures were 0.9824 and 0.9686, respectively. Therefore, the dynamic stability of an asphalt mixture can reflect its creep deformation. The correlation between the deformation strength and the stiffness modulus of the asphalt mixtures was acceptable. The coefficients of determination of the two asphalt mixtures were 0.8863 and 0.9457. Therefore, the deformation strength of an asphalt mixture can approximately reflect its creep deformation.Figure 22
Correlation analysis diagram of the dynamic stability and stiffness modulus of the two asphalts mixtures at the same temperature.Figure 23
Correlation analysis diagram of the deformation strength and stiffness modulus of the two asphalts mixtures at the same temperature.Table 6
Parameters obtained by fitting the dynamic stability, deformation strength, and stiffness modulus of the two asphalt mixtures.
Model and parametersZ=aY+babR2Dynamic stability (Z) and stiffness modulus (Y)AC-13C48.959−1838.8960.9824AC-20C84.392−5194.9090.9686Deformation strength (Z) and stiffness modulus (Y)AC-13C0.0753−2.53060.8863AC-20C0.0650−1.91130.9457


## 4.1. Relationships between the Compressive Strength, the Compressive Resilience Modulus, and the Temperature of the Asphalt Mixtures

Figure10 is the correlation analysis diagram of the compressive strength and the temperature of the AC-13C and AC-20C asphalt mixtures. As the temperature increased, the compressive strength of the two asphalt mixtures decreased gradually. At 40°C, the compressive strength of the AC-13C asphalt mixture was greater than that of the AC-20C mixture. As the temperature increased, this advantage gradually disappeared and became a disadvantage. When the temperature increased to 60°C, the compressive strength of the AC-13C asphalt mixture was slightly lower than that of the AC-20C mixture. As the temperature increased from 40°C to 60°C, the compressive strength of the AC-13C asphalt mixture decreased by 51.82% and that of the AC-20C asphalt mixture decreased by 43.83%. The compressive strength of the AC-13C asphalt mixture was greatly affected by the temperature increase. Moreover, the compressive strength of the AC-13C and AC-20C asphalt mixtures exhibits a linear exponential decrease as the temperature increased, and the coefficients of determination of the two asphalt mixtures were 0.9587 and 0.9630, respectively. Interestingly, in the case of very high temperature (60°C), two asphalt mixtures were observed to possess a strength that was lower than the predicted value of the exponential curve. Because, at this temperature, the contribution of the cohesion between the aggregates to the strength was almost zero, and the strength of the asphalt mixture was probably completely provided by the strength of the aggregate itself and the friction between the aggregates.Figure 10
Correlation analysis of the compressive strength and the temperature of the AC-13C and AC-20C asphalt mixtures.Figure11 presents the correlation analysis diagram of the compressive resilience modulus and the temperature of the asphalt mixture. As the temperature increased, the compressive resilience modulus of the two asphalt mixtures decreased gradually. The compressive resilience modulus of the AC-13C asphalt mixture was lower than that of the AC-20C mixture. As the temperature increased to 60°C, the compressive strength of the AC-13C asphalt mixture decreased by 64.64%, and that of the AC-20C asphalt mixture decreased by 58.42%. The compressive resilience modulus of the two asphalt mixtures exhibited a linear exponential decrease as the temperature increased, and the determination coefficients were 0.99887 and 0.99652, respectively.Figure 11
Correlation analysis between the compressive resilience modulus and the temperature of the AC-13C and AC-20C asphalt mixtures.


## 4.2. Relationships between the Rutting Deformation, Dynamic Stability, and Temperature of the Asphalt Mixtures

Figures12 and 13 show the logarithmic correlation analysis diagrams of the rutting deformation and time for the AC-13C and AC-20C asphalt mixtures, respectively. The rutting deformation of the two asphalt mixtures increased gradually with time. Simultaneously, the higher the temperature was, the greater the rutting deformation of the two asphalt mixtures was. The final rutting deformation of the AC-13C asphalt mixture at 60°C was 2.264 times that at 40°C, and that of the AC-20C mixture at 60°C was 2.160 times that at 40°C. Therefore, the temperature has a great influence on the rutting deformation of the asphalt mixtures. The rutting deformation of the two asphalt mixtures showed a first-order linear exponential growth relationship with the logarithm of time.Figure 12
Correlation analysis of the AC-13C asphalt mixtures rutting deformation and the logarithm of time.Figure 13
Correlation analysis of the AC-20C asphalt mixtures rutting deformation and the logarithm of time.Figure14 exhibits the correlation analysis diagram of the dynamic stability and temperature of the two asphalt mixtures. As the temperature increased, the dynamic stability of the two asphalt mixtures decreased gradually. The dynamic stability of the AC-13C asphalt mixture was lower than that of the AC-20C mixture. When the temperature increased from 40°C to 60°C, the compressive strength of the AC-13C asphalt mixture decreased by 74.14% and that of the AC-20C asphalt mixture decreased by 70.61%. The dynamic stability of the two asphalt mixtures exhibited a first-order linear exponential decrease as the temperature increased. The determinative coefficients of the two asphalt mixtures were 0.98180 and 0.99278.Figure 14
Correlation analysis of the dynamic stability and temperature of the AC-13C and AC-20C asphalt mixtures.


## 4.3. Relationship between the Uniaxial Penetration Creep of the Asphalt Mixtures and Temperature

It can be seen from the data in Figures15 and 16 that the creep curve of asphalt mixtures can be divided into two stages: at Stage 1, the creep rates decreased with time, and at Stage 2, the creep tends to be steady, the steady creep rates to be constant, and the creep curves were similar to straight lines. The creep rates of the two asphalt mixtures at different temperatures are presented in Figures 15 and 16. It can be seen from the figures that the transient strains of AC-13C and AC-20C asphalt mixtures increase as the test temperature increased, and at the same time, the higher the temperature, the greater the creep. At the same temperature, the transient strain of the AC-20C asphalt mixture was smaller than that of the AC-13C asphalt mixture. In stage 2, the creep rates of both asphalt mixtures increase as the temperature increased; however, at the same temperature, the creep rate of the AC-13C asphalt mixture was smaller than that of the AC-20C asphalt mixture.Figure 15
Creep curve of the AC-13C asphalt mixture at different temperatures.Figure 16
Creep curve of the AC-20C asphalt mixture at different temperatures.The stiffness modulus parameters were extracted from the creep curves, and Figure17 presents the variation in the stiffness modulus with temperature. As the temperature increased, the stiffness modulus of the two asphalt mixtures decreased gradually, signifying that as the temperature increased, the cementitious material in the asphalt mixture softened, and the friction between aggregates decreased, thus reducing the deformation resistance of the asphalt mixture. The stiffness modulus of the asphalt mixture showed a good regularity with the temperature. The determination coefficients of the AC-13C and AC-20C mixtures were 0.9961 and 0.9985, respectively.Figure 17
Correlation analysis diagram of the stiffness modulus and the temperature of the AC-13C and AC-20C asphalt mixtures.


## 4.4. Correlation Analysis of the Deformation Strength, Compressive Strength, Compressive Resilience Modulus, and Dynamic Stability of the Asphalt Mixtures

Figure18 shows the correlation analysis diagram between the deformation strength and temperature of the AC-13C and AC-20C asphalt mixtures. As the temperature increased, the deformation strength of both asphalt mixtures decreased gradually. At the same temperature, the deformation strength of the AC-13C asphalt mixture was lower than that of the AC-20C mixture, meaning that the shear strength of the AC-13C asphalt mixture was lower than that of the AC-20C mixture. However, as the temperature increased, the gap gradually decreased. As the temperature increased from 40°C to 60°C, the deformation strength of the AC-13C asphalt mixture decreased by 56.12%, and that of the AC-20C asphalt mixture decreased by 63.67%. The decrease in the deformation strength of the AC-20C asphalt mixture was greatly affected by the temperature increase. The deformation strength of the AC-13C and AC-20C asphalt mixtures exhibited a linear exponential decrease as the temperature increased. The determination coefficients of the AC-13C and AC-20C mixtures were 0.99858 and 0.99837, respectively.Figure 18
Correlation analysis of the deformation strength and temperature of the AC-13C and AC-20C asphalt mixtures.The deformation strength of the two asphalt mixtures was fitted with the compressive strength, the compressive resilience modulus, and the dynamic stability, respectively, and the obtained parameters are shown in Table5.Table 5
Parameters obtained by fitting the deformation strength with the compressive strength, compressive resilient modulus, and dynamic stability.
Model and parametersY=aZ+babR2Deformation strength (Z) and compressive strength (Y)AC-13C0.08500.23540.9292AC-20C0.04260.35290.9528Deformation strength (Z) and compressive resilience modulus (Y)AC-13C45.2581−50.34160.9999AC-20C30.051620.39580.9969Deformation strength (Z) and dynamic stability (Y)AC-13C1045.9359−1929.47190.9756AC-20C703.9401−43.80970.9521The correlation analysis diagram of the compressive strength and deformation strength of the two asphalt mixtures at different temperatures are presented in Figure19. Furthermore, Figure 20 shows the correlation analysis diagram of the compressive rebound modulus and the deformation strength of the two asphalt mixtures at different temperatures. The comparison of Figures 19 and 20 reveals a strong linear correlation between the resilience modulus of the asphalt mixture and the deformation strength. The linear correlation coefficients of the two asphalt mixtures were 0.9999 and 0.9969. The linear correlation between the compressive strength and deformation strength was acceptable, and the linear correlation coefficients of the two asphalt mixtures were 0.9292 and 0.9528. It can be concluded that the compressive performance of an asphalt mixture is approximately reflected by its deformation strength.Figure 19
Correlation analysis chart of the deformation strength and compressive strength of the two asphalt mixtures at different temperatures.Figure 20
Correlation analysis chart of the deformation strength and compressive resilient modulus of the two asphalt mixtures at different temperatures.Figure21 presents the linear correlation analysis diagram of the deformation strength and dynamic stability of the two asphalt mixtures at different temperatures. The linear correlation coefficients of the AC-13C and AC-20C asphalt mixtures were 0.9756 and 0.9521, respectively. A strong linear correlation between the deformation strength and the dynamic stability of the two asphalt mixtures was observed at different temperatures. The high-temperature shear performance of asphalt mixtures can be reflected by the deformation strength.Figure 21
Correlation analysis chart of the deformation strength and dynamic stability of the two asphalt mixtures at different temperatures.


## 4.5. Correlation Analysis of the Dynamic Stability, Deformation Strength, and Stiffness Modulus of the Asphalt Mixtures

Figure22 shows the correlation analysis diagram of the dynamic stability and stiffness modulus of the two asphalt mixtures at different temperatures. Figure 23 shows the correlation analysis diagram of the deformation strength and stiffness modulus of the two asphalt mixtures at the same temperature. The parameters obtained by fitting the dynamic stability, deformation strength, and stiffness modulus of the two asphalt mixtures are shown in Table 6. A good correlation between the dynamic stability and the stiffness modulus of the asphalt mixture was observed, and the coefficients of determination of the two asphalt mixtures were 0.9824 and 0.9686, respectively. Therefore, the dynamic stability of an asphalt mixture can reflect its creep deformation. The correlation between the deformation strength and the stiffness modulus of the asphalt mixtures was acceptable. The coefficients of determination of the two asphalt mixtures were 0.8863 and 0.9457. Therefore, the deformation strength of an asphalt mixture can approximately reflect its creep deformation.Figure 22
Correlation analysis diagram of the dynamic stability and stiffness modulus of the two asphalts mixtures at the same temperature.Figure 23
Correlation analysis diagram of the deformation strength and stiffness modulus of the two asphalts mixtures at the same temperature.Table 6
Parameters obtained by fitting the dynamic stability, deformation strength, and stiffness modulus of the two asphalt mixtures.
Model and parametersZ=aY+babR2Dynamic stability (Z) and stiffness modulus (Y)AC-13C48.959−1838.8960.9824AC-20C84.392−5194.9090.9686Deformation strength (Z) and stiffness modulus (Y)AC-13C0.0753−2.53060.8863AC-20C0.0650−1.91130.9457


## 5. Conclusions

(1)
The compressive strength, compressive resilience modulus, and deformation strength of the asphalt mixtures exhibited a linear exponential decrease as the temperature increased. As the temperature increased from 40°C to 60°C, the initial compressive strength of the AC-13C mixture was lower than that of the AC-20C mixture, but the gap between the two gradually narrowed as the temperature continued to increase. The higher the temperature was, the greater the rutting deformation of the asphalt mixture was. The deformation of the AC-13C mixture was larger than that of the AC-20C mixture under the same load and action time. The rutting deformation of the asphalt mixture exhibited a linear exponential increase with the logarithm of time.(2)
The deformation strength showed an excellent correlation with the compressive rebound modulus, compressive strength, and dynamic stability of the asphalt mixtures. Therefore, the deformation strength can be used as an evaluation index of the high-temperature shear performance of the asphalt mixtures.(3)
The deformation strength correlated with the modulus of stiffness of the asphalt mixtures, signifying that the deformation strength can be used as an index to evaluate the high-temperature shear performance of asphalt mixtures.(4)
This article only conducts related research work on the AC-13C and AC-20C asphalt mixtures. More broadly, more research is also needed to determine whether the related properties of other materials and different types of asphalt mixtures are same as those in this article.



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*Source: 6428018-2021-09-09.xml*