# Comparison of Real Response and Theoretical Modeling of Pavement with Thick Asphalt Layers under Heavy Traffic Load

Authors: Jingsong Shan; Hongmei Shao; Qiuzhong Li; Peili Sun
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

Two kinds of asphalt pavement with thick asphalt layers were used to construct two samples. In structure I, a semirigid base and graded crushed stone subbase were used. In structure II, a granular base and semirigid subbase layer were used. Responses of the two structures under traffic loads were measured using optical fiber sensors, and the differences between theoretical model results and field measurements were analyzed. Field measurements show that vertical compressive stress in structure I is larger than that in structure II. The maximum tensile strain of the asphalt layer is located at the bottom of the AC-25C layer in structure I and at the bottom of the AC-25F layer in structure II. The latter is significantly larger than the former, indicating the possibility of fatigue cracking induced by traffic load is higher in structure II. The measured tensile horizontal strain at the bottom of the semirigid layer is relatively low (<30εμ) in both structure I and structure II. In theoretical model, static modulus, dynamic modulus, and interface bonding ability are considered and theoretical responses are calculated. There are significant differences between the theoretical results and field test data. In the theoretic model, the material properties of layers and bonding status of adjacent layers all influence the results. In order to reduce the difference between the calculated and measured results, numerous material tests and field tests should be carried out.


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## Body

## 1. Introduction

Road paving materials and their mechanical properties are complicated. Ideal theory analysis cannot accurately reflect the true pavement response. So, theoretical calculation results should be revised to agree with pavement response data. In 1989, Mendez et al. proposed embedding fiber grating sensors (FBGs) in reinforced concrete to measure the status of the internal structure [1]. Then, in 1992, Prohaska et al. put FBG in reinforced concrete to measure strain [2]. FBG can also be used to measure asphalt pavement temperature [3]. A regression formula for pavement temperature was formed by combing field data and numerical analysis [4, 5]. Pavement temperature and response were measured, and a simulation model was created based on the field data [6, 7]. With the development of testing technology, pavement three-dimensional response could be tested and analyzed considering load magnitude and loading speed [8]. Vertical strains of the No. 40 Interstate Road in New Mexico, United States were tested, and test data and simulation data were compared [9–11]. In addition, GPR and core sampling were combined to determine the thickness of pavement layers, and the modulus of each layer was back-calculated using Falling Weight Deflectometer (FWD) data [12, 13].In recent years, the mechanics-empirical method has been widely accepted for its connection between field measurements, theoretical calculation results, and pavement distresses. In the theoretical method, road material mechanical parameters must be tested and input into the theoretical model. Mechanical parameters have an important effect on the accuracy of the results [14–16].Real pavement responses can be obtained directly in the field, but a significant amount of manpower and cost is required. On the other hand, theoretical calculations can be carried out easily by computers but are less accurate due to assumptions in the theoretical model. In this study, two types of asphalt pavement with thick asphalt layers are proposed and constructed. Real stress and strain responses in the pavement layers are tested, and the difference between the real responses and theoretical simulation results is analyzed.


## 2. Field Test of Pavement with a Thick Asphalt Layer under Traffic Load

### 2.1. Test Road

In many countries, the major materials used in flexible pavement include hot-mix asphalt (HMA), asphalt stabilized base, cement-treated base (CTB), other chemically treated materials (e.g., lime-fly ash, soil cement, lime-stabilized soils, etc.), and unbound aggregate base/subbase. In China, cement-stabilized material is widely used as the base and subbase layers. However, fatigue and reflective fracturing are inevitable if the chemically treated materials are used directly below asphalt layers. Unbound aggregate can restrain the reflective cracking progress, and thicker asphalt layers can also delay crack propagation within the asphalt layers.Based on the above considerations, the pavement structures illustrated in Figures1 and 2 are proposed as the test load structures. HMA layers with a total thickness of 30 cm are used. In structure I, cement-treated material is used as the base layer, and unbound granular aggregate is used as the subbase layer. Unlike structure I, an unbound aggregate layer is placed between the asphalt and cement-treated layers in structure II. The total thickness of pavement layers is 80 cm. In AC-25C and AC-25F, the symbols C and F denote either a coarse gradation or fine gradation, respectively.Figure 1
Test road pavement structure I.Figure 2
Test road pavement structure II.


### 2.2. Installation of FBG

FBGs have been used to measure pavement structure response in recent years [3]. FBGs are a kind of optical fiber passive component, which have higher accountability, higher accuracy, and less electromagnetic interference compared to other sensors. During construction of the test road, FBGs are placed within pavement layers (Figure 3). FBG installation should adhere to the following rules:(1)
According to the transverse distribution of vehicles, sensors should be placed underneath the wander of the traffic load to ensure the maximum pavement response is recorded.(2)
Two or more sensors are required at the same position to verify the data. If the data from the two sensors are significantly different, further analysis must be conducted.(3)
The distance between structure I and structure II should be as small as possible to link the transmission wire to a common point (Figure3).Figure 3
FBG layout.All sensors and transmission wires must be protected during pavement construction. Grooves should be cut in the pavement first; then the FBG and wires are placed in the groove and covered with road material to ensure that the sensors and wires are protected (Figures4 and 5). All sensors must be examined as soon as possible after construction to verify that the sensor is operable.Figure 4
The instrument and landfill.Figure 5
Protecting the FBG.Three different types of sensors are used: compressive stress sensors, strain sensors, and temperature sensors (Table1). Sensors are linked to a demodulator by fiber wires, and the wavelength variation of all sensors is recorded using the demodulator. Because the asphalt layer response is closely related to temperature, temperature sensors should be placed at the same position as the other sensors. Considering that sensors are easily destroyed by rollers during construction, test sensors are primarily placed in the AC-25C and underlying layers.Table 1
FBG layout.
Test channel
Sensor number
Initial wavelength (nm)
Sensor type
Position
Structure type
Channel one
1-YB-1/1-YB-2
1561.28/1562.65
Strain
Bottom of AC-25F
Structure I
Channel two
2-YB-1/2-YB-2
1557.507/1558.91
Strain
Bottom of AC-25C
2-T-1
1529.092
Temperature
Bottom of SMA
Channel three
3-CS-1/3-CS-2
1550.05/1548.63
Pressure
Top of CTB layer
3-CS-3/3-CS-4
1562.994/1564.31
Pressure
Top of granular base
3-CS-5/1-CS-6
1557.768/1555.923
Pressure
Bottom of AC-25C
Channel four
4-YB-1/4-YB-2
1539.382/1538.102
Strain
Bottom of CTB
Channel five
5-T-1
1552.834
Temperature
Bottom of AC-25F
5-YB-1/5-YB-2
1557.569/1554.43
Strain
Bottom of AC-25F
5-T-2
1544.588
Temperature
Bottom of AC-20C of AC25-C
Channel six
6-YB-1/6-YB-2
1541.914/1542.723
Strain
Bottom of CTB
Structure II
6-YB-3/6-YB-4
1545.33/1547.62
Strain
Bottom of AC-25F
6-YB-5/6-YB-6
1550.016/1548.012
Strain
Bottom of AC-25F
Channel seven
7-CS-1/7-CS-2
1545.966/1544.827
Pressure
Bottom of AC-25C
7-YB-1/7-YB-1
1557.584/1556.791
Strain
Bottom of AC-25C
7-T-1
1553.012
Temperature
Bottom of SMA
7-T-2
1544.609
Temperature
Bottom of AC-25F
Channel eight
8-T-1
1544.693
Temperature
Bottom of AC-20C
8-CS-1/8-CS-2
1537.951/1539.832
Pressure
Top of granular base


## 2.1. Test Road

In many countries, the major materials used in flexible pavement include hot-mix asphalt (HMA), asphalt stabilized base, cement-treated base (CTB), other chemically treated materials (e.g., lime-fly ash, soil cement, lime-stabilized soils, etc.), and unbound aggregate base/subbase. In China, cement-stabilized material is widely used as the base and subbase layers. However, fatigue and reflective fracturing are inevitable if the chemically treated materials are used directly below asphalt layers. Unbound aggregate can restrain the reflective cracking progress, and thicker asphalt layers can also delay crack propagation within the asphalt layers.Based on the above considerations, the pavement structures illustrated in Figures1 and 2 are proposed as the test load structures. HMA layers with a total thickness of 30 cm are used. In structure I, cement-treated material is used as the base layer, and unbound granular aggregate is used as the subbase layer. Unlike structure I, an unbound aggregate layer is placed between the asphalt and cement-treated layers in structure II. The total thickness of pavement layers is 80 cm. In AC-25C and AC-25F, the symbols C and F denote either a coarse gradation or fine gradation, respectively.Figure 1
Test road pavement structure I.Figure 2
Test road pavement structure II.


## 2.2. Installation of FBG

FBGs have been used to measure pavement structure response in recent years [3]. FBGs are a kind of optical fiber passive component, which have higher accountability, higher accuracy, and less electromagnetic interference compared to other sensors. During construction of the test road, FBGs are placed within pavement layers (Figure 3). FBG installation should adhere to the following rules:(1)
According to the transverse distribution of vehicles, sensors should be placed underneath the wander of the traffic load to ensure the maximum pavement response is recorded.(2)
Two or more sensors are required at the same position to verify the data. If the data from the two sensors are significantly different, further analysis must be conducted.(3)
The distance between structure I and structure II should be as small as possible to link the transmission wire to a common point (Figure3).Figure 3
FBG layout.All sensors and transmission wires must be protected during pavement construction. Grooves should be cut in the pavement first; then the FBG and wires are placed in the groove and covered with road material to ensure that the sensors and wires are protected (Figures4 and 5). All sensors must be examined as soon as possible after construction to verify that the sensor is operable.Figure 4
The instrument and landfill.Figure 5
Protecting the FBG.Three different types of sensors are used: compressive stress sensors, strain sensors, and temperature sensors (Table1). Sensors are linked to a demodulator by fiber wires, and the wavelength variation of all sensors is recorded using the demodulator. Because the asphalt layer response is closely related to temperature, temperature sensors should be placed at the same position as the other sensors. Considering that sensors are easily destroyed by rollers during construction, test sensors are primarily placed in the AC-25C and underlying layers.Table 1
FBG layout.
Test channel
Sensor number
Initial wavelength (nm)
Sensor type
Position
Structure type
Channel one
1-YB-1/1-YB-2
1561.28/1562.65
Strain
Bottom of AC-25F
Structure I
Channel two
2-YB-1/2-YB-2
1557.507/1558.91
Strain
Bottom of AC-25C
2-T-1
1529.092
Temperature
Bottom of SMA
Channel three
3-CS-1/3-CS-2
1550.05/1548.63
Pressure
Top of CTB layer
3-CS-3/3-CS-4
1562.994/1564.31
Pressure
Top of granular base
3-CS-5/1-CS-6
1557.768/1555.923
Pressure
Bottom of AC-25C
Channel four
4-YB-1/4-YB-2
1539.382/1538.102
Strain
Bottom of CTB
Channel five
5-T-1
1552.834
Temperature
Bottom of AC-25F
5-YB-1/5-YB-2
1557.569/1554.43
Strain
Bottom of AC-25F
5-T-2
1544.588
Temperature
Bottom of AC-20C of AC25-C
Channel six
6-YB-1/6-YB-2
1541.914/1542.723
Strain
Bottom of CTB
Structure II
6-YB-3/6-YB-4
1545.33/1547.62
Strain
Bottom of AC-25F
6-YB-5/6-YB-6
1550.016/1548.012
Strain
Bottom of AC-25F
Channel seven
7-CS-1/7-CS-2
1545.966/1544.827
Pressure
Bottom of AC-25C
7-YB-1/7-YB-1
1557.584/1556.791
Strain
Bottom of AC-25C
7-T-1
1553.012
Temperature
Bottom of SMA
7-T-2
1544.609
Temperature
Bottom of AC-25F
Channel eight
8-T-1
1544.693
Temperature
Bottom of AC-20C
8-CS-1/8-CS-2
1537.951/1539.832
Pressure
Top of granular base


## 3. Field Data Processing

A heavily loaded truck was used as a test vehicle. The weight of the front and rear axles was 7.46 tons and 23.7 tons, respectively. Before the field test begins, a mark should be made on the road surface over the FBGs to ensure that the test vehicle passes directly over the FBGs. The test truck had a uniform speed of 60 km/h. A demodulator with a frequency of 100 Hz was used to collect wavelength data every 0.01 s. Pavement response can be calculated using the FBG wavelength variation using formulas (1) through (3):(1)P=K1λ1−λ0,(2)ε=K2λ1−λ0,(3)T=K3λ1−λ0,where P is the vertical compressive stress, ε is the horizontal strain, K1 is the stress coefficient (kPa/nm), K2 is the strain coefficient (με/nm), K3 is the temperature coefficient (°C/nm), λ1 is the current wavelength of FBG (nm), and λ0 is the initial wavelength of FBG (nm)


### 3.1. Vertical Compressive Stress

The vertical compressive stress vs. time for structures I and II are plotted in Figures6 and 7, respectively. When the test vehicle passes over the test sensors, the vertical stress response is calculated and recorded. The compressive stress response in the two structures is similar. Two wave peaks resulting from the front and rear axles, respectively, are visible. The response induced by the rear axle is significantly larger than the front axle response because the load magnitude of the rear axle is significantly larger than the front axle.Figure 6
Vertical compressive stress at the top of AC-25F. (a) Structure I. (b) Structure II.
(a)
(b)Figure 7
Vertical compressive stress at the top of the granular layer. (a) Structure I. (b) Structure II.
(a)
(b)The compressive vertical stress in structure I is larger than that in structure II at the same position. For instance, the peak vertical compressive stress at the top of the AC-25F layer is 338.0 kPa in structure I; however, the peak vertical compressive stress is 206.3 kPa in structure II. The former is 1.64 times larger than the latter.In Figure7, the compressive stress response at the granular layer top is plotted. The peak of vertical stress in structure I is 43.0 kPa, which is much less than structure II (169.0 kPa). The difference comes from the granular layer depth. The distance from the granular layer top to pavement surface is 64 cm in structure I; however, this distance is 30 cm in structure II. Therefore, it can be concluded that the semirigid layer transfers and spreads the traffic load well and reduces the possibility of deformation in the granular layer.


### 3.2. Horizontal Strain

Horizontal strain in the pavement layers is plotted in Figures8–10, from which several conclusions can be drawn:(1)
The horizontal strain response in structures I and II are similar when the traffic load passes over the test sensors. Horizontal strains are compressive at the bottom of the AC-25C and AC-25F layers when the test vehicle is not directly over an FBG; however, when the test vehicle is directly over an FBG, the horizontal strain is extensional.(2)
The tensile strain in structure II is significantly larger than that in structure I. For example, the maximum tensile strain at the bottom of the AC-25C layer in structure I is118εμ and 160εμ in structure II. The maximum tensile strain beneath the AC-25F layer in structure I is 60εμ and 283εμ in structure II. As a result, fatigue cracking may be more likely in structure II.(3)
The position of the maximum strain is different in structure I and structure II. The point of maximum tensile strain is at the bottom of the AC-25C layer in structure I but is located at the bottom of the AC-25F layer in structure II.(4)
In structure I and structure II, tensile strain exists beneath the cement stabilized layer; however, the tensile strain magnitude at the bottom of cement stabilized layer is small. Thus, fatigue cracking is less likely in CTB with a thick asphalt layer and thick CTB base layer.Figure 8
Horizontal strain at the bottom of AC-25C.
(a)
(b)Figure 9
Horizontal strain at the bottom of AC-25F.
(a)
(b)Figure 10
Horizontal strain at the bottom of the cement-stabilized base.
(a)
(b)


### 3.3. Temperature in Asphalt Layers

Field tests were conducted from 10 am to 12 am on a sunny day without wind and an atmospheric temperature of 29.2°C. Temperature in the asphalt layers during the test period is plotted in Figure11. Temperature fluctuation exists at the test point, but fluctuations are not greater than 1°C. The average temperature during the test is regarded as the representative temperature at the moment of testing. The temperature at the bottom of the SMA (h = 4 cm), AC-20 (h = 10 cm), AC-25C (h = 20 cm), and AC-25F (h = 30 cm) layers was 39.3°C, 34.6°C, 25.5°C, and 24.7°C, respectively.Figure 11
Measured temperatures in asphalt layers. (a)h = 4 cm, (b) h = 10 cm, (c) h = 20 cm, and (d) h = 30 cm.
(a)
(b)
(c)
(d)


## 3.1. Vertical Compressive Stress

The vertical compressive stress vs. time for structures I and II are plotted in Figures6 and 7, respectively. When the test vehicle passes over the test sensors, the vertical stress response is calculated and recorded. The compressive stress response in the two structures is similar. Two wave peaks resulting from the front and rear axles, respectively, are visible. The response induced by the rear axle is significantly larger than the front axle response because the load magnitude of the rear axle is significantly larger than the front axle.Figure 6
Vertical compressive stress at the top of AC-25F. (a) Structure I. (b) Structure II.
(a)
(b)Figure 7
Vertical compressive stress at the top of the granular layer. (a) Structure I. (b) Structure II.
(a)
(b)The compressive vertical stress in structure I is larger than that in structure II at the same position. For instance, the peak vertical compressive stress at the top of the AC-25F layer is 338.0 kPa in structure I; however, the peak vertical compressive stress is 206.3 kPa in structure II. The former is 1.64 times larger than the latter.In Figure7, the compressive stress response at the granular layer top is plotted. The peak of vertical stress in structure I is 43.0 kPa, which is much less than structure II (169.0 kPa). The difference comes from the granular layer depth. The distance from the granular layer top to pavement surface is 64 cm in structure I; however, this distance is 30 cm in structure II. Therefore, it can be concluded that the semirigid layer transfers and spreads the traffic load well and reduces the possibility of deformation in the granular layer.


## 3.2. Horizontal Strain

Horizontal strain in the pavement layers is plotted in Figures8–10, from which several conclusions can be drawn:(1)
The horizontal strain response in structures I and II are similar when the traffic load passes over the test sensors. Horizontal strains are compressive at the bottom of the AC-25C and AC-25F layers when the test vehicle is not directly over an FBG; however, when the test vehicle is directly over an FBG, the horizontal strain is extensional.(2)
The tensile strain in structure II is significantly larger than that in structure I. For example, the maximum tensile strain at the bottom of the AC-25C layer in structure I is118εμ and 160εμ in structure II. The maximum tensile strain beneath the AC-25F layer in structure I is 60εμ and 283εμ in structure II. As a result, fatigue cracking may be more likely in structure II.(3)
The position of the maximum strain is different in structure I and structure II. The point of maximum tensile strain is at the bottom of the AC-25C layer in structure I but is located at the bottom of the AC-25F layer in structure II.(4)
In structure I and structure II, tensile strain exists beneath the cement stabilized layer; however, the tensile strain magnitude at the bottom of cement stabilized layer is small. Thus, fatigue cracking is less likely in CTB with a thick asphalt layer and thick CTB base layer.Figure 8
Horizontal strain at the bottom of AC-25C.
(a)
(b)Figure 9
Horizontal strain at the bottom of AC-25F.
(a)
(b)Figure 10
Horizontal strain at the bottom of the cement-stabilized base.
(a)
(b)


## 3.3. Temperature in Asphalt Layers

Field tests were conducted from 10 am to 12 am on a sunny day without wind and an atmospheric temperature of 29.2°C. Temperature in the asphalt layers during the test period is plotted in Figure11. Temperature fluctuation exists at the test point, but fluctuations are not greater than 1°C. The average temperature during the test is regarded as the representative temperature at the moment of testing. The temperature at the bottom of the SMA (h = 4 cm), AC-20 (h = 10 cm), AC-25C (h = 20 cm), and AC-25F (h = 30 cm) layers was 39.3°C, 34.6°C, 25.5°C, and 24.7°C, respectively.Figure 11
Measured temperatures in asphalt layers. (a)h = 4 cm, (b) h = 10 cm, (c) h = 20 cm, and (d) h = 30 cm.
(a)
(b)
(c)
(d)


## 4. Comparison of Theoretical Results and Field Data

Although field tests can help to obtain the real inner responses of pavement structures, field tests have some limitations. For instance, the subgrade condition, pavement structure, and testing method can all have an effect on test data, which results in difficulty directly applying test results to pavement design. Field tests are also expensive and time consuming. By comparison, theoretical analysis is cheaper and faster. The following paragraphs focus on comparing theoretical results and field test results in order to improve the accuracy of the theoretic results.In the theoretic model, road pavement is assumed to be composed of multiple elastic layers characterized by an elastic modulus and Poisson's ratio. In this section, the effects of material properties including static modulus, dynamic modulus, and interface contact conditions between layers are analyzed.


### 4.1. Test Truck Load Parameters

The contact parameters between the test truck’s tire and road surface are calculated listed in Table2 and are used as inputs for the theoretic model [17].Table 2
Parameter of test vehicle.
Rear axle load of test vehicleP (kN)
237
Weight of single wheel (kN)
59.25
Contact pressure of tire (MPa)
0.948
Contact area (cm2)
626
Equivalent diameter of single wheeld (cm)
28.2
Center-to-center distance of two wheels (cm)
1.5d


### 4.2. Influence of Static Modulus

Static modulus is widely used in theoretic modeling. Asphalt layer modulus is determined using the real temperature of the test road in Figure11. Because the temperature in the AC-25F and AC-25C layers is similar, the static modulus of the two layers is set to same value. In order to analyze the influence of asphalt modulus on the theoretic model, the modulus of the AC-25C and AC-25F layers is varied while the modulus of other layers is held constant. Three modulus combinations are listed in Table 3.Table 3
Static modulus.
Pavement layers
Modulus (MPa) combination I
Modulus (MPa) combination II
Modulus (MPa) combination III
Poisson’s ratio
SMA-13
450
450
450
0.25
AC-20
700
700
700
0.25
AC-25C, AC-25F
800
1000
1200
0.25
CTB
1400
1400
1400
0.20
Granular
400
400
400
0.25
Subgrade
40
40
40
0.3Variations in asphalt layer modulus have a small effect on the theoretical vertical compressive stress (Figure12). The theoretical compressive vertical stresses in structures I and II are both significantly larger than the corresponding field measurements. For example, compressive vertical stresses at the bottom of the AC-25C and AC-25F layers in structure I are 62.3% and 58.7% larger than the respective measured values. The compressive vertical stresses at the bottom of the AC-25C and AC-25F layers in structure II are 45.8% and 70.1% larger than the respective measured values. The differences between the theoretic and real responses have nothing to do with the asphalt layer static modulus.Figure 12
Comparison of theoretical vertical stress and measured vertical stress. (a) Structure I. (b) Structure II.
(a)
(b)The theoretical tensile strains at the bottom of the AC-25C and AC-25F layers are significantly smaller than the measured values (Figure13). The theoretic horizontal strain at the bottom of the cement treated layer is significantly larger than the corresponding field measurement. With increasing asphalt layer modulus, theoretic tensile strain at the bottom of the AC-25C layer in structure I decreases, but the tensile strain in the AC-25F layer increases slightly. In structure II, tensile strain in the AC-25C layer decreases with increasing asphalt layer modulus, similar to structure I, and the tensile strain at the bottom of the AC-25F layer shows little change. It should be noted that the tensile horizontal strain in asphalt layers may be underestimated, and the tensile strain at the bottom of the CTB layer may be significantly overestimated when the theoretic method is used. Thus, the theoretical results should be revised before applying them to pavement design.Figure 13
Comparison of theoretical horizontal tensile strain and measured tensile strain. (a) Structure I. (b) Structure II.
(a)
(b)


### 4.3. Influence of Semirigid Layer Modulus

In order to analyze the influence of semirigid layer modulus on pavement response, the modulus of all asphalt layers in the theoretical model were fixed, and only the semirigid layer modulus was varied. The modulus of the AC-25C and AC-25F layers were fixed at 1000 MPa, and the modulus of CTB layer was varied from 1000 MPa to 1800 MPa. The parameters of the other layers are listed in Table3.Variation in the CTB base or subbase modulus has little effect on the compressive vertical stress of pavement layers (Table4). However, varying the semirigid layer modulus can influence the tensile strain of asphalt layers (Table 5). With increasing CTB modulus, tensile strains at the bottom of the AC-25C and AC-25F layers decrease, especially in the AC-25F layer. Increasing the CTB layer modulus is conducive to reducing the possibility of fatigue cracking beneath asphalt layers under traffic load. However, it must be noted that the discrepancy between theoretic results and field measurements will grow with increasing CTB modulus in the theoretic model.Table 4
Compressive vertical stress.
Position
Compressive vertical stress (kPa)
Modulus (MPa) combination I
Modulus (MPa) combination II
Modulus (MPa) combination III
Field measured (MPa)
Structure I
AC-25C
524.5
539.7
549.8
338.0
AC-25F
325.1
344.5
357.8
199.6
CTB
42.3
38.7
35.9
39.6
Structure II
AC-25C
446.2
450.0
451.9
206.6
AC-25F
237.0
243.3
247.6
165.4Table 5
Tensile horizontal strain.
Position
Tensile horizontal strain (με)
Modulus (MPa) combination I
Modulus (MPa) combination II
Modulus (MPa) combination III
Measured values
Structure I
AC-25C bottom
56.0
49.8
47.6
115.9
AC-25F
62.1
24.9
3.8
56.8
CTB
145.7
133.6
123.5
10.9
Structure II
AC-25C bottom
73.1
72.9
72.5
156.3
AC-25F
157.5
149.0
144.3
280.6
CTB
167.9
142.5
125.7
24.4


### 4.4. Influence of Asphalt Layer Dynamic Modulus

The dynamic modulus of asphalt mixtures can be tested using laboratory methods, and results were related to loading rate and temperature [18, 19]. In this study, the dynamic modulus of asphalt layers is determined based on past studies. The dynamic modulus of asphalt mixtures under a loading frequency of 10 Hz is listed in Table 6. The theoretical results are listed in Table 7.Table 6
Asphalt dynamic modulus.
Real temperature (°C)
Dynamic modulus (MPa)
Poisson’s ratio
SMA-13
39.4
1900
0.25
AC-20
34.5
5500
0.25
AC-25C
25.5
10000
0.25
AC-25F
24.6
10500
0.25Table 7
Theoretical results.
Structure type
Position
Compressive vertical stress (kPa)
Tensile horizontal strain (με)
Theoretical
Field test
Theoretical
Field test
Structure I
AC-25C
437.7
338.0
8.0
115.9
AC-25F
190.3
199.6
54.1
56.8
CTB
23.2
39.6
83.5
10.9
Structure II
AC-25C
380.5
206.6
10.1
156.3
AC-25F
150.5
165.4
66.0
280.6
CTB
85.7
24.4Theoretical results show that if dynamic modulus is used, the compressive vertical stresses in the asphalt layers are clearly less when using the static modulus. The difference between theoretical compressive stress and measured data decreases when the dynamic modulus is adopted in the theoretical model.The maximum tensile horizontal strain positions appear at the bottom of the AC-25F layer in both structure I and structure II when the dynamic modulus is used in the theoretical model. The maximum tensile strain of asphalt layers in structure II decreased significantly compared with the calculated results using the static modulus model. Thus, the dynamic modulus has a greater effect on the theoretical strain response of structure II.On the whole, using the dynamic modulus leads to a decreased theoretical compressive stress and tensile strain in asphalt layers. As a result, the difference between theoretical vertical compressive stress and field measurements is reduced and the difference in tensile strains is increased.


### 4.5. Interface between the Asphalt Layer and Base Layer

When pavement structures are constructed, the interface between layers may be not fully bonded because the adjacent materials are not same. Bonding conditions are considered in the theoretical model to analyze the effect of interface characteristics on pavement response. Only the bonding status between the lowest asphalt layer and base layer is considered, including a fully bonded boundary and a sliding boundary (Figures14 and 15).Figure 14
Effect of bonding condition on compressive vertical stress. (a) Structure I. (b) Structure II.
(a)
(b)Figure 15
Effect of bonding condition on tensile horizontal strain. (a) Structure I. (b) Structure II.
(a)
(b)The bonding conditions between the asphalt and base layers have the same effect on the compressive vertical stress in structure I and structure II. The sliding boundary led to an increased compressive vertical stress in the AC-25F layer and decreased compressive vertical stress in the AC-25C layer. Overall, the change in compressive vertical stress magnitude is not significant. In contrast, the effects of interface condition on tensile horizontal strain are significant. For a sliding boundary, the theoretical tensile horizontal strains of the AC-25C and AC-25F layers in structure 1 are 3.9 times and 16.5 times larger, respectively, compared to a fully bonded layer. In structure 2, the increase ratio of tensile horizontal strain is 1.9 times and 2.1 times, respectively.The theoretical horizontal strain in asphalt layers is larger than field measurements for a sliding boundary. However, if the boundary is fully bonded, the theoretical results will be less than field measurements. Thus, the interface type has an important effect on the theoretical results. It is necessary to reasonably evaluate the actual interface type in order to decrease the difference between theoretical and real responses.


## 4.1. Test Truck Load Parameters

The contact parameters between the test truck’s tire and road surface are calculated listed in Table2 and are used as inputs for the theoretic model [17].Table 2
Parameter of test vehicle.
Rear axle load of test vehicleP (kN)
237
Weight of single wheel (kN)
59.25
Contact pressure of tire (MPa)
0.948
Contact area (cm2)
626
Equivalent diameter of single wheeld (cm)
28.2
Center-to-center distance of two wheels (cm)
1.5d


## 4.2. Influence of Static Modulus

Static modulus is widely used in theoretic modeling. Asphalt layer modulus is determined using the real temperature of the test road in Figure11. Because the temperature in the AC-25F and AC-25C layers is similar, the static modulus of the two layers is set to same value. In order to analyze the influence of asphalt modulus on the theoretic model, the modulus of the AC-25C and AC-25F layers is varied while the modulus of other layers is held constant. Three modulus combinations are listed in Table 3.Table 3
Static modulus.
Pavement layers
Modulus (MPa) combination I
Modulus (MPa) combination II
Modulus (MPa) combination III
Poisson’s ratio
SMA-13
450
450
450
0.25
AC-20
700
700
700
0.25
AC-25C, AC-25F
800
1000
1200
0.25
CTB
1400
1400
1400
0.20
Granular
400
400
400
0.25
Subgrade
40
40
40
0.3Variations in asphalt layer modulus have a small effect on the theoretical vertical compressive stress (Figure12). The theoretical compressive vertical stresses in structures I and II are both significantly larger than the corresponding field measurements. For example, compressive vertical stresses at the bottom of the AC-25C and AC-25F layers in structure I are 62.3% and 58.7% larger than the respective measured values. The compressive vertical stresses at the bottom of the AC-25C and AC-25F layers in structure II are 45.8% and 70.1% larger than the respective measured values. The differences between the theoretic and real responses have nothing to do with the asphalt layer static modulus.Figure 12
Comparison of theoretical vertical stress and measured vertical stress. (a) Structure I. (b) Structure II.
(a)
(b)The theoretical tensile strains at the bottom of the AC-25C and AC-25F layers are significantly smaller than the measured values (Figure13). The theoretic horizontal strain at the bottom of the cement treated layer is significantly larger than the corresponding field measurement. With increasing asphalt layer modulus, theoretic tensile strain at the bottom of the AC-25C layer in structure I decreases, but the tensile strain in the AC-25F layer increases slightly. In structure II, tensile strain in the AC-25C layer decreases with increasing asphalt layer modulus, similar to structure I, and the tensile strain at the bottom of the AC-25F layer shows little change. It should be noted that the tensile horizontal strain in asphalt layers may be underestimated, and the tensile strain at the bottom of the CTB layer may be significantly overestimated when the theoretic method is used. Thus, the theoretical results should be revised before applying them to pavement design.Figure 13
Comparison of theoretical horizontal tensile strain and measured tensile strain. (a) Structure I. (b) Structure II.
(a)
(b)


## 4.3. Influence of Semirigid Layer Modulus

In order to analyze the influence of semirigid layer modulus on pavement response, the modulus of all asphalt layers in the theoretical model were fixed, and only the semirigid layer modulus was varied. The modulus of the AC-25C and AC-25F layers were fixed at 1000 MPa, and the modulus of CTB layer was varied from 1000 MPa to 1800 MPa. The parameters of the other layers are listed in Table3.Variation in the CTB base or subbase modulus has little effect on the compressive vertical stress of pavement layers (Table4). However, varying the semirigid layer modulus can influence the tensile strain of asphalt layers (Table 5). With increasing CTB modulus, tensile strains at the bottom of the AC-25C and AC-25F layers decrease, especially in the AC-25F layer. Increasing the CTB layer modulus is conducive to reducing the possibility of fatigue cracking beneath asphalt layers under traffic load. However, it must be noted that the discrepancy between theoretic results and field measurements will grow with increasing CTB modulus in the theoretic model.Table 4
Compressive vertical stress.
Position
Compressive vertical stress (kPa)
Modulus (MPa) combination I
Modulus (MPa) combination II
Modulus (MPa) combination III
Field measured (MPa)
Structure I
AC-25C
524.5
539.7
549.8
338.0
AC-25F
325.1
344.5
357.8
199.6
CTB
42.3
38.7
35.9
39.6
Structure II
AC-25C
446.2
450.0
451.9
206.6
AC-25F
237.0
243.3
247.6
165.4Table 5
Tensile horizontal strain.
Position
Tensile horizontal strain (με)
Modulus (MPa) combination I
Modulus (MPa) combination II
Modulus (MPa) combination III
Measured values
Structure I
AC-25C bottom
56.0
49.8
47.6
115.9
AC-25F
62.1
24.9
3.8
56.8
CTB
145.7
133.6
123.5
10.9
Structure II
AC-25C bottom
73.1
72.9
72.5
156.3
AC-25F
157.5
149.0
144.3
280.6
CTB
167.9
142.5
125.7
24.4


## 4.4. Influence of Asphalt Layer Dynamic Modulus

The dynamic modulus of asphalt mixtures can be tested using laboratory methods, and results were related to loading rate and temperature [18, 19]. In this study, the dynamic modulus of asphalt layers is determined based on past studies. The dynamic modulus of asphalt mixtures under a loading frequency of 10 Hz is listed in Table 6. The theoretical results are listed in Table 7.Table 6
Asphalt dynamic modulus.
Real temperature (°C)
Dynamic modulus (MPa)
Poisson’s ratio
SMA-13
39.4
1900
0.25
AC-20
34.5
5500
0.25
AC-25C
25.5
10000
0.25
AC-25F
24.6
10500
0.25Table 7
Theoretical results.
Structure type
Position
Compressive vertical stress (kPa)
Tensile horizontal strain (με)
Theoretical
Field test
Theoretical
Field test
Structure I
AC-25C
437.7
338.0
8.0
115.9
AC-25F
190.3
199.6
54.1
56.8
CTB
23.2
39.6
83.5
10.9
Structure II
AC-25C
380.5
206.6
10.1
156.3
AC-25F
150.5
165.4
66.0
280.6
CTB
85.7
24.4Theoretical results show that if dynamic modulus is used, the compressive vertical stresses in the asphalt layers are clearly less when using the static modulus. The difference between theoretical compressive stress and measured data decreases when the dynamic modulus is adopted in the theoretical model.The maximum tensile horizontal strain positions appear at the bottom of the AC-25F layer in both structure I and structure II when the dynamic modulus is used in the theoretical model. The maximum tensile strain of asphalt layers in structure II decreased significantly compared with the calculated results using the static modulus model. Thus, the dynamic modulus has a greater effect on the theoretical strain response of structure II.On the whole, using the dynamic modulus leads to a decreased theoretical compressive stress and tensile strain in asphalt layers. As a result, the difference between theoretical vertical compressive stress and field measurements is reduced and the difference in tensile strains is increased.


## 4.5. Interface between the Asphalt Layer and Base Layer

When pavement structures are constructed, the interface between layers may be not fully bonded because the adjacent materials are not same. Bonding conditions are considered in the theoretical model to analyze the effect of interface characteristics on pavement response. Only the bonding status between the lowest asphalt layer and base layer is considered, including a fully bonded boundary and a sliding boundary (Figures14 and 15).Figure 14
Effect of bonding condition on compressive vertical stress. (a) Structure I. (b) Structure II.
(a)
(b)Figure 15
Effect of bonding condition on tensile horizontal strain. (a) Structure I. (b) Structure II.
(a)
(b)The bonding conditions between the asphalt and base layers have the same effect on the compressive vertical stress in structure I and structure II. The sliding boundary led to an increased compressive vertical stress in the AC-25F layer and decreased compressive vertical stress in the AC-25C layer. Overall, the change in compressive vertical stress magnitude is not significant. In contrast, the effects of interface condition on tensile horizontal strain are significant. For a sliding boundary, the theoretical tensile horizontal strains of the AC-25C and AC-25F layers in structure 1 are 3.9 times and 16.5 times larger, respectively, compared to a fully bonded layer. In structure 2, the increase ratio of tensile horizontal strain is 1.9 times and 2.1 times, respectively.The theoretical horizontal strain in asphalt layers is larger than field measurements for a sliding boundary. However, if the boundary is fully bonded, the theoretical results will be less than field measurements. Thus, the interface type has an important effect on the theoretical results. It is necessary to reasonably evaluate the actual interface type in order to decrease the difference between theoretical and real responses.


## 5. Conclusion

In this study, two kinds of pavements with thick asphalt layers are designed and used to construct test road samples. The responses of pavement layers under traffic loading are measured. The differences between the theoretical results and field measurements are analyzed, and several conclusions are drawn as follows:(1)
According to field data, the compressive vertical stress in the asphalt layers of structure I is larger than in structure II at the same depth, indicating that the asphalt material in structure I undergoes more severe compression under traffic load.(2)
The position of the maximum horizontal tensile strain in structure I is located at the bottom of the AC-25C layer. The same point is located at the bottom of the AC-25F layer in structure II, and the magnitude of maximum horizontal tensile strain is 2.42 times larger in structure II than in structure I based on field data, indicating fatigue cracking is more likely to occur in structure II with a granular base layer.(3)
The measured tensile strains of a semirigid base layer are relatively low (less than30με), indicating that fatigue cracking induced by traffic load may not initiate at the bottom of the CTB covered with a thick asphalt layer.(4)
Pavement responses calculated using the theoretical model are distinctly different from field measurements. Theoretical compressive vertical stresses are significantly larger than field measurements, and the theoretical tensile strain in asphalt layers is significantly less than field measurements if the interface condition is good. Thus, the predicted service life of pavement will deviate from the actual service life if the theoretical response is directly used to design the pavement.(5)
Material properties and interface bonding condition have significant effects on theoretical pavement response. It is difficult to reduce the difference between theoretical results and field measurements only by varying the material modulus of certain layers or one interface bonding condition. Numerous material tests and field tests must be conducted in order to establish a reasonable relationship between theoretical results and field measurements.



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*Source: 8097890-2019-09-03.xml*