*Article* **Initiation and Propagation of Top-Down Cracking in Asphalt Pavement**

#### **Lijun Sun 1,\*, Gang Wang <sup>2</sup> , Hongchao Zhang <sup>1</sup> and Liping Liu <sup>1</sup>**


Received: 5 April 2018; Accepted: 4 May 2018; Published: 12 May 2018

**Abstract:** Top-down cracking (TDC) alongside the wheel path is one of the commonly seen distress types on asphalt pavements, especially on heavy-duty asphalt pavements. It has been believed that TDC is caused by either tension stress or shear stress in the top asphalt layer(s). In this paper, new initiation and propagation mechanisms of TDC are proposed and validated through both accelerated pavement testing in the field and uniaxial repeated loading penetration tests in the laboratory at different temperatures. The test results clearly show that the uniaxial repeated loading penetration test can simulate both initiation and propagation processes of TDC very closely. Based on these test results, the mechanisms for crack initiation and propagation are further investigated with the finite element (FE) program. The FE analysis results show that under repeated loading, shear damage will occur first in the asphalt layer, then extend horizontally and consequently result in a shear-damaged layer. The damaged layer then led to higher tensile strain in the upper mixture which caused tension cracks and finally propagated upwards to the pavement surface. The whole process of TDC initiation and propagation can be described as "shear damage, then tension propagation", which is the new mechanism proposed in this paper.

**Keywords:** asphalt pavements; top-down cracking mechanism; shear damage; tension propagation

### **1. Introduction**

Cracking alongside the wheel path is one of the common distress types seen on asphalt pavements, especially on heavy-duty ones. Different from the traditional bottom-up fatigue cracking, this type of longitudinal cracking, observed within two to six years after opening to traffic [1–4], initiates at the top part of asphalt layer and then propagates downward, and is often called top-down cracking (TDC). There are two different views on TDC mechanisms. Some researchers believe that TDC is caused by the tensile stress/strain initiated at the surface of the pavement. For example, Molenaar [5] used Australian CIRCLY(a computer program for mechanistic pavement design and analysis) elastic analysis program to analyze the effects of the lateral and vertical contact stresses within the pavement and stresses of the tyre on the pavement within the asphalt layers, and concluded that the surface tensile stress at the tyre edge was the cause for top-down cracking. Similar findings were later published by Hugo [4] and Gerritsen [6], respectively. By using a finite element (FE) program CAPA (FE program developed at Delft University of Technology in the Netherlands), Groenendijk [7] analyzed the pavement structure under the measured non-uniform tyre–pavement contact load with the South African Vehicle-Road Pressure Transducer Array (VRSPTA). He found that higher tensile stress at the surface of the layer is

associated with non-uniform tyre–pavement contact pressure and aging of the asphalt mixture, which ultimately led to TDC. Mayer [8] suggested that longitudinal TDC cracks were caused by principal tension stress due to radial ply tyres. Kim and Roque et al. [9] later developed the models for TDC initiation and propagation based on the "tension cracking mechanism assumption".

The second view on TDC is that it is caused by shear stress/strain. By using the FE method to analyze the pavement stress/strain distributions under tyre loads, Bensalem [10] found that traffic-induced shear strain on the vertical plane at tyre edge was much larger than the lateral tensile strain at same position. Wang [11] computed the stress distributions using the discrete element method (DEM) and bimodal mechanics. The results indicated that the crack was initiated at a depth of 25 mm, and obvious plastic deformation was observed below the cracking zone. He believed that the crack was caused by the shear stress. Based on the calculated octahedral shear strain for three pavement structures, Pellinen et al. [12,13] found that the maximum shear strain location is at the inner side of tyre edge, which indicated that the top-down crack was more likely to occur in the summer time. In recent years, Kim and Roque have shifted their research focuses from the "tension cracking mechanism assumption" to the "shear cracking mechanism assumption" and proposed that TDC was shear-induced or shear-dominant cracking.

This paper, based on the latest findings from TDC-oriented accelerated pavement testing (APT) and laboratory uniaxial repeated penetration tests, develops and validates new TDC initiation and propagation mechanisms. Details are presented in the following sections.

### **2. Field and Laboratory TDC Tests**

In order to investigate the TDC mechanisms, both field accelerated pavement testing with MMLS3 (Model Mobile Load Simulator) and laboratory uniaxial repeated loading penetration tests were conducted. The MMLS3 is a mobile loading system developed in South Africa with a maximum load of 2.9 kN, maximum tyre pressure of 850 kPa, maximum loading rate of 7200 pass/h, and tyre that was 80 mm wide inflated to 700 kPa. Since traffic wander was not considered in the test, the wheel track area was 80 mm wide. The test pavement structures for the field APT are listed in Table 1.



For pavement structure 1, the APT loading was applied under four different temperature conditions: low (Figure 1a), normal (Figure 1b), and two high temperature conditions (Figure 1c). However, pavement structure 2 was tested under the high temperature condition (Figure 1d) only. The number of load repetitions for each test was 1 million. The temperatures at different pavement depth, deformation and cracks on pavement surface were measured during testing. The air temperatures at normal conditions are listed in Table 2.

wheel path.


**Table 2.** Air temperature when testing (normal temperature).

Note: The italic data mean the air temperature was taken at night. Note: The italic data mean the air temperature was taken at night.

**Figure 1.** Pavement temperature variations during testing. (**a**) Low temperature test for structure 1; (**b**) high temperature test for condition 1; (**c**) high temperature test for condition 2; (**d**) high temperature test for condition 3. **Figure 1.** Pavement temperature variations during testing. (**a**) Low temperature test for structure 1; (**b**) high temperature test for condition 1; (**c**) high temperature test for condition 2; (**d**) high temperature test for condition 3.

Pavement deformation from transverse profiles was automatically measured with a laser profilometer (MLS Profilometer Drive-P2003). The data obtained from the profilometer was accurate to within 0.01 mm. For pavement structure 1, the measured pavement deformation was 2.4 mm after one million load repetitions at normal temperature conditions (Table 2). Neither upheave nor visual crack were observed near the outside of the wheel path. Similar observations were made at the low temperature conditions: there was not any significant deformation nor any cracks after applying one million repetitions of MMLS3 loading. In the case of high temperature conditions (Figure 1b), significant deformation occurred alongside the wheel path, and clearly, longitudinal cracking was found within 2 cm outside of the wheel path. Figure 2 shows the measured rutting profiles at the high temperature conditions (Figure 1c) under different loading repetitions, varying from 0 to 1 million. In Figure 2, there is a "rutting zone" in either side of upheave which is circled in red. It was found that the deepest position in the either red circle is around 20 mm away from the tyre edge, Pavement deformation from transverse profiles was automatically measured with a laser profilometer (MLS Profilometer Drive-P2003). The data obtained from the profilometer was accurate to within 0.01 mm. For pavement structure 1, the measured pavement deformation was 2.4 mm after one million load repetitions at normal temperature conditions (Table 2). Neither upheave nor visual crack were observed near the outside of the wheel path. Similar observations were made at the low temperature conditions: there was not any significant deformation nor any cracks after applying one million repetitions of MMLS3 loading. In the case of high temperature conditions (Figure 1b), significant deformation occurred alongside the wheel path, and clearly, longitudinal cracking was found within 2 cm outside of the wheel path. Figure 2 shows the measured rutting profiles at the high temperature conditions (Figure 1c) under different loading repetitions, varying from 0 to 1 million. In Figure 2, there is a "rutting zone" in either side of upheave which is circled in red. It was found

longitudinal cracking occurs more often at higher temperature conditions.

where the longitudinal cracking is located. To further verify this observation, another test was

Similarly, APT testing was performed on pavement structure 2 at the temperature conditions shown in Figure 1d. Similar deformations (Figure 2) and obvious longitudinal cracking were observed within 20 mm of the wheel path. It can be concluded from the APT test results that that the deepest position in the either red circle is around 20 mm away from the tyre edge, where the longitudinal cracking is located. To further verify this observation, another test was conducted at high temperature conditions (Figure 1c) at 10 m away from the test site where longitudinal cracking was observed. Again, longitudinal cracks were found within 20 mm from the wheel path. *Appl. Sci.* **2018**, *8*, x FOR PEER REVIEW 4 of 14

**Figure 2.** Deformation on pavement surface of high temperature test for structure 2. **Figure 2.** Deformation on pavement surface of high temperature test for structure 2.

Figure 3 shows the observed longitudinal cracking located within 20 mm from the tyre edge

with a width of 3 mm. To identify whether or not the longitudinal cracking is TDC, cores were taken and cut in half. It was obvious that the longitudinal cracking observed outside the wheel path was TDC, and that TDC propagated downwards 9 mm from the pavement surface. This observation matches the FE analysis results, which indicates that the maximum shear stresses for pavement structures 1 and 2 at high temperature conditions are located at 10–12 mm below the pavement Similarly, APT testing was performed on pavement structure 2 at the temperature conditions shown in Figure 1d. Similar deformations (Figure 2) and obvious longitudinal cracking were observed within 20 mm of the wheel path. It can be concluded from the APT test results that longitudinal cracking occurs more often at higher temperature conditions. **Figure 2.** Deformation on pavement surface of high temperature test for structure 2.

surface. Figure 3 shows the observed longitudinal cracking located within 20 mm from the tyre edge with a width of 3 mm. To identify whether or not the longitudinal cracking is TDC, cores were taken and cut in half. It was obvious that the longitudinal cracking observed outside the wheel path was TDC, and that TDC propagated downwards 9 mm from the pavement surface. This observation matches the FE analysis results, which indicates that the maximum shear stresses for pavement structures 1 and 2 at high temperature conditions are located at 10–12 mm below the pavement surface. Figure 3 shows the observed longitudinal cracking located within 20 mm from the tyre edge with a width of 3 mm. To identify whether or not the longitudinal cracking is TDC, cores were taken and cut in half. It was obvious that the longitudinal cracking observed outside the wheel path was TDC, and that TDC propagated downwards 9 mm from the pavement surface. This observation matches the FE analysis results, which indicates that the maximum shear stresses for pavement structures 1 and 2 at high temperature conditions are located at 10–12 mm below the pavement surface.

temperature is 60 °C, the loading rate is 1 mm/min, and the loading frequency is 10 Hz. **Figure 3.** Observed longitudinal cracks outside the wheel path. **Figure 3.** Observed longitudinal cracks outside the wheel path.

In addition to field APT testing, a simple laboratory test—uniaxial repeated penetration test [14]—was developed in Tongji University, as shown in Figure 4, that simulates TDC initiation and

In addition to field APT testing, a simple laboratory test—uniaxial repeated penetration test [14]—was developed in Tongji University, as shown in Figure 4, that simulates TDC initiation and propagation. In Figure 4, the specimen diameter is 150 mm, the plunger diameter is 42 mm, test temperature is 60 ◦C, the loading rate is 1 mm/min, and the loading frequency is 10 Hz. *Appl. Sci.* **2018**, *8*, x FOR PEER REVIEW 5 of 14

**Figure 4.** Uniaxial penetration test. **Figure 4.** Uniaxial penetration test.

Figure 5 shows a cracked specimen after the uniaxial repeated penetration test. There is downward deformation beneath the plunger in the specimen, and obvious cracks were observed at the edge of the plunger. Then, the cracked specimen was sliced two times with a diamond saw at Sections A and B, as Figure 5 shows a cracked specimen after the uniaxial repeated penetration test. There is downward deformation beneath the plunger in the specimen, and obvious cracks were observed at the edge of the plunger.

shown in Figure 5. Cross-Section A was sliced perpendicular to the crack alongside the edge of the plunger; Cross-Section B was sliced around 20 mm away from Section A. The cross-sections of Sections A and B are shown in Figure 6. It can be seen that TDC of Cross-Section A was much more severe than that of Cross-Section B. Therefore, it can be excluded that TDC initiates from outside the specimen (Cross-Section B) and moves inside (Cross-Section A). Compared to the field TDC observed on cores taken from the APT site, the cracks observed in Cross-section A were very similar to the longitudinal cracking seen alongside the wheel path in terms of both the characteristic and the formation of cracks via top to downward propagation. Additionally, Figure 6 also shows the variations of shear stress (red line) and tangent tension Then, the cracked specimen was sliced two times with a diamond saw at Sections A and B, as shown in Figure 5. Cross-Section A was sliced perpendicular to the crack alongside the edge of the plunger; Cross-Section B was sliced around 20 mm away from Section A. The cross-sections of Sections A and B are shown in Figure 6. It can be seen that TDC of Cross-Section A was much more severe than that of Cross-Section B. Therefore, it can be excluded that TDC initiates from outside the specimen (Cross-Section B) and moves inside (Cross-Section A). Compared to the field TDC observed on cores taken from the APT site, the cracks observed in Cross-section A were very similar to the longitudinal cracking seen alongside the wheel path in terms of both the characteristic and the formation of cracks via top to downward propagation.

stress (blue line) on the section along its depth. The most severe cracking area occurred at the top part of the specimen (6 mm down from the top surface of specimen)—where the largest shear stress was located—as shown in Figure 6. Meanwhile, tangent stress is compressive stress, rather than tensile stress in this area, and the greatest tangent stress is 40 mm from the top surface, located far away from the severe TDC area. Therefore, it can be concluded that the crack on Cross-Section A was due t shear stress at the edge of the plunger, and initiated at the maximum shear stress area. The uniaxial repeated penetration test result is consistent with the field APT test. Thus, the uniaxial repeated penetration test is a valid test for simulating TDC in the laboratory. Additionally, Figure 6 also shows the variations of shear stress (red line) and tangent tension stress (blue line) on the section along its depth. The most severe cracking area occurred at the top part of the specimen (6 mm down from the top surface of specimen)—where the largest shear stress was located—as shown in Figure 6. Meanwhile, tangent stress is compressive stress, rather than tensile stress in this area, and the greatest tangent stress is 40 mm from the top surface, located far away from the severe TDC area. Therefore, it can be concluded that the crack on Cross-Section A was due t shear stress at the edge of the plunger, and initiated at the maximum shear stress area. The uniaxial repeated penetration test result is consistent with the field APT test. Thus, the uniaxial repeated penetration test is a valid test for simulating TDC in the laboratory.

Section A

**Figure 5.** Cracks in penetration specimen.

Section B

*Appl. Sci.* **2018**, *8*, x FOR PEER REVIEW

cross-section B.

the edge of the plunger.

formation of cracks via top to downward propagation.

repeated penetration test is a valid test for simulating TDC in the laboratory.

**Figure 4.** Uniaxial penetration test.

Figure 5 shows a cracked specimen after the uniaxial repeated penetration test. There is downward deformation beneath the plunger in the specimen, and obvious cracks were observed at

Then, the cracked specimen was sliced two times with a diamond saw at Sections A and B, as shown in Figure 5. Cross-Section A was sliced perpendicular to the crack alongside the edge of the plunger; Cross-Section B was sliced around 20 mm away from Section A. The cross-sections of Sections A and B are shown in Figure 6. It can be seen that TDC of Cross-Section A was much more severe than that of Cross-Section B. Therefore, it can be excluded that TDC initiates from outside the specimen (Cross-Section B) and moves inside (Cross-Section A). Compared to the field TDC observed on cores taken from the APT site, the cracks observed in Cross-section A were very similar to the longitudinal cracking seen alongside the wheel path in terms of both the characteristic and the

Additionally, Figure 6 also shows the variations of shear stress (red line) and tangent tension stress (blue line) on the section along its depth. The most severe cracking area occurred at the top part of the specimen (6 mm down from the top surface of specimen)—where the largest shear stress was located—as shown in Figure 6. Meanwhile, tangent stress is compressive stress, rather than tensile stress in this area, and the greatest tangent stress is 40 mm from the top surface, located far away from the severe TDC area. Therefore, it can be concluded that the crack on Cross-Section A was due t shear stress at the edge of the plunger, and initiated at the maximum shear stress area. The

**Figure 5.** Cracks in penetration specimen. **Figure 5.** Cracks in penetration specimen.

6 of 14

**Figure 6.** Cracks and stress distribution on cross-sections A and B. (**a**) Cross-section A; (**b**) **Figure 6.** Cracks and stress distribution on cross-sections A and B. (**a**) Cross-section A; (**b**) cross-section B.

#### **3. Investigation of the TDC Propagation and Material Modulus Decrease under Uniaxial 3. Investigation of the TDC Propagation and Material Modulus Decrease under Uniaxial Repeated Penetration Test**

#### **Repeated Penetration Test** *3.1. TDC Initiation and Propagation Process under the Uniaxial Repeated Penetration Test*

test simulates the TDC initiation and growth process very well.

**13mm**

*3.1. TDC Initiation and Propagation Process under the Uniaxial Repeated Penetration Test* The uniaxial repeated penetration test was performed on specimens with similar volumetric property. The tests were stopped at 30, 50, 70, 90, and 105 thousand load repetitions. Again, each the specimen was sliced at the same Section A as described previously. Figure 7 shows the TDC growing process. It can be seen that the cracks occur first in the area where the maximum shear stress is located, and then gradually grow downward until going through the whole specimen with an The uniaxial repeated penetration test was performed on specimens with similar volumetric property. The tests were stopped at 30, 50, 70, 90, and 105 thousand load repetitions. Again, each the specimen was sliced at the same Section A as described previously. Figure 7 shows the TDC growing process. It can be seen that the cracks occur first in the area where the maximum shear stress is located, and then gradually grow downward until going through the whole specimen with an increasing number of load repetitions. This process implies that the uniaxial repeated penetration test simulates the TDC initiation and growth process very well.

increasing number of load repetitions. This process implies that the uniaxial repeated penetration

(**a**) 30,000 (**b**) 70,000

**80mm**

**34mm**

**100mm**

**Figure 7.** TDC initiation and propagation downward process.

(**c**) 105,000 (**d**) Failure

cross-section B.

**Repeated Penetration Test**

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

**Figure 6.** Cracks and stress distribution on cross-sections A and B. (**a**) Cross-section A; (**b**)

The uniaxial repeated penetration test was performed on specimens with similar volumetric property. The tests were stopped at 30, 50, 70, 90, and 105 thousand load repetitions. Again, each the specimen was sliced at the same Section A as described previously. Figure 7 shows the TDC growing process. It can be seen that the cracks occur first in the area where the maximum shear stress is located, and then gradually grow downward until going through the whole specimen with an

**3. Investigation of the TDC Propagation and Material Modulus Decrease under Uniaxial** 

*3.1. TDC Initiation and Propagation Process under the Uniaxial Repeated Penetration Test*

test simulates the TDC initiation and growth process very well.

**Figure 7.** TDC initiation and propagation downward process. **Figure 7.** TDC initiation and propagation downward process.

#### *3.2. Modulus Decrease Process under the Uniaxial Repeated Penetration Test*

During the uniaxial repeated penetration test, the deformation vs. number of load repetitions curve was recorded. Based on the relationship between deformation and number of load repetitions, the penetration modulus (tentatively called the dynamic penetration modulus) can be calculated from Equation (1):

$$|\mathbf{E}^{\*p}| = \frac{\sigma\_0}{\varepsilon\_0} \tag{1}$$

where |E ∗*p* | is the dynamic penetration modulus, MPa. *σ*<sup>0</sup> is initial penetration loading intensity, *σ*<sup>0</sup> = *<sup>P</sup> A* , MPa. *P* is penetration load, *A* is area of the plunger, mm<sup>2</sup> . *ε*<sup>0</sup> is the initial vertical strain.

Because there is a settling process at the initial loading stage, the dynamic penetration modulus at the 500th load repetition was defined as the initial modulus of the specimen for comparison. The measured relationship between the dynamic penetration modulus and number of load repetitions for 3 different asphalt mixtures (styrene-butadiene-styrene (SBS) Modified asphalt: AC13/AC20/SMA13) under five levels of penetration loading are shown in Figures 8–10, respectively.

It can be seen from Figures 8–10 that the decreasing trends of the dynamic penetration modulus for 3 SBS modified asphalt mixtures are very similar. For example, when the penetration load is 1.3 MPa or higher, the dynamic penetration modulus curves for all 3 asphalt mixtures deteriorate following an S-shape, and keep decreasing towards 0 with an increasing number of load repetitions. When the dynamic penetration modulus decreases to 1/3 of its initial value, the deterioration rate becomes very rapid for all 3 asphalt mixtures.

from Equation (1):

from Equation (1):

\*p

E

\*p

E

A

A

P

P

where

where

 0 =

 0 =

*3.2. Modulus Decrease Process under the Uniaxial Repeated Penetration Test*

*3.2. Modulus Decrease Process under the Uniaxial Repeated Penetration Test*

is the dynamic penetration modulus, MPa.

is the dynamic penetration modulus, MPa.

, MPa. *P* is penetration load, *A* is area of the plunger, mm<sup>2</sup>

, MPa. *P* is penetration load, *A* is area of the plunger, mm<sup>2</sup>

During the uniaxial repeated penetration test, the deformation vs. number of load repetitions curve was recorded. Based on the relationship between deformation and number of load repetitions, the penetration modulus (tentatively called the dynamic penetration modulus) can be calculated

During the uniaxial repeated penetration test, the deformation vs. number of load repetitions curve was recorded. Based on the relationship between deformation and number of load repetitions, the penetration modulus (tentatively called the dynamic penetration modulus) can be calculated

*Appl. Sci.* **2018**, *8*, x FOR PEER REVIEW 7 of 14

0

0

Because there is a settling process at the initial loading stage, the dynamic penetration modulus at the 500th load repetition was defined as the initial modulus of the specimen for comparison. The measured relationship between the dynamic penetration modulus and number of load repetitions for 3 different asphalt mixtures (styrene-butadiene-styrene (SBS) Modified asphalt:

Because there is a settling process at the initial loading stage, the dynamic penetration modulus at the 500th load repetition was defined as the initial modulus of the specimen for comparison. The measured relationship between the dynamic penetration modulus and number of load repetitions for 3 different asphalt mixtures (styrene-butadiene-styrene (SBS) Modified asphalt:

0

0

> . 0

. 0 

(1)

(1)

is initial penetration loading intensity,

is initial penetration loading intensity,

is the initial vertical strain.

is the initial vertical strain.

\* 0

\* 0

= p

= p

E

E

**Figure 8.** Modulus variation for SBS-AC13. **Figure 8.** Modulus variation for SBS-AC13. **Figure 8.** Modulus variation for SBS-AC13.

It can be seen from Figures 8–10 that the decreasing trends of the dynamic penetration modulus for 3 SBS modified asphalt mixtures are very similar. For example, when the penetration load is 1.3

*3.3. Relationship between Dynamic Penetration Modulus Decrease and TDC Growth*

becomes very rapid for all 3 asphalt mixtures.

damage.

When the dynamic penetration modulus decreases to 1/3 of its initial value, the deterioration rate

Figure 11 shows the relationship between the dynamic penetration modulus deterioration percentage, cracking length percentage (the ratio of cracking length on Cross-Section A to specimen height), and the number of penetration loading repetitions. It can be seen from Figure 11 that there is an obvious consistency between the modulus deterioration percentage and TDC growth ratio. After 80,000 load repetitions, specimens start to show rapid growth in TDC until failure. The threshold for dynamic penetration modulus reduction is about 60–70%, which corresponds to 80,000 load repetitions. The dynamic penetration modulus reduction was found to correlate with the growth of TDC well. The greater the reduction of the dynamic penetration modulus, the more severe the TDC

**Figure 11.** Variation of modulus and crack length.

grows rapidly when the dynamic penetration modulus reaches 1/3 of its initial value.

It can be concluded that the uniaxial repeated penetration test simulates the decreasing process of the dynamic penetration modulus during TDC initiation and growth process very well. The greater the decrease in dynamic penetration modulus, the more severe TDC damage is. The TDC Dynamic Penetration Modulus, MPa

#### *3.3. Relationship between Dynamic Penetration Modulus Decrease and TDC Growth 3.3. Relationship between Dynamic Penetration Modulus Decrease and TDC Growth* Figure 11 shows the relationship between the dynamic penetration modulus deterioration

Figure 11 shows the relationship between the dynamic penetration modulus deterioration percentage, cracking length percentage (the ratio of cracking length on Cross-Section A to specimen height), and the number of penetration loading repetitions. It can be seen from Figure 11 that there is an obvious consistency between the modulus deterioration percentage and TDC growth ratio. After 80,000 load repetitions, specimens start to show rapid growth in TDC until failure. The threshold for dynamic penetration modulus reduction is about 60–70%, which corresponds to 80,000 load repetitions. The dynamic penetration modulus reduction was found to correlate with the growth of TDC well. The greater the reduction of the dynamic penetration modulus, the more severe the TDC damage. percentage, cracking length percentage (the ratio of cracking length on Cross-Section A to specimen height), and the number of penetration loading repetitions. It can be seen from Figure 11 that there is an obvious consistency between the modulus deterioration percentage and TDC growth ratio. After 80,000 load repetitions, specimens start to show rapid growth in TDC until failure. The threshold for dynamic penetration modulus reduction is about 60–70%, which corresponds to 80,000 load repetitions. The dynamic penetration modulus reduction was found to correlate with the growth of TDC well. The greater the reduction of the dynamic penetration modulus, the more severe the TDC damage.

*Appl. Sci.* **2018**, *8*, x FOR PEER REVIEW 8 of 14

0 100000 200000 300000 400000 500000 600000 700000 800000 Accumulated Load Repetitions, passes

It can be seen from Figures 8–10 that the decreasing trends of the dynamic penetration modulus for 3 SBS modified asphalt mixtures are very similar. For example, when the penetration load is 1.3 MPa or higher, the dynamic penetration modulus curves for all 3 asphalt mixtures deteriorate following an S-shape, and keep decreasing towards 0 with an increasing number of load repetitions. When the dynamic penetration modulus decreases to 1/3 of its initial value, the deterioration rate

**Figure 10.** Modulus variation for SBS-SMA13.

**Figure 11.** Variation of modulus and crack length. **Figure 11.** Variation of modulus and crack length.

It can be concluded that the uniaxial repeated penetration test simulates the decreasing process of the dynamic penetration modulus during TDC initiation and growth process very well. The greater the decrease in dynamic penetration modulus, the more severe TDC damage is. The TDC grows rapidly when the dynamic penetration modulus reaches 1/3 of its initial value. It can be concluded that the uniaxial repeated penetration test simulates the decreasing process of the dynamic penetration modulus during TDC initiation and growth process very well. The greater the decrease in dynamic penetration modulus, the more severe TDC damage is. The TDC grows rapidly when the dynamic penetration modulus reaches 1/3 of its initial value.

### **4. Proposed New Mechanisms for TDC Initiation and Propagation**

Inspired by the laboratory observations (Figures 7–11) and the relationship between TDC initiation and propagation and the dynamic penetration modulus deterioration, the authors explored a new way to view TDC initiation and propagation in asphalt pavements. A pavement structure with a geometry of 6 m × 6 m × 15 m was analyzed by FE method. Traffic loading was represented using a 22 × 16 cm rectangle with uniform distribution pressure of 0.7 MPa.

#### *4.1. Simulation of Cracking Initiation and Propagation Process with FE Method*

Based on the field and laboratory test results discussed previously, it was concluded that under repeated loading, shear damage occurs first in areas where maximum shear stress is located. Consequently, the modulus in those areas decreases and pavement stresses/strains are re-distributed within the whole pavement structure. When the modulus of the asphalt mixture in this area decreases to around 1/3 of initial value, the crack starts to grow rapidly. This is simulated by FE method, and detailed steps are described as follows:


Maximum Shear Stress, MPa

as shown in Figure 14.

shear damage failure.

*LB* 

increased from 0 to 20 cm<sup>2</sup>

strain at *x* direction always kept the same order:

*DL* 

and

The element set {e<sup>1</sup> e<sup>2</sup> e<sup>3</sup> . . . e*n*} of the shear damage area constitutes the shear damage area in the asphalt pavement structure under repeated loading.

With an assumed 0.7 MPa loading pressure, the numerical simulation of the shear damage process for various pavement structures (see Table 3) was performed. It can be seen from the simulations that maximum shear stress always occurred at the inner side of the tyre edge at a depth of 40 mm. The element with maximum shear stress is believed to damage first, gradually extending to the adjacent elements in a horizontal direction towards the outside of tyre edge. Finally, a "damaged layer" is formed from a damaged element in the pavement structure. Figure 12 shows an example of pavement structure with a damaged layer (DL). The FE method was employed to investigate the impact of the weakened layer on the shear stresses in the layers above (LA) and beneath (LB) the damaged layer. As shown in Figure 13, after shear damage, the maximum shear stresses *τ* in the pavement structures kept a fixed relationship: *τDL* > *τLA* > *τLB*. Therefore, the maximum shear stress always occurs at the bottom of the damaged layer, 40 mm from the pavement surface. Accordingly, it is anticipated that shear damage in pavements under repeated loading will extend in a horizontal, rather than vertical, direction. Certainly, a shear-damaged layer will be formed. The same conclusion was made when analyzing other types of pavement structures. Horizontal, rather than vertical, extension of shear damage implies that the cause for TDC initiation and propagation may be more complex than initially thought.

**Table 3.** Pavement structures used in finite element method (FEM) simulation.

**Figure 12.** Definition of the damaged layer. **Figure 12.** Definition of the damaged layer.

LA DL LB

Shear Damage Area,

**Figure 13.** Maximum shear stress variation.

Figure 14 shows that the maximum tensile strain in LA, DL, and LB at *x* direction (i.e.,

. When the shear damage area is larger than 4 cm<sup>2</sup>

damage area, the maximum tensile strain in LA increased rapidly, even exceeding the strain in LB. Therefore, there is a possibility that tension damage can occur in LA, and potentially accelerate the

*DL* 

) increased by 140.1%, 75.4% and 1.8%, respectively, when the shear damage area

> *LA* 

> *LB* 

As discussed above, repeated loading results in a damaged layer in the pavement structure. It is obvious that this damaged layer will influence the tensile stress/strain distribution in nearby layers, including both LA and LB. The maximum tensile strains (at *x* direction, which is perpendicular to the traveling direction) in the layers were computed with different assumed shear-damaged areas,

*4.2. Effects of Shear Damage Layer on Pavement Tensile Strain Distribution*

2 *cm*

> *LA* ,

, the maximum tensile

. With an increase in the shear

Layer Above Damaged Layer (LA)

1cm

1cm

1cm

2cm

Layer Beneath Damaged Layer (LB)

**Figure 12.** Definition of the damaged layer.

Damaged Layer (DL)

**Figure 13.** Maximum shear stress variation. **Figure 13.** Maximum shear stress variation.

#### *4.2. Effects of Shear Damage Layer on Pavement Tensile Strain Distribution 4.2. Effects of Shear Damage Layer on Pavement Tensile Strain Distribution*

As discussed above, repeated loading results in a damaged layer in the pavement structure. It is obvious that this damaged layer will influence the tensile stress/strain distribution in nearby layers, including both LA and LB. The maximum tensile strains (at *x* direction, which is perpendicular to the traveling direction) in the layers were computed with different assumed shear-damaged areas, as shown in Figure 14. As discussed above, repeated loading results in a damaged layer in the pavement structure. It is obvious that this damaged layer will influence the tensile stress/strain distribution in nearby layers, including both LA and LB. The maximum tensile strains (at *x* direction, which is perpendicular to the traveling direction) in the layers were computed with different assumed shear-damaged areas, as shown in Figure 14.

Figure 14 shows that the maximum tensile strain in LA, DL, and LB at *x* direction (i.e., *LA* , *DL* and *LB* ) increased by 140.1%, 75.4% and 1.8%, respectively, when the shear damage area increased from 0 to 20 cm<sup>2</sup> . When the shear damage area is larger than 4 cm<sup>2</sup> , the maximum tensile strain at *x* direction always kept the same order: *DL* > *LA* > *LB* . With an increase in the shear damage area, the maximum tensile strain in LA increased rapidly, even exceeding the strain in LB. Therefore, there is a possibility that tension damage can occur in LA, and potentially accelerate the Figure 14 shows that the maximum tensile strain in LA, DL, and LB at *x* direction (i.e., *εLA*, *εDL* and *εLB*) increased by 140.1%, 75.4% and 1.8%, respectively, when the shear damage area increased from 0 to 20 cm<sup>2</sup> . When the shear damage area is larger than 4 cm<sup>2</sup> , the maximum tensile strain at *x* direction always kept the same order: *εDL* > *εLA* > *εLB*. With an increase in the shear damage area, the maximum tensile strain in LA increased rapidly, even exceeding the strain in LB. Therefore, there is a possibility that tension damage can occur in LA, and potentially accelerate the shear damage failure. *Appl. Sci.* **2018**, *8*, x FOR PEER REVIEW 11 of 14

**Figure 14.** Variation of maximum tensile strain in the *x* direction. **Figure 14.** Variation of maximum tensile strain in the *x* direction.

Repeated shear stress can damage the layer and result in the DL modulus reduction to almost 1/3 of its initial value, and even to 0 (assumed to be 0.5 MPa in FE model). Consequently, the

Maximum Tension Strain, με

Area of Damaged Layer,

LA DL LB

(b) Maximum Tension Strain (Modulus of Damage 0.5MPa)

2 *cm*

, the maximum tensile

**Figure 15.** Effects of damaged layer on maximum tensile strain.

strain in LA exceeds 120 με. Based on the laboratory studies and field survey conducted by Marshall [15], Robert [16], Angela [17], and Xu [18], it can be reasonably assumed that in cases where the tensile strain is above 120 με, fatigue cracking might occur. The tensile strain in DL is greater than that in LA, and so will accelerate the failure of the layer or the opening of cracks. For the LB, the tensile strain remains at a level of less than 120 με, indicating a low probability of tension cracking.

It is necessary to take into account the LA modulus reduction and evaluate its impact on the tensile strain in LA. The effects of reduced LA moduli (1, 1/2, 1/4 and 1/6 of its initial value) on the

maximum tensile strain in LA will be more than 120 με, as shown in Figure 15.

2 *cm*

As illustrated in Figure 15, when the shear damage area reaches 3~4 cm<sup>2</sup>

(a) Maximum Tension Strain (Modulus of Damage Layer=1/6 Initial Value) Area of Damaged Layer,

maximum tensile strain in LA are shown in Figure 16.

*4.3. Analysis of TDC Growth Process*

LA DL LB

Maximum Tension Strain, με

Maximum Tension Strain, με

Repeated shear stress can damage the layer and result in the DL modulus reduction to almost 1/3 of its initial value, and even to 0 (assumed to be 0.5 MPa in FE model). Consequently, the maximum tensile strain in LA will be more than 120 µε, as shown in Figure 15. Repeated shear stress can damage the layer and result in the DL modulus reduction to almost 1/3 of its initial value, and even to 0 (assumed to be 0.5 MPa in FE model). Consequently, the maximum tensile strain in LA will be more than 120 με, as shown in Figure 15.

Shear Damage Area,

**Figure 14.** Variation of maximum tensile strain in the *x* direction.

2 *cm*

LA DL LB

*Appl. Sci.* **2018**, *8*, x FOR PEER REVIEW 11 of 14

**Figure 15.** Effects of damaged layer on maximum tensile strain. **Figure 15.** Effects of damaged layer on maximum tensile strain.

As illustrated in Figure 15, when the shear damage area reaches 3~4 cm<sup>2</sup> , the maximum tensile strain in LA exceeds 120 με. Based on the laboratory studies and field survey conducted by Marshall [15], Robert [16], Angela [17], and Xu [18], it can be reasonably assumed that in cases where the tensile strain is above 120 με, fatigue cracking might occur. The tensile strain in DL is greater than that in LA, and so will accelerate the failure of the layer or the opening of cracks. For the LB, the tensile strain remains at a level of less than 120 με, indicating a low probability of tension cracking. As illustrated in Figure 15, when the shear damage area reaches 3~4 cm<sup>2</sup> , the maximum tensile strain in LA exceeds 120 µε. Based on the laboratory studies and field survey conducted by Marshall [15], Robert [16], Angela [17], and Xu [18], it can be reasonably assumed that in cases where the tensile strain is above 120 µε, fatigue cracking might occur. The tensile strain in DL is greater than that in LA, and so will accelerate the failure of the layer or the opening of cracks. For the LB, the tensile strain remains at a level of less than 120 µε, indicating a low probability of tension cracking.

#### *4.3. Analysis of TDC Growth Process 4.3. Analysis of TDC Growth Process*

this was not discussed in detail in this paper.

helped perform the analysis with constructive discussions.

Foundation of China (NSFC) under grant number 51678443. **Conflicts of Interest:** The authors declare no conflict of interest.

**5. Summary and Conclusions**

growth.

It is necessary to take into account the LA modulus reduction and evaluate its impact on the tensile strain in LA. The effects of reduced LA moduli (1, 1/2, 1/4 and 1/6 of its initial value) on the maximum tensile strain in LA are shown in Figure 16. It is necessary to take into account the LA modulus reduction and evaluate its impact on the tensile strain in LA. The effects of reduced LA moduli (1, 1/2, 1/4 and 1/6 of its initial value) on the maximum tensile strain in LA are shown in Figure *Appl. Sci.* **2018**, *8*, x FOR PEER REVIEW 16. 12 of 14

**Figure 16.** Effects of LA modulus variation on tensile strain. **Figure 16.** Effects of LA modulus variation on tensile strain.

Figure 16 clearly shows that the tensile strains with discounted moduli are much higher than 120 με. Thus, longitudinal cracks will occur under repeated loading. It will affect stress and strain responses in the layer above LA, resulting in a strain level higher than 120 με in the layer above LA. At same time, the maximum shear stress will increase from 0.270 MPa to 0.310 MPa. Figure 16 clearly shows that the tensile strains with discounted moduli are much higher than 120 µε. Thus, longitudinal cracks will occur under repeated loading. It will affect stress and strain responses in the layer above LA, resulting in a strain level higher than 120 µε in the layer above LA. At same time, the maximum shear stress will increase from 0.270 MPa to 0.310 MPa.

In summary, this study proposed a new TDC initiation and propagation mechanism: shear damage in the asphalt layer results in increased tensile strain in the LA, which causes tension cracks; these tension cracks finally propagate upwards to the pavement surface. This new TDC mechanism can be described as "shear damage, then tension propagation". After the crack propagates to In summary, this study proposed a new TDC initiation and propagation mechanism: shear damage in the asphalt layer results in increased tensile strain in the LA, which causes tension cracks; these tension cracks finally propagate upwards to the pavement surface. This new TDC mechanism

The TDC initiation and propagation process is much more complex than first believed. The field APT test results showed that under repeated loading, TDC occurred first within 20 mm outside of the wheel path and was more easily induced at higher temperatures. The cracking damage characteristics of specimens under laboratory uniaxial repeated penetration test coincided well with the field TDC. Therefore, the uniaxial repeated penetration test can be used to simulate TDC initiation and propagation processes. With increasing load repetitions, the dynamic penetration modulus of the mixture kept decreasing; this decreasing process is consistent with crack length

Based on field and laboratory test data and extensive FE analyses, this paper concluded that top-down cracking is caused by shear stress, although the crack propagation process is not that simple. Maximum shear stress causes damage, which then extends horizontally and forms a damaged layer; the damaged layer will further cause the increased tensile strain in the upper layer. Higher tensile strain will result in crack initiation and propagation upwards to the pavement surface. The whole process can be summarized as "shear damage, then tension extension". More field, laboratory, and mechanistic analysis is needed to further validate this new TDC mechanism.

**Author Contributions:** Lijun Sun contributed significantly to analysis idea and manuscript preparation; Gang Wang performed the experiments and the data analyses; Hongchao Zhang contributed in mobile APT tests (using MMLS3) and helped revise the manuscript, Liping Liu contributed in APT tests (using MSL66) and

**Acknowledgments:** The authors gratefully acknowledge financial support from National Natural Science

pavement surface, stresses in the pavement structure will be re-distributed, and the maximum shear

can be described as "shear damage, then tension propagation". After the crack propagates to pavement surface, stresses in the pavement structure will be re-distributed, and the maximum shear stress area will move downwards to the place beneath the crack tip. Then, the process of "shear damage, then tension propagation" will be repeated until it completely goes through the entire asphalt layer. It is worth noting that thermal stress will also accelerate crack propagation, although this was not discussed in detail in this paper.

### **5. Summary and Conclusions**

The TDC initiation and propagation process is much more complex than first believed. The field APT test results showed that under repeated loading, TDC occurred first within 20 mm outside of the wheel path and was more easily induced at higher temperatures. The cracking damage characteristics of specimens under laboratory uniaxial repeated penetration test coincided well with the field TDC. Therefore, the uniaxial repeated penetration test can be used to simulate TDC initiation and propagation processes. With increasing load repetitions, the dynamic penetration modulus of the mixture kept decreasing; this decreasing process is consistent with crack length growth.

Based on field and laboratory test data and extensive FE analyses, this paper concluded that top-down cracking is caused by shear stress, although the crack propagation process is not that simple. Maximum shear stress causes damage, which then extends horizontally and forms a damaged layer; the damaged layer will further cause the increased tensile strain in the upper layer. Higher tensile strain will result in crack initiation and propagation upwards to the pavement surface. The whole process can be summarized as "shear damage, then tension extension". More field, laboratory, and mechanistic analysis is needed to further validate this new TDC mechanism.

**Author Contributions:** Lijun Sun contributed significantly to analysis idea and manuscript preparation; Gang Wang performed the experiments and the data analyses; Hongchao Zhang contributed in mobile APT tests (using MMLS3) and helped revise the manuscript, Liping Liu contributed in APT tests (using MSL66) and helped perform the analysis with constructive discussions.

**Acknowledgments:** The authors gratefully acknowledge financial support from National Natural Science Foundation of China (NSFC) under grant number 51678443.

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

### **References**


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