# Initiation and Propagation of Top-Down Cracking in Asphalt Pavement
## 4 Proposed New Mechanisms for TDC Initiation and Propagation
### 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:  
* Step 1: Establish a set of elements for the shear damage area, named set U.
* Step 2: Compute the shear stress in the original pavement structure, and identify the element (say, e\({}_{1}\)) with maximum shear stress, then put this element (i.e., e\({}_{1}\)) into U.
* Step 3: Assign a reduced modulus value to the elements in U, then reanalyze pavement structure with FE program.  
Figure 11: Variation of modulus and crack length.  
* Step 4: Identify again the element (for example, e\({}_{2}\)) with the maximum shear stress in the pavement structure, and put element e\({}_{2}\) into U.
* Step 5: Again, assign the discounted modulus value to the elements in U, then reanalyze pavement structure with the FE program.
* Step 6: Find again the element (say, e\({}_{3}\)) with the maximum shear stress in the pavement structure, and put element e\({}_{3}\) into U.
* Step 7: Repeat above steps.  
The element set {e\({}_{1}\) e\({}_{2}\) e\({}_{3}\)... 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 \(\tau\) in the pavement structures kept a fixed relationship: \(\tau_{DL}>\tau_{LA}>\tau_{LB}\). 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.