*4.3. Vertical Dynamic Stress Analysis*

Figure 14 shows the variation of road vertical dynamic stress with depth when the vehicle travels to about 50 m. It can be seen from the figure that, like the horizontal shear stress, the value of the vertical dynamic stress in the number of road surface layers and the base layer is larger, and the dynamic stress in the middle of the surface layer is 119,373 Pa. The value of vertical dynamic stress in the road subgrade is much smaller, and the vertical dynamic stress in the middle of the subgrade is 5824 Pa. In the vertical direction of the road, the vertical dynamic stress of each layer of the road structure decreases rapidly. In contrast, the dynamic stress on the surface of the asphalt base course is 0.602 times the dynamic stress on the surface course, and when it reaches the bottom of the subbase, the dynamic stress decreases to 0.038 times the surface stress.

**Figure 14.** Diagram of vertical dynamic stress variation with road depth.

Figure 15 shows the time–history variation diagram of the vertical dynamic stress of each layer. It can be seen from the diagram that the vertical dynamic stress of road is sometimes positive and sometimes negative, and the positive value shows tension while the negative value shows compression, and each value shows the maximum value when the asphalt road surface course.

Figure 16 shows the distribution of vertical dynamic stress on asphalt roads. It can be seen from the figure that vertical dynamic stress is mainly concentrated in asphalt road surface and base, within a relatively small range of the whole road length. Due to the alternating action of vertical dynamic stress tension and compression, the damage of road surface is accelerated.

**Figure 16.** Vertical dynamic stress nephogram. (Note: .010711 means 0.010711).

### *4.4. Stress Analysis of Pavement Considering Tire Starting Force and Braking Force*

When the vehicle is running on the road, in addition to the dynamic load in the vertical direction of the vehicle, it also receives the starting force and braking force in the horizontal direction when the vehicle starts and brakes. In fact, when the vehicle is driving on the road, the horizontal starting and braking force are the reasons for the large shear stress on the road surface. China's urban road design code also requires us to consider the horizontal force applied to the road when the vehicle's braking starts.

The horizontal shear stress change mileage curve of the road under the action of vehicle vertical coupling dynamic load, horizontal starting force, and braking force is shown in Figures 17 and 18. The horizontal shear stress of surface course and the base course is obvious during vehicle starting and braking. Compared with normal conditions, the horizontal shear stress of the road during starting and braking is larger. This is not only the main factor affecting vehicle starting and braking but also a factor affecting road service life.

**Figure 18.** Diagram of shear stress time–history during braking. (Note: ×10\*\*1 means ×<sup>10</sup>1, .5 means 0.5).

In the process of vehicle starting and braking, the road surface course and the base course are stressed the most, and the shear stress of the base course is larger than that of the surface course, which is more obvious when the vehicle is braking. From the perspective of the vertical road displacement, the vehicle can affect the front of the road when it is started, and the vehicle can still affect the back road when it is braked, as shown in Figures 19 and 20.

**Figure 19.** Vertical displacement nephogram at startup. (Note: .315 means 0.315, and so on with the other numbers).

**Figure 20.** Vertical displacement nephogram during braking. (Note: .011017 means 0.011017, and so on with the other numbers).
