# Study of the Dynamic Response of a Rigid Runway with Different Void States during Aircraft Taxing
## 4 Analysis of Results and Discussion  
### Calculation Results of VDD with No Void  
The above calculations were completed in ABAQUS finite element software. The load transfer coefficient was calculated to be above 95% by the displacement at the corresponding position of the adjacent panels, which proved that the rigid pavement model had good load transfer performance. When there was no void in the pavement, the time-domain VDD of  
Figure 8: Acquisition path of VDD and vibration signal monitor points.  
the collected pavement was calculated as shown in Figure 9a,b using the acquisition points on the acquisition path of the VDD. As the calculation model is a four-degrees-of-freedom, double-main-landing-gear model, the rollover stiffness was considered in the dynamic load calculation. Therefore, the VDDs in the left and correct symmetrical positions on the runway centerline were different, but the VDD trends were consistent with the changes in position and time. At 0.5 s, the main landing gear was located directly above the acquisition path, and the VDDs in different positions were at their maximum values. The smallest VDDs values were at 10 m on the left and right sides of the runway center, 0.050 mm and 0.044 mm, respectively, while 3.21 m to the left and right sides of the runway center was under the inner tire of the main landing gear, with the largest VDD values of 0.290 mm and 0.270 mm, respectively. The peak value of the time-domain VDD in the runway center was 0.141 mm, similar to the peak value of the time-domain VDD at 6.08 m on both sides.  
The acquisition path of the VDD was offset to the middle and bottom of the base layer along the negative direction of the \(y\)-axis, and the soil base layer depths were 2.1 m, 4.1 m, 6.3 m, 8.4 m, and 10.1 m. There were eight acquisition paths of the VDD with different depths. Figure 10 depicts the VDD results on the eight paths at the 0.5 s moment. The VDDs of the surface and base layers increased first and then decreased from the runway center to both sides, forming an obvious \"W\" shape with the peaks located directly below the left and right main landing gears. The left main landing gear was currently more loaded, and the VDD at the bottom of the base layer was 0.267 mm, which was only 7% less than the VDD in the middle of the surface layer of 0.287 mm. The reduction rates of the soil base layer were approximately 53.6%, 72.1%, 83.3%, 91%, and 96%at the depths of 2.1 m, 4.1 m, 6.3 m, 8.4 m, and 10.1 m, respectively, compared with the VDD of 0.267 mm in the middle of the surface layer. The soil base layer's VDD increased with depth and then decreased. We marked the VDD peak on the left side of the runway center of the eight paths. The maximum VDD of each left path was shifted to the runway center as the acquisition path depth increased, and the shifting amplitude in the interval from the surface layer to the soil base at a depth of 2.1 m was small, about 0.2 m. The maximum value of VDD was about 3 m in the soil base depth range from 2.1 m to 10.1 m, which was close to the runway center. Below the runway center, the VDD of the surface layer and the base layer barely changed. The VDD of the soil base changed uniformly along the runway depth direction. When the acquisition path depth exceeded 6.3 m, the maximum value of VDD decreased noticeably.  
Figure 9: Multipoint dynamic displacement of surface dynamic displacement acquisition path in the time domain.  
Sections 4.2 and 4.3 investigate the runway surface layer's VDD response and vibration signal during aircraft taxiing on runways under different runway pavement void conditions.