## 6 Discussion  
The dynamic excess pore pressure ratio can reflect the liquefaction distribution in the deeply deposited saturated liquefiable soil during earthquakes. When the ratio reaches about 1.0, the saturated soil will be in the state of liquefaction failure.  
Twenty seconds into the earthquake, the distribution of the excess pore pressure ratio in natural foundation, foundation reinforced with isometric gravel piles, and foundation reinforced with subarea long-short gravel piles are as shown in Figure 12a-c, respectively.  
Figure 12: Cont.  
The excess pore pressure ratio in the upper soil of natural foundation was close to 1.0, which indicated that the subgrade was about to be in the state of liquefaction failure. The dynamic excess pore pressure ratio of the subgrade soil was less than 0.15, at a depth of 23.0 m, in the foundation reinforced with isometric gravel piles. Besides, for the foundation reinforced with subarea long-short gravel piles, the dynamic excess pore pressure ratio of the subgrade soil was less than 0.15, at a depth of 22.0 m, in both sides of the roadbed and at a depth of 13.0 m in the midsection of roadbed. Therefore, neither reinforced foundation would be liquefied because the dynamic excess pore pressure ratio at the core of the subgrade is far less than 1.0.  
In the foundation reinforced with subarea long-short gravel piles, a special shielding region, where excess pore water pressure decreased significantly because of the drainage effect in the permeable gravel piles, could be formed between the long gravel piles on the sides of the roadbed and below the short pile in the midsection of the roadbed. This is shown in Figure 13. The long gravel piles on the sides could block the propagation of seismic waves, and the drainage effect of gravel piles resulted in a large dissipation in the dynamic pore pressure around the long gravel piles. At the same time, the increase in excess pore pressure in the midsection could be restrained in the shielding region, below the short gravel piles, through their own drainage actions.  
The excess pore pressure ratio in the shielding region was obviously smaller than that in the same region in natural foundation; therefore, the shielding region must be in the state of non-liquefaction. With the shielding effect, implementation of the foundation reinforced with subarea long-short gravel piles not only greatly reduced the level of excess pore pressure ratio in the shielding region, but it also greatly reduced the length required for gravel piles below the middle of the embankment. In addition, the project's cost can be effectively reduced by using only a few long gravel piles, arranged under the embankment sides, and a large number of short gravel piles arranged beneath the middle of the embankment.  
Figure 12: Distribution of excess pore pressure ratio at 20 s in natural foundation and reinforced foundations. (**a**) Natural foundation. (**b**) Foundation reinforced with isometric gravel piles. (**c**) Foundation reinforced with long-short gravel piles.  
In terms of engineering costs, according to Figures 4 and 5, the total length of gravel piles, used in the isometric gravel piles scheme, is 525 m, while that of gravel piles employed in the subarea long-short gravel piles is only 336 m. This leads to a 36% savings in the cost of gravel piles construction. Due to the existence of the shielding effect in the scheme of foundation reinforced with subarea long-short gravel piles, the consumption of pile is greatly reduced, as to reduce the project cost.  
While considering the anti-liquefaction effect and project cost, we conclude that the subarea long-short gravel piles reinforcement scheme, in which the shielding effect exists, is superior to the isometric gravel piles scheme.