## 4 Response Characteristics of Stabilizing Piles under Seismic Load
### Lateral Pile-Soil Load  
In the dynamic centripetal modeling tests, four earth pressure cells were placed on the stabilizing pile above the bedrock surface. In addition, according to the differential relationship between moment \(M\), shear force \(Q\), and distributed load \(q\) on the stabilizing pile (\(\mathrm{d}M/\mathrm{d}x=Q,\mathrm{d}Q/\mathrm{d}x=q\)), the distributed load \(q\) on the stabilizing pile after each  
Figure 17: Schematic representation of the resistance exerted by a stabilizing pile in the bedrock. shaking event can be roughly obtained (\(\Delta M/\Delta h=\overline{Q},\Delta\overline{Q}/\Delta h=\overline{q}\), where \(\Delta h\) is the distance between two adjacent moment gauges) from the residual moment diagram in Figure 16. The comparison of distributed load increment obtained by moment strain gauge and earth pressure cell (from pressure integral to distributed load) on a stabilizing pile after each shaking event is shown in Figure 18 (the increment of distributed load in EQ1 is almost zero, so is not shown in Figure 18 for clarity). It should be pointed out that the centrifuge model test gave values of pile-soil pressure on only one side surface of the pile, while the distributed load calculated from the bending moment is the pressure transmitted by the soil to the whole pile (four surfaces). There are differences between the two: Figure 18 shows that the distributions of the two are similar, but the values differ significantly when increasing the input PGA. To verify the rationality of the aforementioned differential method, Figure 19 shows the simplified distributed load increment above the slip surface after each shaking event according to Figure 18: the shape of the distributed load increment is the same, but the magnitude increases gradually with the increase inthe input PGA. The increment individributed load in EQ1 is almost zero, and in EQ5 it is equal to that in EQ4. It is noted that the distributed load increment generated by the seismic excitation  
Figure 19: Simplified distributed load increment above the slip surface after each shaking event (unit: kN/m). Figure 18: Comparison of distributed load increment obtained by moment strain gauge and earth pressure cell on a stabilizing pile after each shaking event. in Figure 19 is negative near the slip surface, which indicates that the earth pressure in front of the pile is large. The sliding force generated by the seismic excitation is mainly concentrated in the part above 3.5 m up the slip surface. It can be calculated that the point of action of the resultant force is 7.46 m above the slip surface. The point of action of the resultant force is 1.54 m below the slope surface, which indicates that the earthquake mainly causes shallow sliding of the deposit, resulting in the distribution of the load increment in the upper part of the pile. Taking the simplified distributed load in Figure 19 as the external load, the Mohr--Coulomb model was adopted for the bedrock (with the [PERSON]'s modulus of bedrock set to 5.42 Gpa, and the Poisson's ratio to 0.30). The stabilizing pile (Table 2) was simulated as a Mindlin beam [46] with the help of PLAXIS 2D software [47]. Then, the horizontal displacement, shear force, and bending moment on a stabilizing pile after an earthquake can be obtained (Figure 20). In Figure 20, the horizontal displacements of the pile in each shaking event are obtained by invoking Mindlin beam theory. The horizontal displacements of the pile top from EQ2 to EQ5 are 0.601 mm, 2.08 mm, 8.88 mm, and 8.88 mm, respectively. The pile top horizontal displacements measured by laser displacement transducer LDS-3 are 0.31 mm, 1.48 mm, 6.85 mm, and 6.85 mm, respectively. It can be found that the horizontal displacement of the pile tip obtained by use of Mindlin beam theory is slightly greater than that measured by laser displacement transducer, but the trend of the two is consistent.