# Study on the Optimization of Pile Length of Micropiles in Soil Landslides
## 2 Methods
### Seismic Design Calculation Method of Micropile  
Many feasible methods have been proposed by scholars in the industry for the seismic design calculation of micropiles, such as the time history analysis method, response spectrum method, pseudo-static method, etc. However, for multi-degree-of-freedom systems such as micropiles with complex stress states, it is virtually impossible to perform time history analysis and response spectrum analysis calculations without the use of numerical calculation methods. Therefore, the more traditional pseudo-static method is still recommended in engineering. To ensure the reliability and operability of the seismic design calculation method for micropiles described in this study, this study will also explore the seismic design calculation method for micropiles based on the pseudo-static method. When the pseudo-static method is applied to the calculation of anti-slide structures, the seismic action is actually simplified to the product of the weight of the sliding body and the corresponding seismic coefficient, which is applied as the seismic force on the anti-slide structure to calculate the internal forces and deformations of the anti-slide structure. Essentially, by effectively simulating seismic force, this method enables a complete integration of seismic design calculation with static design calculation, allowing for direct application of the principles and methods of static design calculation in seismic design. Therefore, it can be known that under the vibration action, the thrust force of the loaded section of micropiles is closer to the trapezoidal distribution feature, and there is a more obvious load-sharing feature between each row of piles. Therefore, when dealing with a clearly defined dynamic load, the seismic design calculation for micropiles can be conducted using a method entirely consistent with the static design calculation. As a result, the focus of research on the seismic design calculation of micropiles is simplified to simulating the seismic force acting on them. According to the calculation results of the amplification coefficient in the vibration table test and numerical simulation, referring to the current seismic code [29], the recommended amplification coefficient of 2.25 is used to directly amplify the calculated static load, and the amplified thrust value is taken as the value of the load for dynamic calculation. Table 2 displays a comparison table of the results obtained using the static amplification and dynamic calculation for each row of micropiles. In the table, the measured static load is the result of the static load under the critical failure load in the model test and numerical simulation. The measured dynamic load is compared with the peak acceleration of 0.6 g, which has been selected based on the bearing limit state of the rear row of piles. As can be seen from the table, the calculated load of each row of micropiles after being amplified by the static load is greater than the measured dynamic load. In the test, the static load of the rear row and middle row of piles after being amplified is relatively close to the measured dynamic load result, but because the load-sharing ratio of the front row piles measured in the vibration table test is relatively low, its result deviates significantly from the measured value after multiplying the static load by the amplification coefficient. In the numerical  
simulation, after calculating the load-sharing according to the maximum value of the loaded section, there is also some deviation between the measured dynamic load of each row of piles and the calculated value using the amplification coefficient method, with a smaller deviation for the rear row piles and relatively larger deviation for the middle and front row piles. However, overall, this deviation tends to be conservative, rendering it acceptable for engineering design purposes. Consequently, based on the results obtained from this test and numerical simulation, this calculation method can be deemed fundamentally reliable.