# Study on the Optimization of Pile Length of Micropiles in Soil Landslides
## 2 Methods
### Calculation Method for Static Design of Micropiles  
(1) Determine the monopile load  
According to the conclusions of the model experiments, it can be assumed that micropiles are elastic-plastic materials with a clear yield limit. Under the action of landslide thrust, the rear row of piles that directly resist the thrust will enter the yield stage first. Furthermore, the issue of pile length design, which was not directly addressed by previous model experiments and numerical simulations, was optimized using engineering structural optimization principles to effectively solve practical design problems related to minipiles from an engineering perspective. The specific calculation method is as follows:  
1 Calculation of landslide thrust  
The calculation of landslide thrust can be carried out using the simplified Bishop method or the transfer coefficient method according to the code [27], which will not be further elaborated here. Figure 1: Micropile diameter and deformation coefficient curve. (a) The “m-m” method. (b) The “m-k” method. Figure 2: Schematic diagram of the computational model. (a) Micropile and landslide action model. (b) Landslide thrust distribution model. (c) A monopile calculation model. 2. _Thrust distribution_ The thrust distribution is determined by taking a conservative distribution ratio based on the results of the static tests and numerical simulations mentioned earlier. The specific distribution ratios are determined according to Table 1. Data in Table 1 are derived from the previously conducted tests, and the landslide thrust was actually measured based on the pressure boxes arranged in the middle and back rows of piles before and after the tests, which ultimately resulted in the landslide inference coefficients [28]. (2) Calculation of Pile Length According to the relevant experimental results, it can be assumed that when the micropile is subjected to bending and shear, the pile body will shift from mainly bearing bending and shear to mainly bearing tensile and compressive forces after the pile body bends and cracks. Assuming this premise, if the pile body undergoes excessive deformation leading to plastic failure, the bending and shear resistance of the pile body will cease to increase. However, during the plastic deformation stage, the pile body still exerts a restraining effect on the soil above and below the sliding surface. Consequently, at this juncture, micropiles primarily endure tensile forces. However, with the increase in the tensile force, the micropile may experience a pull-out failure. In order to avoid such failure, the pile length of the micropile needs to be determined based on its anchoring characteristics. Referring to existing calculation theories, assuming the diameter of the micropile is D and the diameter of the longitudinal reinforcement in the pile is d, the pile length required for the micropile to meet the anchoring performance can be calculated according to Formula (2). \[L=\text{max}\bigg{(}\frac{Kf_{s}A_{s}}{\pi Dq_{1}},\frac{Kf_{s}A_{s}}{n\pi d \xi q_{s}}\bigg{)} \tag{2}\]  
According to the formula, \(K\) is the safety factor, which can be obtained from Table 8.2.2 in reference [27]; \(q_{1}\) is the design value of the bond strength between the cement stone and the pile hole wall, which can be selected from Table 8.2.3-2 and Table 8.2.3-3 in reference [27]; \(q_{s}\) is the design value of the bond strength between the cement stone and the steel bar, which is 0.8 times the standard value and can be obtained from Table 8.2.4 in reference [27]; \(n\) is the number of steel bars; \(\hat{\xi}\) is the reduction factor of the interface bond strength when multiple steel bars are used as longitudinal reinforcement, which can be selected from the range of 0.6 to 0.85. By utilizing this approach, the anchorage length of micropiles in both the sliding bed and sliding body can be computed, thereby enabling the determination of Ld and Lu, respectively.