# Study on the Optimization of Pile Length of Micropiles in Soil Landslides
## 2 Methods  
### Micropile Design Calculation Method and Pile Length Optimization Study  
When dealing with landslides, it is important to clarify the load-sharing mechanism of each row of micropiles and the load-carrying mechanism of individual micropiles. Based on this, this chapter summarizes and derives the design calculation method of minipiles in order to obtain a more convenient and practical engineering design calculation method. Simultaneously, the unresolved issue of pile length design in previous model experiments and numerical simulations was addressed through the application of engineering structural optimization principles, thereby effectively resolving the practical design problem of minipiles from an engineering perspective. Numerous experts and scholars have extensively discussed the design and calculation methods of micropiles, including influential approaches such as the ultimate bearing capacity method, p-y curve method, [PERSON] method, and elastic foundation beam method, among others. From the 1970s to 1990s, [PERSON], [PERSON] [23] and [PERSON] et al. [24] proposed a design method for mesh minipile reinforced slopes, but this method relies heavily on subjective experience and judgment, and in China, [PERSON] and [PERSON] et al. [25] also conducted related research and gave an empirical calculation formula foundation beam theory for the normal working phase and tensioning phase of anchors to establish a set of calculation models for the calculation of the interaction between this combined structure and the soil. This study optimizes previous design methods using a \"global to local\" analytical approach, providing a reliable and user-friendly analysis and calculation method for engineering applications. Based on the phenomena and data analyzed in previous model tests and numerical simulations, micropiles within soil landslides exhibit deformation and failure characteristics similar to those of elastic piles. Furthermore, according to the current calculation theory in the code [26], the type of pile can be determined based on the deformation coefficient using the following equation (The definition of the deformation coefficient \(\alpha\) is derived from the specification GB/T38509-2020 Landslide Prevention and Control Design Code [S] and is defined by the equation. ):  
\[\left\{ \begin{array}{l}\alpha=\sqrt[3]{kb_{0}/4 EI}(\mathrm{k-law})\\ \alpha=\sqrt[3]{mb_{0}/EI}(\mathrm{m-law})\end{array} \right. \tag{1}\]  
Equation (1) calculates the type of pile based on the deformation coefficient, where \(k\) is the embedded section foundation coefficient, in the \"k method\" is a constant; \(m\) is the embedded section foundation coefficient scale factor, in the \"m method\" with the depth of z change and linear change; \(b_{0}\) is the calculation width, for the miniature pile such as round small pile, generally take, \(b_{0}\) is the width of the pile, \(b_{0}\) is the width of the pile, \(b_{0}\) is the width of the pile, \(b_{0}\) is the width of the pile, \(b_{0}\) is the width of the pile, \(b_{0}\) is the width of the pile, in general take \(b_{0}=0.9(1.5d+0.5)\), \(d\) is the diameter of the pile. \(d\) is the pile diameter. In practical engineering applications, taking the elastic modulus \(E\) as 3 \(\times\) 10\({}^{7}\) kPa (C30 concrete) and assuming the worst-case scenario for the embedded soil layer, taking \(m\) = 1000 kPa/m\({}^{2}\) and \(k\) = 3 \(\times\) 10\({}^{4}\) kPa/m, the relationship curve between the diameter of the micropile and the deformation coefficient shown in Figure 1 can be calculated.