## 4 Discussion
### Root Mechanical Characteristics  
A significant result of our research is related to the mechanical characteristics of roots. Embedded beam elements were used to simulate the root system. Due to the limitations of embedded beam elements, root slippage caused by large deformations of the root-soil system might not occur. Therefore, potential errors could arise due to the influence of the root-soil interface. Understanding the latest development in root-soil interactions could simulate root-soil interactions more accurately by incorporating friction laws of root-soil interaction [40; 41; 42]. The laws of friction are needed to calculate simple root-soil complexes. Due to the complexity of the model, it is difficult to achieve it in our research. Since the embedded element method turned out to be a good choice in accuracy [30], the stress state of the root system in the slope soil was well simulated, which enabled us to use the model to analyze the mechanical characteristics of different 3D root structures in the soil. The results showed that the thickness, length, and position of the root may strongly affect its force on the slope and its influence on the slope stability. Compared with the root system in the upper part of the slope, the root system stress in the middle and lower parts of the slope is larger, contributing more to the anchorage of the soil [25]. No. 1 lateral root is mainly subjected to tensile stress, while the No. 4 lateral root is mainly subjected to compressive stress, which may be due to the symmetrical growth of the roots on both sides of the slope toe, and the No. 1 lateral root played an anchoring role, while the No. 4 lateral root did not. Additionally, the three rows of tap roots in the middle and lower part of the slope are also subject to greater bending moments, which may be related to the stress concentration of the surrounding soil. The bending moment of the lateral roots of the toe 1, 2, and 3 at the connection with the tap root is the largest, suggesting that when this kind of root structure is stressed in the slope, the lateral roots connected with the tap root are the most prone to bending deformation. It can help us understand how to optimize the root structure, which will have a good influence on the stability of the slope in the future. For the first time, we quoted the mechanical characteristics of the root system in slope stability analysis and specifically explored how the root system exerts its tensile strength to anchor the soil. In this research, due to the lack of specific data on root structure, it is necessary to simplify the root structure and the mechanical properties of certain roots. It is assumed that the mechanical properties of the tap root and lateral roots are the same, but their mechanical properties are not exactly the same. It is generally believed that there are differences due to the root age and physical properties of the root (cellulose, diameter, and water content) [43]. The elastic modulus of the root system used by us is 450 Mpa, which may cause calculation errors on all parameters related to the root system Es. In addition, the simulation did not consider the impact of tree species planting and the weight of the trees on the slope. [PERSON] et al. showed that some trees on the ground  
Figure 15: The shear stress of the soil at the 3 m root slope section: (**a**) The slope toe, (**b**) The second row, (**c**) The third row, (**d**) The fourth row, (**e**) The fifth row, (**f**) The sixth row. had little influence on the total pressure of the slope [23]. Furthermore, this paper did not considere the physiological characteristics of the root system, such as water absorption. This physiological characteristic of roots will have a great impact on the mechanical properties of soil and roots, which are often dynamic and difficult to be simulated and analyzed qualitatively. As [PERSON] et al. mentioned, rainfall was sometimes the determining factor of slope stability [44], though root architecture also had a great effect on soil loss.