# Stability Reinforcement of Slopes Using Vegetation Considering the Existence of Soft Rock
## 2 Materials and Methods
### Numerical Model and Simulation
#### 2.2.2 Numerical Model Development  
In this study, the slope characterized by red-bed in this site with a size of 113 m long and 59 m high was modeled using the 2D finite element program PLAXIS [49]. To consider the effect of root vegetation, six layers on the top of the geometry were divided. The mesh of the numerical model was generated using the triangular element, with local mesh refinement in some parts of the geometry. The 15-node triangle was used due to its fourth-order interpolation for displacements and 12 Gauss points for numerical integration. The mesh distributions of the model were presented in Figure 5, with a total of 5380 elements and 43,837 nodes. The bottom boundary was blocked, with both the horizontal and vertical displacements not allowed. The left and right boundaries of the slope were restrained in the horizontal direction. The top boundary of the slope was normally set as traction-free. However, a surcharge load with a value of 600 Pa due to the presence of trees was applied on the top, which corresponded to the cases of plants of young forest and mature forest with a plantation density of 350 trees/ha [50]. In addition, a rainfall intensity of 10 mm/day (light rain) or 50 mm/day (heavy rain) was also considered for the cases that analyze the slope stability under rainfall conditions. No groundwater table was detected in the borehole within a depth of 25 m during the geotechnical survey in dry seasons. For the convenience of seepage analysis and considering the effect of wet seasons, the groundwater level for the numerical model was set as 6 m above the bottom of the numerical model.  
Mechanical properties of the three soils were represented using the elastic perfectly plastic Mohr-Coulomb constitutive failure criteria. The detailed parameters of the three soils were listed in Table 2. Noticeably, both the average and minimum value of the sandy loess and silts were adopted to investigate the stability of the slope. The hydraulic conductivity of the three soils is also necessary to analyze the stability of the slope with rainfall. The saturated hydraulic conductivity of the sandy loess, silt and mudstone are determined as 1.05 \(\times\) 10\({}^{-6}\), 0.258 \(\times\) 10\({}^{-6}\), 1 \(\times\) 10\({}^{-10}\) m/s, respectively, based on the constant head experiments during the geotechnical investigation report on this site. VanGenuchten function [51] is adopted to describe the water retention behaviors of the soils, which can be further used to determine the relative hydraulic conductivity of soils. The detailed hydraulic parameters for the numerical model implemented in Plaxis 2D are listed in Table 3.  
Figure 4: Root reinforcement: (**a**) four different vegetation; (**b**) Relationships between root additional cohesion and depth (modified from [PERSON] et al. (2016)).  
The factor of safety (FS) of the slope with or without vegetation reinforcement was determined using the strength reduction method (SRM), which successively reduced both the cohesion and friction of the soils while keeping the internal stress field of the slope constant, to cause the failure of the slope [52; 53]. The value of \(\Sigma\)Msf at failure in the Plaxis program indicates the FS of the slope at the current state [49].