## 1 Introduction  
Plant roots have the functions of shallow root reinforcement and deep root anchoring [1; 2; 3; 4], and they can effectively improve the stability of the slope [5]. The current ecological engineering technology mainly uses herbs, shrubs, or herbs combined with engineering protection, which can effectively reduce the occurrence of shallow landslides [6; 7; 8]. For example, vetiver grass can effectively prevent shallow landslides and improve slope stability [9; 10; 11]. As far as all the current ecological engineering protection technologies are concerned, although they have a good reinforcement effect on shallow landslides, they cannot reinforce deep landslides. Slope stabilization with living stumps is a new form of ecological engineering [12; 13], which is to plant or drive living stumps with strong vitality into the soil. After a period of time, the living stumps will grow strong root systems, as shown in Figure 1. The root system of the living stump crosses the potential sliding surface of the slope; therefore, it plays a role in strengthening and protecting the slope. The enhancement of the slope stability by the root system is mainly achieved by the following two methods. (1) Treat the root system as a bar similar to soil nails and add it to the soil for analysis. (2) The rooted soil is regarded as a root-soil complex, and an equivalent reinforcement layer is used to replace the rooted soil layer for analysis. In the current slope stability analysis, 2D models are widely used in numerical simulations [14; 15]. [PERSON] et al. proposed a simple 2D model to estimate the stability of vegetated riverbanks, in which three root-reinforced zones in the upper soil layer of the slope were suggested [16]. [PERSON] et al. investigated the effect of the spatial layout of root reinforcement and slope geometry on slope stability using 2D finite element analysis [17]. The research showed that compared with other locations, the vegetation at the bottom one-third part of the slope had a greater influence on the stability of the slopes. In the middle of the slope, the tap or heart root systems would have sufficient depth to interact with the sliding surface and provide better shearing resistance in soils [18]. In [19; 20; 21] authors applied 2D finite element analysis to study the influence of plant roots on slope stability. [PERSON] et al. analyzed the influence of factors such as root diameter, root length, and root position on slope stability through 2D finite element analysis [22]. However, studies on the influence of plant roots on slope stability, which considered the roots as rod-shaped units or simplified the root-soil complex into homogeneous materials, failed to consider the 3D spatial layout of plant roots. Few scholars considered the 3D characteristics of the root system in slope stability. [PERSON] et al. summarized the root-soil complex as soils with different cohesion in a 3D model and studied the influence of the spatial layout of root structure on slope stability [23]. [PERSON] et al. obtained accurate root structure data from mature oak trees by using 3D in-situ digitization and conducted stability analysis [24]. They concluded that the uniform arrangement of trees had little effect on fixing the soil. The staggered arrangement of trees will improve slope stability. [PERSON] & [PERSON] established a 3D simplified root model (one tap root and four lateral roots) to study the influence of the spatial layout of vegetation on slope stability [25]. In [26] authorsused embedded beam elements to simulate the root system and explored the anchoring mechanism of tree roots under the wind. [PERSON] et al. (from the same research group) established a 3D simplified living stump root system, supported the slope together with bamboo anchors, and analyzed the stability of the slope [27]. It showed that living stumps with developed root systems had a good effect on preventing deep landslides.