STABILITY ASSESSMENT OF ROOT-REINFORCED SLOPES USING FINITE ELEMENT LIMIT ANALYSIS

Slope instability poses serious threats to infrastructure and environmental sustainability. As a result, numerous reinforcement techniques have been used as disaster mitigation attempts to prevent slope failure. Among various traditional slope reinforcement methods, the use of vegetion root is more cost-effective and environmentally friendly. This paper presents stability assessment of root-reinforced slopes. Firstly, slope models were built for case of bare and root-reinforced slopes. The slope angles were varied in the range of 15º~55º. The root zone depth and cohesion of root were adjusted within the ranges of 0~1.5 m and 0~20 kPa, respectively. In this study, slope stability was assessed using finite element limit analysis with a strength reduction technique. The results indicate that factor of safety increases with the increasing of root zone depth and cohesion of root. The best factor of safety was obtained for the case with root zone depth and cohesion of root of 1.5 m and 20 kPa, respectively. Shear dissipation contours of the slope models also show that root reinforcement reduces shear dissipation energy along the failure surface, consequently lowering the possibility of slope failure.


Introduction
Slope failure is considered as one of the high-risk geo-environmental hazards since it has potential to be harmful, resulting in the loss of human life and damage of properties (Gallage et al., 2021;Xue et al., 2016).Generally, various factors contribute to slope instability such as heavy rainfall (Cho et al., 2021;Yang & Zhang, 2024), earthquake (Farichah & Hutama, 2020;Hutama & Farichah, 2020) or shift of stress condition (Taha et al., 2022).As the results, slope reinforcement is essential in order to mitigate slope failure due to those factors.
Many researchers have been investigated the effect of root reinforcement to slope stability.Guo et al. (2024) examined how root properties, such as architecture, orientation, and depth, affect the reliability of vegetated slopes during heavy rainfall.Furthermore, Yamase et al. ( 2024) compared the root system architecture of single and multi-stemmed E. japonica, as well as the impact of soil reinforcement on slope stability.Su et al. (2021) studied the effect of root reinforcement on slope stability while accounting for changes in root distribution and tensile strength throughout soil depths.Lann et al. (2024) investigated the hydromechanical effects of plants on slope stability.Moreover, Song & Tan (2024) investigate the microscopic mechanical reinforcing mechanism of plant roots on stabilization of slope.In general, all studies mentioned above have proved that root reinforcement increases stability of the slope.
Essentially, root reinforcement contributes to slope stability by increasing soil shear strength, which is equivalent to an increase in apparent soil cohesion (Cronkite-Ratcliff et al., 2022;Fata et al., 2022).Numerous researchers have conducted extensive evaluations to determine the values of cohesion of root for varied range of plant species living in a variety of environmental conditions.The majority of the results are in the range of 1 to 20 kPa (Chok et al., 2015).
Computational methodologies for slope stability analysis have emerged over the last few decades (Shiau et al., 2023).The limit equilibrium method (LEM) is frequently used in slope stability analysis because it is simple and effective (Schlotfeldt et al., 2018;Siacara et al., 2020).Nonetheless, a critical prerequisite for this technique is an early assumption concerning the slip surface (Peng et al., 2023;Sarkar & Chakraborty, 2021).In the other hand, Finite Element Method (FEM) outperforms LEM in predicting safety factor of the slopes without assuming a slip surface however the analysis requires longer computational time (Ghadrdan & Mokhtari, 2021;Raghuvanshi, 2019).Furthermore, Finite Element Limit Analysis (FELA) has been utilized to assess stability of slopes under different conditions (Oberhollenzer et al., 2018;Yingchaloenkitkhajorn, 2019).This approach can generate two distinct solutions: lower bound (LB) and upper bound (UB) solutions (Poulsen & Olesen, 2024).The FELA approach automates the search for the safety factor, combining the advantages of finite element and limit analysis methodologies.Furthermore, by using adaptive mesh techniques into the calculation, the slip plane can be identified directly (Hu et al., 2024;Zhang et al., 2021).
This study assessed the root reinforcement contribution to factor of safety using finite element limit analysis.The effects of root zone depth and cohesion of root to factor of safety were investigated.Furthermore, shear dissipation contours were used to highlight the root reinforcement effect to stability of slope.

Slope Geometry
The geometry of slope models for case of bare and root-reinforced slope are presented in Figure 1 and 2, respectively.The height of slope (H) for all cases are 8 m while slope base length slope angle of slopes models are Table 1 presents the input parameters used in this study.It should be noted that for condition of rootr).The slope models are considered to be homogeneous soil slopes.For the case of bare slopes, the parameters of cr and hr equal to zero.

Strength Reduction Finite Element Limit Analysis
The FELA program (Optum G2) was employed for assessing stability of root-reinforced slopes.The slope models were constructed for three adaptive iterations, with an initial mesh of 5000 elements that was automatically updated and increased to the final mesh.The factor of safety (FS) of both bare and root-reinforced slopes was analyzed using the strength reduction finite element limit analysis.The FS is expressed in relation to material strength, which is the ratio between the strength that is utilized and the actual strength of the material (Sarkar & Chakraborty, 2021;Tschuchnigg et al., 2015).

Research Results and Discussion
Effect of Root Zone Depth to FS Figure 3 shows how adjusting the root zone depth (hr) affects the FS of a slope with varied r can be observed that the FS increases with hr.The largest percentage increments in the FS of r = 1.5 m compared to the case of bare slopes (hr = 0) are 3.5, 6.8, 10.3, 13.2, and 16.3%, respectively.15°, 25°, 35°, 45°, and 55°, achieved when hr = 1.50 m compared to bare slopes (hr = 0), are 6.7%, 12.7%, 18.3%, 23.9%, and 29.3%, respectively.The findings of the study, as shown in Figures 3 5, align with the results reported by Chok et al. (2015) who employed the finite element method.This study concluded that the factor of safety for vegetated slopes increases with the enhancement of root zone depth.
Figure 5. Factor of safety versus root zone depth for cr = 20 kPa

Effect of Cohesion of Root to FS
Figure 6 shows the plots of the factor of safety (FS) versus cohesion of root, (cr) for the r = 1 m and other parameters are kept constant.The presented FS in this study is obtained from average value of lower bound (LB) r = 20 kPa and hr = 1 m, the factor of safety for lower bound and upper bound solutions are 3.365 and 3.385, respectively.Therefore, the average factor of safety for that case is 3.375.
Figure 7. Factor of safety versus cohesion of root for hr = 1.25 m Figure 8 depicts the relationship between the factor of safety (FS) and cohesion of root (cr) r = 1.5 m and maintaining constant 35°, 45°, and 55°, achieved when cr = 20 kPa compared to bare slopes (cr = 0), are 6.7%, 12.7%, 18.3%, 23.9%, and 29.3%, respectively.Figures 6 8 show the research findings, which are consistent with the conclusions given by Chok et al. (2015), who used a different methodology, specifically the finite element method, but their findings are comparable in that the factor of safety for vegetated slopes increases with the increase in cohesion of roots.Shear dissipation contours can be used to present the potential sliding surface obtained from finite element limit analysis.The greater shear dissipation energy indicates a greater shear possibility in the area.Figure 9  The results as shown in Figures 9 12 agree with the study of Chok et al. (2015) which proved that the presence of vegetation roots successfully reinforced the slope's weaker zones by providing additional apparent cohesion to the soils and 'pushed' the failure surface deeper into the slope, thereby improving the factor of safety.Additionally, the study of Chok et al. (2015) also concluded that steeper slopes tend to gain more improvement on FS than gentle slopes which is similar to the results of the current study, further validating the effectiveness of root reinforcement in stabilizing steep slopes.Additionally, the effect of root reinforcement on the failure surface of vegetated slopes shown in this section is also consistent with the findings of Burak (2021), which found that roots reinforce soil by serving as soil pins and dissipating stresses.mechanistic understanding is vital for the development of more accurate predictive models for slope stability in vegetated areas.Overall, these findings highlight the critical role of vegetation roots in slope stabilization, particularly for steep slopes.The root reinforcement is proved to be a valuable strategy in geotechnical engineering for managing slope stability in various terrains.This natural reinforcement strategy not only improves safety and reduces the risk of landslides but also supports sustainable environmental practices in geotechnical engineering.

Conclusion
This study finite limit analysis to explore the impact of root reinforcement to soil slope stability.Based on the results, several conclusions can be drawn.For all slope models, root reinforcement has been shown to be successful in enhancing slope stability.The best factor of safety is observed for the model with root zone depth (hr) and cohesion of root (cr) of 1.5 m and 20 kPa, respectively.Furthermore, the results of factor of safety and shear dissipation indicates that the effect of reinforcement of root to shear dissipation is more significant for the case of steep slope compared to gentle slope.This indicates that in steeper slopes, root reinforcement plays a crucial role in reducing shear stresses, thereby enhancing stability more significantly than in slopes with a gentler incline.This effect can be attributed to the increased demand for stabilization in steeper terrains, where the gravitational forces driving potential slope failures are greater.

Figure 1 .
Figure 1.Slope geometry for bare slope

Figure 3 .
Figure 3. Factor of safety versus root zone depth for cr = 10 kPa Figure 4 depicts the plots of factor of safety (FS) versus root zone depth (hr) for slopes with r = 15 kPa and other parameters are kept constant.When hr increments in the FS compared to bare slopes (hr = 0) were 5.3%, 9.7%, 14.5%, 18.9%, and 23.1%, respectively.

Figure 4 .
Figure 4. Factor of safety versus root zone depth for cr = 15 kPa Figure 5 illustrates the relationship between the factor of safety (FS) and the root zone depth r = 20 kPa and maintaining

Figure 6 .
Figure 6.Factor of safety versus cohesion of root for hr = 1 m Figure 7 depicts the plots of factor of safety (FS) versus cohesion of root (cr) for slopes with

Figure 8 .
Figure 8. Factor of safety versus cohesion of root for hr = 1.5 m Effect of Root Reinforcement of Failure Surface

Figure 9 .
Figure 9. Failure surface based on shear dissipation (lower bound) for gentle bare slope with

Figure 11 .
Figure 11.Failure surface based on shear dissipation (lower bound) for steep bare slope r = 20 kPa, hr = 1.5 m

Table 1 .
Input parameters