An optimum tree density for mitigating slope instability associated with root reinforcement and tree surcharge effects: insights from numerical simulations

Shallow landslides commonly occur on vegetated slopes, where trees reinforce the soil through their roots while imposing additional biomass loading. Both effects depend strongly on tree density, which governs competition for water and nutrients, thereby controls root development and biomass allocation. However, how tree density simultaneously influences these competing mechanical effects and overall slope stability remains poorly quantified. This study evaluated the effect of tree density on slope stability using numerical simulations that integrate Root Distribution Model (RDM), Root Bundle Model with Weibull distribution (RBMw), and finite element analysis. Cryptomeria japonica (Japanese cedar) was adopted as a representative shallow-rooted species, with tree densities of 400–3,500 stems/ha, and soil thicknesses of 1–2.5 m. For 1 m soil thickness, vegetated slopes exhibited non-linear variations in the factor of safety (FS), ranging from 1.654 to 1.996, compared with 1.773 for the bare slope. FS increased by up to 11–13% at low to moderate densities (≤ 2,000 stems/ha) but declined at higher densities as tree surcharge outweighed gains in root reinforcement, with the maximum FS occurring at 800 stems/ha. Sensitivity analysis confirmed a strong dependence of FS on tree density under this condition (SI = - 0.233). In contrast, FS became weakly sensitive to tree density (SI = 0.018–0.039) for soil thicknesses > 1 m, and no optimum density emerged, as critical slip surfaces consistently developed beneath the rooting zone. The findings reveal a condition-specific optimum tree density for shallow-rooted species, providing a mechanistic basis for tree density–based landscape management.