Abstract: [Objective] Vegetation is widely used for controlling shallow landslides due to the root additional cohesion (c_r) in reinforcing the soil along slopes. To improve the accuracy of estimation on afforested slope stability, this study investigated correction coefficients of the root additional cohesion Wu's model based on successive fracture process.[Method] Wu and Waldron's Model (WWM) and Fiber Bundle Model (FBM) are commonly used to quantify root additional cohesion. However, the overestimation of root reinforcement by WWM is well documented as the model assumes that all roots break simultaneously during shearing between two soil layers.FBM, on the other hand, assumes a progressive breakage leading to the reduced errors of c_r. In this study, a fracture conservative ratio (k") was introduced aiming at reducing WWM's overestimation based on FBM. To quantify the k", additional cohesion (c_r) of two commonly used ecological restoration tree species composed monospecific 17-year-old plantation stands of Robinia pseudoacacia and Platycladus orientalis grown on slopes in the semiarid Loess Plateau of China was investigated. We estimated c_r by WWM and four different FBMs as a function of load apportioned hypotheses by root cross-section area, root diameter, root number and as a function of identical displacement, respectively.[Result] k" differed significantly depending on species(P<0.001), soil depth(P<0.001) and algorithms (P<0.001). Overall, it was found that k" obtained by identical displacement FBM was significantly higher than that by other FBM algorithms (P<0.001) for both species, and R.pseudoacacia presented much higher correction coefficients than P. orientalis (P<0.001). In addition, fracture correction coefficients were found to be negatively corrected with root area ratio although a threshold existed according to simple linear analysis. Below the root area ratio threshold (R. pseudoacacia:0.14; P. orientalis:0.11), k" significantly decreased with the increase of root area ratio, but k" showed no response to root area ratio when it was higher than the threshold. Due to the high root area ratio, WWM always gave larger over-prediction for top several layers.[Conclusion] Fracture correction coefficents k" differs with algorithms, species and depth. To some extent, k" is negatively corrected with root area ratio. The finding of present study provides useful information for estimating root addition cohesion, as well as for controlling soil erosion and improving shallow landslide stability in the Loess plateau of China.

Key words: shallow landslide, root additional cohesion, Wu's model, fracture correction coefficents, root area ratio