[目的]研究根系黏聚力Wu氏模型的修正系数,可提高Wu氏模型的精确度,进而提高造林边坡稳定性评价的准确性.[方法]针对Wu氏模型对根系黏聚力的高估问题,以刺槐和侧柏根系为研究对象,应用复合材料学的连续破坏理论,阐述根系的渐进失效过程,提出基于连续断裂过程的根系黏聚力Wu氏模型修正系数,即断裂修正系数,并研究不同算法间修正系数的差异性以及修正系数与根截面积比之间的关系.[结果]根系断裂修正系数随算法(P<0.001)、树种(P<0.001)和土层深度(P<0.001)的变化而有显著差异;位移控制式算法引入的修正系数显著高于由拉力控制式算法引入的修正系数(P<0.001);断裂修正系数随深度的增加而增加,表层30 cm内的修正系数显著低于深层根系(P<0.001);根截面积比与断裂修正系数的负相关性存在阈值,当根截面积比小于阈值时(刺槐0.14,侧柏0.11),断裂修正系数随着根截面积比的增加而减少;当根截面积比大于阈值时,断裂修正系数的根截面积比效应不显著.[结论]根系断裂修正系数随算法和树种不同而变化,随土壤深度增加而增大,且在根截面积比阈值范围内(刺槐0.14,侧柏0.11)与根截面积比呈负相关关系.研究结论能为评价造林边坡的稳定性、揭示植物护坡的力学机理提供理论基础,并为水土保持工程植物措施的选择提供科学依据.%[Objective]Vegetation is widely used for controlling shallow landslides due to the root additional cohesion ( cr ) 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 cr . 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 (cr) 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 cr 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.
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