基于渐近均匀化理论的黄土高原草本植物固土效果模拟  

Numerical simulation of root reinforcement for herbs in Loess Plateau based on asymptotic homogenization theory

作　　者：黄建坤 王学林[1,2,3] 及金楠 陈丽华[1,2,3] 张之伟 Huang Jiankun;Wang Xuelin;Ji Jinnan;Chen Lihua;Zhang Zhiwei(Forest Ecosystem Studies,National Observation and Research Station,Beijing Forestry University,Jixian 042200,China;Key Laboratory of State Forestry Administration on Soil and Water Conservation,School of Soil and Water Conservation,Beijing Forestry University,Beijing 100083,China;School of Soil and Water Conservation,Beijing Forestry University,Beijing 100083,China)

机构地区：[1]山西吉县森林生态系统国家野外科学观测研究站,北京林业大学,吉县042200 [2]北京林业大学水土保持学院水土保持国家林业局重点实验室,北京100083 [3]北京林业大学水土保持学院,北京100083

出　　处：《农业工程学报》2020年第9期168-176,共9页Transactions of the Chinese Society of Agricultural Engineering

基　　金：国家自然科学基金(31700637);中央高校基本科研业务费专项资金(2015ZCQ-SB-01)。

摘　　要：黄土高原是中国水土流失和浅层滑坡灾害最严重的地区之一,而植被根系能有效抑制浅层滑坡。黄土高原草系分布广泛,根系在空间配置上具有鲜明的周期重复特征,计算大量根系的边坡固土效果非常复杂。该文利用渐进均匀化理论,构建"根系-土体"复合土体本构关系,通过与已有研究对比说明,该文所述方法计算三维本构关系具有较高精度。为说明均匀化方法在含根群边坡中的准确性和高效性,该文基于有限元软件ANSYS,进一步模拟了含草边坡和无草边坡的应力和应变分布规律。数值模型设置为3组,分别是无草边坡模型、含草边坡的分离式模型,以及基于该文均匀化理论的含草边坡模型。该文进一步采用观察等效塑性应变区是否贯通作为边坡失稳临界状态的标准,利用强度折减法计算了边坡安全系数。研究表明:1)渐进均匀化理论不仅能准确地构建根土复合体本构关系,而且极大地减少了模型计算工作量(减少了95.58%的单元数)。2)披碱草根系能改善边坡浅层土体的应力场,使得根系分布区内的剪应力更加均匀,使坡体浅层更趋于稳定。3)当边坡坡度较小时(坡角为30°),无草边坡安全系数较大(F=4.28),根系对边坡的稳定性加持较小(平均仅提高2.92%);当坡角增大到45°时,无草边坡安全系数下降为2.90,而含草边坡平均安全系数提升了13.45%,根系固土效果更加显著。Loess Plateau is the most severe soil and water loss area in the world,as well subjected to shallow-landslide disaster in China.Currently,grass system has been widely distributed in the Loess Plateau,while the root system shows obviously periodic characteristics in spatial distribution.In order to accurately evaluate the influence of root groups on root reinforcement,and the coupling relationship between roots and soils,a constitutive relation of the“root-soil”composite was constructed via the“unit cell”of the root and soil based on the asymptotic homogenization theory.The“root-soil”composite in the nature similar to the reinforced concrete,can be regarded as a“new composite material”,with a strong coupling relationship between roots and soil.In the deduction,some numerical methods including the perturbation method,periodic boundary conditions,subsection integral method and divergence theorem,were used to derive the expression of the equivalent stiffness matrix,and the equivalent density of the root-soil composite.The detailed solution to these functions was also given based on the finite element method.The two-dimensional elastic parameters of the root-soil composites were calculated by MATLAB program.The three-dimensional equivalent elastic parameters of the root-soil composite were eventually obtained,where the two-dimensional plane strain problem can be extended to three-dimensional one by additional equations.The calculation accuracy and stability of the present method are better than those of the simplified method,particularly on calculating the three-dimensional constitutive relationship.There was a certain deviation(up to 29.4%)in the calculation of equivalent Poisson's ratioυxy,whereas,the calculation errors of other equivalent parameters are less than 7.1%.To illustrate the accuracy and efficiency of the homogenization method in root reinforced slopes,the influence of the Elymus dahuricus’s roots on the stress and strain field of the slope was analyzed based on the finite element soft

关 键 词：边坡稳定性 根系 固土 均匀化理论 有限元法 

分 类 号：TU441[建筑科学—岩土工程]