基于代表体元法的根土复合体本构计算与验证

Calculation and validation of the constitutive relation for root-soil composite based on representative volume element method

传统的根系固土计算方法没有考虑根系的存在对根土复合体弹性参数的影响,难以针对坡面数量庞大的根系进行高效地建模和计算。为研究植被根系对土体的增强作用和对边坡稳定性的影响,将根土复合体视为天然根系纤维增强复合材料,通过引入代表体元(RVE)法,直接建立根土复合体三维本构关系,量化根系对土体的增强作用;现场采集山西吉县刺槐根系及土壤,通过不同埋根方式的直剪试验及反复剪切试验验证RVE法理论结果;最后通过数值模拟验证,RVE法获得的根土复合体等效力学参数用于评价边坡稳定性的可行性。研究表明:RVE法能预测根土复合体的等效弹性参数,其剪切弹性模量提升率与反复剪试验结果相比,相差仅为0.24%。RVE法理论计算得到的强度参数黏聚力c和内摩擦角φ与试验结果仅分别相差2.45 kPa和3°,而Wu模型计算的黏聚力c比试验结果高估约5倍。与素土边坡相比,根土复合体试验结果计算得到的边坡安全系数提高7.20%,RVE模型边坡提高9.78%,而Wu模型边坡安全系数提高29.33%。相比于RVE模型,Wu模型存在高估边坡稳定性的风险;因此,RVE法能准确预测根土复合体的弹性参数和强度参数c和φ的变化,根系对土体的增强作用,不仅体现在黏聚力的增强上,内摩擦角和等效弹性参数同样有变化。代表体元结合数值仿真的方式,为实现含大量根系边坡的稳定计算提供了新的方法和技术手段。

[Background]Tree roots can inhibit shallow landslides.Quantitative evaluation of the effect of root reinforcement is a key step for assessing the effectiveness of vegetation in slope stabilization.The traditional calculation method of root-soil composites did not consider the influence of roots on the elastic parameters of root-soil composites.Meanwhile,it is difficult to calculate a slope with a large number of roots.In fact,trees are often planted in a spatial layout of regular planting arrangement on slopes to create plantations;thus,this research treats periodically arranged tree roots and the surrounding soil as a periodic composite.[Methods]The representative volume element(RVE)method was introduced to directly construct the three-dimensional constitutive relation of root-soil composites.The theoretical results obtained by the RVE method were verified by direct shear tests and repeated shear tests with length-varied roots.The roots and soil used in the test were collected in Jixian,Shanxi.The application feasibility of the equivalent mechanical properties of the root-soil composite obtained by the RVE method to evaluate the slope stability was verified by numerical simulation.[Results]The RVE method can be used to accurately evaluate the equivalent elastic properties of root-soil composites,and the improvement rate of the shear elastic modulus is only 0.24%higher than the repeated shear test.The difference for cohesion c and internal friction angleφis only 2.45 kPa and 3°,respectively.The cohesion calculated by the Wu model is overestimated about 5 times compared to the test results.Compared with the pure soil slope,the safety factor of the vegetated slope with the test data increases by 7.20%and the RVE slope model increases by 9.78%,while the safety factor of the slope with the Wu model increase by 29.33%.The Wu model has the risk of overestimating the slope stability compared with the RVE model.[Conclusions]The RVE method can accurately predict the alterations of the elastic parameters and strength parameters c andφof the root-soil composite.The strengthening effect of roots on the soil not only improves the cohesion,but also changes the internal friction angle and elastic parameters.RVE method combined with numerical simulation provide new method and technical means to realize the stable calculation of the slope with a large number of roots.