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## 非线性准则下三维加筋边坡稳定性的上限分析

(1.合肥工业大学汽车与交通工程学院, 安徽合肥 230009)
(2.格勒诺布尔-阿尔卑斯大学3SR实验室, 伊泽尔格勒诺布尔38041)
(3.中南大学土木工程学院, 湖南长沙 410006)
【知识点链接】极限分析

【摘要】为了研究非线性摩尔-库仑破坏准则下的三维加筋边坡在均匀加筋和三角形加筋2种加筋模式下的稳定性,采用极限分析上限理论,构建加筋边坡破坏的三维破坏机构,推导不同加筋模式下的筋材内能耗散方程,并根据上限定理将三维加筋边坡的稳定性问题转化为显式优化问题,得到三维边坡稳定性指标的计算公式。采用MATLAB软件计算,将结果与已有研究成果进行比较,验证了所提出计算方法的正确性,并进一步讨论了非线性参数m、宽高比B/H、不同加筋模式以及不同加筋强度k0对三维边坡稳定性的影响。结果表明:稳定性系数Ns随着m的增加而非线性减小,在坡角较小(不大于60°)的情况下,m对边坡稳定性系数Ns的影响较大,边坡的非线性特性比较明显;稳定性系数Ns随着B/H的增加而减小,在B/H<5尤其B/H<2时,稳定性系数下降速率较快,B/H越接近10时稳定性系数逐渐趋于稳定;三角形加筋模式的加固效果优于均匀加筋模式,稳定系数性Ns随着加筋强度k0的增加而线性增大,但变化规律并不显著。在实际工程中,建议B/H较小时,要对加筋边坡进行三维分析以符合工程实际;坡角较小时需要考虑土体的非线性破坏特征,选取合适的非线性参数可避免不安全的设计;在工程条件允许的情况下,优先选择三角形加筋模式进行边坡加固。

【关键词】 道路工程;三维稳定性分析;极限分析;三维边坡;加筋边坡;非线性破坏准则;稳定性系数;

【DOI】

【基金资助】 国家重点基础研究发展计划(“九七三”计划)项目(2013CB036004); 国家自然科学基金项目(51408180); 中央高校基本科研业务费专项资金项目(JZ2014HGQC0138,J2014HGBZ0177);

## Upper Bound Analysis of Stability of Three-dimensional Reinforced Slopes Based on Nonlinear Failure Criterion

HOU Chao-qun1 DENG Xin1 SUN Zhi-bin1 DIAS D1,2 XU Jing-shu3

(1.School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, Anhui Province, China 230009)
(2.Laboratory 3SR,Grenoble Alpes University, Grenoble 38041, Isere, France)
(3.School of Civil Engineering, Central South University, Changsha, Hunan Province, China 410006)

【Abstract】In order to investigate the stability of three-dimensional reinforced slopes under two kinds of reinforcement models, namely, uniform reinforcement and triangular reinforcement on the basis of nonlinear Mohr-Coulomb failure criterion, three-dimensional failure mechanism was constructed by dint of upper bound theory in limit analysis. And the internal energy dissipation equations of reinforcement in different reinforced modes were derived. Then the stability problem of three-dimensional reinforced slopes could be transferred into an explicit optimization process, and the formulas of stability coefficient were obtained. The results were calculated by MATLAB software and compared with the previous achievement for validation. Further calculation and discussion were conducted to investigate the effects of nonlinear parameters m, the ratio of slope width to height (B/H), different reinforcement modes and strength (k0) on three-dimensional stability. The results show that the stability coefficient Ns decreases with the increase in m, and with small slope angle (no more than 60°), m has a great impact on Ns. The nonlinear characteristics of the slope are relatively significant. The stability coefficient Ns decreases with the B/H and decreases rapidly when B/H < 5, especially when B/H < 2. Besides, the coefficient Ns becomes stable when B/H approaching 10. Furthermore, the triangular reinforcement is better than uniform reinforcement. The stability coefficient Ns increases linearly with the reinforced strength k0, but the changing rate is not significant. Some project proposals will be provided for the practical use. The three-dimensional analyses are required for reinforced slopes when B/H is small, in order to be consistent with the actual engineering. To avoid unsafe design, the nonlinear characteristic of criterion should be considered when the slope angle is small. The priority goes to the triangular reinforcement if the engineering condition allows.

【Keywords】 road engineering; three-dimensional stability analysis; limit analysis; three-dimensional slope; reinforced slope; nonlinear failure criterion; stability coefficient;

【DOI】

【Funds】 National Basic Research Program of China (973 Program, 2013CB036004); National Natural Science Foundation of China (51408180); Fundamental Research Funds for the Central Universities of Ministry of Education of China (JZ2014HGQC0138,J2014HGBZ0177);

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ISSN:1001-7372

CN: 61-1313/U

Vol 31, No. 02, Pages 124-132

February 2018

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