(3.中南大学土木工程学院, 湖南长沙 410006)
【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
(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;
【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);
 MICHALOWSKI R L, DRESCHER A. Three-dimensional Stability of Slopes and Excavations [J]. Geotechnique, 2009, 59(10): 839–850.
 PAN Q J, XU J S, DIAS D. Three-Dimensional Stability of a Slope Subjected to Seepage Forces [J]. International Journal of Geomechanics, 2017, 17 (8): 04017035
 WANG Zhao, QIAO Li-ping. Research of Critical Height of Reinforced Slopes [J]. Rock and Soil Mechanics, 2006, 27(1): 132–136 (in Chinese).
 CUI Xin-zhuang, YAO Zhan-yong, SHANG Qing-sen, et al. Limit Analysis of Critical Heights of Reinforced Soil Slope [J]. China Journal of Highway and Transport, 2007, 20(1): 1–6 (in Chinese).
 ZHAO Lian-heng, LI Liang, YANG Feng, et al. Dynamic Stability Pseudo-static Analysis of Reinforcement Soil Slopes [J]. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(9): 1904–1917 (in Chinese).
 YANG Xin-guang, CHI Shi-chun, LU Xiao-long. Upper Bound Limit Analysis for Seismic Stability of Reinforced Slopes of Earth-rock Dams [J]. Journal of Hydraulic Engineering, 2014, 45(3): 304–311 (in Chinese).
 AUSILIO E. Seismic Bearing Capacity of Strip Footings Located Close to the Crest of Geosynthetic Reinforced Soil Structures [J]. Geotechnical & Geological Engineering, 2014, 32(4): 885–899.
 GAO Y F, Yang S C, Zhang F, et al. Three-dimensional Reinforced Slopes: Evaluation of Required Reinforcement Strength and Embedment Length Using Limit Analysis [J]. Geotextiles and Geomembranes, 2016, 44(2): 133–142.
 LADE P V. Elasto-plastic Stress-strain Theory for Cohesionless Soil with Curved Yield Surface [J]. International Journal of Solids & Structures, 1977, 13(11): 1019–1035.
 YANG Xiao-li. Limit Analysis Method and Its Application to Geotechnical Engineering with Linear and Nonlinear Failure Criteria [D]. Changsha: Central South University, 2002 (in Chinese).
 ZHANG X J and CHEN W F. Stability Analysis of Slopes with General Nonlinear Failure Criterion [J]. International Journal for Numerical And Analytical Methods in Geomechanics, 1987, 11(1): 33–50.
 Gao Y F, Wu D, Zhang F. Effects of Nonlinear Failure Criterion on the Three-dimensional Stability Analysis of Uniform Slopes [J]. Engineering Geology, 2015, 198: 87–93.
 PORBAHA A, GOODINGS D J. Centrifuge Modeling of Geotextile Reinforced Cohesive Soil Retaining Walls [J]. Journal of Geotechnical Engineering, 1996, 122(10): 840–848.
 LI Xiu-juan. The Application of Upper-Bound Method on Stability Analysis of Reinforcement [D]. Qingdao: Ocean University of China, 2008 (in Chinese).