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)
【Knowledge Link】Limit analysis

【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)

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This Article


CN: 61-1313/U

Vol 31, No. 02, Pages 124-132

February 2018


Article Outline



  • 0 Introduction
  • 1 Nonlinear strength criterion
  • 2 Failure mechanism and energy dissipation of reinforcement
  • 3 Energy rate calculation of the mechanism
  • 4 Comparison and analysis
  • 5 Results and discussion
  • 6 Conclusions
  • References