Rock and Soil Mechanics ›› 2022, Vol. 43 ›› Issue (10): 2735-2743.doi: 10.16285/j.rsm.2021.7080

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Three-dimensional stability limit analysis of cracked loess slopes

ZHU Xue-liang1, SHAO Sheng-jun1, 2, SHEN Xiao-jun3, SHAO Shuai4, LIU Xiao-kang1   

  1. 1. Institute of Geotechnical Engineering, Xi’an University of Technology, Xi’an, Shaanxi 710048, China 2. Shaanxi Key Laboratory of Loess Mechanics and Engineering, Xi’an University of Technology, Xi’an, Shaanxi 710048, China 3. Hanjiang to Weihe River Valley Water Diversion Project Construction Co., Ltd., Xi’an, Shaanxi 710000, China 4. Department of Architecture and Urban Planning, Xi’an University of Technology, Xi’an, Shaanxi 710048, China
  • Online:2022-10-28 Published:2022-11-25
  • Contact: SHAO Shuai, male, born in 1990, PhD, Lecture, mainly engaged in the loess mechanics. E-mail: E-mail:
  • About author:ZHU Xue-liang, male, born in 1996, Master degree candidate, mainly engaged in the loess mechanics and limit analysis of slope stability.
  • Supported by:
    the National Natural Science Foundation of China (52108342), the Shaanxi Province Natural Science Foundation Research Program–Hanjiang-Weihe Joint Fund Project (2019JLP-21, 2019JLZ-13), the Ph.D. Launch Fund of Xi’an University of Technology (107-451122001) and the Shaanxi Water Science and Technology Program (2021slkj-12).

Abstract: The development of vertical cracks in loess slopes often affects slope stability. Compared with the plane strain mechanism, the slope stability analysis under the three-dimensional (3D) failure mechanism is closer to the actual slope instability. Based on the upper bound method of plastic limit analysis, different failure mechanisms (face failure, toe failure and base failure) of 3D loess slope with pre-existing cracks are considered, the energy balance equation and its dimensionless critical height expression γH/c are established, and the upper bound solution of critical height is obtained by random search method. The effects of constraint width, slope angle, internal friction angle and crack depth on the critical height of 3D vertical cracked loess slopes are analyzed. The results indicate that for the toe failure mechanism, the critical height decreases with the increase of crack depth, and the increase in crack depth no longer affects the critical height after reducing to the critical crack depth (δ /H)min. The critical crack depth increases with the increase of slope angle β and decreases with the increase of internal friction angle φ. When the constraint width B/H<0.8, most of the failure mechanism is of face failure. When the constraint width B/H=0.8, internal friction angle φ =10°, and the constraint width B/H=0.6, internal friction angle φ =15°, the failure mechanism of the slope gradually transits from the face failure mechanism to the toe failure mechanism. The loess slope with vertical cracks has a smaller critical height than the intact slope. The constraint width and internal friction angle can affect the failure mechanism of 3D loess slopes.

Key words: slope instability, vertical cracks, failure mechanism, upper bound method