Abstract
In practical engineering, due to the noncontinuity characteristics of joints in rock slopes, in addition to plane failure, stepped sliding failure may occur for intermittently jointed rock slopes. Especially for intermittently bedding jointed rock slopes, the correlation and difference in strength parameters between joints and rock bridges, along with the various failure modes and intermittency of rock bridges, contribute to the complexity of stepped failure modes and the unpredictability of failure regions. Based on the upper-bound limit analysis method and multi-sliders step-path failure mode, considering the shear and tensile failure of rock bridges and the weakened relationship between the strength parameters of rock bridges and jointed surfaces, by introducing the modified M-C failure criterion and the formula for calculating the energy consumption of tensile failure of rock bridges, two failure mechanisms are constructed to obtain the safety factor (Fs) of intermittently jointed rock slopes. The sequential quadratic programming method is used to obtain the optimal upper-bound solution for Fs. The influence of multiple key parameters (slope height H, horizontal distance L, Slope angle β, shear strength parameters of the rock bridge φr and cr, Dimensionless parameter u, weakening coefficients of the internal friction angle and cohesion between the rock bridges and joint surfaces Kφ and Kc) on the stability analysis of intermittently jointed rock slopes under the shear failure mode of rock bridges as well as under the tensile failure mode is also explored. The reliability of the failure mechanisms is verified by comparative analysis with theoretical results, numerical results, and landslide cases, and the variation rules of Fs with each key parameter are obtained. The results show that Fs varies linearly with φr and cr of the rock bridge and with Kφ and Kc, whereas Fs changes nonlinearly with H and L. In particular, with the increase in Kφ and Kc, Fs increases by approximately 52.78% and 171.02% on average, respectively. For rock bridge tensile failure, Fs shows a nonlinearly positive correlation with φr, cr, Kφ and Kc. In particular, with the increase in Kφ and Kc, Fs increases by approximately 13% and 61.69% on average, respectively. Fs decreases rapidly with increasing slope gradient β and decreasing dimensionless parameter μ. When Kφ and Kc are both less than 1.0, the stepped sliding surface occurs more easily than the plane failure surface, especially in the case of tensile failure of the rock bridge. In addition, rock slopes with higher strength parameters, taller heights, and greater weakening coefficients are prone to rock bridge tension failure with lower Fs, and more attention should be given to the occurrence of such accidents in actual engineering.
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Change history
08 April 2024
An Erratum to this paper has been published: https://doi.org/10.1007/s11629-024-8648-2
Abbreviations
- Abb.:
-
Explanation
- α :
-
The angle between the slope top and the horizontal plane
- α i :
-
The angle between the sliders at point O
- BB1 :
-
The tensile fracture
- B1B2 :
-
The upper joint surface
- B2B3 :
-
Rock bridge
- B3B4 :
-
The lower joint surface
- β :
-
Slope angle
- β i :
-
The angle between the slip surface and the horizontal plane
- C :
-
The difference between the angles of adjacent joint surfaces
- D c :
-
The internal dissipation rate
- F s :
-
The safety factor
- f t’:
-
Uniaxial tensile strength
- H :
-
The slope height
- K φ, K c :
-
The weakening coefficients of the internal friction angle and cohesion between the rock bridges and joint surfaces, respectively, and their values range from 0 to 1
- k Y :
-
The fracture connectivity rate.
- L :
-
The horizontal length from the tensile fracture to the top point of the slope
- γ :
-
Bulk density
- S i :
-
The slider area
- μ :
-
Dimensionless parameter (indicates the contribution of tensile strength truncation)
- u i :
-
Slider absolute speed
- u r(i) :
-
Slider relative speed
- W e :
-
The external dissipation rate
- φ j, c j :
-
Shear strength parameters of the joint surface
- φ r, c r :
-
Shear strength parameters of the rock bridge
- δ i :
-
The angle between the sliders at point Bi
- σ s :
-
The ground overload (kpa)
- η :
-
The angle (φr < η < 90°) between the rock bridge and the absolute speed when the rock bridge fails in tensile failure
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Acknowledgements
This study was financially supported by the National Natural Science Foundation of China (Nos. 52208369, 52309138, 52209142, 51978666), the Department of Science and Technology of Sichuan Province (2023NSFSC0284). All financial supports are greatly appreciated.
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LI Dejian: Conceptualization, Software, Validation, Writing-original draft, Writing-review & editing, Resources. FU Junwen: Conceptualization, Software, Investigation, Validation, Writing-original draft. LI Hekai: Investigation, Formal analysis, Validation, Writing-original draft. CHENG Xiao: Formal analysis, Validation, Writing-original draft. ZHAO Lianheng: Conceptualization, Resources, Writing-review & editing. ZHANG Yingbin and PENG Xinyan: Resources, Writing-review & editing.
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Li, D., Fu, J., Li, H. et al. Stability analysis of intermittently jointed rock slopes based on the stepped failure mode. J. Mt. Sci. 21, 1019–1035 (2024). https://doi.org/10.1007/s11629-023-8192-5
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DOI: https://doi.org/10.1007/s11629-023-8192-5