Upper Limit Analysis for the Ultimate Bearing Capacity of a Multilayer Slope with Horizontal Stratification
Publication: International Journal of Geomechanics
Volume 23, Issue 6
Abstract
The ultimate bearing capacity is one of the most important mechanical parameters in the mining and geotechnical fields and has a vital influence on the stability of slopes and the safety of constructions and structures. The determination of the ultimate bearing capacity has become a controversial issue in slope engineering. This study proposes a way to obtain the ultimate bearing capacity of a multilayer slope with horizontal stratification. According to limit analysis theory, three typical multiblock sliding failure modes for a multilayer slope with horizontal stratification are established. The upper limit solution of the ultimate bearing capacity of a multilayer slope, considering the influence of horizontal stratification, is derived. The optimization procedure is carried out to obtain the optimal value of the ultimate bearing capacity by using the sequential quadratic programming algorithm. The accuracy of the present method is proven based on a comparison of calculation results using other analytical methods and the numerical simulation method. The influence analysis of the parameters, involving the slope angle, soil strength, and distance of the foundation from the slope shoulder, is performed. The results indicate that the error between the calculated results of the present method and those of numerical simulation, as well as the error between the calculated results of the present method and those of other existing methods, is less than 10%. The ultimate bearing capacity linearly decreases with increasing slope angle, while it linearly increases with increasing distance of the foundation from the slope shoulder. The analytical method provides a method to analyze the ultimate bearing capacity of a multilayer slope, which effectively solves the problem of heterogeneity of soil layers observed in the natural slope. The results from this study can be used as a guide to estimate the stability of the slope and design of the foundation on a slope considering the load action near the slope.
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Acknowledgments
The authors gratefully acknowledge the support provided by the Special Fundamental Research Project of Hebei Natural Science Foundation (No. E2020402087), the Open Subject of the State Key Laboratory of Geotechnical Mechanics and Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (No. Z018022 and No. SKLGME021013), and the Funded by Science and Technology Project of Hebei Education Department (No. BJ2019023 and QN2021030).
Notation
The following symbols are used in this paper:
- Bi
- intersections of the ith stratum interface and slope surface;
- b
- foundation width;
- ci
- cohesion of the ith soil layer;
- D
- rate of internal energy dissipation;
- Dbase
- rate of internal energy dissipation for a base-failure mode;
- Dface
- rate of internal energy dissipation for a face-failure mode;
- Dtoe
- rate of internal energy dissipation for a toe-failure mode;
- hi
- thickness of the ith soil layer;
- L
- distance of the foundation from the slope shoulder;
- Li
- length of the velocity discontinuity line A2i−1Bi−1;
- l2i
- length of the velocity discontinuity line A2i−1A2i;
- l2i−1
- length of the velocity discontinuity line A2i−2A2i−1;
- n
- number of soil layers;
- Qu
- bearing capacity of the slope;
- bearing capacity for a base-failure mode;
- bearing capacity for a toe-failure mode;
- bearing capacity for a face-failure mode;
- S2i−1, S2i
- area of a block;
- Vi
- volume of the ith sliding blocks;
- v0
- velocity vector;
- W
- rate of work of external forces;
- Wbase
- rate of work of external forces for a base-failure mode;
- Wface
- rate of work of external forces for a face-failure mode;
- WG
- rate of weight work of soil;
- rate of bearing capacity work;
- Wtoe
- rate of work of external forces for a toe-failure mode;
- αi
- angle between the velocity discontinuity line A2i−2A2i−1 and the horizontal line;
- αi(i+1)
- angle between the velocity discontinuity line A2i−1A2i and the horizontal line;
- β
- slope angle;
- assumed field of the admissible deformation rate;
- γi
- unit weight of the ith soil layer;
- ηi
- angle between the velocity discontinuity line A2i−1Bi−1 and the slope surface;
- stress component; and
- φi
- internal friction angle of the ith soil layer.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 6 • June 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jun 19, 2022
Accepted: Dec 12, 2022
Published online: Apr 4, 2023
Published in print: Jun 1, 2023
Discussion open until: Sep 4, 2023
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