Limit Analysis for 3D Stability of Unsaturated Inhomogeneous Slopes Reinforced with Piles
Publication: International Journal of Geomechanics
Volume 23, Issue 4
Abstract
Achieving slope stabilization by placing anti-slide piles has become an effective slope-reinforcement technique in geotechnical engineering. Based on the limit analysis method, this study investigated the 3D stability of unsaturated inhomogeneous piled slopes, incorporating three failure patterns: toe-failure, face-failure, and base-failure. The suction and effective unit weight profile under different effective saturation were considered and the soil cohesion was assumed as varied linearly with depth. A theoretical analysis of the lateral force acting on a row of rigid anti-slide piles with the same spacing in a row through plastically deforming soils is described while considering the soil suction and inhomogeneity. In addition, a new formula was developed to calculate the lateral forces provided by a row of piles. The genetic algorithm (GA) was used to obtain the minimum value of the factor of safety FS and the corresponding critical slip surface. The results of the study were compared with those of the existing literature to verify the feasibility of the proposed approach. In addition, the influences of key parameters on FS of 3D piled slopes were investigated by parametric analysis. The numerical results indicate that piled slope stability will be underestimated when the 3D effects and suction are not considered, and soil inhomogeneity has a negative impact on piled slope stability. It was also found that the probability for the occurrence of face-failure increases with increasing inhomogeneity and decreasing suction-induced effect, and the occurrence of face-failure significantly reduces the pile reinforcement effect. In addition, when the anti-piles are located at the slope toe, the base-failure mechanism yields the critical values of FS in most cases. This study can provide several reasonable suggestions for engineering applications and a theoretical basis for further studies on the stability of slopes reinforced with piles.
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Acknowledgments
The authors would like to thank the editor and the anonymous reviewers for their valuable suggestions to improve this paper. This research was supported by the National Natural Science Foundation of China (Grant No. 41807295). The financial supports are also greatly appreciated. We would like to thank Editage (www.editage.cn) for English language editing.
Notation
The following symbols are used in this paper:
- a, d
- distances from the centerline of the conical volume to the slope crest for toe-failure and base-failure mechanism;
- b
- width of “plane insert”;
- c
- cohesion strength;
- cf
- cohesion strength of the slope face;
- distribution of apparent cohesion along the sliding surface for the 2D portion;
- distribution of apparent cohesion along the sliding surface for the 3D portion;
- D1
- center-to-center spacing between piles;
- D2
- opening between piles;
- Dp
- rate of the internal energy dissipation by the total resistance power of the anti-slide pile;
- DS
- rate of the internal energy dissipation by apparent cohesion;
- Dt
- rate of the internal energy dissipation by soil cohesion;
- e
- distances from the centerline of the conical volume to the slope base;
- GS
- specific gravity of soil;
- h
- integration limit along z′;
- hf
- distance from the slope face to the slope crest;
- ks
- saturated hydraulic conductivity;
- LX
- horizontal distance from the top to the toe of the slope;
- Nφ
- function related to φ;
- n0
- inhomogeneous coefficient;
- q
- vertical steady flow rate;
- q/ks
- influence of normalized flow rate;
- R
- radius of the conical volume;
- r
- radius of log-spiral;
- Rp
- reinforcement effect of pile;
- r′
- radius of inner log-spiral;
- r0
- initial radius of log-spiral OA;
- initial radius inner of log-spiral OA′;
- rh
- final radius of the log-spiral;
- rm
- average radius of the two log-spirals;
- rp
- initial radius of log-spiral OP;
- S
- degree of pore–water saturation;
- Se
- normalized degree of saturation;
- Sr
- residual degree of saturation;
- ua
- pore–air pressure;
- uw
- pore–water pressure;
- ua − uw
- matric suction;
- rate of external forces done by the effective soil weight of the 2D part;
- rate of external forces done by the effective soil weight of the 3D part;
- XF
- horizontal distance between the piles position and slope toe;
- z′
- depth of soil layer from the ground surface;
- z0
- vertical distance from the water table to the slope toe elevation;
- z2D
- vertical distance from a general point on the sliding surface to the water table level for the 2D part;
- z3D
- vertical distance from a general point on the sliding surface to the water table level for the 3D part;
- α
- inverse of air-entry pressure;
- β
- slope inclination angle;
- β′
- auxiliary slope inclination angle;
- γ′
- effective unit weight;
- γsat
- unit weight of saturated soil;
- γw
- unit weight of water;
- σ
- total stress;
- σ′
- effective stress;
- σs
- suction stress;
- φ
- internal friction angle;
- θ0
- initial rotational angle of the failure mechanism;
- θB
- rotational angles from horizontal line to the line passing through point B;
- θC
- rotational angles from horizontal line to the line passing through point C;
- θh
- final rotational angle of log-spiral;
- θe
- rotational angles from horizontal line to the line passing through point E; and
- θp
- rotational angles from horizontal line to the line passing through point P.
References
Anastasiou, E., K. O. Lorentz, G. J. Stein, and P. D. Mitchell. 2014. “Prehistoric schistosomiasis parasite found in the Middle East.” Lancet Infect Dis. 14 (7): 553–554. https://doi.org/10.1016/s1473-3099(14)70794-7.
Cai, F., and K. Ugai. 2000. “Numerical analysis of the stability of a slope reinforced with piles.” Soils Found. 40 (1): 73–84. https://doi.org/10.3208/sandf.40.73.
Chen, H. H., H. H. Zhu, and L. Y. Zhang. 2022a. “An analytical approach to the ultimate bearing capacity of smooth and rough strip foundations on rock mass considering three-dimensional(3D) strength.” Comput. Geotech. 149: 104865. https://doi.org/10.1016/j.compgeo.2022.104865.
Chen, H. H., H. H. Zhu, and L. Y. Zhang. 2022b. “A three-dimensional (3D) analytical solution for the ultimate side shear resistance of rock-socketed shafts.” Int. J. Rock Mech. Min. Sci. 159: 105231. https://doi.org/10.1016/j.ijrmms.2022.105231.
Chen, W. F., M. W. Giger, and H. Y. Fang. 1975. “Method to estimate lateral force acting on stabilizing piles.” Soils Found. 15 (4): 43–59. https://doi.org/10.3208/sandf1960.9.4_23.
Fang, H. W., F. Y. Chen, Z. K. Hou, G. W. Xu, and J. X. Wu. 2020. “Probabilistic analysis of a cohesion-frictional slope using the slip-line field theory in a Monte-Carlo framework.” Comput. Geotech. 120: 103398. https://doi.org/10.1016/j.compgeo.2019.103398.
Gao, Y. F., M. Ye, and F. Zhang. 2015. “Three-dimensional analysis of slopes reinforced with piles.” J. Cent. South Univ. 22 (6): 2322–2327. https://doi.org//10.1007/s11771-0152757-6.
Gao, Y. F., F. Zhang, G. H. Lei, and D. Y. Li. 2013a. “An extended limit analysis of three-dimensional slope stability.” Géotechnique 63 (6): 518–524. https://doi.org/10.1680/geot.12.T.004.
Gao, Y. F., F. Zhang, G. H. Lei, D. Y. Li, Y. X. Wu, and N. Zhang. 2013b. “Stability charts for 3D failures of homogeneous slopes.” J. Geotech. Geoenviron. Eng. 139 (9): 1528–1538. https://doi.org/10.1061/(ASCE)gt.1943-5606.0000866.
Garder, W. R. 1958. “Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table.” Soil Sci. 85 (4): 228–232. https://doi.org/10.1097/00010694-195804000-00006.
Gong, W. B., J. P. Li, and L. Li. 2017. “Limit analysis on seismic stability of anisotropic and nonhomogeneous slopes with anti-slide piles.” Sci. China Technol. Sci. 61 (1): 140–146. https://doi.org/10.1007/s11431-017-9147-8.
He, S. M., C. J. Ouyang, and Y. Luo. 2011. “Seismic stability analysis of soil nail reinforced slope using kinematic approach of limit analysis.” Environ. Earth Sci. 66 (1): 319–326. https://doi.org/10.1007/s12665-011-1241-3.
Ito, T., T. Matsui, and W. P. Hong. 1981. “Design method for stabilizing piles against landslide—One row of piles.” Soils Found. 21 (1): 21–37. https://doi.org/10.3208/sandf1972.21.21.
Li, X. P., L. J. Su, S. M. He, and J. Xu. 2016. “Limit equilibrium analysis of seismic stability of slopes reinforced with a row of piles.” Int. J. Numer. Anal. Methods Geomech. 40 (8): 1241–1250. https://doi.org/10.1002/nag.2484.
Li, Y. N., C. Liu, L. W. Wang, and S. Xu. 2022. “Stability analysis of inhomogeneous slopes in unsaturated soils optimized by a genetic algorithm.” Int J Geomech. 22 (9): 04022151. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002461.
Lu, N., and J. Godt. 2008. “Infinite slope stability under steady unsaturated seepage conditions.” Water Res. 44 (11): W11404. https://doi.org/10.1029/2008wr006976.
Lu, N., J. W. Godt, and D. T. WU. 2010. “A closed-form equation for effective stress in unsaturated soil.” Water Resour. Res. 45 (5): W05515.
Lu, N., and W. J. Likos. 2006. “Suction stress characteristic curve for unsaturated soil.” J. Geotech. Geoenviron. Eng. 132 (2): 131–142. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(131).
Michalowski, R. L. 1995. “Slope stability analysis: A kinematical approach.” Géotechnique 45 (8): 283–293. https://doi.org/10.1680/geot.1995.45.2.283.
Michalowski, R. L., and A. Drescher. 2009. “Three-dimensional stability of slopes and excavations.” Géotechnique 59 (10): 839–850. https://doi.org/10.1680/geot.8.P.136.
Nian, T. K., G. Q. Chen, M. T. Luan, Q. Yang, and D. F. Zheng. 2008. “Limit analysis of the stability of slopes reinforced with piles against landslide in nonhomogeneous and anisotropic soils.” Can. Geotech. J. 45 (8): 1092–1103. https://doi.org/10.1139/T08-042.
Nian, T. K., J. C. Jiang, F. W. Wang, Q. Yang, and M. T. Luan. 2016. “Seismic stability analysis of slope reinforced with a row of piles.” Soil Dyn. Earthquake Eng. 84: 83–93. https://doi.org/10.1016/j.soildyn.2016.01.023.
Pan, Q., J. S. Xu, and D. Dias. 2017. “Three-dimensional stability of a slope subjected to seepage forces.” Int. J. Geomech. 17 (8): 04017035. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000913.
Rao, P., L. X. Zhao, Q. S. Chen, and L. Li. 2017. “Limit analysis approach for accessing stability of three-dimensional (3-D) slopes reinforced with piles.” Mar. Georesour. Geotechnol. 35 (7): 978–985. https://doi.org/10.1080/1064119X.2016.1273982.
Rao, P., L. X. Zhao, Q. S. Chen, and S. Nimbalkar. 2019. “Three-dimensional limit analysis of slopes reinforced with piles in soils exhibiting heterogeneity and anisotropy in cohesion.” Soil Dyn. Earthquake Eng. 121: 194–199. https://doi.org/10.1016/j.soildyn.2019.02.030.
Ray, R. L., J. M. Jacobs, and P. de Alba. 2010. “Impacts of unsaturated zone soil moisture and groundwater table on slope instability.” J. Geotech. Geoenviron. Eng. 136 (10): 1448–1458. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000357.
Sun, D. A., L. Wang, and L. Li. 2019. “Stability of unsaturated soil slopes with cracks under steady-infiltration conditions.” Int. J. Geomech. 19 (6): 04019044. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001398.
Van Genuchten, M. T. 1980. “A closed-form equation predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Wang, L., D. A. Sun, Y. P. Yao, and Y. Z. Tan. 2019. “Seismic stability of 3D piled unsaturated earth slopes using kinematic limit analysis.” Soil Dyn. Earthquake Eng. 126: 105821. https://doi.org/10.1016/j.soildyn.2019.105821.
Wang, L., D. A. Sun, Y. Yao, L. Wu, and Y. Xu. 2020. “Kinematic limit analysis of three-dimensional unsaturated soil slopes reinforced with a row of piles.” Comput. Geotech. 120: 103428. https://doi.org/10.1016/j.compgeo.2019.103428.
Wei, W. B., and Y. M. Cheng. 2009. “Strength reduction analysis for slope reinforced with one row of piles.” Comput. Geotech. 36 (7): 1176–1185. https://doi.org/10.1007/s12517-014-1272-7.
Won, J., K. H. You, S. Jeong, and S. Kim. 2005. “Coupled effects in stability analysis of pile–slope systems.” Comput. Geotech. 32 (4): 304–315. https://doi.org/10.1016/j.compgeo.2005.02.006.
Yang, M. H., and B. Deng. 2019. “Stability study of slope reinforced with piles under steady unsaturated flow conditions.” Comput. Geotech. 109: 89–98. https://doi.org/10.1016/j.compgeo.2019.01.020.
Yang, X. L., and Z. W. Li. 2018. “Comparison of factors of safety using a 3D failure mechanism with kinematic approach.” Int. J. Geomech. 18 (9), https://doi.org/10.1061/(ASCE)GM.1943-5622.0001235.
Yang, X. L., and J. S. Xu. 2017. “Three-dimensional stability of two-stage slope in inhomogeneous soils.” Can. Geotech. J. 17 (7): 06014045. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000867.
Yang, X. L., and S. Zhang. 2020. “Stability analysis of 3D cracked slope reinforced with piles.” Comput. Geotech. 122: 103544. https://doi.org/10.1016/j.compgeo.2020.103544.
Zhang, F., Y. F. Gao, Y. X. Wu, N. Zhang, and Y. Qiu. 2016. “Effects of vertical seismic acceleration on 3D slope stability.” Earthquake Eng. Eng. Vibr. 15 (3): 487–494. https://doi.org/10.1007/s11803-016-0338-9.
Zheng, L., L. Li, and J. P. Li. 2020. “Development of three-dimensional failure mechanisms and genetic algorithm for limit analysis of two-layer slopes.” Nat. Hazard. 103 (3): 3181–3212. https://doi.org/10.1007/s11069-020-04126-1.
Zhou, X. P., and H. Cheng. 2013. “Analysis of stability of three-dimensional slopes using the rigorous limit equilibrium method.” Eng. Geol. 160: 21–33. https://doi.org/10.1016/j.enggeo.2013.03.027.
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© 2023 American Society of Civil Engineers.
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Received: Mar 8, 2022
Accepted: Nov 23, 2022
Published online: Jan 27, 2023
Published in print: Apr 1, 2023
Discussion open until: Jun 27, 2023
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