Abstract
The NMM (numerical manifold method) has shown its ability to solve continuum and discontinuum engineering problems in the same framework. In the present paper, the vector sum NMM (VSNMM) is proposed to investigate the stability of slopes. With the (vector sum numerical manifold method) VSNMM, the FOSs (factors of safety) of slopes are obtained using the real stress fields of the slopes. Compared with the limit equilibrium methods, the deformation and stress field of a slope can be obtained using the VSNMM. Besides, the computational cost of the VSNMM is much less than that of the strength reduction numerical manifold method (SRNMM), since only one elasto-plastic analysis is needed in the VSNMM, while a series of elasto-plastic analyses is needed in the SRNMM. Based on the VSNMM, the stability analyses of two slopes including a homogeneous slope and an inhomogeneous slope with three different materials are conducted. The numerical results based on the two slopes show that the VSNMM can accurately calculate the FOSs of the slopes.
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References
Chen Z (2003) Earth slope stability analysis-theory, method and programs. China Water Power Press, Beijing
Chen L, Yang YT, Zheng H (2018) Numerical study of soil-rock mixture: generation of random aggregate structure. Science China Technol Sci 61:359–369
Chen T, Yang YT, Zheng H, Wu ZJ (2019) Numerical determination of the effective permeability coefficient of soil-rock mixtures using the numerical manifold method. Int J Numer Anal Methods Geomech 43(1):381–414
Deng Q, Guo M, Li C, Ge X (2010) Vector sum method for slope stability analysis based on boundary element method. Rock and Soi1 Mechanics 31(6):1971–1976
Fredlund DG, Scoular REG (1999) Using limit equilibrium concepts in finite element slope stability analysis[C]//Int. Symp. on Slope Stability Engineering, Matsuyama, pp 31–47
Ge XR (2010) A new method for anti-sliding stability analysis — basic principle of vector sum analysis method and its application[C] Proceedings of the 11th National Rock Mechanics and Engineering Conference. Wuhan: Hubei Science and Technology Press: 26–44
Griffiths DV, Lane P (1999) A slope stability analysis by finite elements. Géotechnique 49(3):387–403
Guo MW, Ge XR, Wang SL (2011) Slope stability analysis under seismic load by vector sum analysis method. J Rock Mech Geotech Eng 3(3):282–288
Lee NS, Bathe KJ (1993) Effects of element distortions on the performance of isoparametric elements. Int J Numer Methods Eng 36(20):3553–3576
Luo N, Bathurst RJ (2018) Probabilistic analysis of reinforced slopes using RFEM and considering spatial variability of frictional soil properties due to compaction. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 12(2):87–108
Matsui T, San KC (1992) Finite element slope stability analysis by shear strength reduction technique. Soils Foundations 32(1):59–70
Mohammadnejad T, Khoei AR (2013) An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model. Finite Elem Anal Des 73:77–95
Morgenstern NR, Price VE (1965) The analysis of the stability of general slip surface. Géotechnique 15(1):79–93
Owen DRJ, Hinton E (1980) Finite elements in plasticity: theory and practice. Pineridge Press, Swansea
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H (2010) A simple and robust three-dimensional cracking-particle method without enrichment. Comput Methods Appl Mech Eng 199:2437–2455
Shi GH (1991) Manifold method of material analysis. In: Proceedings of the Transactions of the Ninth Army Conference on Applied Mathematics and Computing: 57–76
Sun GH, Yang YT, Cheng SG, Zheng H (2017) Phreatic line calculation and stability analysis of slopes under the combined effect of reservoir water level fluctuations and rainfall. Can Geotech J 54(5):631–645
Wu Z, Wong LNY (2012) Frictional crack initiation and propagation analysis using the numerical manifold method. Comput Geotech 39(1):38–53
Wu W, Yang Y, Zheng H (2020) Enriched mixed numerical manifold formulation with continuous nodal gradients for dynamics of fractured poroelasticity. Appl Math Model 86:225–258
Xu D, Wu A, Yang Y, Lu B, Liu F, Zheng H (2020) A new contact potential based three-dimensional discontinuous deformation analysis method. Int J Rock Mech Min Sci 127:104206
Yang Y, Chen T, Zheng H (2020a) Mathematical cover refinement of the numerical manifold method for the stability analysis of a soil-rock-mixture slope. Eng Anal Bound Elem 116:64–76
Yang Y, Guo H, Xiaodong F, Zheng H (2018a) Boundary settings for the seismic dynamic response analysis of rock masses using the numerical manifold method. Int J Numer Anal Methods Geomech 42(9):1095–1122
Yang Y, Sun G, Zheng H (2019b) Modeling unconfined seepage flow in soil-rock mixtures using the numerical manifold method. Eng Anal Bound Elem 108:60–70
Yang Y, Sun G, Zheng H (2019b) Stability analysis of soil-rock-mixture slopes using the numerical manifold method. Eng Anal Bound Elem 109:153–160
Yang Y, Sun G, Zheng H (2020b) A high-order numerical manifold method with continuous stress/strain field. Appl Math Model 78:576–600
Yang Y, Sun Y, Sun G, Zheng H (2019d) Sequential excavation analysis of soil-rock-mixture slopes using an improved numerical manifold method with multiple layers of mathematical cover systems. Eng Geol 261:105278
Yang Y, Sun G, Zheng H, Yan C (2020c) An improved numerical manifold method with multiple layers of mathematical cover systems for the stability analysis of soil-rock-mixture slopes. Eng Geol 264:105373
Yang Y, Wu W, Zheng H, Liu X (2020d) A high-order three dimensional numerical manifold method with continuous stress/strain field. Eng Anal Bound Elem 117:309–320
Yang Y, Xu D, Zheng H (2018c) Explicit discontinuous deformation analysis method with lumped mass matrix for highly discrete block system. Int J Geomech 18(9):04018098
Yang Y, Zheng H (2016) A three-node triangular element fitted to numerical manifold method with continuous nodal stress for crack analysis. Eng Fract Mech 162:51–75
Yang Y, Zheng H (2017) Direct approach to treatment of contact in numerical manifold method. Int J Geomech 17(5):E4016012
Yang Y, Zheng H, Sivaselvan MV (2017) A rigorous and unified mass lumping scheme for higher-order elements. Comput Methods Appl Mech Eng 319:491–514
Yang YT, Tang XH, Zheng H, Liu QS, He L (2016) Three-dimensional fracture propagation with numerical manifold method. Engineering Analysis with Boundary Elements 72:65–77
Yang YT, Tang XH, Zheng H, Liu QS, Liu ZJ (2018b) Hydraulic fracturing modeling using the enriched numerical manifold method. Appl Math Model 53:462–486
Yang YT, Sun GH, Zheng H (2019a) Investigation of the sequential excavation of a soil-rock-mixture slope using the numerical manifold method. Eng Geol 256:93–109
Zheng H, Yang Y (2017) On generation of lumped mass matrices in partition of unity based methods. Int J Numer Methods Eng 112(8):1040–1069
Zheng H, Xu DD (2014) New strategies for some issues of numerical manifold method in simulation of crack propagation. Int J Numer Methods Eng 97(13):986–1010
Zheng H, Li CG, Lee CF, Ge X (2002) Finite element method for solving the factor of safety. Chinese Journal of Geotechnical Engineering 24(5):626–628
Zheng H, Liu DF, Li CG (2005) Slope stability analysis based on elasto-plastic finite element method. Int J Numer Methods Eng 64(14):1871–1888
Zhuang X, Augarde CE, Mathisen KM (2012) Fracture modeling using meshless methods and level sets in 3D: framework and modeling. Int J Numer Methods Eng 92:969–998
Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Butterworth-Heinemann, Oxford
Funding
This study is supported by the Youth Innovation Promotion Association CAS, under the grant no. 2020327; and the National Natural Science Foundation of China, under the grant nos. 51609240, 11172313, and 51538001.
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Yang, Y., Wu, W. & Zheng, H. Stability analysis of slopes using the vector sum numerical manifold method. Bull Eng Geol Environ 80, 345–352 (2021). https://doi.org/10.1007/s10064-020-01903-x
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DOI: https://doi.org/10.1007/s10064-020-01903-x