Slope failures in hilly terrain impact the social and economic balance of the community. The major reasons for these slope failures are steeper slopes, climate factors, seismic activity, nearby excavations, and construction. Natural slopes show significant heterogeneity due to the inherent randomness in material properties and geometric nonlinearities. Effective slope stability analysis solutions can be achieved by incorporating probabilistic approaches. We present a comprehensive method to develop and analyze a heterogeneous two-dimensional slope model, utilizing a non-linear-spatial-probabilistic-finite element method under a plane strain condition. The developed slope model encompasses geometrical and material nonlinearity with a uniform random distribution over the space. Also, the present slope model integrates the Mohr-Coulomb's constitutive model for elastoplastic analysis to capture more realistic and complex behavior. A benchmark soil slope problem was modeled using the spatial probabilistic finite element method, comprising all six material properties with uniform spatial uncertainties. These material properties are elastic modulus, unit weight, cohesion, friction angle, and dilation angle. During the numerical simulation, the detailed deformations, stress patterns, strain patterns, potential pre-failure zone, and failure characteristics of heterogeneous slopes were achieved under self-weight and step loading sequences. Nodal failure and probability of nodal failure were introduced as two novel quantitative parameters for more insights into failure investigations. The testbench slope model was subjected to self-weight load and external 100-step loading sequences with a loading increment of -0.1 kN/m. The percentage probability of nodal failure was obtained at 40.46% considering uniformly distributed material uncertainties with a 10% coefficient of variation. The developed testbench slope model was also simulated for different values of the coefficient of variation (ranging from 0% to 50%) and comparatively investigated. The detailed deformation patterns, thorough profiles of stresses-strains, failure zones, and failure characteristics provided valuable insights into geotechnical engineering practices.
Citation: Peeyush Garg, Pradeep Kumar Gautam, Amit Kumar Verma, Gnananandh Budi. Deformation and failure analysis of heterogeneous slope using nonlinear spatial probabilistic finite element method[J]. AIMS Mathematics, 2024, 9(10): 26339-26370. doi: 10.3934/math.20241283
Slope failures in hilly terrain impact the social and economic balance of the community. The major reasons for these slope failures are steeper slopes, climate factors, seismic activity, nearby excavations, and construction. Natural slopes show significant heterogeneity due to the inherent randomness in material properties and geometric nonlinearities. Effective slope stability analysis solutions can be achieved by incorporating probabilistic approaches. We present a comprehensive method to develop and analyze a heterogeneous two-dimensional slope model, utilizing a non-linear-spatial-probabilistic-finite element method under a plane strain condition. The developed slope model encompasses geometrical and material nonlinearity with a uniform random distribution over the space. Also, the present slope model integrates the Mohr-Coulomb's constitutive model for elastoplastic analysis to capture more realistic and complex behavior. A benchmark soil slope problem was modeled using the spatial probabilistic finite element method, comprising all six material properties with uniform spatial uncertainties. These material properties are elastic modulus, unit weight, cohesion, friction angle, and dilation angle. During the numerical simulation, the detailed deformations, stress patterns, strain patterns, potential pre-failure zone, and failure characteristics of heterogeneous slopes were achieved under self-weight and step loading sequences. Nodal failure and probability of nodal failure were introduced as two novel quantitative parameters for more insights into failure investigations. The testbench slope model was subjected to self-weight load and external 100-step loading sequences with a loading increment of -0.1 kN/m. The percentage probability of nodal failure was obtained at 40.46% considering uniformly distributed material uncertainties with a 10% coefficient of variation. The developed testbench slope model was also simulated for different values of the coefficient of variation (ranging from 0% to 50%) and comparatively investigated. The detailed deformation patterns, thorough profiles of stresses-strains, failure zones, and failure characteristics provided valuable insights into geotechnical engineering practices.
| [1] |
A. K. Turner, Social and environmental impacts of landslides, Innov. Infrastruct. Solut., 3 (2018), 70. https://doi.org/10.1007/s41062-018-0175-y doi: 10.1007/s41062-018-0175-y
|
| [2] |
P. Lacroix, A. L. Handwerger, G. Bièvre, Life and death of slow-moving landslides, Nat. Rev. Earth Environ., 1 (2020), 404–419. https://doi.org/10.1038/s43017-020-0072-8 doi: 10.1038/s43017-020-0072-8
|
| [3] | S. T. McColl, Landslide causes and triggers, In: Landslide hazards, risks, and disasters, 2 Eds., Amsterdam: Elsevier, 2022, 13–41. https://doi.org/10.1016/B978-0-12-818464-6.00011-1 |
| [4] |
R. Paranunzio, M. Chiarle, F. Laio, G.. Nigrelli, L. Turconi, F. Luino, New insights in the relation between climate and slope failures at high-elevation sites, Theor. Appl. Climatol., 137 (2019), 1765–1784. https://doi.org/10.1007/s00704-018-2673-4 doi: 10.1007/s00704-018-2673-4
|
| [5] |
J. F. Shroder, L. Cvercková, K. L. Mulhern, Slope-failure analysis and classification: Review of a century of effort, Phys. Geogr., 26 (2005), 216–247. https://doi.org/10.2747/0272-3646.26.3.216 doi: 10.2747/0272-3646.26.3.216
|
| [6] |
M. J. Froude, D. N. Petley, Global fatal landslide occurrence from 2004 to 2016, Nat. Hazards Earth Syst. Sci., 18 (2018), 2161–2181. https://doi.org/10.5194/nhess-18-2161-2018 doi: 10.5194/nhess-18-2161-2018
|
| [7] | A. Braathen, L. H. Blikra, S. S. Berg, F. Karlsen, Rock-slope failures in Norway; type, geometry, deformation mechanisms and stability, Norw. J. Geol., 84 (2004), 67–88. |
| [8] |
J. M. Duncan, State of the art: limit equilibrium and finite-element analysis of slopes, Journal of Geotechnical Engineering, 122 (1996), 577–596. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:7(577) doi: 10.1061/(ASCE)0733-9410(1996)122:7(577)
|
| [9] | Y. H. Huang, Slope stability analysis by the limit equilibrium method: Fundamentals and methods, Reston: ASCE Press, 2013. https://doi.org/10.1061/9780784412886 |
| [10] | W. F. Chen, Limit analysis and soil plasticity, Burlington: Elsevier, 2013. |
| [11] |
B. Leshchinsky, S. Ambauen, Limit equilibrium and limit analysis: comparison of benchmark slope stability problems, J. Geotech. Geoenviron., 141 (2015), 04015043. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001347 doi: 10.1061/(ASCE)GT.1943-5606.0001347
|
| [12] | A. Burman, S. P. Acharya, R. Sahay, D. Maity, A comparative study of slope stability analysis using traditional limit equilibrium method and finite element method, Asian Journal of Civil Engineering, 16 (2015), 467–492. |
| [13] |
R. K. H. Ching, D. G. Fredlund, Some difficulties associated with the limit equilibrium method of slices, Can. Geotech. J., 20 (1983), 661–672. https://doi.org/10.1139/t83-074 doi: 10.1139/t83-074
|
| [14] |
S. Ullah, M. U. Khan, G. Rehman, A brief review of the slope stability analysis methods, Geological Behavior, 4 (2020), 73–77. https://doi.org/10.26480/gbr.02.2020.73.77 doi: 10.26480/gbr.02.2020.73.77
|
| [15] |
Y. N. Zheng, L. F. Zheng, H. Y. Zhan, Q. F. Huang, C. J. Jia, Z. Li, Study on failure mechanism of soil–rock slope with FDM-DEM method, Sustainability, 14 (2022), 17015. https://doi.org/10.3390/su142417015 doi: 10.3390/su142417015
|
| [16] |
Z. Y. Yin, J. C. Teng, H. L. Wang, Y. F. Jin, A MATLAB-based educational platform for analysis of slope stability, Comput. Appl. Eng. Educ., 30 (2022), 575–588. https://doi.org/10.1002/cae.22474 doi: 10.1002/cae.22474
|
| [17] | G. R. Lindfield, J. E. T. Penny, Numerical methods: using MATLAB, 3 Eds., New York: Academic Press, 2012. https://doi.org/10.1016/C2010-0-67189-6 |
| [18] | L. Y. Zhang, W. M. Shi, Y. R. Zheng, The slope stability analysis by FEM under the plane strain condition, Chinese Journal of Geotechnical Engineering, 24 (2002), 487–490. |
| [19] | F. Darve, F. Laouafa, Plane strain instabilities in soil: application to slopes stability, In: Numerical models in geomechanics, Boca Raton: CRC Press, 2020, 85–90. https://doi.org/10.1201/9781003078548-16 |
| [20] | E. M. Dawson, W. H. Roth, Slope stability analysis with FLAC, In: FLAC and numerical modeling in geomechanics, Boca Raton: CRC Press, 2020, 3–9. https://doi.org/10.1201/9781003078531-2 |
| [21] |
Y. L. Tan, J. J. Cao, W. X. Xiang, W. Z. Xu, J. W. Tian, Y. Gou, Slope stability analysis of saturated–unsaturated based on the GEO-studio: a case study of Xinchang slope in Lanping County, Yunnan Province, China, Environ. Earth Sci., 82 (2023), 322. https://doi.org/10.1007/s12665-023-11006-x doi: 10.1007/s12665-023-11006-x
|
| [22] |
A. Torok, A. Barsi, G. Bogoly, T. Lovas, Á. Somogyi, P. Görög, Slope stability and rockfall assessment of volcanic tuffs using RPAS with 2-D FEM slope modelling, Nat. Hazards Earth Syst. Sci., 18 (2018), 583–597. https://doi.org/10.5194/nhess-18-583-2018 doi: 10.5194/nhess-18-583-2018
|
| [23] |
R. Singh, R. K. Umrao, T. N. Singh, Hill slope stability analysis using two and three dimensions analysis: A comparative study, J. Geol. Soc. India, 89 (2017), 295–302. https://doi.org/10.1007/s12594-017-0602-2 doi: 10.1007/s12594-017-0602-2
|
| [24] |
D. V. Griffiths, G. A. Fenton, Probabilistic slope stability analysis by finite elements, J. Geotech. Geoenviron., 130 (2004), 507–518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507) doi: 10.1061/(ASCE)1090-0241(2004)130:5(507)
|
| [25] |
J. M. Duncan, Factors of safety and reliability in geotechnical engineering, J. Geotech. Geoenviron., 126 (2000), 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307) doi: 10.1061/(ASCE)1090-0241(2000)126:4(307)
|
| [26] | K. Farah, M. Ltifi, T. Abichou, H. Hassis, Comparison of different probabilistic methods for analyzing slope stability, Int. J. Civ. Eng., 12 (2014), 264–268. |
| [27] |
V. Renaud, M. A. Heib, Probabilistic slope stability analysis: A novel distribution for soils exhibiting highly variable spatial properties, Probabilist. Eng. Mech., 76 (2024), 103586. https://doi.org/10.1016/j.probengmech.2024.103586 doi: 10.1016/j.probengmech.2024.103586
|
| [28] |
M. Matsuo, K. Kuroda, Probabilistic approach to design of embankments, Soils Found., 14 (1974), 1–17. https://doi.org/10.3208/sandf1972.14.2_1 doi: 10.3208/sandf1972.14.2_1
|
| [29] | A. Alfredo, H. Wilson, Probability concepts in engineering planning and design, New York: John Wiley & Sons, 1975. |
| [30] |
E. E. Alonso, Risk analysis of slopes and its application to slopes in Canadian sensitive clays, Geotechnique, 26 (1976), 453–472. https://doi.org/10.1680/geot.1976.26.3.453 doi: 10.1680/geot.1976.26.3.453
|
| [31] |
E. H. Vanmarcke, Reliability of earth slopes, Journal of the Geotechnical Engineering Division, 103 (1977), 1247–1265. https://doi.org/10.1061/AJGEB6.00005 doi: 10.1061/AJGEB6.00005
|
| [32] |
O. Ditlevsen, P. Bjerager, Methods of structural systems reliability, Struct. Saf., 3 (1986), 195–229. https://doi.org/10.1016/0167-4730(86)90004-4 doi: 10.1016/0167-4730(86)90004-4
|
| [33] |
H. El-Ramly, N. R. Morgenstern, D. M. Cruden, Probabilistic slope stability analysis for practice, Can. Geotech. J., 39 (2002), 665–683. https://doi.org/10.1139/t02-034 doi: 10.1139/t02-034
|
| [34] | O. D. Ditlevsen, H. O. Madsen, Structural reliability methods, Chichester: John Wiley & Sons, 1996. |
| [35] |
I. E. Zevgolis, A. V. Deliveris, N. C. Koukouzas, Probabilistic design optimization and simplified geotechnical risk analysis for large open pit excavations, Comput. Geotech., 103 (2018), 153–164. https://doi.org/10.1016/j.compgeo.2018.07.024 doi: 10.1016/j.compgeo.2018.07.024
|
| [36] |
C. Obregon, H. Mitri, Probabilistic approach for open pit bench slope stability analysis–A mine case study, Int. J. Min. Sci. Techno., 29 (2019), 629–640. https://doi.org/10.1016/j.ijmst.2019.06.017 doi: 10.1016/j.ijmst.2019.06.017
|
| [37] |
V. Merrien-Soukatchoff, T. Korini, A. Thoraval, Use of an integrated discrete fracture network code for stochastic stability analyses of fractured rock masses, Rock Mech. Rock Eng., 45 (2012), 159–181. https://doi.org/10.1007/s00603-011-0136-7 doi: 10.1007/s00603-011-0136-7
|
| [38] |
L. J. Wu, H. X. Zhang, X. H. Yang, F. R. Wang, A second-order finite difference method for the multi-term fourth-order integral–differential equations on graded meshes, Comp. Appl. Math., 41 (2022), 313. https://doi.org/10.1007/s40314-022-02026-7 doi: 10.1007/s40314-022-02026-7
|
| [39] |
X. H. Yang, Z. M. Zhang, Analysis of a new NFV scheme preserving DMP for two-dimensional sub-diffusion equation on distorted meshes, J. Sci. Comput., 99 (2024), 80. https://doi.org/10.1007/s10915-024-02511-7 doi: 10.1007/s10915-024-02511-7
|
| [40] |
W. Wang, H. X. Zhang, Z. Y. Zhou, X. H. Yang, A fast compact finite difference scheme for the fourth-order diffusion-wave equation, Int. J. Comput. Math., 101 (2024), 170–193. https://doi.org/10.1080/00207160.2024.2323985 doi: 10.1080/00207160.2024.2323985
|
| [41] |
X. H. Yang, W. L. Qiu, H. X. Zhang, L. Tang, An efficient alternating direction implicit finite difference scheme for the three-dimensional time-fractional telegraph equation, Comput. Math. Appl., 102 (2021), 233–247. https://doi.org/10.1016/j.camwa.2021.10.021 doi: 10.1016/j.camwa.2021.10.021
|
| [42] |
M. L. Napoli, M. Barbero, E. Ravera, C. Scavia, A stochastic approach to slope stability analysis in bimrocks, Int. J. Rock Mech. Min., 101 (2018), 41–49. https://doi.org/10.1016/j.ijrmms.2017.11.009 doi: 10.1016/j.ijrmms.2017.11.009
|
| [43] | I. Molchanov, Foundations of stochastic geometry and theory of random sets, In: Stochastic geometry, spatial statistics and random fields, Berlin: Springer, 2012, 1–20. https://doi.org/10.1007/978-3-642-33305-7_1 |
| [44] |
D. V. Griffiths, J. S. Huang, G. A. Fenton, Influence of spatial variability on slope reliability using 2-D random fields, J. Geotech. Geoenvirong., 135 (2009), 1367–1378. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099 doi: 10.1061/(ASCE)GT.1943-5606.0000099
|
| [45] |
A. M. Afrapoli, M. Osanloo, Determination and stability analysis of ultimate open-pit slope under geomechanical uncertainty, Int. J. Min. Sci. Techno., 24 (2014), 105–110. https://doi.org/10.1016/j.ijmst.2013.12.018 doi: 10.1016/j.ijmst.2013.12.018
|
| [46] |
H. Shen, S. M. Abbas, Rock slope reliability analysis based on distinct element method and random set theory, Int. J. Rock Mech. Min., 61 (2013), 15–22. https://doi.org/10.1016/j.ijrmms.2013.02.003 doi: 10.1016/j.ijrmms.2013.02.003
|
| [47] | R. G. Ghanem, P. D. Spanos, Stochastic finite elements: A spectral approach, New York: Dover Publications, 2003. https://doi.org/10.1007/978-1-4612-3094-6 |
| [48] |
X. Li, Q. L. Liao, J. M. He, In-situ tests and a stochastic structural model of rock and soil aggregate in the Three Gorges Reservoir area, China, Int. J. Rock Mech. Min., 41 (2004), 702–707. https://doi.org/10.1016/j.ijrmms.2004.03.122 doi: 10.1016/j.ijrmms.2004.03.122
|
| [49] |
B. Pandit, G. Tiwari, G. M. Latha, G. L. S. Babu, Stability analysis of a large gold mine open-pit slope using advanced probabilistic method, Rock Mech. Rock Eng., 51 (2018), 2153–2174. https://doi.org/10.1007/s00603-018-1465-6 doi: 10.1007/s00603-018-1465-6
|
| [50] | S. Sharma, I. Roy, Slope failure of waste rock dump at Jayant opencast mine, India: A case study, International Journal of Applied Engineering Research, 10 (2015), 33006–33012. |
| [51] | M. R. Bishwal, P. Sen, M. Jawed, Characterization of shear strength properties of spoil dump based on their constituent material, International Journal of Applied Engineering Research, 12 (2017), 8590–8594. |
| [52] |
C. Oggeri, R. Vinai, Characterisation of geomaterials and non-conventional waste streams for their reuse as engineered materials, E3S Web of Conferences, 2020, 06002. https://doi.org/10.1051/e3sconf/202019506002 doi: 10.1051/e3sconf/202019506002
|
| [53] |
I. E. Zevgolis, Geotechnical characterization of mining rock waste dumps in central Evia, Greece, Environ. Earth Sci., 77 (2018), 566. https://doi.org/10.1007/s12665-018-7743-5 doi: 10.1007/s12665-018-7743-5
|
| [54] |
I. E. Zevgolis, A. I. Theocharis, A. V. Deliveris, N. C. Koukouzas, C. Roumpos, A. M. Marshall, Geotechnical characterization of fine-grained spoil material from surface coal mines, J. Geotech. Geoenviron., 147 (2021), 04021050. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002550 doi: 10.1061/(ASCE)GT.1943-5606.0002550
|
| [55] |
K. Arai, K. Tagyo, Determination of noncircular slip surface giving the minimum factor of safety in slope stability analysis, Soils Found., 25 (1985), 43–51. https://doi.org/10.3208/sandf1972.25.43 doi: 10.3208/sandf1972.25.43
|
| [56] |
S. H. Li, L. Z. Wu, An improved salp swarm algorithm for locating critical slip surface of slopes, Arab. J. Geosci., 14 (2021), 359. https://doi.org/10.1007/s12517-021-06687-2 doi: 10.1007/s12517-021-06687-2
|
| [57] |
J. Singh, A. K. Verma, H. Banka, R. Kumar, A. Jaiswal, Optics-based metaheuristic approach to assess critical failure surfaces in both circular and non-circular failure modes for slope stability analysis, Rock Mechanics Bulletin, 3 (2024), 100084. https://doi.org/10.1016/j.rockmb.2023.100084 doi: 10.1016/j.rockmb.2023.100084
|
| [58] |
A. R. Kashani, R. Chiong, S. Mirjalili, A. H. Gandomi, Particle swarm optimization variants for solving geotechnical problems: review and comparative analysis, Arch. Computat. Methods Eng., 28 (2021), 1871–1927. https://doi.org/10.1007/s11831-020-09442-0 doi: 10.1007/s11831-020-09442-0
|
| [59] |
J. Singh, H. Banka, A. K. Verma, Locating critical failure surface using meta-heuristic approaches: A comparative assessment, Arab. J. Geosci., 12 (2019), 307. https://doi.org/10.1007/s12517-019-4435-8 doi: 10.1007/s12517-019-4435-8
|
| [60] |
Z. Y. Xiao, B. Tian, X. C. Lu, Locating the critical slip surface in a slope stability analysis by enhanced fireworks algorithm, Cluster Comput., 22 (2019), 719–729. https://doi.org/10.1007/s10586-017-1196-6 doi: 10.1007/s10586-017-1196-6
|
| [61] |
N. Himanshu, A. Burman, V. Kumar, Assessment of optimum location of non-circular failure surface in soil slope using unified particle swarm optimization, Geotech. Geol. Eng., 38 (2020), 2061–2083. https://doi.org/10.1007/s10706-019-01148-w doi: 10.1007/s10706-019-01148-w
|
| [62] | O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu, The finite element method: its basis and fundamentals, Oxford: Butterworth-Heinemann, 2013. https://doi.org/10.1016/C2009-0-24909-9 |
| [63] | K. H. Huebner, D. L. Dewhirst, D. E. Smith, T. G. Byrom, The finite element method for engineers, 4 Eds., New York: John Wiley & Sons, 2001. |
| [64] |
H. Nguyen‐Xuan, S. Bordas, H. Nguyen‐Dang, Smooth finite element methods: convergence, accuracy and properties, Int. J. Numer. Meth. Eng., 74 (2008), 175–208. https://doi.org/10.1002/nme.2146 doi: 10.1002/nme.2146
|
| [65] |
P. Duxbury, X. K. Li, Development of elasto-plastic material models in a natural coordinate system, Comput. Method. Appl. M., 135 (1996), 283–306. https://doi.org/10.1016/0045-7825(95)00950-7 doi: 10.1016/0045-7825(95)00950-7
|
| [66] | L. E. Baker, R. S. Sandhu, Application of Elasto-Plastic analysis in rock mechanics by finite element method, The 11th U.S. Symposium on Rock Mechanics (USRMS), Berkeley, California,, 1969. |
| [67] |
H. Zheng, D. F. Liu, C. G. Li, Slope stability analysis based on elasto‐plastic finite element method, Int. J. Numer. Meth. Eng., 64 (2005), 1871–1888. https://doi.org/10.1002/nme.1406 doi: 10.1002/nme.1406
|
| [68] |
X. H. Yang, H. X. Zhang, The uniform l1 long-time behavior of time discretization for time-fractional partial differential equations with nonsmooth data, Appl. Math. Lett., 124 (2022), 107644. https://doi.org/10.1016/j.aml.2021.107644 doi: 10.1016/j.aml.2021.107644
|
| [69] |
X. H. Yang, H. X. Zhang, Q. Zhang, G. W. Yuan, Z. Q. Sheng, The finite volume scheme preserving maximum principle for two-dimensional time-fractional Fokker–Planck equations on distorted meshes, Appl. Math. Lett., 97 (2019), 99–106. https://doi.org/10.1016/j.aml.2019.05.030 doi: 10.1016/j.aml.2019.05.030
|
Figures(22) / Tables(2)
Peeyush Garg, Pradeep Kumar Gautam, Amit Kumar Verma, Gnananandh Budi. Deformation and failure analysis of heterogeneous slope using nonlinear spatial probabilistic finite element method[J]. AIMS Mathematics, 2024, 9(10): 26339-26370. doi: 10.3934/math.20241283
DownLoad: