Postfailure Analysis of Slopes by Random Generalized Interpolation Material Point Method
Publication: International Journal of Geomechanics
Volume 21, Issue 3
Abstract
In this paper, the generalized interpolation material point (GIMP) method will be utilized to simulate the postfailure behavior of slopes that accounts for spatial variability. Because the spatial variability of soil has not been considered in the analysis of the postfailure behavior of slopes, the local average subdivision (LAS) will be used to model the spatial variability of soil properties. By combining these two methods with Monte Carlo simulation, a random generalized interpolation material point (RGIMP) method will be proposed. A homogeneous slope will first be analyzed to verify the correctness of the GIMP implementation used in this paper. Then, a strain-softening slope will be analyzed as an illustrative example to investigate the influence of the spatial variability of soil on the postfailure behavior using the RGIMP. The results show that the runout distance, the retrogression distance, and the sliding volume of the slope that considers spatial variability have significant variations compared with the homogeneous slope. In addition, the kinetic energy of the slope will be investigated. The maximum and average global kinetic energy of the slope that considers spatial variability show obvious differences compared with the homogeneous slope. According to the Pearson correlation coefficient, this shows that there were relatively strong correlations between the maximum (average) global kinetic energy and the runout distance. However, there was no apparent correlation between the maximum global kinetic energy and the retrogression distance (sliding volume).
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Acknowledgments
The research was supported by the Natural Science Foundation of China (Grant No. 51908175 and No. 41807223); the Natural Science Foundation of Anhui Province (Grant No. 1908085QE242). The financial support is gratefully acknowledged.
References
Abe, K., K. Soga, and S. Bandara. 2014. “Material point method for coupled hydromechanical problems.” J. Geotech. Geoenviron. Eng. 140 (3): 04013033. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001011.
Alonso, E. E. 1976. “Risk analysis of slopes and its application to slopes in Canadian sensitive clays.” Géotechnique 26 (3): 453–472. https://doi.org/10.1680/geot.1976.26.3.453.
Andersen, S., and L. Andersen. 2010. “Modelling of landslides with the material-point method.” Comput. Geosci. 14 (1): 137–147.
Bandara, S., A. Ferrari, and L. Laloui. 2016. “Modelling landslides in unsaturated slopes subjected to rainfall infiltration using material point method.” Int. J. Numer. Anal. Methods Geomech. 40 (9): 1358–1380. https://doi.org/10.1002/nag.2499.
Bandara, S., and K. Soga. 2015. “Coupling of soil deformation and pore fluid flow using material point method.” Comput. Geotech. 63: 199–214. https://doi.org/10.1016/j.compgeo.2014.09.009.
Bardenhagen, S. G., J. U. Brackbill, and D. Sulsky. 2000. “The material-point method for granular materials.” Comput. Methods Appl. Mech. Eng. 187 (3–4): 529–541. https://doi.org/10.1016/S0045-7825(99)00338-2.
Bardenhagen, S. G., J. E. Guilkey, K. Roessig, J. U. Brackbill, W. Witzel, and J. Foster. 2001. “An improved contact algorithm for the material point method and application to stress propagation in granular material.” Comput. Model. Eng. Sci. 2 (4): 509–522.
Bardenhagen, S. G., and E. M. Kober. 2004. “The generalized interpolation material point method.” Comput. Model. Eng. Sci. 5 (6): 477–496.
Beuth, L., Z. Więckowski, and P. A. Vermeer. 2011. “Solution of quasi-static large-strain problems by the material point method.” Int. J. Numer. Anal. Methods Geomech. 35 (13): 1451–1465.
Buzzi, O., D. M. Pedroso, and A. Giacomini. 2008. “Caveats on the implementation of the generalized material point method.” Comput. Model. Eng. Sci. 31 (2): 85–106.
Ceccato, F., L. Beuth, P. A. Vermeer, and P. Simonini. 2016. “Two-phase material point method applied to the study of cone penetration.” Comput. Geotech. 80: 440–452. https://doi.org/10.1016/j.compgeo.2016.03.003.
Chen, W., and T. Qiu. 2012. “Numerical simulations for large deformation of granular materials using smoothed particle hydrodynamics method.” Int. J. Geomech. 12 (2): 127–135. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000149.
Cherubini, C. 2000. “Reliability evaluation of shallow foundation bearing capacity on c′, ϕ′ soils.” Can. Geotech. J. 37 (1): 264–269.
Cho, S. E. 2012. “Probabilistic analysis of seepage that considers the spatial variability of permeability for an embankment on soil foundation.” Eng. Geol. 133–134: 30–39. https://doi.org/10.1016/j.enggeo.2012.02.013.
Cornell, C. A. 1972. “First-order uncertainty analysis of soil deformation and stability.” In Proc., 1st Int. Conf. on Applications of Probability and Statistics in Soil and Structural Engineering, 129–144. Hong Kong, China: University of Hong Kong Press.
De Groot, D. J., and G. B. Baecher. 1993. “Estimating autocovariance of in-situ soil properties.” J. Geotech. Eng. 119 (1): 147–166. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:1(147).
Fenton, G. A., and D. V. Griffiths. 2003. “Bearing-capacity prediction of spatially random c-φ soils.” Can. Geotech. J. 40 (1): 54–65. https://doi.org/10.1139/t02-086.
Fenton, G. A., F. Naghibi, and D. V. Griffiths. 2016. “On a unified theory for reliability-based geotechnical design.” Comput. Geotech. 78: 110–122. https://doi.org/10.1016/j.compgeo.2016.04.013.
Fenton, G. A., and E. H. Vanmarcke. 1990. “Simulation of random fields via local average subdivision.” J. Eng. Mech. 116 (8): 1733–1749. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:8(1733).
Fern, E. J., and K. Soga. 2016. “The role of constitutive models in MPM simulations of granular column collapses.” Acta Geotech. 11 (3): 659–678. https://doi.org/10.1007/s11440-016-0436-x.
Griffiths, D. V., and G. A. Fenton. 1993. “Seepage beneath water retaining structures founded on spatially random soil.” Géotechnique 43 (4): 577–587. https://doi.org/10.1680/geot.1993.43.4.577.
Griffiths, D. V., G. A. Fenton, and N. Manoharan. 2002. “Bearing capacity of rough rigid strip footing on cohesive soil: Probabilistic study.” J. Geotech. Geoenviron. Eng. 128 (9): 743–755. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743).
Guilkey, J. E., J. B. Hoying, and J. A. Weiss. 2006. “Computational modeling of multicellular constructs with the material point method.” J. Biomech. 39 (11): 2074–2086. https://doi.org/10.1016/j.jbiomech.2005.06.017.
Hicks, M. A., and K. Samy. 2002. “Influence of heterogeneity on undrained clay slope stability.” Q. J. Eng. Geol. Hydrogeol. 35 (1): 41–49. https://doi.org/10.1144/qjegh.35.1.41.
Hicks, M. A., and W. A. Spencer. 2010. “Influence of heterogeneity on the reliability and failure of a long 3D slope.” Comput. Geotech. 37 (7–8): 948–955. https://doi.org/10.1016/j.compgeo.2010.08.001.
Hsu, S. C., and P. P. Nelson. 2006. “Material spatial variability and slope stability for weak rock masses.” J. Geotech. Geoenviron. Eng. 132 (2): 183–193. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(183).
Huang, P., S.-L. Li, H. Guo, and Z.-M. Hao. 2015. “Large deformation failure analysis of the soil slope based on the material point method.” Comput. Geosci. 19 (4): 951–963. https://doi.org/10.1007/s10596-015-9512-9.
Jahanfar, A., M. Amirmojahedi, B. Gharabaghi, B. Dubey, E. McBean, and D. Kumar. 2017. “A novel risk assessment method for landfill slope failure: Case study application for Bhalswa Dumpsite, India.” Waste Manage. Res. 35 (3): 220–227. https://doi.org/10.1177/0734242X16686412.
Jassim, I., D. Stolle, and P. A. Vermeer. 2013. “Two-phase dynamic analysis by material point method.” Int. J. Numer. Anal. Methods Geomech. 37 (15): 2502–2522. https://doi.org/10.1002/nag.2146.
Kermani, E., T. Qiu, and T.-B. Li. 2015. “Simulation of collapse of granular columns using the discrete element method.” Int. J. Geomech. 15 (6): 04015004. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000467.
Krizek, R. J., R. B. Corotis, and H. H. El-Moursi. 1977. “Probabilistic analysis of predicted and measured settlements.” Can. Geotech. J. 14 (1): 17–33.
Li, D.-Q., X.-H. Li, Z.-J. Cao, X.-S. Tang, W. Zhou, K. K. Phoon, and C.-B. Zhou. 2015. “Reliability analysis of strip footing considering spatially variable undrained shear strength that linearly increases with depth.” Soils Found. 55 (4): 866–880. https://doi.org/10.1016/j.sandf.2015.06.017.
Li, L., Y. Wang, L. M. Zhang, C. Choi, and C. W. W. Ng. 2019. “Evaluation of critical slip surface in limit equilibrium analysis of slope stability by smoothed particle hydrodynamics.” Int. J. Geomech. 19 (5): 04019032. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001391.
Liu, K., P. J. Vardon, M. A. Hicks, and P. Arnold. 2017. “Combined effect of hysteresis and heterogeneity on the stability of an embankment under transient seepage.” Eng. Geol. 219: 140–150. https://doi.org/10.1016/j.enggeo.2016.11.011.
Liu, X., Y. Wang, and D.-Q. Li. 2019. “Investigation of slope failure mode evolution during large deformation in spatially variable soils by random limit equilibrium and material point methods.” Comput. Geotech. 111: 301–312. https://doi.org/10.1016/j.compgeo.2019.03.022.
Lumb, P. 1966. “The variability of natural soils.” Can. Geotech. J. 3 (2): 74–97. https://doi.org/10.1139/t66-009.
Mast, C. M., P. Arduino, P. Mackenzie-Helnwein, and G. R. Miller. 2015. “Simulating granular column collapse using the material point method.” Acta Geotech. 10 (1): 101–116. https://doi.org/10.1007/s11440-014-0309-0.
Phoon, K.-K., and F. H. Kulhawy. 1999. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/t99-038.
Phuong, N. T. V., A. F. van Tol, A. S. K. Elkadi, and A. Rohe. 2016. “Numerical investigation of pile installation effects in sand using material point method.” Comput. Geotech. 73: 58–71. https://doi.org/10.1016/j.compgeo.2015.11.012.
Potts, D. M., G. T. Dounias, and P. R. Vaughan. 1990. “Finite element analysis of progressive failure of Carsington embankment.” Géotechnique 40 (1): 79–101. https://doi.org/10.1680/geot.1990.40.1.79.
Pramanik, R., D. K. Baidya, and N. Dhang. 2020. “Reliability analysis for bearing capacity of surface strip footing using fuzzy finite element method.” Geomech. Geoeng. 15 (1): 29–41. https://doi.org/10.1080/17486025.2019.1601268.
Puła, W., and M. Chwała. 2015. “On spatial averaging along random slip lines in the reliability computations of shallow strip foundations.” Comput. Geotech. 68: 128–136. https://doi.org/10.1016/j.compgeo.2015.04.001.
Rackwitz, R. 2000. “Reviewing probabilistic soils modelling.” Comput. Geotech. 26 (3–4): 199–223. https://doi.org/10.1016/S0266-352X(99)00039-7.
Samy, K. 2003. Stochastic analysis with finite elements in geotechnical engineering. Manchester, UK: Univ. of Manchester.
Shin, W. K. 2009. Numerical simulation of landslides and debris flows using an enhanced material point method. Seattle: Univ. of Washington.
Sivakumar Babu, G. L., and D. S. Murthy. 2005. “Reliability analysis of unsaturated soil slopes.” J. Geotech. Geoenviron. Eng. 131 (11): 1423–1428.
Sivakumar Babu, G. L., A. Srivastava, and D. S. Murthy. 2006. “Reliability analysis of the bearing capacity of a shallow foundation resting on cohesive soil.” Can. Geotech. J. 43 (2): 217–223. https://doi.org/10.1139/t05-099.
Smith, I. M., D. V. Griffiths, and L. Margetts. 2013. Programming the finite element method. 5th ed. London: John Wiley & Sons.
Sołowski, W. T., and S. W. Sloan. 2015. “Evaluation of material point method for use in geotechnics.” Int. J. Numer. Anal. Methods Geomech. 39 (7): 685–701. https://doi.org/10.1002/nag.2321.
Spencer, W. A. 2007. Parallel stochastic and finite element modelling of clay slope stability in 3D. Manchester, UK: Univ. of Manchester.
Srivastava, A., G. L. Sivakumar Babu, and S. Haldar. 2010. “Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis.” Eng. Geol. 110 (3–4): 93–101. https://doi.org/10.1016/j.enggeo.2009.11.006.
Suchomel, R., and D. Mašín. 2010. “Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c–ϕ soil.” Comput. Geotech. 37 (1–2): 132–140. https://doi.org/10.1016/j.compgeo.2009.08.005.
Sulsky, D., Z. Chen, and H. L. Schreyer. 1994. “A particle method for history-dependent materials.” Comput. Methods Appl. Mech. Eng. 118 (1–2): 179–196. https://doi.org/10.1016/0045-7825(94)90112-0.
Tang, W. H., M. S. Yucemen, and A. H.-S. Ang. 1976. “Probability-based short term design of soil slopes.” Can. Geotech. J. 13 (3): 201–215. https://doi.org/10.1139/t76-024.
Wang, B., M. A. Hicks, and P. J. Vardon. 2016. “Slope failure analysis using the random material point method.” Géotech. Lett. 6 (2): 113–118. https://doi.org/10.1680/jgele.16.00019.
Wang, B., P. J. Vardon, and M. A. Hicks. 2018. “Rainfall-induced slope collapse with coupled material point method.” Eng. Geol. 239: 1–12. https://doi.org/10.1016/j.enggeo.2018.02.007.
Wang, Y., Z.-W. Qin, X. Liu, and L. Li. 2019. “Probabilistic analysis of post-failure behavior of soil slopes using random smoothed particle hydrodynamics.” Eng. Geol. 261: 105226.
Wieckowski, Z. 2004. “The material point method in large strain engineering problems.” Comput. Methods Appl. Mech. Eng. 193 (39–41): 4417–4438. https://doi.org/10.1016/j.cma.2004.01.035.
Wu, T. H., and L. M. Kraft. 1970. “Safety analysis of slopes.” J. Soil Mech. Found. Div. 96 (2): 609–630.
Xu, X., F. Jin, Q. Sun, K. Soga, and G. G. D. Zhou. 2019. “Three-dimensional material point method modeling of runout behavior of the Hongshiyan landslide.” Can. Geotech. J. 56 (9): 1318–1337. https://doi.org/10.1139/cgj-2017-0638.
Yerro, A., E. E. Alonso, and N. M. Pinyol. 2015. “The material point method for unsaturated soils.” Géotechnique 65 (3): 201–217. https://doi.org/10.1680/geot.14.P.163.
Yuan, W.-H., K. Liu, W. Zhang, B.-B. Dai, and Y. Wang. 2020. “Dynamic modeling of large deformation slope failure using smoothed particle finite element method.” Landslides 17 (7): 1591–1603. https://doi.org/10.1007/s10346-020-01375-w.
Yuan, W.-H., B. Wang, W. Zhang, Q. Jiang, and X.-T. Feng. 2019a. “Development of an explicit smoothed particle finite element method for geotechnical applications.” Comput. Geotech. 106: 42–51. https://doi.org/10.1016/j.compgeo.2018.10.010.
Yuan, W.-H., H.-C. Wang, W. Zhang, B.-B. Dai, K. Liu, and Y. Wang. 2021. “Particle finite element method implementation for large deformation analysis using Abaqus.” Acta Geotech. https://doi.org/10.1007/s11440-020-01124-2.
Yuan, W.-H., W. Zhang, B.-B. Dai, and Y. Wang. 2019b. “Application of the particle finite element method for large deformation consolidation analysis.” Eng. Comput. 36 (9): 3138–3163. https://doi.org/10.1108/EC-09-2018-0407.
Zhang, W., W.-H. Yuan, and B.-B. Dai. 2018a. “Smoothed particle finite-element method for large-deformation problems in geomechanics.” Int. J. Geomech. 18 (4): 04018010. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001079.
Zhang, X., S. W. Sloan, and E. Oñate. 2018b. “Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity.” Int. J. Numer. Anal. Methods Geomech. 42 (15): 1806–1822. https://doi.org/10.1002/nag.2815.
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Received: Apr 23, 2020
Accepted: Oct 23, 2020
Published online: Jan 13, 2021
Published in print: Mar 1, 2021
Discussion open until: Jun 13, 2021
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