Document Type : Article

**Authors**

School of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155/9567, Iran

**Abstract**

This paper presents an integrated two-dimensional numerical framework for simulating rainfall-induced landslides from instability initiation to post-failure flow. To describe the entire process, three steps are considered in this study: 1) a coupled hydro-stability analysis which detects the failure plane using the Finite Element Method (FEM) (pre-failure stage), 2) computing the local rheology of the failed mass (wet sandy soil) based on the water saturation at the onset of failure, using the saturation-based rheological model (transition stage), and 3) a continuum-based propagation analysis which solves the flow of the wet material by employing the Smoothed Particle Hydrodynamics (SPH) method (post-failure stage). Finally, to investigate the influence of rheological model on the post-failure behavior, the computed final deposition profile and flow kinetic energy are compared with those of a viscoplastic model.

**Keywords**

References:

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34. Bogaard, T. and Greco, R. "Landslide hydrology: from hydrology to pore pressure", WIREs Water, 3, pp. 439-459 (2015).

35. Farthing, M. and Ogden, F. "Numerical solution of Richards' equation: A review of advances and challenges", Soil Science Society of America Journal, 81, pp. 1257-1269 (2017).

36. van Genuchten, M. and Pachepsky, Y. "Hydraulic properties of unsaturated soils", Encyclopedia of Earth Sciences Series, Springer, pp. 368-376 (2011).

37. Guellouz, L., Askri, B., Jaffre, J., et al. "Estimation of the soil hydraulic properties from field data by solving an inverse problem", Scientific Reports, 10, p. 9359 (2020).

38. van Genuchten, M. "A closed-form equation for predicting the hydraulic conductivity of unsaturated soils", Soil Science Society of America Journal, 44, pp. 892-898 (1980).

39. Mualem, Y. "A new model for predicting the hydraulic conductivity of unsaturated porous media", Water Resources Research, 12, pp. 513-522 (1976).

40. Shanmugam, M., Kumar, G., Narasimhan, B., et al. "Effective saturation-based weighting for interblock hydraulic conductivity in unsaturated zone soil water flow modelling using one-dimensional vertical finite difference model", Journal of Hydroinformatics, 22, pp. 423-439 (2019).

41. Zhang, G., Modelling Hydrological Response at the Catchment Scale, Eburon Academic Publishers, p. 145 (2007).

42. List, F. and Radu, F. "A study on iterative methods for solving Richards' equation", Computational Geosciences, 20, pp. 341-353 (2016).

43. Hashemi, M., Fatehi, R., and Manzari, M. "A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows", International Journal of Non-Linear Mechanics, 47, pp. 626-638 (2012).

44. Park, M. "Behavior analysis by model slope experiment of artificial rainfall", Natural Hazards and Earth System Sciences, 16, pp. 789-800 (2016).

45. Ceccato, F., Leonardi, A., Girardi, V., et al. "Numerical and experimental investigation of saturated granular column collapse in air", Soils and Foundations, 60, pp. 683-696 (2020).

2. Shen, P., Zhang, L., Chen, H., et al. "EDDA 2.0: integrated simulation of debris flow initiation and dynamics considering two initiation mechanisms", Geoscientific Model Development, 11, pp. 2841-2856 (2018).

3. Chen, X., Zhang, L., Zhang, L., et al. "Modelling rainfall-induced landslides from initiation of instability to post-failure", Computers and Geotechnics, 129, p. 103877 (2021).

4. Cascini, L., Cuomo, S., Pastor, M., et al. "Modeling of rainfall-induced shallow landslides of the flow-type", Journal of Geotechnical and Geoenvironmental Engineering, 136, pp. 85-98 (2010).

5. Gallage, C., Abeykoon, T., and Uchimura, T. "Instrumented model slopes to investigate the effects of slope inclination on rainfall-induced landslides", Soils and Foundations, 61, pp. 160-174 (2021).

6. Marin, R., and Velasquez, M. "Influence of hydraulic properties on physically modelling slope stability and the definition of rainfall thresholds for shallow landslides", Geomorphology, 351, p. 106976 (2020).

7. Manenti, S., Amicarelli, S., Palazzolo, N., et al. "Postfailure dynamics of rainfall-induced landslide in oltrep pavese", Water, 12, p. 2555 (2020).

8. Hungr, O. "A model for the runout analysis of rapid flow slides, debris flows, and avalanches", Canadian Geotechnical Journal, 32, pp. 610-623 (1995).

9. Abramson, L., Slope Stability and Stabilization Methods, 2nd Ed., New York: Wiley (1996).

10. Liu, S., Shao, L., and Li, H. "Slope stability analysis using the limit equilibrium method and two finite element methods", Computers and Geotechnics, 63, pp. 291-298 (2015).

11. Duncan, J. "State of the art: Limit equilibrium and finite-element analysis of slopes", Journal of Geotechnical Engineering, 122, pp. 577-596 (1996).

12. Griths, D. and Lane, P. "Slope stability analysis by finite elements", Geotechnique, 49, pp. 387-403 (1999).

13. Sharma, A., Raju, P., Sreedhar, V., et al. "Slope stability analysis of steep-reinforced soil slopes using finite element method", Geotechnical Applications, 13, pp. 163-171 (2019).

14. Ho, I., Li, S., and Ma, L. "Analysis of partially saturated clayey slopes using finite element method", Soil Mechanics and Foundation Engineering, 56, pp. 382-389 (2020).

15. Xie, F., Liu, C., Zhao, T., et al. "Slope stability analysis via discrete element method and Monte Carlo simulations", IOP Conference Series: Earth and Environmental Science, 861, p. 032023 (2021).

16. Zhang, W., Meng, F., Chen, F., et al. "Effects of spatial variability of weak layer and seismic randomness on rock slope stability and reliability analysis", Soil Dynamics and Earthquake Engineering, 146, p. 106735 (2021).

17. Zhao, C., Yin, Z., and Hicher, P. "A multiscale approach for investigating the effect of microstructural instability on global failure in granular materials", International Journal for Numerical and Analytical Methods in Geomechanics, 42, pp. 2065-2094 (2018).

18. Beuth, L., Benz, T., Vermeer, P., et al. "Large deformation analysis using a quasi-static material point method", Journal of Theoretical and Applied Mechanics, 38, pp. 45-60 (2008).

19. Nikooei, M. and Manzari, M. "Studying effect of entrainment on dynamics of debris flows using numerical simulation", Computers & Geosciences, 134, p. 104337 (2020).

20. Lu, C., Tang, C., Chan, Y., et al. "Forecasting landslide hazard by the 3D discrete element method: A case study of the unstable slope in the Lushan hot spring district, central Taiwan", Engineering Geology, 183, pp. 14-30 (2014).

21. Yamaguchi, Y., Takase, S., Moriguchi, S., et al. Solidliquid coupled material point method for simulation of ground collapse with fluidization", Computational Particle Mechanics, 7, pp. 209-223 (2019).

22. Guo, N. and Zhao, J. "A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media", International Journal for Numerical Methods in Engineering, 99, pp. 789-818 (2014).

23. Li, X. and Zhao, J. "A unified CFD-DEM approach for modeling of debris flow impacts on flexible barriers", International Journal for Numerical and Analytical Methods in Geomechanics, 42, pp. 1643-1670 (2018).

24. Liu, W. and Wu, C. "Modelling Complex Particle- Fluid Flow with a Discrete Element Method Coupled with Lattice Boltzmann Methods (DEM-LBM)", Chem Engineering, 4, p. 55 (2020).

25. Zhao, T., Dai, F., and Xu, N. "Coupled DEM-CFD investigation on the formation of landslide dams in narrow rivers", Landslides, 14, pp. 189-201 (2016).

26. Mast, C., Arduino, P., Mackenzie-Helnwein, P., et al. "Simulating granular column collapse using the material point method", Acta Geotechnica, 10, pp. 101-116 (2014).

27. Fern, E. and Soga, K. "The role of constitutive models in MPM simulations of granular column collapses", Acta Geotechnica, 11, pp. 659-678 (2016).

28. Ceccato, F. and Simonini, P. "Granular flow impact forces on protection structures: MPM numerical simulations with different constitutive models", Procedia Engineering, 158, pp. 164-169 (2016).

29. Wang, D., Li, L., and Li, Z. "A regularized Lagrangian meshfree method for rainfall infiltration triggered slope failure analysis", Engineering Analysis with Boundary Elements, 42, pp. 51-59 (2014).

30. Schwarze, R., Gladkyy, A., Uhlig, F., et al. "Rheology of weakly wetted granular materials: a comparison of experimental and numerical data", Granular Matter, 15, pp. 455-465 (2013).

31. Zhao, C., Salami, Y., Hicher, P., et al. "Multiscale modeling of unsaturated granular materials based on thermodynamic principles", Continuum Mechanics and Thermodynamics, 31, pp. 341-359 (2018).

32. Willett, C., Adams, M., Johnson, S., et al. "Capillary bridges between two spherical bodies", Langmuir, 16, pp. 9396-9405 (2000).

33. Ghorbani, R., Manzari, M., and Hajilouy-Benisi, A. "Development of a saturation-based Mu(I)-rheology for wet granular materials using discrete element method", Scientia Iranica, 28, pp. 2719-2732 (2021).

34. Bogaard, T. and Greco, R. "Landslide hydrology: from hydrology to pore pressure", WIREs Water, 3, pp. 439-459 (2015).

35. Farthing, M. and Ogden, F. "Numerical solution of Richards' equation: A review of advances and challenges", Soil Science Society of America Journal, 81, pp. 1257-1269 (2017).

36. van Genuchten, M. and Pachepsky, Y. "Hydraulic properties of unsaturated soils", Encyclopedia of Earth Sciences Series, Springer, pp. 368-376 (2011).

37. Guellouz, L., Askri, B., Jaffre, J., et al. "Estimation of the soil hydraulic properties from field data by solving an inverse problem", Scientific Reports, 10, p. 9359 (2020).

38. van Genuchten, M. "A closed-form equation for predicting the hydraulic conductivity of unsaturated soils", Soil Science Society of America Journal, 44, pp. 892-898 (1980).

39. Mualem, Y. "A new model for predicting the hydraulic conductivity of unsaturated porous media", Water Resources Research, 12, pp. 513-522 (1976).

40. Shanmugam, M., Kumar, G., Narasimhan, B., et al. "Effective saturation-based weighting for interblock hydraulic conductivity in unsaturated zone soil water flow modelling using one-dimensional vertical finite difference model", Journal of Hydroinformatics, 22, pp. 423-439 (2019).

41. Zhang, G., Modelling Hydrological Response at the Catchment Scale, Eburon Academic Publishers, p. 145 (2007).

42. List, F. and Radu, F. "A study on iterative methods for solving Richards' equation", Computational Geosciences, 20, pp. 341-353 (2016).

43. Hashemi, M., Fatehi, R., and Manzari, M. "A modified SPH method for simulating motion of rigid bodies in Newtonian fluid flows", International Journal of Non-Linear Mechanics, 47, pp. 626-638 (2012).

44. Park, M. "Behavior analysis by model slope experiment of artificial rainfall", Natural Hazards and Earth System Sciences, 16, pp. 789-800 (2016).

45. Ceccato, F., Leonardi, A., Girardi, V., et al. "Numerical and experimental investigation of saturated granular column collapse in air", Soils and Foundations, 60, pp. 683-696 (2020).

Transactions on Mechanical Engineering (B)

September and October 2022Pages 2304-2316