Landslide Hazard Assessment Model for Slope Stability Analysis
Abstract - 33


Slope stability
Factor of safety
Limit equilibrium analysis

How to Cite

De Santis, G., Egidi, N., Giacomini, J., Gioia, E., Maponi, P., & Spadoni, L. (2023). Landslide Hazard Assessment Model for Slope Stability Analysis. Journal of Advances in Applied & Computational Mathematics, 10, 77–87.


Soil moisture dynamics is a complex phenomenon that depends on the atmospheric conditions, the geomorphological characteristics of the region under study, and the corresponding land use. It can be formally described by a diffusion model based on Darcy’s law and the law of mass continuity. In this work, the obtained numerical solution of the hydrological model has been exploited to evaluate the soil moisture in a given region and build a risk map for the slope stability of this region. More in detail, the infinite slope model from slope stability analysis has been used for evaluating the safety factor and constructing the corresponding quantitative hazard maps. Some results of the proposed method applied to a real case study are shown and discussed.


Brown WM, Cruden DM, Denison JS. The directory of the world landslide inventory. U.S. Geological Survey; 1992, Open-File Report 92-427-A.

Lacasse S, Nadim F, Kalsnes B. Living with landslide risk. Geotech Eng J SEAGS AGSSEA 2010; 41: 239-67.

Crescenzo G, Pirone M, Santo A, Urciuoli G, Leroi E. SafeLand Living with landslide risk in Europe: Assessment, effects of global change, and risk management strategies. European Union; 2010.

Busslinger M. Landslide time-forecast methods. Rapperswil: HSR University of Applied Sciences; 2009.

Guzzetti F, Peruccacci S, Rossi M, Stark CP. Rainfall thresholds for the initiation of landslides in central and southern Europe. Meteorl Atmos Phys. 2007; 98: 239-67.

Baum RL, Godt JW. Early warning of rainfall-induced shallow landslides and debris flows in the USA. Landslides. 2010; 7: 259-72.

Baum RL, Savage WZ, Godt JW. TRIGRS: a Fortran program for transient rainfall infiltration and grid-based regional slope-stability analysis, version 2.0. US Geological Survey Open-File Report 2008.

Polarski M. Distributed rainfall-runoff model incorporating channel extension and gridded digital maps. Hydrol Processes. 1997; 11: 1-11.<1::AID-HYP388>3.0.CO;2-G

Schreider SY, Jakeman AJ, Pittock AB. Modeling rainfall-runoff from large catchment to basin scale: The Goulburn Valley, Victoria. Hydrol Processes. 1996; 10: 863-76.<863::aid-hyp376>;2-8

Giacomini J, Khamitova G, Maponi P, Vittori S, Fioretti L. Water flow and transport in porous media for in-silico espresso coffee. Int J Multiph Flow. 2020; 126: 103252.

Giacomini J, Invernizzi MC, Maponi P, Verdoya M. Testing a model of flow and heat transfer for u-shaped geothermal exchangers. Adv Model Anal A. 2018; 55: 151-7.

Richards LA. Capillary conduction of liquids through porous mediums. Physics. 1931; 1: 318-33.

Haverkamp R, Vauclin M, Touma J, Wierenga PJ, Vachaud G. A comparison of numerical simulation models for one-dimensional infiltration. Soil Sci So Am J. 1977; 41: 285-94.

Kirkland MR, Hills RG, Wierenga PJ. Algorithms for solving Richards’ equation for variably saturated soils. Water Resour Res. 1992; 28: 2049-58.

Onda Y. Influence of water storage capacity in the regolith zone on hydrological characteristics, slope processes, and slope form. Zeitschrift Für Geomorphologie. 1992; 36: 165-78.

Cheng YM, Lau CK. Slope stability and stabilization new methods and insight, second edition. London: Taylor & Francis; 2014.

Huang C-C, Tsai C-C, Chen Y-H. Generalized method for three-dimensional slope stability analysis. J Geotech Geoenviron Eng. 2002; 128: 836-48.

Coulomb CA. Essai sur une application des règles de maximis et minimis à quelques problèmes de Statique, relatifs à l’Architecture. Mem Div Sav Acad 1773.

Mohr O. Abhandlungen aus dem Gebiete der Technischen Mechanik, 2nd ed. Berlin: W Ernst & Sohn 1914.

Yokoi H. Relationship between soil cohesion and shear strength. Soil Sci Plant Nutr. 1968; 14: 89-93.

Haefeli R. The stability of slopes acted upon by parallel seepage. International Conference on Soil Mechanics and Foundation Engineering, Rotterdam: 1948, p. 57-62.

Duncan JM, Wright SG, Brandon TL. Soil strength and slope stability. 2nd ed. John Wiley & Sons; 2014.

Pinder GF, Celia MA. Subsurface hydrology. John Wiley & Sons; 2006.

Hill MC, Banta ER, Harbaugh AW, Anderman ER. MODFLOW-2000, the US geological survey modular ground-water model; user guide to the observation, sensitivity, and parameter-estimation processes and three post-processing programs. U.S. Geological Survey; Denver: 2000, Open-File Report 2000-184.

Beven K. Rainfall-runoff modelling: the primer. Wiley; 2012.

van Genuchten MT. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J. 1980; 44: 892-8.

Burdine NT. Relative permeability calculations from pore size distribution data. J Pet Technol. 1953; 5: 71-8.

Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour Res. 1976; 12: 513-22.

Spadoni L, Gioia E, Egidi N, Maponi P. The moisture dynamics in saturated-unsaturated soil. In: IMACS Series in Computational and Applied Mathematics. Rome: Rosa Maria Spitaleri, Daniela Mansutti; 2017, vol. 20: pp. 161-70.

Freeze RA. Three-dimensional, transient, saturated-unsaturated flow in a groundwater basin. Water Resour Res. 1971; 7: 347-66.

Hanks RJ, Bowers SA. Numerical solution of the moisture flow equation for infiltration into layered soils. Soil Sci Soc Am J. 1962; 26: 530-4.

Harbaugh A. MODFLOW-2005, the US Geological Survey modular ground-water model: the ground-water flow process. VA: 2005.

Diersch H-JG. FEFLOW: finite element modeling of flow, mass and heat transport in porous and fractured media. Berlin, Heidelberg: Springer Science & Business Media; 2013.

Forsyth PA, Wu YS, Pruess K. Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media. Adv Water Resour. 1995; 18: 25-38.

Li CW. A simplified Newton Iteration Method with linear finite elements for transient unsaturated flow. Water Resour Res. 1993; 29: 965-71.

Abriola LM, Lang JR. Self-adaptive hierarchic finite element solution of the one-dimensional unsaturated flow equation. Int J Numer Methods Fluids. 1990; 10: 227-46.

Egidi N, Gioia E, Maponi P, Spadoni L. A numerical solution of Richards equation: a simple method adaptable in parallel computing. Int J Comput Math. 2020; 97: 2-17.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2023 Giulia De Santis, Nadaniela Egidi, Josephin Giacomini, Eleonora Gioia, Pierluigi Maponi, Lorenza Spadoni