Three-dimensional limit equilibrium analysis of slopes

Abstract

A general method of three-dimensional slope stability analysis using the limit equilibrium concept is proposed. The failure mass is assumed to be symmetrical and divided into many vertical columns. The inter-slice forces have the same inclination throughout the mass, and the inter-column shear forces are parallel to the base of the column and function of their positions. Force and moment equilibria are satisfied for each column as well as for the total mass. The analysis is illustrated for several slope angles, soil parameters and pore water pressure conditions. The factors of safety are compared with those obtained with two-dimensional stability analyses and the ordinary method of columns. In addition, a three-dimensional finite element computer program is presented. This program can calculate the local factors of safety at selected points along a failure surface as well as the mean factor of safety for a chosen failure mass. The results obtained by the two methods, limit equilibrium and finite element, are compared. L'article propose une méthode générale pour l'analyse tridimensionnelle de la stabilité des talus basée sur l'idée d'équilibre limite. On admet que le volume de rupture est symmétrique et divisée en beaucoup de tranches verticales. Les efforts entre les tranchés ont la même inclinaison dans la masse entière, tandis que les efforts de cisaillement entre les tranches sont parallèles à la base de la tranche et fonction de leurs positions. Les équilibres des efforts et des moments sont satisfaits pour chaque tranche, aussi bien que pour le volume total. L'analyse est illustrée pour plusieurs angles de talus, paramètres du sol et conditions de pression de l'eau interstitielle. Les coefficients de sécurité sont comparés avec ceux obtenus par des analyses bidimensionelles de stabilité et la méthode ordinaire des tranches. Un programme d'ordinateur à éléments finis tridimensionnels est aussi présenté. Avec ce programme on peut calculer les coefficients locaux de sécurité en des points sélectionnés le long d'une surface de rupture, aussi bien que le coefficient moyen de sécurité pour un volume de rupture choisi. On fait une comparaison entre les résultats obtenus par les deux méthodes (équilibre limite et éléments finis).

Arch Action Over an Excavated Pit on a Stable Scarp Investigated by Physical Model Tests

“…Several analysis methods have been developed to address the eŠects of three-dimensional geometry (Chen and Chameau, 1983;Gens et al, 1988; Leshchinsky and Baker, 1986;Leshchinsky and Huang, 1992;Michalowski, 2010). Despite the availability of threedimensional computer programs for analyzing deformation and stability in slopes, the calculations require many assumptions with regard to lateral forces, the initial stress distribution and other criteria of the critical slip surfaces which is sometimes lacking (Gri‹ths and Marquez, 2007;Loehr et al, 2004;Ugai and Leshchinsky, 1995;Wei et al, 2009).…”

A rigorous method for three-dimensional asymmetrical slope stability analysis

“…In recent years, there have been a number of 3-d limit equilibrium methods (LEM) developed for slope, or landslide, stability analysis: these D r a f t 4 have been presented on the basis of extensions of corresponding 2-d methods (Chen and Chameau 1982;Baker and Leshchinsky 1987;Zhang 1988;Hungr et al 1989;Leshchinsky and Huang 1992;Lam and Fredlund 1993;Zheng 2012;Sun et al 2012;Zhou and Cheng 2013). Since a symmetric plane, or sliding direction, needs to be pre-determined in the analysis, these 3-d methods are only appropriate for landslides with a symmetrical geometry.…”

Stability estimation of slopes having their slip surface determined by means of the STAB-3D method based on sliding body equilibrium analysis

“…Re sults ob tained so far are lim ited to a great extent, be ing some times sub ject to many mod i fi ca tions; in some cases there are no sat is fy ing re sults. For over 30 years, many work ers have dealt with this sub ject mat ter, for ex am ple Chen and Chemeau (1983), Hutch in son and Sarma (1985), Hungr (1987), Zhang (1988), Michalowski (1989), Huang and Tsai (2000), Huang et al (2002), Cheng et al (2005), Griffiths and Marquez (2007), Wei et al (2009) and Kalatehjari et al (2015), who tried to con sider the 3D pro file of slope sta bil ity anal y sis.…”