Engineering Geology 281 (2021) 105968
Available online 16 December 2020
0013-7952/© 2020 Elsevier B.V. All rights reserved.
Insights and perspectives into the limit equilibrium method from 2D and
3D analyses
Bekir Salih Firincioglu
a
, Murat Ercanoglu
b, *
a
Civil Engineering Department, Cyprus International University, Mersin 10, Nicosia, Turkey
b
Geological Engineering Department, Hacettepe University, Beytepe/Ankara 06800, Turkey
A R T I C L E INFO
Keywords:
Limit equilibrium method
2D analyses
3D analyses
Scenario-based analyses
Slope stability
ABSTRACT
Stability analyses of slopes have been a hot topic for several decades and numerous methodologies have been
introduced since the beginning of these analyses. One of these methodologies is the limit equilibrium theory, and
it has been applied in different forms to various cases for almost a hundred years. Although numerous in-
vestigations and works have been carried out on this methodology, there are still wide gaps needed to be
investigated. Various methods have been introduced through the years including two- and three-dimensional
solutions to the slope stability. However, an extensive investigation on the effects of real-life scenarios is still
absent in the literature. Therefore, this study was aimed at modelling and evaluating the slope stability
considering different scenarios in two (2D) and three dimensions (3D). Available methods have been investigated
in both 2D and 3D separately by considering well known cases in the literature. Also, a comparison has been
conducted between two- and three-dimensional versions of the same methods. Five different hypothetical cases
and a multitude of scenarios representing the possible conditional changes on the slopes were investigated during
the analyses. Thus, three distinctive comparisons have been conducted by analyzing 942 data related to the
factor of safety. Many intriguing results have been discovered throughout the analyses and some of them have
been found against the literature. A considerable amount of the computations has produced lower factors of
safety in three-dimensional models. This outcome is arguably the most signifcant fnding of this study.
1. Introduction
Natural or engineered slopes such as highway slopes and open-pit
mines, or any inclined natural earth surfaces could be prone to fail if
the suitable conditions are met. Prevention of such failures is vital for
preserving human-life and of great importance in terms of economic
losses for large scale projects in addition to the loss of properties. Hence,
investigation of this problematic subject with the appropriate type of
stability analyses is one of the most important stages of any engineering
work.
In the last century, many scientists and engineers have aimed to gain
new perspectives for slope stability problems by developing new the-
ories under various names. Some of these methods were based on
satisfying static equilibrium, compatibility and boundary conditions
such as Limit Equilibrium Method (LEM) and Limit Analysis Method
(LAM), and some were based on the principles of continuum mechanics
such as Finite Element Method (FEM), Boundary Element Method
(BEM), Finite Difference Method (FDM), and others were derived from
discontinuum mechanics as Discrete Element Method (DEM), Discon-
tinuous Deformation Analysis (DDA) and Particle Flow Code (PFC).
Moreover, some hybrid methods have been developed to compensate
the disadvantages of each theory such as Discrete Finite Element Method
(DFEM) and Finite Discrete Element Method (FDEM). All of these above-
mentioned methods have pros and cons, therefore, they should be used
cautiously by considering all the limitations and capabilities of each
theory. However, the limit equilibrium method has been around for
almost a hundred years, and it is still one of the most commonly used
methodologies throughout the world.
Slope stability analyses can be performed in both two and three di-
mensions by simply drawing the cross-sections or creating sophisticated
three dimensional models of the related structures. Stability analyses by
limit equilibrium methods generally have been done by considering
plane strain assumption which yields a two dimensional factor of safety
for the problem considered; but in reality, failures of engineering de-
signs such as embankments, vertical cuts, retaining walls and as well as
natural slopes occur in three dimensions. The signifcance of this
* Corresponding author.
E-mail address: murate@hacettepe.edu.tr (M. Ercanoglu).
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Engineering Geology
journal homepage: www.elsevier.com/locate/enggeo
https://doi.org/10.1016/j.enggeo.2020.105968
Received 5 December 2019; Received in revised form 10 December 2020; Accepted 10 December 2020