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in the case of variational approach) in a global sense and
produces a stable solution. FEM encompasses all the methods
for connecting many simple element equations over many small
subdomains, named finite elements, to approximate a
larger domain. Similar to FDM, the origin of FEM is not so
straightforward. As summarized by Oden (1987), it probably
dates back to the time of Hrennikoff (1941) and Courant (1943).
However, this idea was not further pursued then since
computers were still largely unavailable. Decades later, the term
“finite element method” was coined by the renowned structural
and earthquake engineer Clough in 1960 when he involved in
the design of wings of Boeing aeroplane (Clough, 1960, 1980).
The first finite element book is “The Finite Element Method in
Structural ad Continuum Mechanics” by O.C. Zienkiewicz
(1967). At least 29 of these papers stated explicitly that finite
element method (FEM) was employed. Among the available
commerical FEM softwares, the most popular ones are
ABAQUS and PLAXIS. Papers used ABAQUS include Elkady
(2013), Hamann and Grabe (2013), Lyngs et al. (2013), Rezaei
et al. (2013), Sadrekarimi and Monfared (2013), and Yapage et
al. (2013). The name and logo of ABAQUS are based on
the abacus calculation tool and is a product of Dassault
Systemes Simulia Corp. founded in USA. Those used PLAXIS
include Balakumar et al. (2013), Chang et al. (2013), Dong and
Anagnostou (2013), Everaars and Peters (2013), and Mirmoradi
and Ehrlich (2013). PLAXIS is a FEM software intended for 2-
Dimensional and 3-Dimensional geotechnical analysis of
deformation and stability of soil structures, as well as
groundwater and heat flow, in geo-engineering applications
such as excavation, foundations, embankments and
tunnels. Some researchers used custom-made or more
specialized FEM softwares, such COTHMA (Yoneda 2013),
FREW (Smith et al. 2013), GeoFEA (Chaudhary et al. 2013),
CORONA (Hoshina and Isobe 2013), SVSLOPE (Lu et al.
2013), EQWEAP (Chang et al. 2013), and MUESA (Lehtonen
and Lansivaara 2013). In addition, Yesuf et al. (2013) did not
give the name of the FEM that you used. A special form of
FEM called random FEM (or RFEM) is used by Huang et al.
(2013) in considering bearing capacity of clay with
nonhomogeneous properties. Although FEM is probbaly the
most popular numerical methods used in geotechnical problems,
it is not suitable for problems suffering from very large
deformation such that the mesh is highly distorted.
2.1.3
Smoothed particle hydrodynamics
For the less conventional numerical techniques, smoothed
particle hydrodynamics (SPH) was used by Kamalzare et al.
(2013) and Bui et al. (2013). The SPH method belongs to
mesh-free technique which has been widely adopted in other
areas of mechanics. Smoothed particle hydrodynamics (SPH) is
a computational method used for simulating fluid flows. It was
developed by Gingold and Monaghan in 1977 (Gingold and
Monaghan 1977) and Lucy in 1977 (Lucy 1977) initially for
astrophysical problems. It is a mesh-free Lagrangian method in
which the coordinates move with the fluid, and the resolution of
the method can easily be adjusted with respect to variables such
as the density. This technique can handle very large deformation
and are more suitable for post-failure analysis. In particular,
Kamalzare et al. (2013) used SPH method to invetsiagte levee’s
erosion due to overtopping of water; and Bui et al. (2013)
considered post-failure simulations of retaining walls using SPH.
In fact, SPH has been used in other geomechanics analysis.
For example, McDougall and Hungr (2004, 2005) had
developed a SPH model for debris flow simulations for 3-D
terrain. Both erosion and entrainment have been incorparoted
into their model. This SPH approach appears better than the
traditional FDM appraoch used by Chau and Lo (2000)
2.1.4
Material point method
A numerical technique called material point method (MPM)
was empolyed by Yerro et al. (2013) to model static-dynamic
transition of slope failure. This MPM tecnique is particular
useful in modeling large deformation problems, such as
landslides, runouts or anchor pull-out. This formulation uses a
dual description of the media by using Lagrangian material
points and an Eulerian numerical mesh. The MPM, is an
extension of the Particle-in-cell Method (a method developed in
Los Alamos National Laboratory in 1957) in computational
fluid dynamics to computational solid dynamics, and is a Finite
element method (FEM)-based particle method. It is primarily
used for multiphase simulations, because of the ease of
detecting contact without inter-penetration. It can also be used
as an alternative to dynamic FEM methods to simulate large
material deformations, because there is no re-meshing required
by the MPM. It was originally proposed by Sulsky et al.
(1995).
2.1.5
Neural networks
There are three papers adopted neural networks (NN) models in
considering capacity of piles and constitutive modeling. In
particular, Hashash et al. (2013) presented the integration of
self-learning simulations (SelfSim), which is based on neural
network based material model, with laboratory testing to extract
soil-behavior, whereas Shahin (2013) and Wardani et al. (2013)
considered the load-settlement and ultimate bearing capacity of
a single pile respectively. These NN model can be considered
as a kind of artificial intelligence. An artificial neural network,
often just named a neural network, is a mathematical
model inspired by biological neural networks. A neural network
consists of an interconnected group of artificial neurons, and it
processes
information
using
a connectionist approach
to computation. In most cases a neural network is an adaptive
system changing its structure during a learning phase. Neural
networks are used for modeling complex relationships between
inputs and outputs or to find patterns in data.
2.1.6
Genetic algorithm
Pereira et al. (2013) implemented the explicit finite difference
code FLAC and its calibration was done using a Genetic
Algorithm (GA) with Hill Climbing procedure implemented in
MATLAB. The use of these two programs with complete
distinct objectives (MATLAB to the fitting process and FLAC
to the numerical calculations) provides great flexibility to the
implementation of any constitutive model to reproduce the
results from experimental tests. Javadi et al. (2013) incorporated
numerical modelling of seawater intrusion with an genetic
algorithm (GA) to examine different scenarios to control
seawater intrusion including different combinations of
abstraction, desalination and recharge. A Genetic Algorithm
(GA) is a search heuristic that mimics the process of
natural evolution. It is routinely used to generate solutions to
problems of optimization and solution searching.
2.1.7
Finite volume method
"Finite volume" refers to the small volume surrounding each
node point on a mesh, resulting from discretization of the body.
In the finite volume method, volume integrals in a partial
differential equation that contain a divergence term are
converted to surface integrals, using the divergence theorem.
These terms are then evaluated as fluxes at the surfaces of each
finite volume. Because the flux entering a given volume is
identical to that leaving the adjacent volume, these methods
are conservative. FVM is best for solving conservative law in
integral form and can solve for discontinuous solutions. The
most fundamental hyperbolic wave problem with a jump
discontinuity is called the Riemann problem (LeVeque, 2002).
In fact, most of the current nite volume methods make use of
the Riemann problem as the building block, and therefore FVM
literally uses Riemann solver. Most of the FVM solution
schemes used nowadays are of the Godunov-type (Godunov,
