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1959, LeVeque, 2002). Another advantage of the finite volume
method is that it is easily formulated to allow for unstructured
meshes. Fujisawa and Murakami (2013) presented a three-
dimensional numerical analysis of embankment breaching
based on the finite volume method, with a Riemann solver, in
solving the shallow water equations for computing the overflow
onto the embankments and the changes in configuration of the
embankment profiles based on the erosion rates of the
embankment materials as a function of the bed shear stress. As
mentioned above, the erosion of levees has been considered by
Kamalzare et al. (2013) using smoothed particle hydrodynamics
(SPH). Therefore, it is recognized that numerical simulations of
the coupling between geomaterials and water become more
important in the case of geohazards, such as strom surges and
tsunami.
2.2
Failure criteria
2.2.1
Mohr-Coulomb failure model
Among the 52 papers, 14 of them adopted the Mohr-Coulomb
failure model in their numerical simulations. They include Biru
et al. (2013), Chaudhary et al. (2013), Dong and Anagnostou
(2013), Everaars and Peters (2013), Hoshina and Isobe (2013),
Kwon et al. (2013), Lehtonen and Lansivaara (2013), Lu et al.
(2013), Lyngs et al. (2013), Mayoral et al. (2013), Rezaei et al.
(2013), Sturm (2013), Yapage et al. (2013), and Yerro et al.
(2013). This failure model remains the most popuplar one.
2.2.2
Plastic potential of Drucker-Prager
The plastic potential of Drucker-Prager was employed by 7
authors, including Biru et al. (2013), Bui et al. (2013), Dong
and Anagnostou (2013), Hoshina and Isobe (2013), Lehtonen
and Lansivaara (2013), Sadrekarimi and Monfared (2013), and
Siddiquee and Islam (2013). The Drucker-Prager model allows
for non-associated flow rule, which is more appropriate for
geomaterials.
2.2.3
Matsuoka-Nakai failure model
In considering the calibration of models for kakriritic rocks,
Dong and Anagnostou (2013) replaced the original Mohr-
Coulomb yield surface by the Matsuoka-Nakai criterion, which
does not have the yield vertex as the Mohr-Coulomb model
does. Thus, potential singularity problem at sharp corner on
yield surface can be avoided (Chau, 2013).
2.2.4
Hoek-Brown failure criterion
When considering the blasting problems for granite, Yerro et al.
(2013) used both Mohr-Coulomb as well as Hoek-Brown failure
crietria in their MPM simulations. The Hoek-Brown failure
model has a nonlinear failure envelop (comparing to the straight
line envelop of Mohr-Coulomb) that appears to fit triaxial tests
data for rocks better.
2.2.5
Cam clay model
Cam clay model has been adopted in Wanatowski et al. (2013)
for soil-liquefaction, in Yao et al. (2013) for elastic-viscous-
plastic modeling in overconsolidated clays, in Yamada and
Noda (2013) for delayed failure in natural clays, in Pereira et al.
(2013) in modeling hard soils. As demonstrated by Davis and
Selvadurai (2002) and Chau (2013), cam clay model is a natural
consequence of balancing the rate of plastic work and rate of
dissipation (which is assumed as a linear function of shear strain
rate) with normality assumed.
2.3
Analysis by limit equilibrium
A number of studies have adopted the results of limit
equilibrium (LEM) for comparison with their numerical results.
These include Hoshina and Isobe (2013) Lehtonen and
Lansivaara (2013), Lu et al. (2013), Sadrekarimi and Monfared
(2013), and Bui et al. (2013).
2.4
Soil versus rock
Among the 52 papers nearly all of them are related to problems
on soils, and only 4 papers considered the deformation in rocks.
These authors are Dong and Anagnostou (2013), James et al.
(2013), Pereira et al. (2013), and Yerro et al. (2013).
2.5
Types of loading conditions
2.5.1
Earthquake loadings
Kwon et al. (2013) considered the soil-pile-structure interaction
under earhquake loadings. Lyngs et al. (2013) considered soil-
structure interaction for the seismic analyses of the Izmit Bay
Bridge. When considering the performance of waste rock
inclusions on tailings impoundment, James (2013) also included
earthquake analysis. Wanatowski et al. (2013) considered the
possibility of earthquake induced liquefaction across a wide
spectrum of soils. Siddiquee and Islam (2013) modeled a visco-
elasto-plastic material under cyclic loading, and its application
is clearly related to seismic excitation. Chang et al. (2013)
considered the seismic responses of piles subjected to
earthquake excitations.
2.5.2
Dynamic loadings
There at least 9 papers address the dynamic effects in their
analyses. These include Breugnot et al. (2013), Bennani et al.
(2013), Hoshina and Isobe (2013), Kwon et al. (2013), Yamada
and Noda (2013), Hamann et al. (2013), Lyngs et al. (2013),
Yerro et al. (2013), and Stickle et al. (2013).
All other studies mainly deal with static problems.
2.6
Applications to geo-structures
2.6.1
Pile analyses
There are 14 papers out of 52 papers considered the
deformations in piles. They include Balakumar et al. (2013),
Breugnot et al. (2013), Elkady (2013), Tan et al. (2013), Kwon
et al. (2013), Hamann and Grabe (2013), Lyngs et al. (2013),
Wardani et al. (2013), Everaars et al. (2013), Smith et al. (2013),
Sturm (2013), Shahin (2013), Chaudhary et al. (2013), and
Chang et al. (2013). Therefore, behavoir of piles remains an
area of active research. It probably is due to soil nonlinearity
and both static and dynamic soil-pile interactions. The
interaction is particularly important in the case of earthquake
excitations. Although equivalent springs with stiffnesses
depending on the frequency and damping was commonly
calibrated by geotechnical engineers and used by structural
engineers, nonlinearity is seldom incorporated. The study by
Chau and Yang (2001) provided the first step forward in this
direction. Koo et al. (2003) proposed a fully coupled continuum
model for pile-soil-structure interaction and the resonant
frequency and the amplification factor of the coupled system
can differ from those of the soil, pile or structure alone. A 3-D
version of this analysis is given by Chau and Yang (2005).
Shaking table tests by Chau et al. (2009) illustrated that
nonlinear pounding between piles and soil (separation of soil
and pile following by impacts) will cause spikes in the dynamic
responses at the pile cap level. Special contact element needed
to be installed at the interface between soil and piles (Chau et al.,
2009).
In short, we expect pile analysis, especially under seismic
loads, remains an area of active research.
2.6.2
Tunnels
There are 7 papers considered the construction and design for
tunnels. They include Kholmyansky and Sheynin (2013), Dong
and Anagnostou (2013), Rezaei et al. (2013), Tan et al. (2013).
Mayoral et al. (2013), Everaars and Peters (2013), Smith et al.
(2013). We want to emphasize here that some of these tunnels
were proposed in urban areas with existing structures. Such
