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Future evolution of slope stability analysis created by SPH method
Évolution future de l'analyse de stabilité des pentes créé par la méthode SPH
Nonoyama H.
Nagoya University, Japan
Yashima A., Moriguchi S.
Gifu University, Japan
ABSTRACT: In this paper, the SPH (Smoothed Particle Hydrodynamics) method is applied to slope stability problems. This method
can handle large deformation problems because it is based on the free mesh system. In addition, the constitutive models of
geomaterials can be used directly. First, a simulation of a simple shear test is carried out to validate the SPH method. Then, slope
stability analysis considering countermeasures is carried out. The numerical results are compared with results of the safety factors
calculated by the Fellenius method. Based on the obtained results, the effectiveness of the SPH method for slope stability analysis is
discussed.
RÉSUMÉ : Dans cet article, la méthode SPH (hydrodynamique des particules lissées) est appliquée à des problèmes de stabilité des
pentes. La méthode peut traiter des problèmes de grandes déformations parce qu'elle est basée sur le système de maillage libre. En
outre, les modèles de comportement des géomatériaux peuvent être utilisés directement. Dans un premier temps, une simulation
d'essai de cisaillement simple a été réalisée afin de valider la méthode SPH. Ensuite, une analyse de stabilité des pentes considérant
des contre-mesures a été réalisée. Les résultats numériques ont été comparés avec les résultats des facteurs de sécurité calculés par la
méthode Fellenius. Sur la base des résultats obtenus, l'efficacité de la méthode SPH pour l'analyse de la stabilité des pentes a été
discutée.
KEYWORDS: slope stability analysis, meshfree method, constitutive model
1 INTRODUCTION
In terms of the slope stability problems, design of structures and
evaluation of countermeasures are carried out using a safety
factor of slope obtained from circular slippage calculations at
the practical level. In this approach, the safety factor of the
slope is easily obtained from equilibrium of force. However, it
is not possible to take into account of the deformation of slope.
If it is possible to predict the deformation of slope, more
detailed design of structures and evaluation of countermeasures
can be facilitated. A lot of deformation analyses using the Finite
Element Method (FEM) with developed constitutive models
have been reported. It is, however, still difficult to solve large
deformation problems using the FEM due to the distortion of
the mesh. On the other hand, to solve such problems, various
numerical approaches have been proposed, such as a modeling
based on the computational fluid dynamics (CFD) and the
discrete modeling (Cundall and Strack 1979). In the method
based on CFD, it is not necessary to pay attention to mesh
distortion, because the mesh is fixed in space. However, soils
are assumed to be a kind of non-Newtonian fluids (Moriguchi
2005). Thus this modeling is an effective tool for flow
problems, but is difficult to apply to static deformation
problems. In addition, it is difficult to use constitutive models
based on solid mechanics, because they cannot easily handle the
history information of soils during deformation. The discrete
modeling uses an assembly of discrete elements, and is
inappropriate for dealing with constitutive models based on a
continuum approximation.
Against these backgrounds, the purpose of this research is to
express the large deformation behavior of geomaterials in the
framework of continuum mechanics. The smoothed particle
hydrodynamics (SPH) method, proposed by Lucy (1977) and
Gingold and Monaghan (1977), is based on a mesh-free
Lagrangian scheme, and is one of the effective numerical
methods. The method can solve large deformation problems
without mesh distortion. Moreover, it can handle the governing
equations and existing constitutive models for geomaterials,
since it is based on a continuum approximation. The method has
already been used to solve many types of geotechnical
problems, and a number of interesting achievements have been
published (e.g., Maeda et al. 2004, Bui 2007). From these
achievements, it is shown that the SPH is applicable to
geotechnical problems. However, as far as the introduction of
the constitutive models of geomaterial into the SPH method,
detailed discussions have not been carried out.
In this paper, the SPH method was applied to slope stability
problems. In order to validate the method, a simulation of the
simple shear test for elasto-plastic materials is carried out. Then,
a slope stability analysis considering countermeasures is carried
out. The numerical results are compared with the results of the
Fellenius method. Based on the obtained results, the
effectiveness of the SPH method for slope stability analysis is
discussed.
2 NUMERICAL METHOD
2.1
Basic theory of SPH method
In the SPH method, an object is expressed as an assembly of
particles. If the motions of the particles are solved individually,
the deformation behavior of the continuum cannot be
represented by this technique. In order to treat an object as a
continuum, a unique interpolation theory is used. This
interpolation theory includes two key approximations: a kernel
approximation and a particle approximation. The first step is a
kernel approximation of the field functions. The kernel
approximations are based on neighboring particles
located at
points
x
within the support domain
d
h
of a smoothing function
W
for a reference particle
located at point
x
, as shown in Fig.
1. In the first step of the interpolation, we define a smoothed
