Model Study of Slope Stability in Open Pit by Numerical Modeling Using the Finite Element Method

The finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It theoretically satisfies all requirements that must be met for a complete solution to a slope stability problem [1]. The material behavior in FEM is described by an elastic, perfectly plastic model complying with the MohrCoulomb failure criterion [2]. This model takes into account shear strength and deformation parameters. Three additional parameters, along with the aforementioned ones, are the modulus of elasticity, E, Poisson’s ratio, ν, and angle of dilatancy, ψ. Several authors [3-4] have shown that the deformation parameters E and ν, as well as the domain size, have an insignificant influence on the factor of safety value.


Introduction
The majority of geotechnical work undertaken at open pit mines in the past was focused on two-dimensional (2D) methods of slope stability analyses. These methods may not be adequate as the data provided by mining machines cannot be fully incorporated in 2D models.
The finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It theoretically satisfies all requirements that must be met for a complete solution to a slope stability problem [1]. The material behavior in FEM is described by an elastic, perfectly plastic model complying with the Mohr-Coulomb failure criterion [2]. This model takes into account shear strength and deformation parameters. Three additional parameters, along with the aforementioned ones, are the modulus of elasticity, E, Poisson's ratio, ν, and angle of dilatancy, ψ. Several authors [3][4] have shown that the deformation parameters E and ν, as well as the domain size, have an insignificant influence on the factor of safety value.
Duncan [5] proposed that the stability and deformation of slope can be analyzed by finite element method (FEM). Griffiths & Lane [6] discussed several examples of FEM based slope stability analysis by comparing with other solution methods. Zhang et al. [7] evaluated the channel slope stability of the East Route of the South-North Water Diversion Project, China. Typical channel cross section in Sanding Province was evaluated using SSR. To describe the stress-strain relationship of the soils, Duncan-Chang nonlinear constitutive model was employed. The factor of safety calculated by strength reduction method was compared with LEM. He & Zhang [8] described the stability analysis of a homogeneous slope and showed that the equivalent criterion was suitable for the stability analysis of slope.

Description of the Study Area
The study of instability aims at a side of a slope located in career of limestone LAFARGE, M'sila ALGERIA. The career is excavated as benches with 20 m in height, and 10 to 20 m in width. The depth of mine is 180 m (Figure 1).

Tension modeling and stability of Chouf Amar career
The model of study is represent three layers of sol, the marl layer of 5 m thickness is situated between of two layers of limestone .Based on laboratory results, the properties of each soil type are associated with the layer that represents it on the geometric model. The following table summarizes these geotechnical parameters (Table 1). Generation of the mesh When a geometric model is fully defined and the properties of the materials are assigned to all layers, the geometry must be divided into finite elements in order to perform the finite element calculation. For more precise results we use a fine mesh (Figure 2).

The calculation
Depending on the case studied, the calculation is done in two phases. In the first one applies the gravity, one takes into account the hydraulic conditions and like type of calculation one chooses the plastic one, nevertheless in the second phase one makes the calculation of the factor of safety, where the points chosen for the calculation are at the peak talus, center, foot.

The deformed mesh:
The deformed mesh is a representation of the mesh with the finite elements in its deformed state, superimposed on a representation of the undistorted geometry ( Figure 3).

Results of Safety factor
It is observed that the instability is well confirmed by the finite element method; the safety factor is of value of 0.981 and is less than 1. The latter is located in the upper part of the embankment, about 7 m deep from the slope. -the traction crack that moves 2.5 to 3 m away from the downstream side of the slope of career -The most damaged area is also located on the downstream part of the crest of the slope.
-Instability is of circular slip type.