Abstract
A three-dimensional limit analysis of slopes is presented in this paper, based on a right circular cone failure surface. The associated translational mechanism appears to yield better assessment of the safety in isotropic rock than the traditional wedge-type mechanism. The strength of a bonded geomaterial was described using a linear strength envelope truncated in the tensile regime. The tensile strength cut-off so introduced constitutes a non-linear portion of the strength envelope, and it allows constructing failure mechanisms that include rupture modes, in addition to the shear deformation mode. Consequently, the mechanisms in materials with tension cut-off are more critical than those in materials with a traditional linear strength envelope. It is also demonstrated that the failure mechanism based on the right circular cone failure surface in vertical slopes yields results as good as or better than the more complex rotational mechanisms, although the difference is not very significant.
Highlights
The stability of rock and soil slopes has been considered by many, but the subject of three-dimensional (3D) limit analysis of slopes has received less attention
The wedge failure mechanism is considered in an isotropic medium, with strength determined by the classical M-C function where the tensile strength is uniquely related to the compressive strength (Equation 7)
The analysis presented in this paper includes a mechanism with 3D geometry and a material whose strength is truncated in the tensile range, which leads to a non-linear strength envelope in the low-stress regime
Summary
The stability of rock and soil slopes has been considered by many, but the subject of three-dimensional (3D) limit analysis of slopes has received less attention. The admissibility of the mechanism requires that the kinematics be consistent with the normality rule of plastic flow and the boundary conditions of the problem The former requires that vectors of velocity be inclined at the angle of internal friction to the shear failure surfaces or the angle of rupture at the surfaces governed by tension cut-off. The wedge failure mechanism is considered in an isotropic medium, with strength determined by the classical M-C function where the tensile strength is uniquely related to the compressive strength (Equation 7) This mechanism is illustrated in Figure 2; it is revisited here in order to assess its effectiveness in isotropic formations when compared to a conical collapse mechanism. With angle q calculated in Equation 37, the area of the shaded portion Ac of the circular cross-section is given as
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