1、附录一 外文文献 Slope Stability Analysis with Nonlinear Failure Criterion Introduction The determination of the slope stability is a very important issue to geotechnical engineers. Many researchers have attempted to develop and elaborate the methods for slope stability evaluation. The proposed methods in t
2、he past for stability analysis may be classied into the following four categories: 1! the limit equilib-rium including the traditional slices method, 2! the characteristic line method, 3! the limit analysis method including upper and lower bound approaches, and 4! the nite element or nite difference
3、 numerical techniques. Among them, the slices method has almost dominated the geotechnical profession for estimating the stability of soil and rock slopes. This is due to the fact that the slices method is very simple, cumulated on the use of the method, and the method is the most known and widely a
4、ccepted by practicing engineers. Until now, a linear MC failure criterion is commonly used in the limit analysis of stability problems. The reason is probably that a linear MC failure criterion can be expressed as circles. This characteristic makes it possible to approximate the circles by a failure
5、 surface, which is a linear function of the stresses in the stress space for plane strain problems. Thus, based on the upper and lower bound theorems, formulations of the stability or bearing capacity problems are linear programming problems. However, experiments have shown that the strength envelop
6、e of geomaterials has the nature of nonlinearity Hoek 1983； Agaret al. 1985； Santarelli 1987!. When applying an upper bound theorem to estimate the inuences of a nonlinear failure criterion on bearing capacity or stability, the main problem, which many researchers have encountered, is how to calcula
7、te the rate of work done by external forces and the rate of energy dissipation along velocity discontinuities. Suitable methods for solving this problem can be mainly classied into two types. The rst type of method is using a variational calculus technique. Baker and Frydman 1983! applied the variat
8、ional calculus technique to derive the governing equations for the bearing capacity of a strip footing resting on the top horizontal surface of a slope. Zhang and Chen 1987! converted the complex differential equations obtained using the variational calculus technique into an initial value problem a
9、nd presented an effective numerical procedure, called an inverse method, for solving a plane strain stability problem using a general nonlinear failure criterion. They gave numerical results of stability factors of a simple innite homogenous slope without surcharge. The second type of method is usin
10、g a tangential technique. Drescher and Christopoulos 1988! andCollinset al. 1988! proposed a simpler alternative tangent technique to evaluate the stability factors of an innite and homogeneous slope without surcharge. They showed that upper bound limit analysis solutions could be obtained by means
11、of a series of linear failure surfaces which are tangent to an exceed the actual nonlinear failure surface, together with utilizing the previously calculated linear stability factors, NL, given by Chen 1975!. This paper develops an improved method using a generalized tangential technique. This metho
12、d employs the tangential line a linear MC failure criterion!, instead of the actual nonlinear failure criterion, to formulate the work and energy dissipation. A Generalized Tangential Technique A limit load computed from a linear failure surface, which always circumscribes the actual nonlinear failu
13、re surface, will be an upper bound value on the actual limit load Chen 1975!. This is due to the fact that the strength of the circumscribing the actual nonlinear failure surface is equal to or larger than that of the actual failure surface. In the present analysis, a tangential line to a nonlinear
14、failure criterion at point M is used and shown in Fig. It can be seen that the strength of the tangential line equals or exceeds that of a nonlinear failure criterion at the same normal stress. Thus, the linear failure criterion represented by the tangential line will give an upper bound on the actu
15、al load for the material, whose failure is governed by a nonlinear failure criterion.In fact, many researchersLymser 1970； Sloan 1989； Sloan andKleeman 1995； Yu et al. 1998； Kim et al. 1999, 2002!Have adopted this approach in their limit analyses. Upper Bound Solutions with a Nonlinear Failure Crite
16、rion In an upper bound limit analysis, solutions depend on the choices of kinematically admissible velocity elds. To obtain better solutions lower upper bounds!, work has to be done for trial kinematically admissible velocity elds, as many as possible. Rotational failure mechanisms have been conside
17、red when using an upper bound approach Chen 1975!. In the stability analysis of a slope, comparing with different translational failure mechanisms,Chen 1975! concluded that a rotational failure mechanism is the most efcient one and that the rotational failure mechanisms lead to lower critical height
18、s or stability factors than those obtained by using other translational failure mechanisms. The kinematical admissibility condition in the upper bound theorem requires that the rotational failure surface for a perfect-plastic body collapse must be a log-spiral surface log-spiral line for plane strai
19、n problems!.Basic ideas in Chen 1975! on the rotational log-spiral surfacesare adopted in the method of the paper. Conclusions An improved method using a generalized tangential technique approximating a nonlinear failure criterion is developed based on the upper bound theorem of plasticity and is us
20、ed to analyze the stability of slopes in this paper. For a slope as shown in Fig. without surcharge, the values of the stability factor calculated using the proposed upper bound method are almost equal to those obtained by Zhang and Chen 1987! For a translational failure mechanism of the vertical cut slope identical solutions are obtained using the present upper bound method and a lower bound method.
