【正文】 the basis of many modern ,9 However, most of these methods use the sums of the terms for all slices which make the calculations involved in slope stability analysis a repetitive and laborious process. Locating the slip surface having the lowest factor of safety is an important part of analyzing a slope stability problem. A number of puter techniques have been developed to automate as much of this process as possible. Most puter programs use systematic changes in the position of the center of the circle and the length of the radius to find the critical circle. Unless there are geological controls that constrain the slip surface to a noncircular shape, it can be assumed with a reasonable certainty that the slip surface is Spencer (1969) found that consideration of circular slip surfaces was as critical as logarithmic spiral slip surfaces for all practical purposes. Celestino and Duncan (1981), and Spencer (1981) found that, in analyses where the slip surface was allowed to take any shape, the critical slip surface found by the search was essentially circular. Chen (1970), Baker and Garber (1977), and Chen and Liu maintained that the critical slip surface is actually a log spiral. Chen and Liu12 developed semianalytical solutions using variational calculus, for slope stability analysis with a logspiral failure surface in the coordinate system. Earthquake e!ects were approximated in terms of inertiaforces (vertical and horizontal) defined by the corresponding seismic coe$cients. Although this is one of the prehensive and useful methods, use of /coordinate system makes the solution procedure attainable but very plicated. Also, the solutions are obtained via numerical means at the end. Chen and Liu12 have listed many constraints, stemming from physical considerations that need to be taken into account when using their approach in analyzing a slope stability problem. The circular slip surfaces are employed for analysis of clayey slopes, within the framework of an analytical approach, in this study. The proposed method is more straightforward and simpler than that developed by Chen and Liu. Earthquake effects are included in the analysis in an approximate manner within the general framework of static loading. It is acknowledged that earthquake effects might be better modeled by including accumulated displacements in the analysis. The planar slip surfaces are employed for analysis of sandy slopes. A closedform expression for the factor of safety is developed, which is diferent from that developed by Das. STABILITY ANALYSIS CONDITIONS AND SOIL STRENGTH There are two broad classes of soils. In coarsegrained cohesionless sands and gravels, the shear strength is directly proportional to the stress level: 39。s, and the method of slices. The proposed method is straightforward, easy to use, and less timeconsuming in locating the most critical slip surface and calculating the minimum factor of safety for a given slope. Copyright ( 1999) John Wiley amp。 planar failure surface。frictional39。 must not exceed the resisting force R of the body. The factor of safety, Fs , in the slope can be defined in terms of effective force by ratio R/T, that is 1 ta n 2ta nta n ( s in c o s ) s in ( )s kcF k H k? ?? ? ? ? ? ????? ? ? （ 7） It can be observed from equation (7) that Fs is a function of a. Thus the minimum value of Fs can be found using Powell39。39。s method, the key is to specify some initial values of a and b. Wellassumed initial values of a and b can result in a quick convergence. If the values of a and b are given inappropriately, it may result in a delayed convergence and certain values would not produce a convergent solution. Generally, a should be assumed within$184。 and the cohesion c is kPa. Using the conventional method of slices, Liu obtained the minimum safety factor min ? Using the proposed method, one can get the minimum value of safety factor from equation (20) as min ? for k=0, which is very close to the value obtained from the slice method. When k0)1, 0)15, or 0)2, one can get min , ? , and 1)23, respectively,which shows the dynamic e!ect on the slope stability to be significant. CONCLUDING REMARKS An analytical method is presented for analysis of slope stability involving cohesive and noncohesive soils. Earthquake e!ects are considered in an approximate manner in terms of seismic coe$cientdependent forces. Two kinds of failure surfaces are considered in this study: a planar failure surface, and a circular failure surface. Three failure conditions for circular failure surfaces namely toe failure, face failure, and base failure are considered for clayey slopes resting on a hard stratum. The proposed method can be viewed as an extension of the method of slices, but it provides a more accurate treatment of the forces because they are represented in an integral form. The factor of safety is obtained by using theminimization technique rather than by a trial and error approach used monly. The factors of safety obtained from the proposed method are in good agreement with those determined by the local minimum factorofsafety method (finite element methodbased approach), the Bishop method, and the method of slices. A parison of these methods shows that the proposed analytical approach is more straightforward, less timeconsuming, and simple to use. The analytical solutions presented here may be found useful for (a) validating results obtained from other approaches, (b) providing initial estimates for slope stability, and (c) conducting parametric sensitivity analyses for various geometric and soil conditions. REFERENCES 1. D. Brunsden and D. B. Prior. Slope Instability, Wiley, New York, 1984. 2. B. F. Walker and R. Fell. Soil Slope Instability and Stabilization, Rotterdam, Sydney, 1987. 3. C. Y. Liu. Soil Mechanics, China Railway Press, Beijing, P. R.