【正文】 INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech., 23, 439}449 (1999) SHORT COMMUNICATIONS ANALYTICAL METHOD FOR ANALYSIS OF SLOPE STABILITY JINGGANG CAOs AND MUSHARRAF M. ZAMAN*t School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019, . SUMMARY An analytical method is presented for analysis of slope stability involving cohesive and noncohesive effects are considered in an approximate manner in terms of seismic coe$cientdependent forces. Two kinds of failure surfaces areconsidered in this study: a planar failure surface, and a circular failure surface. The proposed method can be viewed as an extension of the method of slices, but it provides a more accurate etreatment of the forces because they are represented in an integral form. The factor of safety is obtained by using the minimization technique rather than by a trial and error approach used monly. The factors of safety obtained by the analytical method are found to be in good agreement with those determined by the local minimum factorofsafety, Bishop39。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。 Sons, Ltd. Key words: analytical method。 slope stability。 cohesive and noncohesive soils。 dynamic effect。 planar failure surface。 circular failure surface。 minimization technique。 factorofsafety. INTRODUCTION One of the earliest analyses which is still used in many applications involving earth pressure was proposed by Coulomb in 1773. His solution approach for earth pressures against retaining walls used plane sliding surfaces, which was extended to analysis of slopes in 1820 by Francais. By about 1840, experience with cuttings and embankments for railways and canals in England and France began to show that many failure surfaces in clay were not plane, but signicantly curved. In 1916, curved failure surfaces were again reported from the failure of quay structures in Sweden. In analyzing these failures, cylindrical surfaces were used and the sliding soil mass was divided into a number of vertical slices. The procedure is still sometimes referred to as the Swedish method of slices. By mid1950s further attention was given to the methods of analysis using circular and noncircular sliding surfaces . In recent years, numerical methods have also been used in the slope stability analysis with the unprecedented development of puter hardware and software. Optimization techniques were used by Nguyen,10 and Chen and Shao. While finite element analyses have great potential for modelling field conditions realistically, they usually require signicant e!ort and cost that may not be justied in some cases. The practice of dividing a sliding mass into a number of slices is still in use, and it forms 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。39。tanf? ? ?? （ 1） where f? is the shear stress at failure, /? the effective normal stress at failure, and