【正文】 /? the effective angle of shearing resistance of soil. In finegrained clays and silty clays, the strength depends on changes in pore water pressures or pore water volumes which take place during shearing. Under undrained conditions, the shear strength cu is largely independent of pressure, that is u? =0. When drainage is permitted, however, both amp。cohesive39。 and amp。frictional39。 ponents 39。39。( , )c? are observed. In this case the shear strength is given by (2) Consideration of the shear strengths of soils under drained and undrained conditions, and of the conditions that will control drainage in the field are important to include in analysis of slopes. Drained conditions are analyzed in terms of effective stresses, using values of 39。39。( , )c? determined from drained tests, or from undrained tests with pore pressure measurement. Performing drained triaxial tests on clays is frequently impractical because the required testing time can be too long. Direct shear tests or CU tests with pore pressure measurement are often used because the testing time is relatively shorter. Stability analysis involves solution of a problem involving force and/or moment equilibrium problem can be formulated in terms of (1) total unit weights and boundary water pressure。 or (2) buoyant unit weights and seepage forces. The first alternative is a better choice, because it is more straightforward. Although it is possible, in principle, to use buoyant unit weights and seepage forces, that procedure is fraught with conceptual diffculties. PLANAR FAILURE SURFACE Failure surfaces in homogeneous or layered nonhomogeneous sandy slopes are essentially planar. In some important applications, planar slides may develop. This may happen in slope, where permeable soils such as sandy soil and gravel or some permeable soils with some cohesion yet whose shear strength is principally provided by friction exist. For cohesionless sandy soils, the planar failure surface may happen in slopes where strong planar discontinuities develop, for example in the soil beneath the ground surface in natural hillsides or in manmade cuttings. ???圖 平面破壞 Figure 1 shows a typical planar failure slope. From an equilibrium consideration of the slide body ABC by a vertical resolution of forces, the vertical forces across the base of the slide body must equal to weight w. Earthquake effects may be approximated by including a horizontal acceleration kg which produces a horizontal force k= acting through the centroid of the body and neglecting vertical For a slice of unit thickness in the strike direction, the resolved forces of normal and tangential ponents N and 185。 can be written as (c os s in )N W k???? （ 3） (si n c os )T W k???? （ 4） where is the inclination of the failure surface and w is given by 02( ta n ta n ) ( ta n )( c o t c o t )2LW x x d x H x d xH? ? ? ? ?? ??? ? ? ????? （ 5） where ? is the unit weight of soil, H the height of slope, c ot , c ot ,L H l H? ? ??? is the inclination of the slope. Since the length of the slide surface AB is /sincH ? , the resisting force produced by cohesion is cH/sin a. The friction force produced by N is (c os si n ) ta nWk? ? ?? . The total resisting or antisliding force is thus given by ( c os si n ) t a n / si nR W k c H? ? ? ?? ? ? （ 6） For stability, the downslope slide force 185。 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。s minimization technique18 from equation (7). Das reported a similar expression for Fs with k=0, developed directly from equation (2) by assuming that /s f dF ??? , where f? is the average shear strength of the soil, and d? the average shear stress developed along the potential failure surface. For cohesionless soils where c=0, the safety factor can be readily written from equation (7) as 1 ta n ta nta ns kF k ? ???? ? （ 8） It is obvious that the minimum value of Fs occurs when a=b, and the failure bees independent of slope height. For such cases (c=0 and k=0), the factors of safety obtainedfrom the proposed method and from Das are identical. CIRCULAR FAILURE SURFACE Slides in mediumstif clays are often deepseated, and failure takes place along curved surfaces which can be closely approximated in two dimensions by circular surfaces. Figure 2 shows a potential circular sliding surface AB in two dimensions with centre O and radius r. The first step in the analysis is to evaluate the sliding39。 or disturbing moment Ms about the centre of the circle O. This should include the selfweight w of the sliding mass, and other terms such as crest loadings from stockpiles or railways, and water pressures acting externally to the slope. Earthquake effects is approximated by including a horizontal acceleration kg which produces a horiazontal force kd=acting through the centroid of each slice and neglecting vertical inertia. When the soil above AB is just on the point of sliding, the average shearing resistance which is required along AB for limiting equilibrium is given by equation (2). The slide mass is divided into vertical slices, and a typical slice DEFG is shown. The selfweight of the slice is dW hdx?? . The method assumes that the resultant forces Xl and Xr on DE and FG, respectively, are equal and opposite, and parallel to the base of the slice EF. It is realized that these assumptions are necessary to keep the analytical solutio