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made whenever a slide does develop, as an aid in the choice of remedial works. In the design of eatth dams the slopes are usually firs[ chosen on the basis of experi- ence and then checked by a full analysis. As will be discussed in Chapter 3l, the methods presented in [his chaplet are primarily useful for checking long-term stability; e.g., stability of the downs[ream slope of an Earth dam once steady seepage has been established through the dam, or stability oC a cu[ slope some years alter cutting. Although some questions remain regarding the accuracy of the mechanics of slope stability analysis, in practical si[uations the greatest uncertainties lie in the estimation of the pore pressures and especially in the selection of strength parameters. As defined in Eq. 24.4, a safely factor indicates [he degree to which the expected strength parameters can be reduced before failure would occur, and hence essen[ially is a safety factor against an error in the estimation of these parameters. For intact homogeneous soils, when the strength parameters have been chosen on the basis of eood laboratory tests and a careful estima[e of pore pressure has been made, a safety factor of at leas[ I,5 is commonly employed. With fissured clays and for nonhomogeneous soils larger un- artain[ies wilt generally axis[ and more caution is necessary. Peck (1967} has recently documented the difficulties and frustrations in estimating stability in a particularly difficult problem. 24.10 SUMMARY OF MA1N POINTS In evaluating the forces on a free body element of soil, one can correctly account (or the e[fects of water by considering either: I. Boundary water forces along with [he total soil weight. 2. Seepage forces along with the buoyant soil weight. These two approaches give identical results since the - boundary water t'orces equal buoyancy plus seepage. In stability problems it is usually more convenient to work with boundary water forces and total soil weight. r• The study of infinite slopes is helpful, both because the z fundamentals of stability problems can clearly be seen and because the results are useful in certain practical .~~i problems. The maximum stable slope oC a submerged '.,~ sand is approximately the same as for the sand in a dry condition. For both cases ice,,, equals the strength angle ~. Seepage within a slope generally reduces stability. Ch, 14 Earth Slopes with Drained Cortditiorts 373 A general slope stability problem is statically indeter- minate. There are various techniques for solving stability problems, depending on which assumption is used to make the problem determinate. The Bishop method and wedge method give good accuracy and aze recommended Cor practiral use, especially where calculations must be made by hand. Where computer facilities aze available, the engineer may use the more sophisticated Morgen- stern method to check simpler solutions and for cases where neither circular nor wedge-shaped failure surfaces are suitable. The greatest uncertainties in stability problems grist in the selection of the pore pressure and strength param- eters. The error associated tvi[h the method of analysis, of the order of 10% difference in computed factor of safety for the better available techniques, is small compared to that arising from the selection of strength parameters. This is the reason why a factor of safety against loss of strength is used for stability problems. PROBLEMS 24.1 An infinite slope at i = 28° consists of sand wi[h a friction angle ~ equal to 30°, a dry unit weight of 1101b/(ta, and a void ratio of 0.32. During a heavy rain [he sand becomes sa[ura[ed and vertical downward seepage under a gradien[ of uni[y occurs, Will the slope flat[en? What is the maximum stable slope during the rain? 24.2 Compute the maximum sable slope angle for a layer of normally consolidated Weald clay having a vertical thickness of 20 f[ and with seepage parallel to the slope. The slope is infinite. 24.3 Wi[h the numerical values in the table prepared in Example 24.4, show on sketches the forces acting on slices 3 and 6. Are these forces in equilibrium? Explain. 24.4 Repeat Problem 24.J but use the numerical values in the [able prepared in Example 24.3. 24.3 Repeat Example 24.3, using a failure arc centered over the boundary between slices 2A and 7 with the center 23 ft above the firm stratum. 24.6 Repeal Example 24.4 using the failure arc described in Problem 245. 24.7 Repeal Example 24.3 using the failure arc described in Problem 24.3. 24.8 Repeal Example 24.6 with the following variations: a. Assume the angle a is equal to the inclination of the slope. b. Using : _ gym, and keeping the location of point A [he same, move point B up the slope so that AB is inclined 10' to the vertical. r. Using i = ~m and with .4B vertical, move points A and B downslope so that OA is inclined at 3°.