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~. ¢. ) ,. made whenever a slide does develop, as an aid in the choice of remedial works. In the design of earth dams the slopes are usually first chosen on the basis of experi- ence and then checked by a full analysis. As will be discussed in Chapter 31, the methods presented in this chapter are primarily useful for checking (ong-term stability; e.g., stability of the downstream slope of an earth dam once steady seepage has been established through the dam, or stability of a cut slope some years after cutting. Although some questions remain regarding the accuracy of the mechanics of slope stability analysis, in practical situations 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 safety factor indicates the degree to which the expected strength parameters can be reduced before failure would occur, and hence essentially is a safety factor against an error in the estimation of these parameters. For intact homogeneous soils, when the strength parameters have 6cen chosen on the basis of good laboratory tests and a careful estimate of pore pressure has been made, a safety factor of at least I.5 is comroott{y employed. With fissured clays and for ttonhomogeneous soils larger un- certainties wilt generally exist 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 MAfN POINTS Jn evaluating the forces on a free body element of soil, one can correctly account for the effects of water by considering either: Boundary w:tter forces along with the total soil weight. 2. Seepage forces along with the buoyant soil weight These two approaches give identical results since the boundary water forces equal buoyancy plus seepage. In stability problems it is usually more convenient to work with boundary water forces and total soil weight. The study of infinite slopes is helpful, both because the fundamentals of stability problems can clearly be seen and because the results are useful in certain practical problems. The maximum stable slope of a submerged sand is approximately the same as Cor the sand in a dry condition. For both cases im„x equals the strength angle ~. Seepage within a slope generally reduces stability. Ch. 24 Earrb Slopes with Drained tronditioixs 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 m~:thod and wedge method give good accuracy and are recommended For practical use, especially where calculations must be made by hand. Where computer facilities are 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 unanainties in stability problems arise in the selection of the pore pressure and strength param- eters. The error associated with the method of analysis, of the order of 10% difference in computed factor of safety for the better available techniquet„ 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 with a friction angle ~ equal to 30°, a dry unit weight of I IO lb/fts, and a void ratio of 0.52. During a heavy rain the sand becomes saturated and vertical downward seepage under a gradient of unity occurs. Will the slope (fatten? What is the maximum stable slope during the rain? 24.2 Compute the maximum stable slope angle for a layer of normally consolidated Weald clay having; a vertical thickness of 20 ft and with seepage parallel to thr, slope. 'The slope is infinite. 24.3 1Vith the numerical values in the table prepared in Example 24,4, show on sketches the Corces acting on slices 3 and 6. Are these forces in equilibrium? Explain. 24.4 Repeat Problem 24.3 but use the numerical values in the table prepared in Example 24.5. 24.5 Repeat Example 24.3, using a failure arc centered over the boundary between slices 2A and 3 with the center 25 ft above the firm stratum. 24.6 Repeat Example 24.4 using the (allure arc described in Problem 24.5. 24.7 Repeat Example 24.5 using the failure arc described in Problem 24.5. 24.6 Repeat Example 24.6 with the following variations: a. Assume the angle a is equal to the inclination of the slope. 6. Using a = ~M, and keeping the location of point A the same, move point B up the slope so that AB is inclined 10° to the vertical. c. Using a = ~,,, and with .4B vettical, move laoints A and B downslope so that OA is inclined at 5°. ~` i; ~i t y i.i t :~ Ir ;. i it ~~.