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356 PART IV SOIL WITH WATER—NO FLOW OR STEADY FLOW > Example 24.2 Given, H =10ft, y, =122.4pcef, ¢ = 12°, submerged slope without seepage. ; Find. Combinations of slope angle and @ which will give failure. Solution. From Eq, 24.3: é = A, cos? i (tani — tan ¢) = 600 cos? i (tani — 0.212) Values of @ and i satisfying this equation are plotted in Fig. E24.2. 200 150 & 100 e 50 0 0 10 20 30 i (degrees) Fig. E24.2 4 Equations 24.2 and 24.3 have practical value in cases where soil overlies a rock surface at shallow depth and parallel to the slope.? In addition, there have been numerous cases in which a shallow slide, with sliding plane parallel to the slope, develops in a soil mass of great depth. This happens because the strength param- eters of an overconsolidated soil are not constant with depth. A typical situation is depicted in Fig. 24.7. Here weathering has weakened the soil near the surface, destroying most of the cohesion intercept. The sliding plane develops on the stronger, less weathered soil which exists at depth. Equations 24.2 and 24.3 may be used to analyze the equilibrium of such slides. If a clay has no cohesion intercept, then of course the maximum slope angle is related directly to the friction angle, as in the case of sands. The safety factor F for a slope is usually defined as P= available shear strength ~~ shear stress required for equilibrium (24.4) This safety factor must be evaluated for the most critical surface through the slope. For the case of soil having vertical thickness H overlying rock, this critical surface is the soil-rock interface. Thus, for seepage parallel to the slopes pattatang E+ nH cos*itan g r Hsin icosi (245) » See page 431 of Taylor (1948) for a similar equation which applies when the top flow line is parallel to but at some distance below the sloping ground surface. Shear stress required for equilibrium and shear strength Weathered shale Unweathered shale Fig. 24.7 Development of failure plane within weathered sx or rock, 7 If the strength parameters ¢ and ¢ vary with depth, as Fig. 24.7, then F must be evaluated for several dept’ until the minimum value of F is found. For a slope with a given inclination and a given seepa condition, the shear stress required for equilibrium c: be determined with great accuracy. Uncertainty as tot stability hence arises from uncertainty as to the shc strength, The

tion and a given seepa condition, the shear stress required for equilibrium c: be determined with great accuracy. Uncertainty as tot stability hence arises from uncertainty as to the shc strength, The safety factor F for an infinite slope thus ¢ presses the amount by which the shear strength can be error and still have equilibrium. When an infinite slope nature fails, it usually means that the shear strength the soil has decreased through weathering and ot! geological processes. Such a failure may take the fo: of a gradual downhill creep or may involve a vc sudden and extensive slip. Actually, the depth tot phreatic surface will generally vary somewhat throughe the year, and so too will the shear stress required | equilibrium. The worst condition usually occurs duri severe rains, and most failures also occur during su periods. In evaluating F for an infinite slope, the wo condition—the phreatic line at the surface of the slope- generally assumed. 24.3. GENERAL BEHAVIOR OF SLOPES OF LIMITED HEIGHT ‘ In many problems ¢ is large enough so that the criti: depth becomes quite large: 25 ft, 100 ft, or even mv more. When H, approaches the height of the slope, 1 problem must be treated as a slope of limited height. The first signs of imminent failure of a slope i usually an outward or upward bulging near the toe a the development of cracks near the crest of the slo Failure involves a downward and outward motion soil until a new position of equilibrium is achiev During this movement the sliding mass often breaks into smaller blocks. Often the surface of sliding is m: or less circular, as in Fig. 24.84. In some problems location of the failure surface and the shape of sliding mass are influenced by weak strata within soil, as indicated in Figs. 24.86 and 24.8c, -