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INDIAN INSTITUTE OF TECHNOLOGY MADRAS, CHENNAI Department of Civil Engineering

CE 3350 Geotechnical Engineering Tutorial # 5: Stability of Slopes, Sheet Pile Walls and Braced Cuts

Note: Make suitable assumptions wherever necessary. 1. (a) You are writing a computer program to

perform slope stability computations. This program will consider only circular failure surfaces. What procedure might you use to locate the critical failure surface? Provide a detailed explanation.

(b) A 45° slope is excavated to a depth of 8 m in a deep layer of saturated clay of unit weight 19 kN/m3: the shear strength parameters are cu = 65 kPa and ϕu = 0. Determine the factor of safety (FS) for the trial failure surface specified in Fig. 1.

Fig. 1

2. Using the Fellenius method of slices, determine the FS, in terms of effective stress, of the slope shown in Fig. 2 for the given failure surface (a) using peak strength parameters c' = 10 kN/m2 and φ' = 29° and (b) using critical state parameter φ'cs = 31°. The unit weight of the soil both above and below the water table is 20 kN/m3.

Fig. 2

3. For the given failure surface, determine the FS in terms of total stress for the slope detailed in Fig. 3. The unit weight for both soils is 19 kN/m3. The undrained strength (cu) is 30 kN/m2 for Soil 1 and 45 kN/m2 for Soil 2. What is the FS if allowance is made for the development of a tension crack?

Fig. 3 4. A cutting 9 m deep is to be excavated in a saturated clay of unit weight 19 kN/m3. The design shear

strength parameters are cu = 30 kN/m2 and φu = 0. A hard stratum underlies the clay at a depth of 11 m below ground level. Using Taylor’s stability coefficients, determine the slope angle at which failure would occur. What is the allowable slope angle if a FS of 1.2 is specified?

5. A long slope is to be formed in a soil of unit weight 19 kN/m3

6. (a) Determine the height of a finite slope (1V: 2H) that should have a FS of 2 against sliding. For the soil, the following values are given: c' =18 kN/m

for which the shear strength parameters are c' = 0 and φ' = 36°. A firm stratum lies below the slope. It is to be assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Using the traditional method, determine the maximum slope angle to ensure a FS of 1.5, assuming a potential failure surface parallel to the slope. What would be the FS of the slope, formed at this angle, if the water table were well below the surface?

2, φ' = 20°, and ρ = 1700 kg/m3. Assume the critical surface for sliding to be a plane. (b) A cut slope is to be made in a saturated clay. Given: cu = 30 kN/m2 (φu = 0 condition) and γ = 17

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kN/m3

7. (a) For the given failure surface, determine the FS in terms of effective stress for the slope detailed in Fig. 4, using the Fellenius method of slices. The unit weight of the soil is 21 kN/m

. The slope makes an angle, β, of 60° with the horizontal. Determine the maximum depth up to which the cut could be made. Assume that the critical surface for sliding is circular. What is the nature of the critical circle (that is, toe, slope, or midpoint)?

3 and the shear strength parameters are: c' = 8 kN/m2 and φ' =32°. (b) Repeat the analysis of the slope detailed above using the Bishop routine method of slices.

Fig. 4

8. Using the Bishop routine method of slices, determine the FS in terms of effective stress for the slope detailed in Fig. 5 for the specified failure surface. The value of ru is 0.20 and the unit weight of the soil is 20 kN/m3. The shear strength parameters are: c' = 0 and φ' = 33°.

Fig. 5

9. Determine the FS in terms of effective stress of the slope shown in Fig. 6 using the Fellenius method of slices. The relevant soil properties are: c' = 10 kN/m2, φ' = 32°; γ = 20 kN/m3.

10. Figure 7 shows a cantilever sheet pile wall penetrating a granular soil. Here, L1 = 2 m, L2 = 3 m, γ = 15.9 kN/m3, γsat

= 19.33 kN/m3, and φ' = 32°. (a) What is the theoretical depth of embedment, D? (b) For a 30% increase in D, what should be the total length of the sheet piles? (c) What should be the minimum section modulus of the sheet piles? Use σall = 172 MN/m2.

Fig. 7

Fig. 9

Fig. 6 11. Using the free-earth support method, calculate

the depth of embedment of the sheet pile and the pull in the anchor rod for the anchored bulkhead system shown in Fig. 8.

Fig. 8 12. Refer to the braced cut shown in Fig. 9. Given: γ = 16 kN/m3

, φ' = 32°, and c' = 0. The struts are located at 3.5 m center-to-center in the plan. Draw the earth-pressure envelope and determine the strut loads at levels A, B, and C.