For a slope, given: Slope: 3H:1V c’ = 12 kN/m2 H = 12.63 m = 19 kN/m3 ’= 25° ru = 0.25 Use Spencer’s chart to determine the factor of safety, Fs.
> The moist weight of 0.2 ft3 of a soil is 23 lb. The moisture content and the specific gravity of the soil solids are determined in the laboratory to be 11% and 2.7, respectively. Calculate the following. Moist unit weight (lb/ft3) Dry unit weight (lb/f
> The moist weight of a soil is 17.8 kN/m3 and the moisture content is 14%. If the specific gravity of the soil solids is 2.69, calculate the following. Dry unit weight Void ratio Degree of saturation
> Repeat Problem 2.3 with the following data.
> The following are the results of a sieve analysis Determine the percent finer than each sieve and plot a grain-size distribution curve. Determine D10, D30, and D60 for each soil. Calculate the uniformity coefficient Cu. Calculate the coefficient o
> The following values for a soil are given: D10 = 0.24 mm, D30 = 0.82 mm, and D60 =1.81 mm. Determine Cu and Cc.
> Figure 14.35 shows a retaining wall that is restrained from yielding. For each problem, determine the magnitude of the lateral earth force per unit length of the wall. Also, find the location of the resultant, z, measured from the bottom of the wall.
> For a soil with D60 = 0.41 mm, D30 = 0.22 mm, and D10 = 0.08 mm, calculate the uniformity coefficient and the coefficient of gradation.
> Refer to the boring log shown in Figure 18.17. Estimate the average drained friction angle, ’, using the Kulhawy and Mayne correlation [Eq. (18.28)]. Assume pa × 100 kN/m2 .
> Assuming the soil in Problem 18.7 is a clean, medium fine sand, use the Meyerhof (1957) method [Eq. (18.23)] to estimate the variation of relative densities with depth.
> A 0.4 m3 moist soil sample has the following. Moist mass 5 711.2 kg Dry mass 5 623.9 kg Specific gravity of soil solids 5 2.68 Estimate: Moisture content Moist density Dry density Void ratio Porosity
> Following are the results of a standard penetration test in fine dry sand. For the sand deposit, assume the mean grain size, D50, to be 0.26 mm and the unit weight of sand to be 15.5 kN/m3 . Estimate the variation of relative density with depth using
> Repeat Problem 18.5 using Eq. (18.30).
> Refer to Problem 18.3. Using Eq. (18.29), determine the average value of the soil friction angle ’ between z = 1.5 m to 7.5 m.
> For the soil profile given in Problem 18.3, estimate the average soil friction angle, ’, using the Kulhawy and Mayne correlation [Eq. (18.28)]. Assume pa ≈ 100 kN/m2 .
> The following are the results of a standard penetration test in sand. Determine the corrected standard penetration numbers, (N1)60, at the various depths given. Note that the watertable was not found during the boring operation. Assume that the average u
> During a soil exploration program, the following choices were available for soil sampling: Shelby tube A: Outside diameter, Do = 101.6 mm; inside diameter, Di = 98.4 mm Shelby tube B: Outside diameter, Do = 89 mm; inside diameter, Di = 85.7 mm Split-s
> During a field exploration program, rock was cored for a length of 4.5 m and the length of the rock core recovered was 2.5 m. All the rock pieces recovered having a length of 101.6 mm or more had a combined length of 2.1 m. Determine the recovery ratio a
> Refer to the footing in Problem 18.12 and Figure 18.18. Estimate the average friction angle, ’, within the 2B zone. Assume the average dry unit weight of the soil within this zone to be 17 kN/m3 . Estimate the aver
> Based on the soil type of the 2B zone determined in Problem 18.12, what would be the average N60 for that soil? Use Figure 18.14.
> The cone penetration resistance (qc) and sleeve-frictional resistance (fc) obtained during a subsoil exploration program are shown in Figure 18.18. A square footing (B = 1.5 m) is to be constructed at a depth of 1 m. Estimate the type of soil within a di
> A saturated soil has w =23% and Gs = 2.62. Determine its saturated and dry densities in kg/m3.
> A cone penetration test was conducted in a layer of saturated clay. The cone tip resistance, qc, at 5.5 m below the ground surface was found to be 1150 kN/m2 . If the unit weight of the saturated clay is 17.8 kN/m3 , estimate the undrained shear strength
> Refer to Figure 18.17. Estimate the variation of cone penetration resistance, qc, with depth, using Eq. (18.46) and values of c and a given by Anagnostopoulos (2004) (Table 18.7). Assume D50 = 0.46 mm
> The following dimensions are for thin-walled steel tubes to be used for collecting samples of soil for geotechnical purposes: Calculate the area ratio for each case and determine which sampler would be appropriate for the following soil characterizatio
> Repeat Problem 17.8 with the following: density of soil above the groundwater table, r = 1800 kg/m3 ; saturated soil density below the groundwater table, rsat = 1980 kg/m3 ; c9 = 23.94 kN/m2 ; 9 = 25o; B = 1.8 m; = 1.2 m; and h = 2 m.
> A square footing is shown in Figure 17.23. Determine the gross allowable load, Qall, that the footing can carry. Use Terzaghi’s equation for general shear failure (Fs = 3). Given:  = 105 lb/ft3 , sat
> A continuous footing is shown in Figure 17.22. Given:  = 16.8 kN/m3 , c’ = 14 kN/m2 , ’ = 288,  = 0.7 m, and B = 0.8 m. Determine the gross al
> Repeat Problem 17.3 using Eq. (17.31), Table 17.2, and Eqs. (17.35) through (17.37).
> Repeat Problem 17.2 using Eq. (17.31), Table 17.2, and Eqs. (17.35) through (17.37).
> Repeat Problem 17.1 using Eq. (17.31), Table 17.2, and Eqs. (17.35) through (17.37).
> Repeat Problem 17.1 with the following: = 17.7 kN/m3 , cu= 48 kN/m2 , = 08, = 0.6 m, B = 0.8 m, and factor of safety = 4.
> The dry density of a soil is 1780 kg/m3 . Given Gs =2.68, what would be the moisture content of the soil when saturated?
> Repeat Problem 17.1 with the following: = 17.5 kN/m3 , c’= 14 kN/m2 , ’ = 20o, = 1.0 m, B = 1.2 m, and factor of safety = 3.
> Figure 17.26 shows a continuous foundation with a width of 1.8 m constructed at a depth of 1.2 m in a granular soil. The footing is subjected to an eccentrically inclined loading with e = 0.3 m and  = 10°. Determine the gros
> Refer to the footing in Problem 17.14. Determine the gross ultimate load the footing can carry using the Patra et al. (2015) reduction factor method for rectangular foundations given in Eqs. (17.53), (17.55), and (17.56).
> A square footing on sand is subjected to an eccentric load, as shown in Figure 17.24. Using Meyerhof’s effective area concept, determine the gross allowable load that the footing could carry with Fs = 4. Given: = 16 kN/m3 , c’ = 0, ’ = 29o, = 1.3 m
> A square footing is subjected to an inclined load, as shown in Figure 17.25. If the size of the footing is B = 2.25 m, determine the gross ultimate load, Q, that the footing can safely carry. Given:  = 12° and Fs = 3.5. Use
> A square footing is shown in Figure 17.24. The footing is subjected to an eccentric load. For the following cases, determine the gross allowable load that the footing could carry. Use Eq. (17.45) and Meyerhof’s bearing capacity, shape,
> Repeat Problem 17.8 using Eqs. (17.31), (17.33), (17.34), (17.36), and (17.37).
> A square footing (B × B) must carry a gross allowable load of 42,260 lb. The base of the footing is to be located at a depth of 3 ft below the ground surface. For the soil, we are given that = 110 lb/ft3 , c’ = 200 lb/ft2 , and ’ = 20o. If the require
> A continuous footing is shown in Figure 17.22. Using Terzaghi’s bearing capacity factors, determine the gross allowable load per unit area (qall) that the footing can carry. Assume general shear failure. Given:  = 115
> Refer to the slope in Problem 16.7. Assume that the shear strength of the soil is improved by soil stabilization methods, and the new properties are as follows: = 22 kN/m3 , ’ = 32o, and c’ = 75 kN/m2 . What would be the improved factor of safety agai
> For a given soil, show the following. /
> Refer to Problem 16.7. With all other conditions remaining the same, what would be the factor of safety against sliding for the trial wedge ABC if the height of the slope was 9 m?
> Figure 16.50 shows a slope with an inclination of b 5 588. If AC represents a trial failure plane inclined at an angle u = 32o with the horizontal, determine the factor of safety against sliding for the wedge ABC. Given: H = 6 m,  = 19
> For a finite slope such as that shown in Figure 16.10, assume that the slope failure would occur along a plane (Culmann’s assumption). Find the height of the slope for critical equilibrium. Given: ’ = 25°, c’ = 400 lb/ft2 , = 115 lb/ft3 , and = 50°.
> Refer to Figure 16.8. Given H = 6 m, = 0.4, = 28°, = 16 kN/m3 , ’ = 26°, c’ = 15 kN/m2 , and sat = 18.6 kN/m3 . Determine the factor of safety against sliding along plane AB.
> For the infinite slope shown in Figure 16.49, find the factor of safety against sliding along the plane AB given that H = 25 ft, Gs = 2.6, e = 0.=, ’ = 22°, and c’ = 600 lb/ft2 . Note tha
> Refer to Figure 16.48. If there were seepage through the soil and the groundwater table coincided with the ground surface, what would be the value of Fs? Use H = 8 m, sat(saturated density of soil) = 1900 kg/m3 ,  = 20
> Use Spencer’s chart to determine the value of Fs for a given slope: = 20°, H = 15 m, ’ = 15°, c’ = 20 kN/m2 , = 17.5 kN/m3 , and ru = 0.5
> Determine the minimum factor of safety of a slope with the following parameters: H = 6 m, = 18.43°, ’ = 20°, c’ = 6 kN/m2 , = 20 kN/m3 , and ru = 0.5 Use Bishop and Morgenstern’s method.
> Determine the minimum factor of safety of a slope with the following parameters: H = 25 ft = 26.57°, ’ = 20° c’ = 300 lb/ft2 = 120 lb/ft3 ru = 0.5 Use Bishop and Morgenstern’s method.
> A loose, uncompacted sand fill 6 ft in depth has a relative density of 40%. Laboratory tests indicated that the minimum and maximum void ratios of the sand are 0.46 and 0.90, respectively. The specific gravity of solids of the sand is 2.65. What is the
> Referring to Figure 16.52 and using the ordinary method of slices, find the factor of safety with respect to sliding for the following trial cases.  = 45°, ’= 20°, câ
> Refer to Problem 16.19. Assume that the slope is subjected to earthquake forces. Let kh = 0.4 and kv = 0.5kh ((). Determine Fs using the procedure outlined in Section 16.11.
> Refer to Figure 16.51. Using Figure 16.24, find the factor of safety, Fs with respect to sliding for a slope with the following. Slope: 2.5H:1V = 16.5 kN/m3 ’ = 12° H = 12 ft c’ = 24 lb/ft2
> For the slope shown in Figure 16.48, find the height, H, for critical equilibrium. Given:  = 22°,  = 100 lb/ft3 , ’ = 15°, and c’ = 200 lb/f
> Refer to Figure 16.51. Using Figure 16.24, find the factor of safety, Fs with respect to sliding for a slope with the following. Slope: 1H:1V = 115 lb/ft3 ’ = 20° H = 30 ft c’ = 400 lb/ft2
> Refer to Figure 16.51. Using Figure 16.24, find the factor of safety, Fs with respect to sliding for a slope with the following. Slope: 2H:1V = 110 lb/ft3 ’ = 10° H = 50 ft c’ = 700 lb/ft2
> Refer to Figure 16.51. Use Figure 16.28 (’ > 0) to solve the following. If n’ = 2, ’ = 20°, c’ = 20 kN/m2 , and ï&se
> A clay slope is built over a layer of rock. Determine the factor of safety with kh = 0.4 for the slope with the following values. Height, H = 16 m Slope angle, = 30° Saturated unit weight of soil, sat = 17 kN/m3 Undrained shear strength, cu = 50 k
> A cut slope was excavated in a saturated clay. The slope angle, b, is equal to 40° with the horizontal. Slope failure occurred when the cut reached a depth of 8.5 m. Previous soil explorations showed that a rock layer was located at a depth of 12 m below
> Refer to Problem 16.13. What should the critical height of the slope be? What is the nature of the critical circle?
> The moisture content of a soil sample is 18.4%, and its dry unit weight is 100 lb/ft3 . Assuming that the specific gravity of solids is 2.65, Calculate the degree of saturation. What is the maximum dry unit weight to which this soil can be compacted wi
> Using the graph given in Figure 16.13, determine the height of a slope (1 vertical to 1 horizontal) in saturated clay with an undrained shear strength of 24 kN/m2 . The desired factor of safety against sliding is 2.5. Given: = 18 kN/m3 and D = 1.20.
> For the cut slope described in Problem 16.11, if we need a factor of safety of 2.0 against sliding, how deep should the cut be made?
> A cut slope is to be made in a saturated clay. Given: cu = 30 kN/m2 (f = 0 condition) and = 17 kN/m3 . The slope makes an angle b of 60° with the horizontal. Determine the maximum depth up to which the cut could be made. Assume that the critical surfac
> Refer to Figure 16.10. Using the soil parameters given in Problem 16.6, find the height of the slope, H, that will have a factor of safety of 2 against sliding. Assume that the critical surface for sliding is a plane.
> Refer to Figure 16.48. Given:  = 30°,  = 15.5 kN/m3 , ’ = 20°, and c’ = 15 kN/m2 . Find the height, H, which will have a factor of safety (F
> Redo Problem 15.8 when u = 10o and  = 0o.
> Refer to Figure 15.22. Given: u = 0,  = 0o, H = 5 m,  = 15 kN/m3 , ’ = 30o, and ’ = 15o. Estimate the passive force, Pp, per unit length of t
> Refer to the retaining wall shown in Figure 15.22. Given: u = 10o,  = 0,  = 19.2 kN/m3 , ’ = 35o, ’ = 21o, and H = 6 m. Estimate the passive
> Refer to Figure 15.22. Given: H = 5 m, = 0, = 0, = 18.7 kN/m3 , ’ = 30o, and ’ = 2/3 ’. Estimate the passive force, Pp, per unit length of the wall using the Kp values given by Shields and Tolunay’s (1973) method of slices (Table 15.1).
> Refer to the retaining wall in Problem 15.1. Estimate the passive force, Pp, per unit length of the wall using Sokolowskiı˘ (1965) solution by the method of characteristics (Table 15.3).
> For a given sandy soil, the maximum and minimum dry unit weights are 108 lb/ft3 and 92 lb/ft3 , respectively. Given Gs = 2.65, determine the moist unit weight of this soil when the relative density is 60% and the moisture content is 8%.
> Assume that the retaining wall shown in Figure 14.35 is frictionless. For each problem, determine the Rankine active force per unit length of the wall, the variation of active earth pressure with depth, and the location of the resultant.
> Refer to the retaining wall in Problem 15.1. Estimate the passive force, Pp, per unit length of the wall using Lancellotta’s (2002) analysis by the lower bound theorem of plasticity. Use Table 15.2.
> Refer to the retaining wall in Problem 15.1. Estimate the passive force, Pp, per unit length of the wall using Zhu and Qian’s (2000) method of triangular slices. Use Eq. (15.18).
> Refer to the retaining wall in Problem 15.1. Estimate the passive force, Pp, per unit length of the wall using Shields and Tolunay’s (1973) method of slices (Table 15.1).
> The cross section of a braced cut supporting a sheet pile installation in a clay soil is shown in Figure 15.25. Given: H = 12 m, clay = 17.9 kN/m3 ,  = 0, c = 75 kN/m2 , and the center-to-center spacing of struts in
> The elevation and plan of a bracing system for an open cut in sand are shown in Figure 15.24. Using Peck’s empirical pressure diagrams, determine the design strut loads. Given: sand = 18 kN/m3 , &ac
> A braced wall is shown in Figure 15.23. Given: H = 7 m, naH = 2.8 m, ’ = 30o, ’ = 20o,  = 18 kN/m3 , and c’ = 0. Determine the act
> Refer to the retaining wall described in Problem 15.8. If there is seepage in the backfill (as shown in Figure 15.8), what would be the magnitude of Pp based on the theory described in Section 15.7? Assume kx = kz and sat = 18 kN/m3 .
> Redo Problem 15.8 when ( = 0o and = 12o (Figure 15.7 and Table 15.6).
> A retaining wall has a vertical back face with a horizontal granular backfill. Given: H = 6 m, = 18.5 kN/m3 , ’ = 408, and ’ = 1/2’. Estimate the passive force, Pp, per unit length of the wall using Terzaghi and Peck’s (1967) wedge theory (Figure 15
> Refer to Section 14.13 and Figure 14.28. Determine the seismic earth pressure from the soil backfill on the retaining wall, considering = 110o, = 12o, ’ = 21o, ’ = 2/3 ’ = 14o, c’ = 30 kN/m2 , c’ a = 15 kN/m2 , H = 10 m, = 19 kN/m3 , q = 5 kN/m
> For a given sandy soil, emax = 0.75, emin = 0.46, and Gs = 2.68. What will be the moist unit weight of compaction (kN/m3) in the field if Dr = 78% and w = 9%?
> Refer to Section 14.13 and Figure 14.28. Determine the seismic earth pressure from the soil backfill on the retaining wall, considering = 105o, = 8o, ’ = 30o, ’ = 2/3 ’ = 20o, c’ = 0 kN/m2 , c’ a = 0 kN/m2 , H = 15 m, = 16.5 kN/m3 , q = 5 kN/m2
> Figure 14.10 provides a generalized case for the Rankine active pressure on a frictionless retaining wall with an inclined back and a sloping granular backfill. You are required to develop some compaction guidelines for the backfill soil when u = 10o and
> Refer to Figure 14.24. Given: H = 7.5 m, u = 10°, = 5°, = 17.9 kN/m3 , ’ = 28o, ’ = 1/2 ’, kh = 0.3, and kv = 0. Determine the active force, Pae, per unit length of the retaining wall. Also find the location of the resultant line of action of Pae.
> Consider the retaining wall shown in Figure 14.37. The height of the wall is 5 m, and the unit weight of the sand backfill is 18 kN/m3 . Using Coulomb’s equation, calculate the active force, Pa, on the wall for the following values of t
> Refer to the frictionless retaining wall shown in Figure 14.10. Given: H = 6 m, = 10°, u = 6°, ’ = 308, and ’ = 17 kN/m3 . Determine the magnitude, direction, and location of the active force Pa.
> Redo Problem 14.19, assuming that a surcharge pressure of 20 kN/m2 is applied on top of the backfill.
> An 8.5 m high retaining wall with a vertical back face retains a homogeneous, saturated soft clay. The saturated unit weight of the clay is 19.6 kN/m3 . Laboratory tests showed that the undrained shear strength, cu, of the clay is 22 kN/m2 . Make the ne
> For the data given in Problem 14.17, determine the Rankine passive force, Pp, per unit length of the wall, its location, and its direction.
> Figure 14.12 shows a frictionless wall with a sloping granular backfill. Given: H = 7 m, = 12°, ’ = 288, and = 18.6 kN/m3 . Determine the magnitude of active pressure, ’ , at the bottom of the wall. Determine the Rankine active force, Pa, per u
> For the partially submerged backfill in Problem 14.13 (Figure 14.36), determine the Rankine passive force per unit length of the wall and the location of the resultant.
> For a given sand, the maximum and minimum void ratios are 0.78 and 0.43, respectively. Given Gs = 2.67, determine the dry unit weight of the soil in kN/m3 when the relative density is 65%.
> A retaining wall is shown in Figure 14.36. For each problem, determine the Rankine active force, Pa, per unit length of the wall and the location of the resultant.
> A retaining wall is shown in Figure 14.36. For each problem, determine the Rankine active force, Pa, per unit length of the wall and the location of the resultant.
