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 and the rock quality designation. Use Table 18.9 to comment on the quality of the rock.
> Calculate the variation of dry density (kg/m3) of a soil (Gs = 2.67) at w = 10% and 20% for degree of saturation (S) = 80%, 90%, and 100%.
> Repeat Problem 6.1= with the following values. D10 = 0.09 mm D20 = 0.2= mm D50 = 0.61 mm
> The backfill material for a vibroflotation project has the following grain sizes. D10 = 0.11 mm D20 = 0.19 mm D50 = 1.3 mm
> Following are the results of a field unit weight determination test on a soil using the sand cone method. Calibrated dry density of Ottawa sand = 1667 kg /m3 Calibrated mass of Ottawa sand to fill the cone = 0.117 kg Mass of jar 1 cone 1 sand (before use
> The relative compaction of a sand in the field is 90%. The maximum and minimum dry unit weights of the sand are 108 lb/ft3 and 93 lb/ft3, respectively. For the field conditions, determine: Dry unit weight Relative density of compaction Moist unit weig
> The maximum and minimum dry densities of a sand were determined in the laboratory to be 1682 kg/m3 and 1510 kg/m3, respectively. In the field, if the relative density of compaction of the same sand is 70%, what are its relative compaction (%) and dry den
> The maximum and minimum dry unit weights of a sand were determined in the laboratory to be 104 lb/ft3 and 93 lb/ft3, respectively. What would be the relative compaction in the field if the relative density is 78%?
> Repeat Problem 6.9 using Matteo’s (2009) method.
> Given Gs = 2.75, calculate the zero-air-void unit weight in lb/ft3 for a soil at w = 5%, 8%, 10%, 12%, and 15%.
> The grain-size characteristics are given in the following table. Draw the grain-size distribution curve. Determine the percentages of gravel, sand, silt, and clay: According to the USDA system According to the AASHTO system
> 9% of a soil is retained on No. 4 sieve, and 11% passes the No. 200 sieve. It is also known that 10%, 30%, and 60% of the soil is smaller than 0.1 mm, 0.8 mm, and 1.9 mm, respectively. When Atterberg limit tests are conducted, it is found that the liquid
> Classify the following soils using the Unified soil classification system. Give group symbols and group names.
> Classify the following soils using the Unified soil classification system. Give the group symbols and the group names
> The sieve analysis of ten soils and the liquid and plastic limits of the fraction passing through the No. 40 sieve are given here. Classify the soils using the AASHTO soil classification system and give the group indexes.
> Classify the following soils by the AASHTO soil classification system. Give the group index for each soil.
> Classify the following soils by the AASHTO soil classification system. Give the group index for each soil.
> Liquidity index, LI, defined by Eq. (4.15), can indicate probable engineering behavior depending on the natural or current state of moisture content. For example, the material behavior can vary from a brittle solid (LI  1) to viscous
> Refer to the same soil in Problem 4.7. A single test was conducted with the fall cone device, and the following results were obtained: d =17 mm and w = 28.5%. Using Eqs. (4.5), (4.6), and (4.7), estimate the liquid limit by the one-point method.
> The following results were obtained for a liquid limit test using a fall cone device. Estimate the liquid limit of the soil and the flow index.
> Using the results of Problem 4.3 and Eq. (4.14), estimate the shrinkage limit of the soil.
> The following are the results of a sieve and hydrometer analysis Draw the grain-size distribution curve. Determine the percentages of gravel, sand, silt, and clay according to the MIT system. Repeat Part b according to the USDA system. Repeat Part
> Using the results of Example 4.1 and Eq. (4.14), estimate the shrinkage limit of the soil. Assume PL = 12.2.
> Refer to Problem 4.3. Determine the liquidity index of the soil when the in situ moisture content is 26%.
> Results from liquid and plastic limit tests conducted on a soil are given here. Liquid limit tests: Plastic limit tests: PL = 18.7% Draw the flow curve and obtain the liquid limit. What is the plasticity index of the soil?
> Determine the liquidity index of the soil in Problem 4.1, if
> Consider Soil No. 3 of Problem 4.9. Using the % of clay size fraction and the liquid limit of the soil, estimate: Plastic limit (use Eq. 4.10) Plasticity index (use Eq. 4.11) Activity (use Eq. 4.19)
> Results from liquid and plastic limit tests conducted on a soil are given here. Liquid limit tests: Plastic limit tests: PL = 13.4% Draw the flow curve and obtain the liquid limit. What is the plasticity index of the soil?
> The moist density of a soil is 1680 kg/m3. Given w = 18% and Gs = 2.73, determine: Dry density Porosity Degree of saturation Mass of water, in kg/m3, to be added to reach full saturation
> Refer to Problem 3.7. Determine the weight of water, in pounds, to be added per cubic foot of soil for 80% degree of saturation 100% degree of saturation
> For a given soil, the following are given: Gs = 2.67; moist unit weight, g = 112 lb/ft3; and moisture content, w = 10.8%. Determine: Dry unit weight Void ratio Porosity Degree of saturation
> The unit weight of a soil is 95 lb/ft3. The moisture content of this soil is 19.2% when the degree of saturation is 60%. Determine: Void ratio Specific gravity of soil solids Saturated unit weight
> Repeat Problem 2.3 with the following data.
> The saturated unit weight of a soil is 19.8 kN/m3. The moisture content of the soil is 17.1%. Determine the following. Dry unit weight Specific gravity of soil solids Void ratio
> 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
> 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
> 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.
> 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
