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Principles of Geotechnical Engineering 8th edition Braja M.Das - Solutions

Following are the results of a laboratory consolidation test on a sample of undisturbed clay obtained from the field. Pressure, σ' (kg/cm2) Final height of specimen
Refer to Figure 11.43. Considering the soil to be a uniform clay layer, estimate the primary consolidation settlement due to the foundation load. Given: P = 150 kN; B = 3 m; L = 3 m; Df = 1.5 m; H = 8 m; e = 0.7; Gs = 2.72; and LL = 42. Assume that the clay is normally consolidated, and the
Redo Problem 11.6 using the weighted average method [Eq. (11.68)] to calculate the stress increase in the clay layer.In problem 11.6Refer to Figure 11.43. Considering the soil to be a uniform clay layer, estimate the primary consolidation settlement due to the foundation load. Given: P = 150 kN; B
Consider the soil profile shown in Figure 11.44 subjected to the uniformly distributed load, Î”s, on the ground surface. Given: Î”Ïƒ = 26 kN/m2; H1 = 1.83 m; H2 = 3.66 m; and H3 = 5.5 m. Soil characteristics are as follows:SandClay Estimate the primary consolidation
Refer to Figure 11.44. Estimate the primary consolidation settlement in the clay layer. Given: Î”Ïƒ = 85 kN/m2; H1 = 2 m; H2 = 4 m; and H3 = 6 m. Soil characteristics are as follows:€¢ Sand: e = 0.65; Gs = 2.66€¢ Clay: LL = 54; e = 0.98; Gs = 2.74
Foundation engineers are often challenged by the existence of soft compressible soils at the construction site. Figure 11.46 shows a soil profile with a silty sand (Î³ = 15 kN/m3; Î³ sat = 17 kN/m3) underlain by high-plasticity clay (Î³ sat = 17 kN/m3) and a peat layer (Î³ sat = 16 kN/m3),
Following data are given for a direct shear test conducted on dry sand: • Specimen dimensions: 63 mm x 63 mm x 25 mm (height) • Normal stress: 105 kN/m2 • Shear force at failure: 300 N a. Determine the angle of friction, ϕ' b. For a normal stress of 180 kN / m2, what shear force is required
In a consolidated-drained triaxial test on clay, the specimen failed at a deviator stress of 124 kN / m2. If the effective stress friction angle is known to be 31°, what was the effective confining pressure at failure?
Consider the clay sample in Problem 12.10. A consolidated-undrained triaxial test was conducted on the same clay with a chamber pressure of 103 k N/m2. The pore pressure at failure (Δud)f = 33 kN/m2. What would be the major principal stress, σ'1, at failure?
Following are the results of consolidated-undrained triaxial tests on undisturbed soils retrieved from a 4-m-thick saturated clay layer in the field (Î³sat = 19 kN/m3).a. Estimate graphically the Mohr-Coulomb shear strength parameters c' and Ï•'.b. Estimate the shear strength
A consolidated-drained triaxial test was conducted on a normally consolidated clay with a chamber pressure, σ3 = 172 kN / m2. The deviator stress at failure, (Δσd)f = 227 kN/m2. Determine: a. The angle of friction, ϕ' b. The angle θ that the failure plane makes with the major principal
The results of two consolidated-drained triaxial tests on a clay are given below:Calculate the shear strength parameters of the soil.
Consider the triaxial tests in Problem 12.14.a. What are the normal and shear stresses on a plane inclined at 40° to the major principal plane for Specimen I?b. What are the normal and shear stresses on the failure plane at failure for Specimen II?In problem 12.14
A clay sample was consolidated in a triaxial test chamber under an all-around confining pressure of 152 k N/m2. The sample was then loaded to failure in undrained condition by applying an additional axial stress of 193 k N/m2. A pore water pressure sensor recorded an excess pore pressure, (Δud)f =
The shear strength of a normally consolidated clay can be given by the equation τf = σ' tan 27°. Following are the results of a consolidated-undrained test on the clay. • Chamber-confining pressure = 150 k N/m2 • Deviator stress at failure = 120 k N/m2 a. Determine the consolidated-undrained
If a consolidated-drained test is conducted on the clay specimen of Problem 12.17 with the same chamber-confining pressure of 150 k N/m2, what would be the deviator stress at failure?
A consolidated-undrained triaxial test was conducted on dense sand with a chamber-confining pressure of 138 k N/m2. Results showed that ϕ' = 24° and ϕ = 31°. Determine the deviator stress and the pore water pressure at failure. If the sand were loose, what would have been the expected behavior?
Consider the specimen in Problem 12.1b. a. What are the principal stresses at failure? b. What is the inclination of the major principal plane with the horizontal? In problem 12.1b For a normal stress of 180 kN / m2, what shear force is required to cause failure?
Undisturbed samples from a normally consolidated clay layer were collected during a field exploration program. Drained triaxial tests showed that the effective friction angle ϕ' = 28°. The unconfined compressive strength, qu, of a similar specimen was found to be 148 k N/m2. Determine the pore
Results of two consolidated-drained triaxial tests on a clayey soil are as follows:Using the failure envelope equation given in Example 12.10 (q' = m + p'tanÎ±), determine the following (do not plot a graph): a. m and Î± b. c' and Ï•'
A 10-m-thick normally consolidated clay layer is shown in Figure 12.57. The plasticity index of the clay is 23. Using Skempton's equation (12.35), estimate the
For a dry sand specimen in a direct shear test box, the following are given: • Size of specimen: 63.5 mm x 63.5 mm x 31.75 mm (height) • Angle of friction: 33° • Normal stress: 193 kN/m2 Determine the shear force required to cause failure
The following are the results of four drained direct shear tests on undisturbed normally consolidated clay samples having a diameter of 50 mm. and height of 25 mm.Draw a graph for shear stress at failure against the normal stress and determine the drained angle of friction from the graph.
Repeat Problem 12.4 with the following data. Given: Specimen diameter = 50 mm; specimen height = 25 mm.
Consider the clay soil in Problem 12.5. If a drained triaxial test is conducted on the same soil with a chamber confining pressure of 208 k N/m2, what would be the deviator stress at failure?
For the triaxial test on the clay specimen in Problem 12.6, a. What is the inclination of the failure plane with the major principal plane? b. Determine the normal and shear stress on a plane inclined at 30° with the major principal plane at failure. Also explain why the specimen did not fail
The relationship between the relative density, Dr, and the angle of friction, ϕ', of a sand can be given as ϕ' = 28 + 0.18Dr (Dr in %). A drained triaxial test was conducted on the same sand with a chamber-confining pressure of 150 kN/m2. The sand sample was prepared at a relative density of 68%.
For a normally consolidated clay specimen, the results of a drained triaxial test are as follows: • Chamber-confining pressure = 125 kN/m2 • Deviator stress at failure = 175 kN/m2 Determine the soil friction angle, ϕ'.
A soil element in the field may go through various complicated stress paths during the lifetime of a geotechnical structure. It is sometimes possible to simulate these field conditions by advanced triaxial stress path testing, in which the axial and confining pressures are independently controlled
Figure 13.36 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, measured from the bottom of the wall.
A retaining wall is shown in Figure 13.37. For each problem, determine the Rankine active force, Pa, per unit length of the wall and the location of the resultant
For the partially submerged backfill in Problem 13.13 (Figure 13.37), determine the Rankine's passive force per unit length of the wall and the location of the resultantIn problem 13
Figure 13.10 shows a frictionless wall with a sloping granular backfill. Given: H = 4 m, Î± = 10°, Ï•' = 33°, and Î³ = 19 kN/m3.a. Determine the magnitude of active pressure, Ïƒ'a, at the bottom of the wall. Also, state the direction of
For the data given in Problem 13.17, determine the Rankine passive force, Pp, per unit length of the wall, and its location and direction. In problem 13.17 a. Determine the magnitude of active pressure, σ'a, at the bottom of the wall. Also, state the direction of application of σ'a b. Determine
A 5-m-high retaining wall with a vertical back face retains a homogeneous saturated soft clay. The saturated unit weight of the clay is 21 kN/m3. Laboratory tests showed that the undrained shear strength, cu, of the clay is 17 kN/m2. a. Make the necessary calculation and draw the variation of
Redo Problem 13.19, assuming that a surcharge pressure of 11 kN/m2 is applied on top of the backfill. In Problem 13.19 a. Make the necessary calculation and draw the variation of Rankine's active pressure on the wall with depth. b. Find the depth up to which tensile crack can occur. c. Determine
A 10-m-high retaining wall with a vertical back face has a c' - ϕ' soil for backfill material. Properties of the backfill material are as follows: γ = 19.1 k N/m3, c' = 35.9 k N/m2, and ϕ' = 28°. Considering the existence of the tensile crack, determine the Rankine active force, Pa, per unit
Consider the retaining wall shown in Figure 13.38. The height of the wall is 9.75 m, and the unit weight of the sand backfill is 18.7 k N/m3. Using Coulomb's equation, calculate the active force, Pa, on the wall for the following values of the angle of wall friction. Also, comment on the direction
Referring to Figure 13.39, determine Coulomb's active force, Pa, per unit length of the wall for the following cases. Use Culmann's graphic construction procedure.a. H = 4.57 m, Î² = 85°, n = 1, H1 = 6.1 m, Î³ = 20.12 k N/m3, Ï•' = 38°, Î´' = 20°b. H = 5.5 m, Î² = 80°, n = 1, H1 =
Refer to Figure 13.24. Given: H = 6 m, Î¸ = 12°, a = 14°, Î³ = 19 kN/m3, Ï•' = 30°,Determine the active force, Pae, per unit length of the retaining wall.
Assume that the retaining wall shown in Figure 13.36 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.
Assume that the retaining wall shown in Figure 13.36 is frictionless. For each problem, determine the Rankine passive force per unit length of the wall, the variation of active earth pressure with depth, and the location of the resultant.
Figure A.2 in Appendix A provides a generalized case for Rankine active pressure on a frictionless retaining wall with inclined back and a sloping granular backfill. You are required to develop some compaction guidelines for the backfill soil when θ = 10°, and a = 0°, 10°, and 20°. Laboratory
Refer to the retaining wall shown in Figure 14.18. Given: Î¸ = 15°, a = 0, Î³ = 17.8 kN/m3, Ï•' = 30°, Î´' = 18°, and H = 5 m. Estimate the passive force, Pp, per unit length of the wall using Zhu and Qian's method of triangular slices
The cross section of a braced cut supporting a sheet pile installation in a clay soil is shown in Figure 14.21. Given: H = 8 m, Î³clay = 19 kN/m3, Ï• = 0, c = 42 kN/m2, and the center-to-center spacing of struts in plan view, s = 3.5 m. a. Using Peck's empirical pressure
Refer to Figure 14.18. Given: H = 4.26 m, θ = 0, a = 0, γ = 17.56 kN/m3, ϕ' = 35°, and δ' = 2/3 ϕ'. Estimate the passive force, Pp, per unit length of the wall using the Kp values given by Shields and Tolunay's method of slices (Figure 14.5).
A retaining wall has a vertical back face with a horizontal granular backfill. Given: H = 4 m, δ = 19 kN/m3, ϕ' = 30°, and δ' = 2/3 ϕ'. Estimate the passive force, Pp, per unit length of the wall using the Terzaghi and Peck's wedge theory (Figure 14.4).
Solve Problem 14.3 using Zhu and Qian's method (Tables 14.2 and 14.3).
Refer to Figure 14.18. Given: Î¸ = 0, a = 10°, H = 4.75 m, Î´ = 16.8 kN/m3, Ï•' = 30°, and Î´' = 18°. Estimate the passive force, Pp, per unit length of the wall
Refer to Figure 14.3a. Given: Î³ = 18.5 kN/m3, .Ï•' = 30°, Î´' = 15°, and H = 4.57 m, kv = 0, and kh = 0.25. Calculate Ppe for the retaining wall (Section 14.7).
A braced wall is shown in Figure 14.19. Given: H = 5.5 m, naH = 2.75 m, Ï•' = 40°, Î´' = 15°, Î³ = 15.8 kN / m3, and c' = 0. Determine the active thrust, Pa, on the wall using the general wedge theory.
Repeat Problem 14.7 with the following data: H = 6.4 m, naH = 1.98 m, Ï•' = 25°, Î´' = 15°, Î³ = 18.97 kN / m3, and c' = 12.18 kN / m2. Assume
The elevation and plan of a bracing system for an open cut in sand are shown in Figure 14.20. Using Peck's empirical pressure diagrams, determine the design strut loads. Given: Î³sand = 18 kN / m3, Ï•' = 32°, x = 1.83 m, z = 0.91 m, and s = 3.05 m.
Refer to the infinite slope shown in Figure 15.47. Given: ( = 25°, ( = 17.8 kN/m3, (' = 28°, and c' = 31 kN/m2. Find the height, H, such that a factor of safety, Fs, of 2.75 is maintained against sliding along the soil-rock interface.
The inclination of a finite slope is 1 vertical to 2 horizontal. Determine the slope height, H, that will have a factor of safety of 2.3 against sliding. Given: ( = 1800 kg/m3, (' = 17°, and c' = 20 kN/m2. Assume that the critical sliding surface is a plane?
A cut slope is to be made in a saturated clay. Given: The un-drained shear strength, cu = 26 kN/m2 (( = 0 condition), and ( = 18.5 kN/m3. The slope makes an angle, ( = 55° with the horizontal. Assuming that the critical sliding surface is circular, determine the maximum depth up to which the cut
For the cut slope described in Problem 15.11, how deep should the cut be made to ensure a factor of safety of 2.5 against sliding?
Using the graph shown in Figure 15.13, determine the height of a slope (1 vertical to 2 horizontal) in saturated clay with an undrained shear strength of 38 kN/m2 and a unit weight of 18.7 kN/m3. The desired factor of safety against sliding is 2.5. Given: D = 1.50?
A cut slope was excavated in a saturated clay with a slope angle, ( = 48°, with the horizontal. Slope failure occurred when the cut reached a depth of 10 m. Previous soil explorations showed that a rock layer was located at a depth of 14 m below the ground surface. Assuming an undrained condition
Refer to Figure 15.52. Using Michalowski's solution given in Figure 15.25 ((' > 0), determine the critical height of the slope for the following conditions. a. n' = 2, (' = 12o, c' = 36 kN/m2, and ( = 18.5 kN/m3 b. n' = 1, (' = 18o, c' = 30 kN/m2, and ( = 17 kN/m3
Refer to Figure 15.52. Using Taylor's stability chart (Figure 15.21), determine the factor of safety, Fs, against sliding for the slopes with the following characteristics: Slope: 2.5H: 1V, ( = 18.8 kN / m3, ( = 14°, H = 18.3 m, and c' = 24 kN/m2?
Repeat Problem 15.17 with the following data: Slope: 1H: 1V, ( = 18 kN/m3, (' = 20o, H = 10 m, and c' = 32 kN/m2?
Repeat Problem 15.17 using the design chart given in Figure 15.27 (Steward Sivakugan, Shukla, and Das, 2011)?
For the slope shown in Figure 15.47, determine the height, H, for critical equilibrium. Given: ( = 30°, ( = 18.05 kN/m3, (' = 21°, and c' = 14.3 kN/m3?
Refer to Figure 15.53. Using the ordinary method of slices, find the factor of safety with respect to sliding for the following trial cases:a. H = 15.2m, ( = 45o, ( = 30o, ( = 70°, ( = 18.9 kN/m3,( = 18°, and c' = 31 kN/m2b. H = 8 m, ( = 45o, ( = 30o, ( = 80o, ( = 17 kN/m3,(' = 20o, and c'
Determine the minimum factor of safety of a slope with the following parameters: H = 14 m, ( = 26.56°, ( = 19 kN/m3, ( = 25°, c' = 20 kN/m2, and ru = 0.5. Use Bishop and Morgenstern's method.
Determine the minimum factor of safety of a slope with the following parameters: H = 12.2 m, ( = 18.43°, ( = 18.4 kN/m3, (' = 20°, c' = 23 kN/m2, and ru = 0.5. Use Bishop and Morgenstern's method?
Use Spencer's chart to determine the value of Fs for a slope with the following characteristics: H = 17 m, ( = 26°, ( = 19 kN/m3, (' = 21°, c' = 21 kN/m2, and ru = 0.5?
The following parameters are given for a slope with steady-state seepage: Slope angle: 3H: 1V, (' = 24°, c' = 27 kN/m2, ( = 17.5 kN/m3, H = 18 m, and ru = 0.25. Determine the factor of safety, Fs, using
Determine the factor of safety, Fs, for the infinite slope shown in Figure 15.48, where seepage is occurring through the soil and the groundwater table coincides with the ground surface. Given: H = 11 m, ( = 18°, (sat = 19.2 kN/m3, (' = 22°, and c' = 46 kN/m2?
Figure 15.48 shows an infinite slope with H = 8.22 m, and the groundwater table coinciding with the ground surface. If there is seepage through the soil, determine the factor of safety against sliding along the plane AB. The soil properties are as follows: Gs = 2.73, e = 0.69, ( = 28°, (' = 18°,
An infinite slope is shown in Figure 15.49. The shear strength parameters at the interface of soil and rock are ( = 26°, and c' = 21 kN/m2. Given: ( = 1950 kg/m3.a. If H = 5 m and ( = 18°, find the factor of safety against sliding on the rock surface.b. If ( = 27°, find the height, H, for which
A slope is shown in Figure 15.50. If AC represents a trial failure plane, determine the factor of safety against sliding for the wedge ABC. Given: ( = 18 kN/m3, (' = 25°, and c' = 19.1 kN/m3.
For the finite slope shown in Figure 15.51, assume that the slope failure would occur along a plane (Culmann's assumption). Find the height of the slope for critical equilibrium. Given: ( = 58°, ( = 16.5 kN/m3, (' = 14°, and c' = 28 kN/m2?
Refer to Figure 15.51. Using the soil parameters given in Problem 15.7, find the height of the slope, H, that will have a factor of safety of 2.5 against sliding. Assume that the critical sliding surface is a plane?
Refer to Figure 15.51. Given that ( = 45°, ( = 18.5 kN/m3, (' = 22°, c' = 34 kN/m2, and H = 9.4 m, determine the factor of safety with respect to sliding. Assume that the critical sliding surface is a plane?
A continuous footing is shown in Figure 16.18. 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: ( = 17.5 kN/m3, c' = 21 kN/m2, (' = 32°, Df = 1 m, B = 1.5 m, and factor of safety =
A square footing (B ( B) must carry a gross allowable load of 1111 kN. The base of the footing is to be located at a depth of 1.37 m below the ground surface. If the required factor of safety is 4, determine the size of the footing. Use Terzaghi's bearing-capacity factors and assume general shear
Repeat Problem 16.10 with the following: gross allowable load = 550 kN, ( = 19 kN/m3, c' = 0, (' = 25°, Df = 2.1 m, and required factor of safety = 2.5?
Repeat Problem 16.7 using the modified general ultimate bearing capacity?
A square footing is shown in Figure 16.20. The footing is subjected to an eccentric load. For the following cases, determine the gross allowable load that the footing could carry with Fs = 5. Use shape factors by De Beer (1970), depth factors by Hansen (1970), and inclination factors by Meyerhof
A plate-load test was conducted on a sandy soil in which the size of the bearing plate was 610 mm ( 610 mm. The ultimate load per unit area (qu) for the test was found to be 325.5 kN/m2. Estimate the maximum allowable load for a footing of size 1524 mm ( 1524 mm. Use a factor of safety of 5?
A plate-load test was conducted on a clay using a circular plate having a diameter of 762 mm. The ultimate load per unit area (qu) for the test was found to be 320 kN/m2. What should be the maximum allowable load of a column footing having a diameter of 2.5 m? Use a factor of safety of 4.
The following table shows the boring log at a site where a multistory shopping center would be constructed. Soil classification and the standard penetration number, N60, are provided in the boring log. All columns of the building are supported by square footings that must be placed at a depth of
Repeat Problem 16.1 with the following: ( = 18.5 kN/m3, c' = 71.8 kN/m2, (' = 24°, Df = 1.21 m, B = 1.83 m, and factor of safety = 4?
Repeat Problem 16.1 with the following: ( = 19.5 kN/m3, cu = 37 kN/m2, (' = 0, Df = 0.75 m, B = 2.5 m, and factor of safety = 6?
Repeat Problem 16.1 using the method general ultimate bearing capacity?
Repeat Problem 16.2 using the modified general ultimate bearing capacity, Eq. (16.31)?
Repeat Problem 16.3 using the modified general ultimate bearing capacity, Eq. (16.31)?
A square footing is shown in Figure 16.19. Determine the gross allowable load, Qall, that the footing can carry. Use Terzaghi's equation for general shear failure (Fs = 3.5). Given: ( = 16 kN/m3, (sat = 18.9 kN/m3, c' = 17 kN/m3,(' = 32°, Df = 1.2 m, h = 0.9 m, and B = 1.75 m?
If the water table in Problem 16.7 drops down to 0.5 m below the foundation level, what would be the change in the factor of safety for the same gross allowable load?
Repeat Problem 16.7 with the following: density of soil above the groundwater table, ( = 1750 kg/m3; saturated soil density below the groundwater table, (sat = 1950 kg/m3; c' = 28 kN/m3,( = 22°, Df = 1.5 m, h = 2.5 m, and B = 2 m.
During a soil exploration program, the following choices were available for soil sampling: • Shelby tube A: outside diameter, Do = 76.2 mm; inside diameter, Di = 73 mm • Shelby tube B: outside diameter, Do = 88.9 mm; inside diameter, Di = 85.72 mm • Split spoon sampler: outside diameter, Do =
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. That the water table was not found within 12 m below the ground surface. Assume that the average unit weight of sand is 17 kN/m3. Use Liao
For the soil profile given in Problem 17.2, estimate the average soil friction angle, (, using the Kulhawy and Mayne correlation [Eq. (17.20)]. Assume pa = 100 kN/m2?
Following are the results of a standard penetration test in dry sand. Depth (m) W60 1.5...........................9 3...........................10 4.5........................14 6.............................8 7.5...........................20 For the sand deposit, assume the mean grain size, D50,
Refer to the boring log shown in Figure 17.15. Estimate the average drained friction angle, (', based on corrected standard penetration number, (N1)60. Use Eqs. (17.10) and (17.24)?
Refer to Problem 17.5 and Figure 17.15. Suppose a footing (2 m ( 2 m) is constructed at a depth of 1.5 m.a. Estimate the design values for N60 and (.b. What is the net allowable load that the footing can carry? The maximum allowable settlement is 25 mm?
Refer to Figure 17.15. Estimate the variation of cone penetration resistance, qc, with depth using Eq. (17.39). Assume D50 = 0.28 mm?
Refer to the footing in Problem 17.6. For calculating elastic settlement under the footing, it is necessary to estimate the elastic modulus of the foundation soil. Using qc from Problem 17.7 and Eq. (17.33), estimate the variation of elastic modulus with depth for the soil profile shown in Figure

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