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All Textbook Solutions for Principles of Foundation Engineering (MindTap Course List)

2.1P 2.2P 2.3P 2.4P 2.5P 2.6P 2.7P 2.8P 2.9P 2.10P 2.11P 2.12P 2.13P 2.14P 2.15P For a normally consolidated soil, the following is given: Determine the following: a. The compression index, Cc. b. The void ratio corresponding to pressure of 200 kN/m2 2.17P 2.18P 2.19P 2.20P 2.21P 2.22P 2.23P 2.24P 2.25P 2.26P 2.27P 3.1P 3.2P Refer to Figure P3.3. Use Eqs. (3.10) and (3.11) to determine the variation of OCR and preconsolidation pressure c. FIGURE P3.3 3.4P 3.5P 3.6P 3.7P 3.8P 3.9P 3.10P 3.11P Following are the standard penetration numbers determined from a sandy soil in the Field: Using Eq. (3.30), determine the variation of the peak soil friction angle, . Estimate an average value of for the design of a shallow foundation. (Note: For depth greater than 20 ft, the unit weight of soil is 118 lb/ft3.)3.13P 3.14P 3.15P 3.16P 3.17P 3.18P 3.19P 3.20P 3.21P 3.22P 3.23P 3.24P 3.25P 3.26P 3.27P For the following cases, determine the allowable gross vertical load-bearing capacity of the foundation. Use Terzaghi’s equation and assume general shear failure in soil. Use FS = 4. Parameters for Problem 6.1 A square column foundation has to carry a gross allowable load of 1805 kN (FS = 3). Given: Df = 1.5 m, =15.9 kN/m3, = 34, and c = 0. Use Terzaghis equation to determine the size of the foundation (B). Assume general shear failure.4.3P The applied load on a shallow square foundation makes an angle of 20° with the vertical. Given: B = 5 ft, Df = 3 ft, γ = 115 lb/ft3, ф′ = 25°, and c′ = 600 lb/ft2. Use FS = 3 and determine the gross inclined allowable load. Use Eq. (6.28). A column foundation (Figure P6.9) is 3 m × 2 m in plan. Given: Df = 1.5 m, ф′ = 25°, c′ = 70 kN/m2. Using Eq. (6.28) and FS = 3, determine the net allowable load [see Eq. (6.24)] the foundation could carry. Figure P6.9 4.6P For the design of a shallow foundation, given the following: Soil: = 20 c = 72 kN/m2 Unit weight, = 17 kN/m3 Modulus of elasticity, Es = 1400 kN/m2 Poissons ratio, s = 0.35 Foundation: L = 2 m B = 1 m Df = 1 m Calculate the ultimate bearing capacity. Use Eq. (6.42).An eccentrically loaded foundation is shown in Figure P6.11. Use FS of 4 and determine the maximum allowable load that the foundation can carry. Use Meyerhof’s effective area method. Figure P6.11 4.9P For an eccentrically loaded continuous foundation on sand, given B = 1.8 m, Df = 0.9 m, e/B = 0.12 (one-way eccentricity), γ = 16 kN/m3, and ф′ = 35°. Using the reduction factor method [Eq. (6.64)], estimate the ultimate load per unit length of the foundation. An eccentrically loaded continuous foundation is shown in Figure P6.18. Determine the ultimate load Qu per unit length that the foundation can carry. Use the reduction factor method [Eq. (6.67)]. Figure P6.18 A square foundation is shown in Figure P6.19. Use FS = 6, and determine the size of the foundation. Use Prakash and Saran’s method [Eq. (6.59)]. Figure P6.19 The shallow foundation shown in Figure 6.25 measures 1.5 m × 2.25 m and is subjected to a centric load and a moment. If eB = 0.12 m, eL = 0.36 m, and the depth of the foundation is 0.8 m, determine the allowable load the foundation can carry. Use a factor of safety of 4. For the soil, we are told that unit weight γ = 17 kN/m3, friction angle ф′ = 35°, and cohesion c′ = 0. Use Eqs (6.75), (6.76), and (6.77). Figure 6.25 Analysis of foundation with two-way eccentricity Consider a continuous foundation of width B = 1.4 m on a sand deposit with c = 0, = 38, and = 17.5 kN/m3. The foundation is subjected to an eccentrically inclined load (see Figure 6.33). Given: load eccentricity e = 0.15 m, Df = 1 m, and load inclination = 18. Estimate the failure load Qu(ei) per unit length of the foundation a. for a partially compensated type of loading [Eq. (6.89)] b. for a reinforced type of loading [Eq. (6.90)]5.1P Repeat Problem 5.1 with the following data: B = 1.5 m, L = 1.5 m, Df = 1 m, H = 0.6 m, = 35, c = 0, and = 15 kN/m3. Use FS = 3. Refer to Figure 5.2 and consider a rectangular foundation. Given: B = 1.5 m, L = 2.5 m, Df = 1.2 m, H = 0.9 m, = 40, c = 0, and = 17 kN/m3. Using a factor of safety of 3, determine the gross allowable load the foundation can carry. Use Eq. (5.3).Refer to Figure 5.2. Given: B = L = 1.75 m, Df = 1 m, H = 1.75 m, = 17 kN/m3, c = 0, and = 30. Using Eq. (5.6) and FS = 4, determine the gross allowable load the foundation can carry.5.4P 5.5P 5.6P 5.7P 5.8P 5.9P 5.10P 5.11P Two continuous foundations are constructed alongside each other in a granular soil. Given for the foundation: B = 1.2 m, Df = 1 m, and center-to-center spacing = 2 m. The soil friction angle ' = 35. Estimate the net allowable bearing capacity of the foundations. Use FS = 4 and a unit weight of soil, = 16.8 kN/m3.5.13P A continuous foundation with a width of 1 m is located on a slope made of clay soil. Refer to Figure 7.19 and let Df = 1 m, H = 4 m, b = 2 m, γ = 16.8 kN/m3, c = cu = 68 kN/m2, ϕ = 0, and β = 60°. Determine the allowable bearing capacity of the foundation. Let FS = 3. Plot a graph of the ultimate bearing capacity qu if b is changed from 0 to 6 m. A continuous foundation is to be constructed near a slope made of granular soil (see Figure 7.19). If B = 4 ft, b = 6 ft, H = 15 ft, Df = 4 ft, = 30, = 40, and = 110 lb/ft3, estimate the ultimate bearing capacity of the foundation.5.16P 5.17P 5.18P 5.19P A flexible circular area is subjected to a uniformly distributed load of 150 kN/m2 (Figure 6.2). The diameter of the load area is 2 m. Determine the stress increase in a soil mass at points located 3 in below the loaded area at r = 0, 0.4 m, 0.8 m, and 1 m. Use Boussinesqs solution.Point loads of magnitude 100, 200, and 400 kN act at B, C, and D, respectively (Figure P6.2). Determine the increase in vertical stress at a depth of 6 m below point A. Use Boussincsqs equation. Figure P6.2 Refer to Figure P6.3. Determine the vertical stress increase at point A with the values q1, = 90 kN/m, q2 = 325 kN/m, x1 = 4 m, x2 = 2.5 m, and z = 3 m. Figure P6.3 Refer to Figure P6.4. A strip load of q = 900 lb/ft2 is applied over a width B = 36 ft. Determine the increase in vertical stress at point A located z = 15 ft below the surface. Given: x = 27 ft. Figure P6.4 Refer to Figure 6.6, which shows a flexible rectangular area. Given: B1 = 4 ft, B2 = 6 ft, L1, = 8 ft, and L2 = 10 ft. If the area is subjected to a uniform load of 3000 lb/ft2, determine the stress increase at a depth of 10 ft located immediately below point O. Figure 6.6 Stress below any point of a loaded flexible rectangular area Repeat Problem 6.5 with B1 = 4 ft, B2 = 10 ft, L1 = 8 ft, L2 = 12 ft, and the uniform load on the flexible area = 2500 lb/ft2. Determine the stress increase below point O at a depth of 20 ft. Use Eq. (6.39) and s = 0. 6.5 Refer to Figure 6.6, which shows a flexible rectangular area. Given: B1 = 4 ft, B2 = 6 ft, L1, = 8 ft, and L2 = 10 ft. If the area is subjected to a uniform load of 3000 lb/ft2, determine the stress increase at a depth of 10 ft located immediately below point O. Figure 6.6 Stress below any point of a loaded flexible rectangular area Use Eq. (6.14) to determine the stress increase () at z = 10 ft below the center of the area described in Problem 6.5. 6.5 Refer to Figure 6.6, which shows a flexible rectangular area. Given: B1 = 4 ft, B2 = 6 ft, L1, = 8 ft, and L2 = 10 ft. If the area is subjected to a uniform load of 3000 lb/ft2, determine the stress increase at a depth of 10 ft located immediately below point O. Figure 6.6 Stress below any point of a loaded flexible rectangular area 6.8P 6.9P 6.10P 6.11P Refer to Problem 6.1. Using Eqs. (6.3) and (6.29), estimate the average stress increase (Δσav) below the center of the loaded area between depths of 3 m and 6 m. 6.1 A flexible circular area is subjected to a uniformly distributed load of 150kN/m2 (Figure 6.2). The diameter of the load area is 2 m. Determine the stress increase in a soil mass at points located 3 m below the loaded area at r = 0. 0.4 m, 0.8 m, and 1 m. Use Boussinesq’s solution. Figure 6.2 Increase in pressure under a uniformly loaded flexible circular area Redo Problem 6.12 using Figure 6.15. 6.12 Refer to Problem 6.1. Using Eqs. (6.3) and (6.29), estimate the average stress increase (av) below the center of the loaded area between depths of 3 m and 6 m. 6.1 A flexible circular area is subjected to a uniformly distributed load of 150 kN/m2 (Figure 6.2). The diameter of the load area is 2 m. Determine the stress increase in a soil mass at points located 3 m below the loaded area at r = 0, 0.4 m, 0.8 m, and 1 m. Use Boussinesqs solution. Figure 6.2 Increase in pressure under a uniformly loaded flexible circular area 7.1P A planned flexible load area (see Figure P7.2) is to be 3 m × 4.6 m and carries a uniformly distributed load of 180 kN/m2. Estimate the elastic settlement below the center of the loaded area. Assume that Df = 2 m and H = . Use Eq. (7.4). 7.3P 7.4P 7.5P 7.6P 7.7P 7.8P Solve Problem 7.8 using Eq. (7.29). Ignore the post-construction settlement. 7.8 Solve Problem 7.4 with Eq. (7.20). Ignore the correction factor for creep. For the unit weight of soil, use γ = 115 lb/ft3. 7.4 Figure 7.3 shows a foundation of 10 ft × 6.25 ft resting on a sand deposit. The net load per unit area at the level of the foundation, qo, is 3000 lb/ft2. For the sand, μs = 0.3, Es = 3200 lb/in.2, Df = 2.5 ft, and H = 32 ft. Assume that the foundation is rigid and determine the elastic settlement the foundation would undergo. Use Eqs. (7.4) and (7.12). A continuous foundation on a deposit of sand layer is shown in Figure P9.10 along with the variation of the cone penetration resistance qc. Assuming and creep is at the end of ten years after construction, calculate the elastic settlement of the foundation using the strain influence factor method. Use Eqs. (9.30) and (9.36). Solve Problem 9.10 using Eqs. (9.39), (9.40), and (9.41). 9.10 A continuous foundation on a deposit of sand layer is shown in Figure P9.10 along with the variation of the cone penetration resistance qc. Assuming and creep is at the end of ten years after construction, calculate the elastic settlement of the foundation using the strain influence factor method. Use Eqs. (9.30) and (9.36). 7.12P 7.13P 7.14P 7.15P 8.1P Following are the results of a standard penetration test in the field (sandy soil): Estimate the net allowable bearing capacity of a mat foundation 6.5 m × 5 m in plan. Here, Df = 1.5 m and allowable settlement = 50 mm. Assume that the unit weight of soil, γ = 16.5 kN/m3. Repeat Problem 8.2 for an allowable settlement of 25 mm. 8.2 Following are the results of a standard penetration test in the field (sandy soil): Estimate the net allowable bearing capacity of a mat foundation 6.5 m × 5 m in plan. Here, Df = 1.5 m and allowable settlement = 50 mm. Assume that the unit weight of soil, γ = 16.5 kN/m3. 8.4P 8.5P 8.6P 8.7P From the plate load test (plate dimensions 1 ft × 1 ft) in the field, the coefficient of subgrade reaction of a sandy soil is determined to be 60 lb/in3. What will be the value of the coefficient of subgrade reaction on the same soil for a foundation with dimensions of 20 ft × 20 ft? Refer to Problem 8.8. If the full-sized foundation had dimensions of 70 ft × 30 ft, what will be the value of the coefficient of subgrade reaction? 8.8 From the plate load test (plate dimensions 1 ft × 1 ft) in the field, the coefficient of subgrade reaction of a sandy soil is determined to be 60 lb/in3. What will be the value of the coefficient of subgrade reaction on the same soil for a foundation with dimensions of 20 ft × 20 ft? The subgrade reaction of a sandy soil obtained from the plate load test (plate dimensions 1 m × 0.7 m) is 18 MN/m3. What will be the value of k on the same soil for a foundation measuring 5 m × 3.5 m? A 20 m long concrete pile is shown in Figure P12.2. Estimate the ultimate point load Qp by a. Meyerhofs method b. Vesics method c. Coyle and Castellos method Use m = 600 in Eq. (12.28).Refer to the pile shown in Figure P9.1. Estimate the side resistance Qs by Using Eqs. (9.40) through (9.42). Use K = 1.5 and Coyle and Castello’s method [Eq. (9.44)] 9.3P A driven closed-ended pile, circular in cross section, is shown in Figure P12.7. Calculate the following. The ultimate point load using Meyerhof’s procedure. The ultimate point load using Vesic’s procedure. Take Irr = 50. An approximate ultimate point load on the basis of parts (a) and (b). The ultimate frictional resistance Qs. [Use Eqs. (12.42) through (12.44), and take K = 1.4 and δ′ = 0.6ϕ′.] The allowable load of the pile (use FS = 4). 9.5P 9.6P 9.7P 9.8P 9.9P A concrete pile 16 in. 16 in. in cross section is shown in Figure P12.13. Calculate the ultimate skin friction resistance by using the a. method [use Eq. (12.61) and Table 12.11] b. method c. method Use R=20 for all clays, which are normally consolidated.9.11P Solve Problem 12.13 using Eqs. (12.59) and (12.60). 12.13 A concrete pile 16 in. × 16 in. in cross section is shown in Figure P12.13. Calculate the ultimate skin friction resistance by using the α method [use Eq. (12.61) and Table 12.11] λ method β method Use for all clays, which are normally consolidated. 9.13P 9.14P A steel pile (H-section; HP 310 125; see Table 12.1a) is driven into a layer of sandstone. The length of the pile is 25 m. Following are the properties of the sandstone: unconfined compression strength = qu(lab) = 80 MN/m2 and angle of friction = 36. Using a factor of safety of 3, estimate the allowable point load that can be carried by the pile. Use [qu(design) = qu(lab)/5].A concrete pile is 20 m long and has a cross section of 0.46 m × 0.46 m. The pile is embedded in a sand having γ = 17 kN/m3 and ϕ′ = 38°. The allowable working load is 1200 kN. If 700 kN are contributed by the frictional resistance and 500 kN are from the point load, determine the elastic settlement of the pile. Given: Ep = 2.1 × 106 kN/m2, Es = 30 × 103 kN/m2, μs = 0.38, and ξ = 0.57 [Eq. (9.81)]. 9.17P 9.18P Solve Problem 12.23 using the method of Broms. Assume that the pile is flexible and free headed. Let the soil unit weight, = 16 kN/m3; the soil friction angle, = 30; and the yield stress of the pile material. FY = 21 MN/m2. 12.23 A 30 m long concrete pile is 305 mm 305 mm in cross section and is fully embedded in a sand dcposit. If nh = 9200 kN/m2, the moment at ground level Mg = 0, the allowable displacement of pile head = 12 mm; Ep = 21 106 kN/m2, and FY(pile) = 21,000 kN/m2, calculate the allowable lateral load, Qg, at the ground level. Use the elastic solution method.9.20P Solve Problem 12.25 using the modified EN formula. (See Table 12.17.) Use FS = 3. 12.25 A steel H-pile (section HP 13 100) is driven by a hammer. The maximum rated hammer energy is 40 kipft, the weight of the ram is 12 kip, and the length of the pile is 90 ft. Also, we have coefficient of restitution = 0.35, weight of the pile cap 2.4 kip, hammer efficiency = 0.85, number of blows for the last inch of penetration = 10, and Ep = 30 106 lb/in2. Estimate the pile capacity using Eq. (12.122). Take FS = 6.Solve Problem 12.25 using the modified Danish formula. (See Table 12.17.) Use FS = 3. 12.25 A steel H-pile (section HP 13 × 100) is driven by a hammer. The maximum rated hammer energy is 40 kip·ft, the weight of the ram is 12 kip, and the length of the pile is 90 ft. Also, we have coefficient of restitution = 0.35, weight of the pile cap 2.4 kip, hammer efficiency = 0.85, number of blows for the last inch of penetration = 10, and Ep = 30 × 106 lb/in2. Estimate the pile capacity using Eq. (12.122). Take FS = 6. Figure 12.49a shows a pile. Let L = 15 m, D (pile diameter) = 305 mm, Hf = 3 m, fill = 17.5 kN/m3, and fill = 25. Determine the total downward drag force on the pile. Assume that the fill is located above the water table and that ' = 0.5fill.Redo Problem 12.30 assuming that the water table coincides with the top of the fill and that sat(fill) = 19.8 kN/m3. If the other quantities remain the same, what would be the downward drag force on the pile? Assume ' = 0.5fill. 12.30 Figure 12.49a shows a pile. Let L = 15 m, D (pile diameter) 305 mm, Hf = 3 m, fill = 17.5 kN/m3, and fill = 25°. Determine the total downward drag force on the pile. Assume that the fill is located above the water table and that = 0.5fill. Refer to Figure 12.49b. Let L = 18 m, fill = 17 kN/m3, sat(clay) = 19 8 kN/m3, clay = 20, Hf = 3.5 m, and D (pile diameter) = 406 mm. The water table coincides with the top of the clay layer. Determine the total downward drag force on the pile. Assume ' = 0.6clay.A concrete pile measuring 16 in. × 16 in. in cross section is 60 ft long. It is fully embedded in a layer of sand. The following is an approximation of the mechanical cone penetration resistance (qc) and the friction ratio (Fr) for the sand layer. Estimate the allowable bearing capacity of the pile. Use FS = 4. The plan of a group pile is shown in Figure P12.34. Assume that the piles are embedded in a saturated homogeneous clay having a cu = 90 kN/m2. Given: diameter of piles (D) = 316 mm, center-to-center spacing of piles = 600 mm, and length of piles = 20 m. Find the allowable load-carrying capacity of the pile group. Use Table 12.11 and FS = 3. 9.28P The section of a 4 × 4 group pile in a layered saturated clay is shown in Figure P9.29. The piles are square in cross section (356 mm × 356 mm). The center-to-center spacing (d) of the piles is 1 m. Determine the allowable load-bearing capacity of the pile group. Use FS = 3 and Table 9.10. 9.30P 10.1P Redo Problem 10.1, this time using Eq. (10.5). Let Es = 600pa. 10.1 A drilled shaft is shown in Figure P10.1. Determine the net allowable point bearing capacity. Given Use Eq. (10.18). For the drilled shaft described in Problem 10.1, what skin resistance would develop in the top 6 m, which are in clay? Use Eqs. (10.37) and (10.39). 10.1 A drilled shaft is shown in Figure P10.1. Determine the net allowable point bearing capacity. Given 10.4P 10.5P 10.6P 10.7P 10.8P 10.9P 10.10P 10.11P 10.12P 10.13P Figure P13.9 shows a drilled shaft extending into clay shale. Given: qu (clay shale) = 1.81 MN/m2. Considering the socket to be rough, estimate the allowable load-carrying capacity of the drilled shaft. Use FS = 4. Use the Zhang and Einstein procedure.A free-headed drilled shaft is shown in Figure P13.10. Let Qg = 260 kN, Mg = 0, = 17.5 kN/m3, = 35, c' = 0, and Ep = 22 106 kN/m2. Determine a. The ground line deflection, xo b. The maximum bending moment in the drilled shaft c. The maximum tensile stress in the shaft d. The minimum penetration of the shaft needed for this analysis 10.16P 11.1P 11.2P 11.3P 11.4P 11.5P 11.6P 11.7P Refer to Figure 15.26b. For the drilled shaft with bell, given: Thickness of active zone, Z = 9 m Dead load = 1500 kN Live load = 300 kN Diameter of the shaft, Ds = 1 m Zero swell pressure for the clay in the active zone = 600 kN/m2 Average angle of plinthsoil friction, ps=20 Average undrained cohesion of the clay around the bell = 150 kN/m2 Determine the diameter of the bell, Db. A factor of safety of 3 against uplift is required with the assumption that dead load plus live load is equal to zero.11.9P 12.1P 12.2P 12.3P 12.4P 12.5P 12.6P 12.7P 12.8P 12.9P 12.10P 12.11P 12.12P 12.13P 12.14P 12.15P 13.1P 13.2P 13.3P 13.4P 13.5P 13.6P 13.7P 13.8P 13.9P 13.10P 14.1P Redo Problem 14.1 with the following: L1 = 3m, L2 = 6 m, γ = 17.3 kN/m3, γsat = 19.4 kN/m3, and ϕ′ = 30°. 14.1 Figure P14.1 shows a cantilever sheet-pile wall penetrating a granular soil. Here, L1 = 4 m, L2 = 8 m, γ = 16.1 kN/m3, γsat = 18.2 kN/m3, and ϕ′ = 32°. What is the theoretical depth of embedment, D? For a 30% increase in D, what should be the total length of the sheet piles? Determine the theoretical maximum moment of the sheet pile. 14.3P 14.4P 14.5P 14.6P 14.7P 14.8P 14.9P 14.10P 14.11P 14.12P 14.13P 15.1P 15.2P 15.3P 15.4P 15.5P 15.6P 15.7P 15.8P 15.9P 15.10P 15.11P 16.1P 16.2P 16.3P 16.4P 16.5P 16.6P 16.7P 16.8P 16.9P 16.10P 16.11P 16.12P

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