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All Textbook Solutions for Fundamentals of Geotechnical Engineering (MindTap Course List)

2.1P Following are the results of a sieve analysis: a. Determine the percent finer than each sieve size and plot a grain-size distribution curve. b. Determine D10, D30, and D60 from the grain-size distribution curve. c. Calculate the uniformity coefficient, Cu. d. Calculate the coefficient of gradation, Cc.For a soil, given: D10 = 0.08 mm D30 = 0.22 mm D60 = 0.41 mm Calculate the uniformity coefficient and the coefficient of gradation of the soil.For a soil, given: D10 = 0.08 mm D30 = 0.22 mm D60 = 0.41 mm Calculate the uniformity coefficient and the coefficient of gradation of the soil. 2.4 Repeat Problem 2.3 for the following: D10 = 0.24 mm D30 = 0.82 mm D60 = 1.81 mm Repeat Problem 2.2 with the following results of a sieve analysis: 2.2 Following are the results of a sieve analysis: a. Determine the percent finer than each sieve size and plot a grain-size distribution curve. b. Determine D10, D30, and D60 from the grain-size distribution curve. c. Calculate the uniformity coefficient. Cu. d. Calculate the coefficient of gradation, Cc.Repeat Problem 2.2 with the following results of a sieve analysis: 2.2 Following are the results of a sieve analysis: a. Determine the percent finer than each sieve size and plot a grain-size distribution curve. b. Determine D10, D30, and D60 from the grain-size distribution curve. c. Calculate the uniformity coefficient, Cu. d. Calculate the coefficient of gradation, Cc.The particle characteristics of a soil are given below. Draw the particle-size distribution curve and find the percentages of gravel, sand, silt, and clay according to the MIT system (Table 2.3).Redo Problem 2.7 according to the USDA system (Table 2.3). 2.7 The particle characteristics of a soil are given below. Draw the particle-size distribution curve and find the percentages of gravel, sand, silt, and clay according to the MIT system (Table 2.3).Redo Problem 2.7 according to the AASHTO system (Table 2.3). 2.7 The particle characteristics of a soil are given below. Draw the particle-size distribution curve and find the percentages of gravel, sand, silt, and clay according to the MIT system (Table 2.3).In a hydrometer test, the results are as follows: Gs = 2.60, temperature of water = 24, and hydrometer reading = 43 at 60 min after the start of sedimentation. What is the diameter, D, of the smallest-size grains that have settled beyond the zone of measurement at that time (that is, t = 60 min)?2.11P 2.12P 2.13P 2.14P In concrete work, Fuller and Thompson (1907) suggested that a dense packing of grains can be achieved if the percent finer (p) and grain size (D) are related by the following equation, where n is a constant varying in the range of 0.3-0.6. Dmax is the size of the largest grain within the soil. p=(DDmax)n100 This equation is sometimes used in roadwork for selecting the aggregates. a. For n = 0.5, show that the soil is well graded. b. If n = 0.5 and Dmax = 19.0 mm, find the percentages of gravel, sand, and fines within the soil. Use the Unified Soil Classification System.3.1P 3.2P 3.3P 3.4P 3.5P 3.6P 3.7P 3.8P 3.9P 3.10P 3.11P 3.12P 3.13P 3.14P 3.15P 3.16P 3.17P Following are the results from the liquid and plastic limit tests for a soil. Liquid limit test: Plastic limit test: PL = 18.7% a. Draw the flow curve and obtain the liquid limit. b. What is the plasticity index of the soil?3.19P 3.20CTP 3.21CTP State whether the following are true or false. a. In the AASHTO classification Table 4.1, the soils that are more suitable for roadwork are located on the left than right. b. In AASHTO classification system, the better performing fine grained soils are the ones with lower group indices. c. In AASHTO classification system, sands are classified as grains with 0.075-4.75 mm diameter. d. The USCS symbol for clayey gravel is CG. e. A soil with USCS symbol SM is sandy silt.In AASHTO, which group are the following soils likely to fall into? a. A well graded gravel with approximately 10% fines. b. A well graded sand with approximately 10% fines. c. A uniform fine sand. d. A high plastic clay.4.3P 4.4P 4.5P For soils that are classified by the following USCS symbols, what would be the most likely AASHTO symbols? (Reference: Liu, 1970) Gravels: GW, GP, GM, GC Sands: SW, SP, SM, SC Fines: ML, CL, MH, CH For the soils that are classified by the following AASHTO symbols, what would be the most likely USCS symbols? (Reference: Liu, 1970) Gravels sands: A-l-a, A-l-b, A3, A-2-4, A-2-5, A-2-6, A-2-7 Fines: A-4, A-5, A-6, A-7-5, A-7-6 5.1P 5.2P 5.3P 5.4P 5.5P 5.6P 5.7P 5.8P 5.9P 5.10P 5.11P 5.12P 5.13P 5.14P 5.15P 5.16P 5.17CTP 6.1P 6.2P 6.3P 6.4P 6.5P 6.6P 6.7P 6.8P 6.9P 6.10P 6.11P 6.12P 6.13P 6.14P 6.15P 6.16P 6.17CTP 7.1P 7.2P 7.3P 7.4P 7.5P 7.6P 7.7CTP 8.1P 8.2P 8.3P 8.4P 8.5P 8.6P 8.7P 8.8P 8.9P The soil profile at a site consists of 10 m of gravelly sand underlain by a soft clay layer. The water table lies 1 m below the ground level. The moist and saturated unit weights of the gravelly sand are 17.0 kN/m3 and 20.0 kN/m3, respectively. Due to some ongoing construction work, it is proposed to lower the water table to 3 m below the ground level. What will be the change in the effective stress on top of the soft clay layer?8.11P 8.12P 8.13P 8.14P A sand has Gs = 2.66. Calculate the hydraulic gradient that will cause boiling for e = 0.35, 0.45, 0.55, 0.7, and 0.8.8.16P A point load of 1000 kN is applied at the ground level. Plot the variation of the vertical stress increase z with depth at horizontal distances of 1 m, 2 m, and 4 m from the load.Point loads of magnitude 9, 18, and 27 kN act at A, B, and C, respectively (Figure 8.23). Determine the increase in vertical stress at a depth of 3 m below point D. Use Boussinesqs equation. FIG. 8.23 Refer to Figure 8.13. The magnitude of the line load q is 45 kN/m. Calculate and plot the variation of the vertical stress increase, between the limits of x = 10 m and x = +10 m, given z = 4 m. FIG. 8.13 Line load over the surface of a semiinfinite soil mass Refer to Figure 8.24. Determine the vertical stress increase, , at point A with the following values: q1 = 100 kN/m x1 = 3 m z = 2 m q2 = 200 kN/m x2 = 2 m FIG. 8.24 Stress at a point due to two line loads Consider a circularly loaded flexible area on the ground surface. Given: radius of the circular area, R = 3 m; uniformly distributed load, q = 250 kN/m2. Calculate the vertical stress increase at a point located 5 m (z) below the ground surface (immediately below the center of the circular area).A flexible circular footing of radius R carries a uniform pressure q. Find the depth (in terms of R) at which the vertical stress below the center is 20% of q.The plan of a flexible rectangular loaded area is shown in Figure 8.25. The uniformly distributed load on the flexible area (q) is 400 kN/m2. Determine the increase in the vertical stress () at a depth of z = 5 m below a. Point A b. Point B c. Point C FIG. 8.25 Refer to Figure 8.26. The circular flexible area is uniformly loaded. Given: q = 320 kN/m2. Determine the vertical stress increase at point A. FIG. 8.26 Refer to Figure 8.27. The flexible area is uniformly loaded. Given: q = 300 kN/m2. Determine the vertical stress increase at point A located at depth 3 m below point A (shown in the plan). FIG. 8.27 8.26CTP 8.27CTP 9.1P 9.2P 9.3P 9.4P 9.5P The coordinates of two points on a virgin compression curve are as follows: e1 = 0.82 1=125kN/m2 e2 = 0.70 2=200kN/m2 Determine the void ratio that corresponds to a pressure of 300 kN/m2.9.7P 9.8P The coordinates of two points on a virgin compression curve are as follows: e1 = 1.7 1=150kN/m2 e2 = 1.48 2=400kN/m2 a. Determine the coefficient of volume compressibility for the pressure range stated. b. Given that cv = 0.002 cm2/sec, determine k in cm/sec corresponding to the average void ratio.9.10P 9.11P 9.12P 9.13P 9.14P 9.15P 9.16P 9.17P 9.18P 9.19CTP 9.20CTP 10.1P 10.2P 10.3P 10.4P 10.5P 10.6P 10.7P 10.8P 10.9P 10.10P 10.11P 10.12P 10.13P 10.14P 10.15P 10.16P 10.17P 10.18P 10.19P 10.20P 10.21P 10.22P 10.23P 10.24CTP 10.25CTP 11.1P 11.2P 11.3P 11.4P 11.5P 11.6P 11.7P 11.8P 11.9P 11.10CTP 12.1P 12.2P A soil profile is shown in Figure 12.30 along with the standard penetration numbers in the clay layer. Use Eqs. 12.5 to determine and plot the variation of cu with depth. Use K = 4.4 kN/m2. FIG. 12.30 12.4P 12.5P 12.6P The table gives the standard penetration numbers determined from a sandy soil deposit in the field: Using Eq. (12.19), 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 6 m, the unit weight of soil is 18.55 kN/m3.12.8P 12.9P 12.10P 12.11P 12.12P 12.13P 12.14P 12.15P 12.16P 12.17P 12.18P 13.1P 13.2P 13.3P 13.4P 13.5P 13.6P 13.7P 13.8P 13.9P 13.10P 13.11P 13.12P 13.13P 13.14P 13.15P 13.16P 13.17P 13.18P 13.19P 13.20P 13.21P 13.22P 13.23P 13.25P 13.26P 13.27CTP 13.28CTP 13.29CTP State whether the following are true or false. a. The higher the friction angle, the higher the value ofK0. b. K0is greater for normally consolidated clays than overconsolidatedclays. c. Active earth pressure coefficient is greater than the passive one. d. The larger the cohesion, the larger is the depth of the tensile cracks inclays in active state. e. Lateral earth pressures increase linearly with depth.14.2P 14.3P 14.4P 14.5P 14.6P 14.7P 14.8P 14.9P 14.10P 14.11P 14.12P 14.13P 14.14P 14.15P 14.16CTP 14.17CTP 14.18CTP 14.19CTP 15.1P 15.2P 15.3P 15.4P 15.5P 15.6P 15.7P 15.8P 15.9P 15.10P 15.11P 15.12P 15.13P 15.14P 15.15P Refer to the braced cut in Figure 15.50, for which = 17 kN/m3, =30, and c = 0. The struts are located at 3 m on center in the plan. Draw the earth pressure envelope and determine the strut loads at levels A, B, and C. FIG. 15.50 For the braced cut described in Problem 15.16, assume that all = 170 MN/m2. a. Determine the sheet pile section (section modulus) b. What is the section modulus of the wales at level A? 15.16 Refer to the braced cut in Figure 15.50, for which = 17 kN/m3, = 30, and c = 0. The struts are located at 3 m on center in the plan. Draw the earth pressure envelope and determine the strut loads at levels A, B, and C. FIG. 15.50 Refer to Figure 15.51 in which = 17.5 kN/m3, c = 60 kN/m2, and center-to-oenter spacing of struts is 5 m. Draw the earth pressure envelope and determine the strut loads at levels A, B, and C. FIG. 15.51 Refer to Figure 15.27a. For the braced cut, H = 6 m, Hs = 2 m, s = 16.2 kN/m3, angle of friction of sand, s=34, Hc = 4 m, c = 17.5 kN/m3, and the unconfined compression strength of the clay layer, qu = 68 kN/m2. a. Estimate the average cohesion, cav, and the average unit weight, av, for development of the earth pressure envelope. b. Plot the earth pressure envelope. FIG. 15.27 Layered soils in braced cuts 15.20P Determine the factor of safety against bottom heave for the braced cut described in Problem 15.18. Use Eqs. (15.66) and (15.70). For Eq. (15.70), assume the length of the cut, L = 18 m. 15.18 Refer to Figure 15.51 in which = 17.5 kN/m3, c = 60 kN/m2, and center-to-center spacing of struts is 5 m. Draw the earth pressure envelope and determine the strut loads at levels A, B, and C. FIG. 15.51 15.22P The water table at a site is at 5 m below the ground level, and it is required to excavate to this level. The soil profile consists of a thick bed of sand where the unit weight is m = 17.0 kN/m3 above the water table and sat = 20.0 kN/m3 below the water table. The friction angle of the sand is 37. The wall of the excavation will be supported by cantilever sheet piles. How deep would you drive the sheet piles? Use the simplified analysis (Figure 15.37) with a factor of safety of 1.5 on the passive resistance. Determine the maximum bending moment in the sheet pile and the required section modulus for the sheet pile section (given an allowable stress of 190 MN/m2).15.24P 15.25CTP Figure 15.53 below shows a cantilever sheet pile driven into a granular soil where the water table is 2 m below the top of the sand. The properties of thesand are: ' = 40, m = 17.5 kN/m3, and sat = 19 kN/m3. It is proposed toexcavate to a depth of 6 m below the ground level. Determine the depth towhich the sheet pile mast be driven, using the net lateral pressure diagram. Fig. 15.53 16.1P A 2.0 m wide continuous foundation carries a wall load of 350 kN/m in a clayey soil where = 19.0 kN/m3, c = 5 kN/m2 and =23. The foundation depth is 1.5 m. Determine the factor of safety of this foundation.Determine the maximum column load that can be applied on a 1.5 m 1.5 m square foundation, placed at a depth of 1.0 m within a soil, where = 19.0 kN/m3, c = 10 kN/m2 and =24. Allow a factor of safety of 3.0.A 2.0 m wide strip foundation is placed in sand at 1.0 m depth. The properties of the sand are: = 19.5 kN/m3, c = 0 and =34. Determine the maximum wall load that the foundation can carry, with a factor of safety of 3.0, using a. Terzaghis original bearing capacity equation with his bearing capacity factors b. Meyerhofs modified bearing capacity equation with appropriate factors (Tables 16.2 and 16.3).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). The applied load on a shallow square foundation makes an angle of 15 with the vertical. Given: B = 1.83 m, Df = 0.91 m, = 18.08 kN/m3, =25, and c = 23.96 kN/m2. Use FS = 4 and determine the gross allowable (vertical component) load. Use Eq. (16.9).The applied load on a shallow square foundation makes an angle of 15 with the vertical. Given: B = 1.83 m, Df = 0.91 m, = 18.08 kN/m3, =25, and c = 23.96 kN/m2. Use FS = 4 and determine the gross allowable (vertical component) load. Use Eq. (16.9).A column foundation (Figure 16.23) is 3 m 2 m in plan. Given: Df = 1.5 m, =25, c = 70 kN/m2. Using Eq. (16.9) and FS = 3, determine the net allowable load [see Eq. (16.16)] the foundation could carry. FIG. 16.23 16.8P A 2 m 3 m spread foundation placed at a depth of 2 m carries a vertical load of 3000 kN and a moment of 300 kNm, as shown in Figure 16.24. Determine the factor of safety. FIG. 16.24 An eccentrically loaded foundation is shown in Figure 16.25. Use FS of 4 and determine the maximum allowable load that the foundation can carry. Use Meyerhofs effective area method. FIG. 16.25 For an eccentrically loaded continuous foundation on sand, given B = 1.8 m, Df = 0.9 m, e/B = 0.12 (one-way eccentricity), = 16 kN/m3, and =35. Using the reduction factor method [Eq. (16.26)], estimate the ultimate load per unit length of the foundation.The shallow foundation shown in Figure 16.12 measures 1.2 m 1.8 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 1 m, determine the allowable load the foundation can carry. Use a factor of safety of 3. For the soil, we are told that unit weight = 17 kN/m3, friction angle =35, and cohesion c = 0. FIG. 16.12 Analysis of foundation with two-way eccentricity A mat foundation measuring 14 m 9 m has to be constructed on a saturated clay. For the clay, cu = 93 kN/m2 and =0. The depth, Df, for the mat foundation is 2 m. Determine the net ultimate bearing capacity.Repeat Problem 16.13 with the following: Mat foundation: B = 8 m, L = 20 m, and Df = 2 m Clay: =0 and cu = 130 kN/m2 16.13 A mat foundation measuring 14 m 9 m has to be constructed on a saturated clay. For the clay, cu = 93 kN/m2 and =0. The depth, Df, for the mat foundation is 2 m. Determine the net ultimate bearing capacity.16.15P For the mat in Problem 16.15, what will be the depth, Df, of the mat for FS = 3 against bearing capacity failure? 16.15 Consider a mat foundation with dimensions of 18 m 12 m. The combined dead and live load on the mat is 44.5 MN. The mat is to be placed on a clay with cu = 40.7 kN/m2 and = 17.6 kN/m3. Find the depth, Df, of the mat for a fully compensated foundation.16.17CTP 16.18CTP A 2.0 m 2.0 m square pad footing will be placed in a normally consolidated clay soil to carry a column load Q. The depth of the footing is 1.0 m. The soil parameters are: c = 0, =26, = 19 kN/m3, cu = 60 kN/m2 (=0 condition). Determine the maximum possible value for Q, considering short-term and long-term stability of the footing.17.1P A 3 m 4 m footing, founded at 2 m depth in a clay, applies a net pressure of 200 kN/m2. The bed rock lies 10 m below the footing. The modulus of elasticity of the clay is 30 MN/m2. Using Janbus generalized relationship [Eq. (17.1)], assuming undrained conditions and flexible footing carrying uniform pressure, estimate the expected settlement.A planned flexible load area (sec Figure 17.13) is to be 2 m 3.2 m and carries a uniformly distributed load of 210 kN/m2. Estimate the elastic settlement below the center of the loaded area. Assume that Df = 1.6 m and H=. Use Eq. (17.2). FIG. 17.13 17.4P 17.5P 17.6P 17.7P 17.8P 17.9P 17.10P 17.11P 17.12P 17.13P Following are the results of standard penetration tests in a granular soil deposit. What will be the net allowable bearing capacity of a foundation planned to be 1.5 m 1.5 m? Let Df = 1 m and the allowable settlement = 25 mm, and use the relationships presented in Section 17.7.A shallow square foundation for a column is to be constructed. It must carry a net vertical load of 1000 kN. The soil supporting the foundation is sand. The standard penetration numbers (N60) obtained from field exploration are as follows: FIG. 17.15 The groundwater table is located at a depth of 12 m. The unit weight of soil above the water table is 15.7 kN/m3, and the saturated unit weight of soil below the water table is 18.8 kN/m3. Assume that the depth of the foundation will be 1.5 m and the tolerable settlement is 25 mm. Determine the size of the foundation.17.16CTP 17.17CTP State whether the following are true or false. a. Load carrying capacities of timber piles are less than those of steel or concrete piles. b. If the load carried by the pile cross section decreases linearly with depth, the frictional resistance per unit remains the same at all depths. c. The point load is mobilized well before the shaft load. d. Soil-pile friction angle can be greater than the friction angle of the soil . e. Bored piles are high displacement piles.A 1500 kN load was applied on two 20 m long and 500 mm diameter driven piles that were instrumented for measuring the load variation with depth. a. The variation of frictional resistance per unit area f(z) with depth for the first pile is shown Figure 18.33a. Draw the variation of pile load Q(z) with depth. b. The variation of pile load Q(z) with depth for the second pile is shown Figure 18.33b. Draw the variation of frictional resistance per unit area f(z) with depth. FIG. 18.33 A 500 mm diameter and 20 m long concrete pile is driven into a sand where = 18.5 kN/m3 and = 32. Assuming = 0.7 and K = 1.5 Ko, determine the load carrying capacity of the pile with a factor of safety of 3.A 400-mm diameter and 15 m long concrete pile is driven into a sand where = 18.0 kN/m3 and = 31. Assuming = 0.65 and K = 1.4 Ko, determine the load carrying capacity of the pile with a factor of safety of 3.A 400 mm 400 mm square precast concrete pile of 15 m length is driven into a sand where = 18.0 kN/m3 and = 33. Assuming = 0.7 and K = 1.4Ko, determine the load carrying capacity of the pile with factor of safety of 3.0.18.6P 18.7P

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