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

For a gravel with D60 = 0.48 mm, D30 = 0.25 mm, and D10 = 0.11 mm, calculate the uniformity coefficient and the coefficient of gradation. Is it a well-graded or a poorly graded soil?2.2P 2.3P The following are the results of a sieve analysis. a. Determine the percent finer than each sieve and plot a grain-size distribution curve. b. Determine D10, D30, and D60 for each soil. c. Calculate the uniformity coefficient Cu. d. Calculate the coefficient of gradation Cc.Repeat Problem 2.4 with the following data. 2.4 The following are the results of a sieve analysis. a. Determine the percent finer than each sieve and plot a grain-size distribution curve. b. Determine D10, D30, and D60 for each soil. c. Calculate the uniformity coefficient Cu. d. Calculate the coefficient of gradation Cc.Repeat Problem 2.4 with the following data. 2.4 The following are the results of a sieve analysis. a. Determine the percent finer than each sieve and plot a grain-size distribution curve. b. Determine D10, D30, and D60 for each soil. c. Calculate the uniformity coefficient Cu. d. Calculate the coefficient of gradation Cc.Repeat Problem 2.4 with the following data. 2.4 The following are the results of a sieve analysis. a. Determine the percent finer than each sieve and plot a grain-size distribution curve. b. Determine D10, D30, and D60 for each soil. c. Calculate the uniformity coefficient Cu. d. Calculate the coefficient of gradation Cc.The following are the results of a sieve and hydrometer analysis. a. Draw the grain-size distribution curve. b. Determine the percentages of gravel, sand, silt and clay according to the MIT system. c. Repeat Part b according to the USDA system. d. Repeat Part b according to the AASHTO system.Repeat Problem 2.8 using the following data. 2.8 The following are the results of a sieve and hydrometer analysis. a. Draw the grain-size distribution curve. b. Determine the percentages of gravel, sand, silt and clay according to the MIT system. c. Repeat Part b according to the USDA system. d. Repeat Part b according to the AASHTO system.Repeat Problem 2.8 using the following data. 2.8 The following are the results of a sieve and hydrometer analysis. a. Draw the grain-size distribution curve. b. Determine the percentages of gravel, sand, silt and clay according to the MIT system. c. Repeat Part b according to the USDA system. d. Repeat Part b according to the AASHTO system.The grain-size characteristics of a soil are given in the following table. a. Draw the grain-size distribution curve. b. Determine the percentages of gravel, sand, silt, and clay according to the MIT system. c. Repeat Part b using the USDA system. d. Repeat Part b using the AASHTO system.Repeat Problem 2.11 with the following data. 2.11 The grain-size characteristics of a soil are given in the following table. a. Draw the grain-size distribution curve. b. Determine the percentages of gravel, sand, silt, and clay according to the MIT system. c. Repeat Part b using the USDA system. d. Repeat Part b using the AASHTO system.Repeat Problem 2.11 with the following data. 2.11 The grain-size characteristics of a soil are given in the following table. a. Draw the grain-size distribution curve. b. Determine the percentages of gravel, sand, silt, and clay according to the MIT system. c. Repeat Part b using the USDA system. d. Repeat Part b using the AASHTO system.A hydrometer test has the following result: Gs = 2.65, temperature of water = 26 C, and L = 10.4 cm at 45 minutes after the start of sedimentation (see Figure 2.25). What is the diameter D of the smallest-size particles that have settled beyond the zone of measurement at that time (that is, t = 45 min)? Figure 2.25 ASTM 152H type of hydrometer placed inside the sedimentation cylinder (Courtesy of Khaled Sobhan, Florida Atlantic University, Boca Raton, Florida)Repeat Problem 2.14 with the following values: Gs = 2.75, temperature of water = 21C, t = 88 min, and L = 11.7 cm. 2.14 A hydrometer test has the following result: Gs = 2.65, temperature of water = 26 C, and L = 10.4 cm at 45 minutes after the start of sedimentation (see Figure 2.25). What is the diameter D of the smallest-size particles that have settled beyond the zone of measurement at that time (that is, t = 45 min)? Figure 2.25 ASTM 152H type of hydrometer placed inside the sedimentation cylinder (Courtesy of Khaled Sobhan, Florida Atlantic University, Boca Raton, Florida)Three groups of students from the Geotechnical Engineering class collected soil-aggregate samples for laboratory testing from a recycled aggregate processing plant in Palm Beach County, Florida. Three samples, denoted by Soil A, Soil B, and Soil C, were collected from three locations of the aggregate stockpile, and sieve analyses were conducted (see Figure 2.35). (a) (b) Figure 2.35 (a) Soil-aggregate stockpile; (b) sieve analysis (Courtesy of Khaled Sobhan, Florida Atlantic University, Boca Raton, Florida) a. Determine the coefficient of uniformity and the coefficient of gradation for Soils A, B, and C. b. Which one is coarser: Soil A or Soil C? Justify your answer. c. Although the soils are obtained from the same stockpile, why are the curves so different? (Hint: Comment on particle segregation and representative field sampling.) d. Determine the percentages of gravel, sand and fines according to Unified Soil Classification System.Refer to Problem 2.C.1. Results of the sieve analysis for Soils A, B, and C are given below. To obtain a more representative sample for further geotechnical testing, a ternary blend is created by uniformly mixing 8000 kg of each soil. Answer the following questions. a. If a sieve analysis is conducted on the mixture using the same set of sieves as shown above, compute the mass retained (as a percentage) and cumulative percent passing in each sieve. b. What would be the uniformity coefficient (Cu) and the coefficient of gradation (Cc) of the mixture?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 3.18P 3.19P 3.20P 3.21P 3.22P 3.23P 3.24P For a given sandy soil, emax = 0.75 and emin = 0.52. If Gs = 2.67 and Dr = 65%, determine the void ratio and the dry unit weight.For a given sandy soil, the maximum and minimum void ratios are 0.77 and 0.41, respectively. If Gs = 2.66 and w = 9%, what is the moist unit weight of compaction (kN/m3) in the field if Dr = 90%?3.27P 3.28P 3.29P 3.1CTP 3.2CTP 3.3CTP During Atterberg limit tests in the soil mechanics laboratory, the students obtained the following results from a clayey soil. Liquid limit tests: Plastic limit tests: Students conducted two trials and found that PL = 17.2% for the first trial and PL = 17.8% for the second trial. a. Draw the flow curve and obtain the liquid limit. b. What is the plasticity index of the soil? Use an average value of PL from the two plastic limit trails.4.2P 4.3P Results from a liquid limit test conducted on a soil are given below. a. Determine the liquid limit of the soil. b. If it is known that the PI = 6.5, what would be the plastic limit of the soil? c. Determine the liquidity index of the soil if win situ = 23.8%The following data were obtained by conducting liquid limit and plastic limit tests on a soil collected from the site. Liquid limit tests: Plastic limit test: PL = 19.3% a. Draw the flow curve and determine the liquid limit. b. Using the Casagrande plasticity chart (Figure 4.21), determine the soil type.Refer to the soil in Problem 4.5. Using the Casagrande plasticity chart, graphically estimate the shrinkage limit of the soil as shown in Figure 4.22. 4.5 The following data were obtained by conducting liquid limit and plastic limit tests on a soil collected from the site. Liquid limit tests: Plastic limit test: PL = 19.3% a. Draw the flow curve and determine the liquid limit. b. Using the Casagrande plasticity chart (Figure 4.21), determine the soil type.Following results are obtained for a liquid limit test using a fall cone device. Estimate the liquid limit of the soil and the flow index.4.8P 4.9P 4.10P 4.11P 4.12P The properties of seven different clayey soils are shown below (Skempton and Northey, 1952). Investigate the relationship between the strength and plasticity characteristics by performing the following tasks: a. Estimate the plasticity index for each soil using Skemptons definition of activity [Eq. (4.28)]. b. Estimate the probable mineral composition of the clay soils based on PI and A (use Table 4.3) c. Sensitivity (St) refers to the loss of strength when the soil is remolded or disturbed. It is defined as the ratio of the undisturbed strength (f-undisturbed) to the remolded strength (f-remolded)) at the same moisture content [Eq. (12.49)]. From the given data, estimate f-remolded for the clay soils. d. Plot the variations of undisturbed and remolded shear strengths with the activity, A, and explain the observed behavior.4.2CTP 5.1P 5.2P 5.3P 5.4P 5.5P 5.6P 5.7P 5.8P 5.9P 5.10P The subsurface characteristics for a highway pavement rehabilitation project in the southeastern United States are shown in a boring log in Figure 5.13. The highway structure consists of the asphalt pavement underlain by four different soil strata up to a depth of 20 ft, after which the boring was terminated. Some data on the grain size and plasticity characteristics are also provided for each stratum. Perform the following tasks: 1. Determine the AASHTO soil classification and the group index (GI) for each layer. 2. Determine the most probable group symbols and group names for the various layers according to the Unified soil classification system. Use Table 5.3 and the soil characteristics given in the boring log.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 6.17P Since laboratory or field experiments are generally expensive and time consuming, geotechnical engineers often have to rely on empirical relationships to predict design parameters. Section 6.6 presents such relationships for predicting optimum moisture content and maximum dry unit weight. Let us use some of these equations and compare our results with known experimental data. The following table presents the results from laboratory compaction tests conducted on a wide range of fine-grained soils using various compactive efforts (E). Based on the soil data given in the table, determine the optimum moisture content and maximum dry unit weight using the empirical relationships presented in Section 6.6. a. Use the Osman et al. (2008) method [Eqs. (6.15) through (6.18)]. b. Use the Gurtug and Sridharan (2004) method [Eqs. (6.13) and (6.14)]. c. Use the Matteo et al. (2009) method [Eqs. (6.19) and (6.20)]. d. Plot the calculated wopt against the experimental wopt, and the calculated d(max) with the experimental d(max). Draw a 45 line of equality on each plot. e. Comment on the predictive capabilities of various methods. What can you say about the inherent nature of empirical models?7.1P 7.2P 7.3P 7.4P 7.5P 7.6P 7.7P 7.8P 7.9P 7.10P 7.11P 7.12P 7.13P 7.14P 7.15P 7.16P 7.17P 7.18P 7.19P 7.20P 7.21P Refer to Figure 7.24. The following data were collected during the field permeability measurement of a confined aquifer using a pumping test. Determine the hydraulic conductivity of the permeable layer. Use Eq. (7.49). Thickness of the aquifer, H = 4.5 m Piezometric level and radial distance of the first observation well: h1 = 2.9 m; r1 = 17.8 m Piezometric level and radial distance of the second observation well: h2 = 1.8 m; r2 = 8.1 m Rate of discharge from pumping, q = 0.5 m3/min 7.23P 7.1CTP 8.1P 8.2P 8.3P 8.4P 8.5P 8.6P 8.7P 8.8P 8.9P 8.10P 8.11P 8.12P 8.1CTP 9.1P 9.2P 9.3P 9.4P 9.5P 9.6P 9.7P 9.8P 9.9P 9.10P 9.11P 9.12P 9.13P 9.14P 9.15P 10.1P 10.2P 10.3P 10.4P 10.5P 10.6P Point loads of magnitude 125, 250, and 500 kN act at B, C, and D, respectively (Figure 10.40). Determine the increase in vertical stress at a depth of 10 m below the point A. Use Boussinesqs equation. Figure 10.40 Refer to Figure 10.41. Determine the vertical stress increase, z, at point A with the following values: q1 = 110 kN/m, q2 = 440 kN/m, x1 = 6 m, x2 = 3 m, and z = 4 m. Figure 10.41 For the same line loads given in Problem 10.8, determine the vertical stress increase, z, at a point located 4 m below the line load, q2. Refer to Figure 10.41. Determine the vertical stress increase, z, at point A with the following values: q1 = 110 kN/m, q2 = 440 kN/m, x1 = 6 m, x2 = 3 m, and z = 4 m. Figure 10.41 Refer to Figure 10.41. Given: q2 = 3800 lb/ft, x1 = 18 ft, x2 = 8 ft, and z = 7 ft. If the vertical stress increase at point A due to the loading is 77 lb/ft2, determine the magnitude of q1. Figure 10.41 Refer to Figure 10.42. Due to application of line loads q1 and q2, the vertical stress increase at point A is 58 kN/m2. Determine the magnitude of q2. Figure 10.42 Refer to Figure 10.43. A strip load of q = 1450 lb/ft2 is applied over a width with B = 48 ft. Determine the increase in vertical stress at point A located z = 21 ft below the surface. Given x = 28.8 ft. Figure 10.43 Repeat Problem 10.12 for q = 700 kN/m2, B = 8 m, and z = 4 m. In this case, point A is located below the centerline under the strip load. 10.12 Refer to Figure 10.43. A strip load of q = 1450 lb/ft2 is applied over a width with B = 48 ft. Determine the increase in vertical stress at point A located z = 21 ft below the surface. Given x = 28.8 ft. Figure 10.43 10.14P For the embankment shown in Figure 10.45, determine the vertical stress increases at points A, B, and C. Figure 10.45 Refer to Figure 10.46. A flexible circular area of radius 6 m is uniformly loaded. Given: q = 565 kN/m2. Using Newmarks chart, determine the increase in vertical stress, z, at point A. Figure 10.46 Refer to Figure 10.47. A flexible rectangular area is subjected to a uniformly distributed load of q = 330 kN/m2. Determine the increase in vertical stress, z, at a depth of z = 6 m under points A, B, and C. Figure 10.47 Refer to the flexible loaded rectangular area shown in Figure 10.47. Using Eq. (10.36), determine the vertical stress increase below the center of the loaded area at depths z = 3, 6, 9, 12, and 15 m. Figure 10.47 10.19P 10.20P Refer to Figure 10.48. If R = 4 m and hw = height of water = 5 m, determine the vertical stress increases 2 m below the loaded area at radial distances where r = 0, 2, 4, 6, and 8 m. Circular contact area of radius R on the ground surface Figure 10.48 Refer to Figure 10.49. For the linearly increasing vertical loading on an infinite strip of width 5 m, determine the vertical stress increase, z, at A. Figure 10.49 EB and FG are two planes inside a soil element ABCD as shown in Figure 10.50. Stress conditions on the two planes are Plane EB: EB = 25 kN/m2; EB = +10 kN/m2 Plane FG: FG = 10 kN/m2; FG = 5 kN/m2 (Note: Mohrs circle sign conventions for stresses are used above) Given ; = 25, determine: a. The maximum and minimum principal stresses b. The angle between the planes EB and FG c. The external stresses on planes AB and BC that would cause the above internal stresses on planes EB and FG A soil element beneath a pave ment experiences principal stress rotations when the wheel load, W, passes over it and moves away, as shown in Figure 10.51. In this case, the wheel load has passed over points A and B and is now over point C. The general state of stress at these points is similar to the one shown by a stress block at point D. The phenomenon of principal stress rotation influences the permanent deformation behavior of the pavement layers. Investigate how the magnitude and the orientations of the principal stresses vary with distance from the point of application of the wheel load. Consider the case shown in Figure 10.51. An unpaved aggregate road with a thickness of 610 mm and unit weight of 19.4 kN/m3 is placed over a soil subgrade. A typical single-axle wheel load, W = 40 kN, is applied uniformly over a circular contact area with a radius of R = 150 mm (tire pressure of 565 kN/m2). The horizontal and shear stresses at each point are calculated from a linear elastic finite element analysis for a two-layer pavement and are presented in the following table. a. Use Eq. (10.28) to calculate the vertical stress increases at soil elements A, B, and C that are located at radial distances 0.457,0.267, and 0 m, respectively, from the center of the load. Determine the total vertical stress (y) due to wheel load, the overburden pressure at each point, and enter these values in the table. b. Use the pole method to determine the maximum and minimum principal stresses (1 and 3) for elements A, B, and C. Also determine the orientation (s) of the principal stress with respect to the vertical. Enter these values in the table. c. Plot the variations of 1 and s, with normalized radial distance, r/R, from the center of loading.11.1P 11.2P 11.3P 11.4P 11.5P The coordinates of two points on the virgin compression curve are as follows: Determine the void ratio that corresponds to a pressure of 6300 lb/ft2.11.7P 11.8P 11.9P 11.10P 11.11P 11.12P 11.13P 11.14P 11.15P 11.16P 11.17P 11.18P 11.19P 11.20P 11.21P 11.1CTP 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 Following are the results of consolidated-undrained triaxial tests on undisturbed soils retrieved from a 4-m thick saturated clay layer in the field (sat = 20.7 kN/m3). a. Estimate graphically the Mohr-Coulomb shear strength parameters c' and '. b. Estimate the shear strength in the middle of the clay layer.12.15P 12.16P 12.17P 12.18P 12.19P 12.20P 12.21P 12.22P 12.23P 12.24P 12.1CTP 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 13.24P 13.25P 13.26P 13.27P 13.1CTP 14.1P 14.2P 14.3P 14.4P 14.5P 14.6P 14.7P 14.8P 14.9P 14.10P 14.11P A braced wall is shown in Figure 14.20. Given: H = 7 m, naH = 2.8 m, =30, =20, = 18 kN/m3, and c = 0. Determine the active thrust, Pa, on the wall using the general wedge theory. Figure 14.20 14.13P The elevation and plan of a bracing system for an open cut in sand are shown in Figure 14.21. Using Pecks empirical pressure diagrams, determine the design strut loads. Given: sand = 18 kN/m3, ' = 38, x = 3 m, z = 1.25 m, and s = 3 m.The cross section of a braced cut supporting a sheet pile installation in a clay soil is shown in Figure 14.22. Given: H = 12 m, clay = 17.9 kN/m3, = 0, c = 75 kN/m2, and the center-to-center spacing of struts in plan view, s = 3 m. a. Using Pecks empirical pressure diagrams, draw the earth-pressure envelope. b. Determine the strut loads at levels A, B, and C.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 15.16P 15.17P 15.18P 15.19P 15.20P 15.21P 15.22P 15.23P 15.27P 15.28P 15.29P 15.30P 15.31P 15.32P A continuous footing is shown in Figure 16.17. Using Terzaghis bearing capacity factors, determine the gross allowable load per unit area (qall) that the footing can carry. Assume general shear failure. Given: = 19 kN/m3, c = 31kN/m2, =28, Df = 1.5 m, B = 2 m, and factor of safety = 3.5. Figure 16.17 Refer to Problem 16.1. If a square footing with dimension 2 m 2 m is used instead of the wall footing, what would be the allowable bearing capacity? 16.1 A continuous footing is shown in Figure 16.17. Using Terzaghis bearing capacity factors, determine the gross allowable load per unit area (qall) that the footing can carry. Assume general shear failure. Given: = 19 kN/m3, c = 31kN/m2, =28, Df = 1.5 m, B = 2 m, and factor of safety = 3.5. Figure 16.17 Redo Problem 16.1 with the following: = 115 lb/ft3, c = 1100 lb/ft2, =35, Df = 3.5 ft, B = 5 ft, and factor of safety = 4. 16.1 A continuous footing is shown in Figure 16.17. Using Terzaghis bearing capacity factors, determine the gross allowable load per unit area (qall) that the footing can carry. Assume general shear failure. Given: = 19 kN/m3, c = 31kN/m2, =28, Df = 1.5 m, B = 2 m, and factor of safety = 3.5. Figure 16.17 Redo Problem 16.1 with the following: = 16.5 kN/m3, cu = 41 kN/m3, =0, Df = 1.5 m, and factor of safety = 5. 16.1 A continuous footing is shown in Figure 16.17. Using Terzaghis bearing capacity factors, determine the gross allowable load per unit area (qall) that the footing can carry. Assume general shear failure. Given: = 19 kN/m3, c = 31kN/m2, =28, Df = 1.5 m, B = 2 m, and factor of safety = 3.5. Figure 16.17 Redo Problem 16.1 using the modified general ultimate bearing capacity Eq. (16.31). 16.1 A continuous footing is shown in Figure 16.17. Using Terzaghis bearing capacity factors, determine the gross allowable load per unit area (qall) that the footing can carry. Assume general shear failure. Given: = 19 kN/m3, c = 31kN/m2, =28, Df = 1.5 m, B = 2 m, and factor of safety = 3.5. Figure 16.17 Redo Problem 16.2 using the modified general ultimate bearing capacity Eq. (16.31). 16.1 A continuous footing is shown in Figure 16.17. Using Terzaghis bearing capacity factors, determine the gross allowable load per unit area (qall) that the footing can carry. Assume general shear failure. Given: = 19 kN/m3, c = 31kN/m2, =28, Df = 1.5 m, B = 2 m, and factor of safety = 3.5. Figure 16.17 6.2 Refer to Problem 16.1. If a square footing with dimension 2 m 2 m is used instead of the wall footing, what would be the allowable bearing capacity?Redo Problem 16.3 using the modified general ultimate bearing capacity Eq. (16.31). 16.1 A continuous footing is shown in Figure 16.17. Using Terzaghis bearing capacity factors, determine the gross allowable load per unit area (qall) that the footing can carry. Assume general shear failure. Given: = 19 kN/m3, c = 31kN/m2, =28, Df = 1.5 m, B = 2 m, and factor of safety = 3.5. Figure 16.17 16.3 Redo Problem 16.1 with the following: = 115 lb/ft3, c = 1100 lb/ft2, =35, Df = 3.5 ft, B = 5 ft, and factor of safety = 4.Redo Problem 16.4 using the modified general ultimate bearing capacity Eq. (16.31). 16.1 A continuous footing is shown in Figure 16.17. Using Terzaghis bearing capacity factors, determine the gross allowable load per unit area (qall) that the footing can carry. Assume general shear failure. Given: = 19 kN/m3, c = 31kN/m2, =28, Df = 1.5 m, B = 2 m, and factor of safety = 3.5. Figure 16.17 16.4 Redo Problem 16.1 with the following: = 16.5 kN/m3, cu = 41 kN/m3, =0, Df = 1.5 m, and factor of safety = 5.16.9P If the water table in Problem 16.9 drops down to 0.25 m below the foundation level, what would be the change in the factor of safety for the same gross allowable load? 16.9 A square footing is shown in Figure 16.18. Determine the gross allowable load, Qall, that the footing can carry. Use Terzaghis equation for general shear failure (Fs = 4). Given: = 17 kN/m3, sat = 19.2 kN/m3, c = 32 kN/m3, =26, Df = 1 m, h = 0.5 m, and B = 1.5 m. Figure 16.18 16.11P A square footing is subjected to an inclined load as shown in Figure 16.19. If the size of the footing, B = 2.25 m, determine the gross allowable inclined load, Q, that the footing can safely carry. Given: = 12 and Fs = 3.5. Figure 16.19 A square footing (B B) must carry a gross allowable load of 1160 kN. The base of the footing is to be located at a depth of 2 m below the ground surface. If the required factor of safety is 4.5, determine the size of the footing. Use Terzaghis bearing capacity factors and assume general shear failure of soil. Given: = 17 kN/m3, c = 48 kN/m2, =31.

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