The hydraulic conductivity of a sand at a void ratio of 0.5 is 0.022 cm/s. Estimate its hydraulic conductivity at a void ratio of 0.7. Use Eq. (7.31).
> Halfway through the season, a basketball player has made 72% of her free throws. What is the probability that her next free throw will be successful?
> What is the probability of a 100-year flood happening this year?
> Every possible correlation coefficient must lie between the values of ____ and____.
> After recording the forecasts of your local meteorologist for 30 days, you conclude that she gave a correct forecast for 26 days. What is the probability that her next forecast will be correct?
> Suppose you randomly select a family with four children. Assume that births of boys and girls are equally likely. a. How many birth orders are possible? List them in a probability distribution table. b. What is the probability that the family has four ch
> Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. a. How many birth orders are possible? List them in a probability distribution table. b. What is the probability of two boys and a girl? c.
> The New England College of Medicine uses an admissions test with many multiple-choice questions, each with five possible answers, only one of which is correct. If you guess randomly on every question, what score might you expect to get? (Express the answ
> A bag contains 13 red M&Ms, 25 orange M&Ms, 8 yellow M&Ms, 8 brown M&Ms, 27 blue M&Ms, and 19 green M&Ms. When randomly selecting one M&M, what is the probability of drawing a red M&M? A blue M&M? A yellow M&M? An M&M that is not orange?
> What is the probability of not buying a defective smart phone when quality control surveys indicate that 2% of all smart phones purchased are defective?
> What is the probability of randomly selecting a person and getting someone who does not have type O blood, given that 45% of people have type O blood?
> What is the probability of finding that the next President of the United States was not born on Saturday?
> What is the probability that a 75% free-throw shooter will miss her next free throw?
> What is the probability of randomly selecting a day of the week and not picking a day whose name includes the letter “t”?
> Find the probability of getting someone who failed the exam or was in Group A.
> A Las Vegas handicapper can correctly predict the winner in a professional basketball game 60% of the time. What is the probability that she is wrong in her next prediction?
> Refer to Figure 9.29. For the variables given, calculate and plot , u, and ’ with depth.
> Refer to Figure 9.29. For the variables given, calculate and plot , u, and ’ with depth.
> From the sieve analysis of a sand, the effective size was determined to be 0.18 mm. Using Hazen’s formula, Eq. (9.34), estimate the range of capillary rise in this sand for a void ratio of 0.65.
> Refer to Figure 9.26. Calculate , u, and ’ at A, B, C, and D for the following cases, and plot the variations with depth. (Note: e = void ratio,  = moisture content, Gs = specific
> Repeat Problem 8.8 using L. Casagrande’s method.
> An earth dam is shown in Figure 8.32. Determine the seepage rate, q, in m3 /day/m length. Given: a1 = 358, a2 = 408, L1 = 5 m, H = 7 m, H1 = 10 m, and k = 3 × 10-4 cm/s. Use Schaffernak’s solution.
> For the weir shown in Figure 8.31, calculate the seepage in the permeable layer in m3/day/m for x9 = 1 m and x9 = 2 m. Use Figure 8.13.
> Draw a flow net for the weir shown in Figure 8.30. Calculate the rate of seepage under the weir.
> Refer to Problem 8.4. Using the flow net drawn, calculate the hydraulic uplift force at the base of the hydraulic structure per meter length (measured along the axis of the structure).
> For the hydraulic structure shown in Figure 8.29, draw a flow net for flow through the permeable layer and calculate the seepage loss in m3 /day/m.
> The porosity of a soil is 0.35. Given Gs = 2.69, calculate: Saturated unit weight (kN/m3 ) Moisture content when moist unit weight 5 17.5 kN/m3
> Refer to Figure 8.28. Given: H1 = 4 m D1 = 6 m H2 = 1.5 m D = 3.6 m Calculate the seepage loss in m3/day per meter length of the sheet pile (at right angles to the cross section shown). Use Figure 8.12.
> Draw a flow net for the single row of sheet piles driven into a permeable layer as shown in Figure 8.28. Given: H1 = 3 m D = 1.5 m H2 = 0.5 m D1 = 3.75 m Calculate the seepage loss per meter length of the sheet pile (at right angles to the cross s
> An earth dam section is shown in Figure 8.33. Determine the rate of seepage through the earth dam using Pavlovsky’s solution. Use k = 4 × 10-5 mm/s.
> Solve Problem 8.10 using L. Casagrande’s method.
> Refer to the cross section of the earth dam shown in Figure 8.19. Calculate the rate of seepage through the dam (q in m3/min/m) using Schaffernak’s solution.
> Refer to Figure 8.28. Given: H1 = 6 m D = 3 m H2 = 1.5 m D1 = 6 m Draw a flow net. Calculate the seepage loss per meter length of the sheet pile (at a right angle to the cross section shown).
> Refer to Figure 7.31. Find the flow rate in m3 /s/m (at right angles to the cross section shown) through the permeable soil layer. Given: H = 5 m, H1 = 2.8 m; h = 3.1 m, L = 60 m,  = 5°, and k = 0.05 cm/s.
> A permeable layer is underlain by an impervious layer, as shown in Figure 7.30. With k = 5.2 ×10-4 cm/s for the permeable layer, calculate the rate of seepage through it in m3 /hr/m if H = 3.8 m and α = 12°.
> A sand layer of the cross-sectional area shown in Figure 7.29 has been determined to exist for an 800 m length of the levee. The hydraulic conductivity of the sand layer is 2.8 m/day. Determine the quantity of water which flows into the ditch in m3 /min.
> For a falling-head permeability test, the following are given: Length of the soil specimen = 700 mm Area of the soil specimen = 20 cm2 Area of the standpipe = 1.05 cm2 Head difference at time t = 0 is 800 mm Head difference at time t = 8 min is 500 mm De
> A hydrometer test has the following results: Gs = 2.6, temperature of water = 24°C, and R = 43 at 60 minutes after the start of sedimentation (see Figure 2.30). What is the diameter D of the smallest-size particles that have settled beyond the zone of me
> For a falling-head permeability test, the following are given: length of specimen = 380 mm; area of specimen = 6.5 cm2; k = 0.175 cm/min. What should the area of the standpipe be for the head to drop from 650 cm to 300 cm in 8 min?
> For a falling-head permeability test, the following are given: Length of the soil specimen = 500 mm Area of the soil specimen = 26 cm2 Area of the standpipe = 1.3 cm2 Head difference at time t = 0 is 760 mm Head difference at time t = 10 min is 300 mm De
> In a constant-head permeability test in the laboratory, the following are given: L = 305 mm and A = 95 cm2. If the value of k = 0.015 cm/s and a flow rate of 7300 cm3/hr must be maintained through the soil, what is the head difference, h, across the spec
> Refer to Figure 7.5. For a constant-head permeability test in a sand, the following are given: L = 300 mm A = 175 cm2 h = 500 mm Water collected in 3 min = 620 cm3 Void ratio of sand = 0.58 Determine: Hydraulic conductivity, k (cm/s) Seepage veloc
> Consider the setup shown in Figure 7.34 in which three different soil layers, each 200 mm in length, are located inside a cylindrical tube of diameter 150 mm. A constant-head difference of 470 mm is maintained across the soil sample. The porosities and h
> A layered soil is shown in Figure 7.33. Estimate the ratio of equivalent hydraulic conductivity, kH(eq)/kV(eq).
> A layered soil is shown in Figure 7.32. Given: H1 = 1.5 m k1 = 10-5 cm/s H2 = 2.5 m k2 = 3.0 × 10-3 cm/s H3 = 3.0 m k3 = 3.5 × 10-5 cm/s Estimate the ratio of equivalent permeability, kH(eq)/kV(eq).
> The in situ void ratio of a soft clay deposit is 2.1, and the hydraulic conductivity of the clay at this void ratio is 0.91 ×10-6 cm/s. What is the hydraulic conductivity if the soil is compressed to have a void ratio of 1.1? Use Eq. (7.34).
> For a normally consolidated clay, the following are given: Estimate the hydraulic conductivity at a void ratio e = 0.9. Use Eq. (7.36).
> The sieve analysis for a sand is given in the following table. Estimate the hydraulic conductivity of the sand at a void ratio of 0.5. Use Eq. (7.30) and SF =6.5
> Assume that the retaining wall shown in Figure 14.35 is frictionless. For each problem, determine the Rankine passive force per unit length of the wall, the variation of passive earth pressure with depth, and the location of the resultant.
> For a sandy soil, the following are given: Maximum void ratio = 0.7 Minimum void ratio = 0.46 D10 = 0.2 mm
> The hydraulic conductivity of a sand at a void ratio of 0.5 is 0.022 cm/s. Estimate its hydraulic conductivity at a void ratio of 0.7. Use Eq. (7.31).
> Refer to the constant-head arrangement shown in Figure 7.5. For a test, the following are given: L = 450 mm A = area of the specimen = 23 cm2 Constant-head difference = h = 700 mm Water collected in 3 min = 350 cm3 Calculate the hydraulic conductivity (c
> For a clayey soil, given: LL = 38, PI = 16, and Gs = 2.68. If a modified Proctor test is conducted, estimate wopt and d(max)/w. Use the method of Gurtug and Sridharan (2004).
> A proposed embankment fill requires 8000 m3 of compacted soil. The void ratio of the compacted fill is specified as 0.7. Four borrow pits are available as described in the following table, which lists the respective void ratios of the soil and the cost p
> The in situ moisture content of a soil is 18%, and the moist unit weight is 105 lb/ft3. The specific gravity of soil solids is 2.75. This soil is to be excavated and transported to a construction site for use in a compacted fill. If the specifications ca
> A field unit weight determination test for the soil described in Problem 6.5 yielded the following data: moisture content = 10.5% and moist density = 1705 kg/m3. Determine the relative compaction.
> The results of a standard Proctor test are given in the following table. Determine the maximum dry density (kg/m3) of compaction and the optimum moisture content.
> For the soil described in Problem 6.3, if Gs = 2.72, determine the void ratio and degree of saturation at optimum moisture content
> The grain-size characteristics of a soil are given in the following table 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
> The results of a standard Proctor test are given here. Determine the maximum dry unit weight of compaction and the optimum moisture content.
> 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 .
