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Refer to Figure 7.29. Find the flow rate in m'/sec/m length (at right angles to the cross section shown) through the permeable soil layer. Given: H = 5 m, H, = 2.8 m, h = 3.1 m, L = 60 m, a = 5°, k = 0.05 cm/sec.

Refer to Figure 7.29. Find the flow rate in m'/sec/m length (at right angles to the cross section shown) through the permeable soil layer. Given: H = 5 m, H, = 2.8 m, h = 3.1 m, L = 60 m, a = 5°, k = 0.05 cm/sec.

Principles of Geotechnical Engineering (MindTap Course List)
Principles of Geotechnical Engineering (MindTap Course List)
9th Edition
ISBN:9781305970939
Author:Braja M. Das, Khaled Sobhan
Publisher:Braja M. Das, Khaled Sobhan
Chapter7: Permeability
Section: Chapter Questions
Problem 7.5P
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Braja Das Principles of Geotechnical Engineering Chapter 7

Problems 195 Direction of flow D Impervious layer Figure 7.29 7.9 Refer to Figure 7.29. Find the flow rate in m/sec/m length (at right angles to the cross section shown) through the permeable soil layer. Given: H = 5 m, H = 2.8 m, h = 3.1 m, L = 60 m, a = 5°, k = 0.05 cm/sec. 7.10 The hydraulic conductivity of a sand at a void ratio of 0.5 is 0.022 cm/sec. Estimate its hydraulic conductivity at a void ratio of 0.7. Use Eq. (7.31). 7.11 For a sand, the following are given: porosity, n = 0.31 and k = 0.2 ft/min. Determine k when n = 0.4. Use Eq. (7.31). 7.12 The maximum dry density determined in the laboratory for a quartz sand is 1800 kg/m³. In the field, if the relative compaction is 80%, determine the hydraulic conductivity of the sand in the field-compaction condition (given that D10 = 0.15 mm, C, = 2.2 and G, = 2.66). Use Eq. (7.34). 7.13 For a sandy soil, the following are given: • Maximum void ratio = 0.7 • Minimum void ratio = 0.46 D10 = 0.2 mm Determine the hydraulic conductivity of the sand at a relative density of 60%. Use Eq. (7.32). 7.14 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. TT U.S. Sieve No. Percent passing 30 100 40 60 68 100 28 200
Transcribed Image Text:Problems 195 Direction of flow D Impervious layer Figure 7.29 7.9 Refer to Figure 7.29. Find the flow rate in m/sec/m length (at right angles to the cross section shown) through the permeable soil layer. Given: H = 5 m, H = 2.8 m, h = 3.1 m, L = 60 m, a = 5°, k = 0.05 cm/sec. 7.10 The hydraulic conductivity of a sand at a void ratio of 0.5 is 0.022 cm/sec. Estimate its hydraulic conductivity at a void ratio of 0.7. Use Eq. (7.31). 7.11 For a sand, the following are given: porosity, n = 0.31 and k = 0.2 ft/min. Determine k when n = 0.4. Use Eq. (7.31). 7.12 The maximum dry density determined in the laboratory for a quartz sand is 1800 kg/m³. In the field, if the relative compaction is 80%, determine the hydraulic conductivity of the sand in the field-compaction condition (given that D10 = 0.15 mm, C, = 2.2 and G, = 2.66). Use Eq. (7.34). 7.13 For a sandy soil, the following are given: • Maximum void ratio = 0.7 • Minimum void ratio = 0.46 D10 = 0.2 mm Determine the hydraulic conductivity of the sand at a relative density of 60%. Use Eq. (7.32). 7.14 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. TT U.S. Sieve No. Percent passing 30 100 40 60 68 100 28 200
196 Chapter 7: Permeability 7.15 For a normally consolidated clay, the following are given: Void ratio, e k (cm /sec) 0.8 1.2 x 10-6 1.4 3.6 x 10-6 Estimate the hydraulic conductivity of the clay at a void ratio, e = 0.9. Use Eq. (7.38). 7.16 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/sec. What is the hydraulic conductivity if the soil is compressed to have a void ratio of 1.1. Use Eq. (7.36). 7.17 A layered soil is shown in Figure 7.30. Given that • H = 1.5 m • H = 2.5 m k = 10-5 cm/sec • k2 = 3.0 x 10-³ cm/sec kz =3.5 x 10-5 cm/sec Estimate the ratio of equivalent hydraulic conductivity, kĦeg/kv{cq}• 7.18 A layered soil is shown in Figure 7.31. Estimate the ratio of equivalent hydraulic H3 = 3.0 m conductivity, kµeq/kvieg)• 1.5 m 1.5 m H2 H3 k = 2 x 10-3 cm/sec (top layer) | k = 2 × 10-4 cm/sec k = 10-4 cm/sec k = 3 x 10-4 cm/sec (bottom layer) Figure 7.30 Figure 7.31
Transcribed Image Text:196 Chapter 7: Permeability 7.15 For a normally consolidated clay, the following are given: Void ratio, e k (cm /sec) 0.8 1.2 x 10-6 1.4 3.6 x 10-6 Estimate the hydraulic conductivity of the clay at a void ratio, e = 0.9. Use Eq. (7.38). 7.16 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/sec. What is the hydraulic conductivity if the soil is compressed to have a void ratio of 1.1. Use Eq. (7.36). 7.17 A layered soil is shown in Figure 7.30. Given that • H = 1.5 m • H = 2.5 m k = 10-5 cm/sec • k2 = 3.0 x 10-³ cm/sec kz =3.5 x 10-5 cm/sec Estimate the ratio of equivalent hydraulic conductivity, kĦeg/kv{cq}• 7.18 A layered soil is shown in Figure 7.31. Estimate the ratio of equivalent hydraulic H3 = 3.0 m conductivity, kµeq/kvieg)• 1.5 m 1.5 m H2 H3 k = 2 x 10-3 cm/sec (top layer) | k = 2 × 10-4 cm/sec k = 10-4 cm/sec k = 3 x 10-4 cm/sec (bottom layer) Figure 7.30 Figure 7.31
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