Permeability

P a g e | 7‐1 Chapter 7 Permeability 1. Soils are permeable due to the existence of (a) fines. (b) voids. (c) interconnected voids. (d) large particles. 2. The discharge velocity of water (a) is the quantity of water flowing in unit time through a unit gross cross-sectional area of the soil. (b) is the quantity of water flowing in unit time through a unit gross cross-sectional area of the soil at right angles to the direction of flow. (c) has the SI unit as m/s. (d) both (b) and (c). 3. Select the incorrect statement. (a) Elevation head at a given point is its vertical distance above or below a datum plane. (b) Pressure head at a given point is the water pressure at this point divided by the unit weight of water. (c) The SI unit of head is m. (d) None of the above. 4. For the flow of water through a porous soil medium, the total head at any point can be adequately represented by the sum of (a) elevation head and pressure head. (b) elevation head and velocity head. (c) pressure head and velocity head. (d) None of the above. 5. The hydraulic gradient (a) is dimensionless. (b) is a ratio of head loss between two points to the distance between these points. (c) both (a) and (b). (d) is similar to the velocity gradient. 6. In which of the following flow zones, the discharge velocity bears a linear relationship to the hydraulic gradient? (a) Laminar flow zone (b) Transition flow zone (c) Turbulent flow zone (d) All of the above 7. For the flow of water through the void spaces of most saturated soils, (a) discharge velocity is proportional to the hydraulic gradient. (b) discharge velocity is proportional to the square of hydraulic gradient. (c) discharge velocity is inversely proportional to the hydraulic gradient. (d) discharge velocity is inversely proportional to the square of hydraulic gradient. P a g e | 7‐2 8. Darcy’s law relates the discharge velocity (v) to the hydraulic gradient (i) and the hydraulic conductivity (k) as (a) / (b) / (c) (d) none of the above. 9. The SI unit of hydraulic conductivity is (a) m. (b) m/s. (c) m/s2. (d) m/s3. 10. The actual velocity of water through the void spaces of soil is called (a) flow rate. (b) discharge velocity. (c) seepage velocity. (d) seepage pressure. 11. If discharge velocity of water through a soil is 24 cm/hr and soil porosity is 30%, the seepage velocity will be (a) 24 cm/hr. (b) 72 cm/hr. (c) 80 cm/hr. (d) None of the above. 12. The hydraulic conductivity of soil does not depend on (a) unit weight of soil solids. (b) unit weight of water flowing through the void spaces of the soil. (c) viscosity of water flowing through the void spaces of the soil. (d) void ratio of the soil. 13. The hydraulic conductivity of soil is (a) proportional to the unit weight of water flowing through the soil. (b) inversely proportional to the unit weight of water flowing through the soil. (c) inversely proportional to the viscosity of water flowing through the soil. (d) both (a) and (c). 14. The hydraulic conductivity of fine sand typically ranges from (a) 100 to 1 cm/s. (b) 1.0 to 0.1 cm/s. (c) 0.01 to 0.001 cm/s. (d) 0.001 to 0.0001 cm/s. 15. The absolute permeability of soil is expressed in (a) m (b) m2 (c) m/s (d) m3/s P a g e | 7‐3 16. The laboratory test used for determining permeability of fine-grained soils is (a) falling head permeability test. (b) constant head permeability test. (c) pumping test. (d) all of the above. 17. For fairly uniform sand, the hydraulic conductivity k (in cm/s) is related to the effective size D10 (in mm) of the soil particles as (a) (b) (c) / (d) / where c is a constant that varies from 1.0 to 1.5. 18. The hydraulic conductivity k of soil is related to its void ratio e as (a) (b) (c) (d) 19. If the hydraulic conductivity of a sand at a void ratio of 0.6 is 0.03 cm/s, its value at the void ratio of 0.75 will be (a) 0.03. (b) 0.05. (c) 0.07. (d) none of the above. 20. If a soil deposit consists of two layers having thickness of 1 m and 1.5 m with hydraulic conductivity values of 3 × 10-3 m/s and 5 × 10-4 m/s, respectively, the equivalent hydraulic conductivity of the soil deposit in the horizontal direction will be (a) 1.5 × 10–3 m/s (b) 1.5 × 10–4 m/s (c) 7.5 × 10–4 m/s (d) 7.5 × 10–3 m/s P a g e | 7‐4 Answers, Hints and Discussion 1. (c) 2. (d) 3. (d) 4. (a) 5. (c) 6. (a) 7. (a) 8. (c) Hint: See Eq. (7.6). 9. (b) 10. (c) 11. (c) Discussion: Eq. (7.10): . 80 / . 12. (a) Hint: Read Sec. 7.4 to know about all the factors that affect hydraulic conductivity of soils. 13. (d) 14. (c) Hint and Discussion: See Table 7.1, (a) is correct for clean gravel, (b) for coarse sand, and (d) for silty clay. 15. (b) Hint: See Eq. (7.13). 16. (a) Discussion: (c) is correct for field permeability test. 17. (b) Hint: See Eq. (7.23). 18. (c) Hint: See Eq. (7.24). 19. (b) Hint: See Example 7.6. 20. (a) Discussion: Eq. (7.40): 1 1.5 10 / 1 1 10 1.5 1.5 10 2.5 (c) is correct for equivalent hydraulic conductivity of the soil deposit in the vertical direction, this can be obtained using Eq. (7.45)