Seepage

P a g e | 8‐1 Chapter 8 Seepage 1. When the flow of water through soil is not in one direction only, and it is not uniform over the entire area perpendicular to the flow, the groundwater flow is conveniently calculated by the use of (a) Darcy’s law. (b) Bernoulli’s theorem. (c) Laplace’s equation of continuity. (d) flow nets. 2. The concept of the flow net is based on (a) Darcy’s law. (b) Bernoulli’s theorem. (c) Laplace’s equation of continuity. (d) none of the above. 3. For anisotropic soils, (a) (b) (c) (d) where kx and kz are the hydraulic conductivities of soil in the horizontal and vertical directions, respectively. 4. If the soil is isotropic with respect to the hydraulic conductivity, the Laplace’s equation of continuity for two dimensional flow in the horizontal (x-) and vertical (z-) directions is (a) (b) ∂ ∂ ∂ ∂ 0 0 (c) 0 (d) 0 where h is the total head at a point in water under motion. 5. If piezometers are placed at different points along an equipotential line, the water level will rise to the (a) same (b) different (c) top (d) mid-point level in all of them. P a g e | 8‐2 6. Select the incorrect statement. (a) A combination of number of flow lines and equipotential lines is called a flow net. (b) Flow nets are constructed to calculate the groundwater flow in the soil media. (c) To complete the graphic construction of a flow net, one must draw the flow and equipotential lines in such a way that the equipotential lines intersect the flow lines at right angles and the flow elements formed are approximate squares. (d) None of the above. 7. A flow channel is (a) a line along which a water particle will travel from the upstream to the downstream sides in the permeable soil medium. (b) a line along which the potential head at all points is equal. (c) the strip between any two adjacent flow lines. (d) a water flow direction. 8. The rate of seepage through the isotropic soil foundation per unit length of the hydraulic structures supported by the soil foundation is (a) (b) (c) (d) where k is the hydraulic conductivity of soil foundation, H is the difference between the upstream and downstream sides (or total head loss), Nd is the number of potential drops, Nf is the number of flow channels, n is the width-to-length ratio the flow elements. 9. If the rate of seepage through the isotropic soil foundation per unit length of the hydraulic structures supported by the soil foundation is , with k as the hydraulic conductivity of soil foundation, H as the difference between the upstream and downstream sides, (a) (b) (c) (d) where, Nd is the number of potential drops, Nf is the number of flow channels, and n is the width-to-length ratio the flow elements. 10. For anisotropic soils, the Laplace equation of continuity represents two families of curves that (a) meet at 90°. (b) are parallel. (c) do not meet at 90°. (d) have no well-defined orientations. P a g e | 8‐3 11. If in the flow net for an anisotropic soil drawn in transformed section, kx = 4 m/day, kz = 2 m/day, Nf = 4, Nd = 10, and the total head loss H = 6 m, the rate of seepage in m3/day/m will be (a) 1.13. (b) 6.79. (c) 42.43. (d) none of the above. 12. For proper selection of the filter material, the size of the voids in the filter material should be small enough to hold the larger particles of the protected material in place. To satisfy this filter condition, Terzaghi and Peck (1948) provided the following criteria: D (a) 15( F ) ≤ 4 to 5 D 85( S ) (b) (c) (d) D15( F ) D 85( S ) D15( F ) D15( S ) D15( F ) D15( S ) ≥ 4 to 5 ≥ 4 to 5 ≤ 4 to 5 13. For proper selection of the filter material, it should have a high hydraulic conductivity to prevent build-up of large seepage forces and hydrostatic pressures in the filters. To satisfy this filter condition, Terzaghi and Peck (1948) provided the following criteria: D (a) 15( F ) ≤ 4 to 5 D 85( S ) (b) (c) (d) D15( F ) D 85( S ) D15( F ) D15( S ) D15( F ) D15( S ) ≥ 4 to 5 ≥ 4 to 5 ≤ 4 to 5 P a g e | 8‐4 Answers, Hints and Discussion 1. (d) 2. (c) 3. (b) Discussion: (a) is correct for isotropic soils. 4. (c) 5. (a) Discussion: An equipotential line is a line along which the potential head at all points is equal. For more details, see Sec. 8.4. 6. (d) 7. (c) Discussion: (a) is correct for flow line, and (b) is correct for equipotential line. 8. (b) 9. (a) 10. (c) 11. (b) Discussion: Eq. (8.28): 4 2 12. (a) Discussion: See inequality (8.41). 13. (c) Discussion: See inequality (8.42). 6.79 / .