Seepage Analysis Practice Questions

Two soils of permeabilities $k_{1}$ and $k_{2}$ are placed in a horizontal flow apparatus, as shown in the figure. For Soil $1, L_{1}=50 \mathrm{~cm}$ , and $k_{1}=0.055 \mathrm{~cm} / \mathrm{s}$ ; for Soil $2, L_{2}=30 \mathrm{~cm}$ , and $\mathrm{k}_{2}=0.035 \mathrm{~cm} / \mathrm{s}$ . The cross sectional area of the horizontal pipe is $100 \mathrm{~cm}^{2}$ , and the head difference ( $\Delta \mathrm{h}$ ) is 150 cm . The discharge (in $\mathrm{cm}^{3} / \mathrm{s}$ ) through the soils is _________ (rounded off to 2 decimal places).

Consider the statements $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ . P: $\quad$ Compacted fine-grained soils with flocculated structure have isotropic permeability. Q: Phreatic surface/line is the line along which the pore water pressure is always maximum. R: $\quad$ The piping phenomenon occuring below the dam foundation is typically known as blowout piping. Which of the following option(s) is/are CORRECT?

For the flow setup shown in the figure (not to scale), the hydraulic conductivities of the two soil samples, Soil 1 and Soil 2, are $10 \mathrm{~mm} / \mathrm{s}$ and $1 \mathrm{~mm} / \mathrm{s}$ , respectively. Assume the unit weight of water as $10 \mathrm{kN} / \mathrm{m}^{3}$ and ignore the velocity head. At steady state, what is the total head (in $m$ , rounded off to two decimal places) at any point located at the junction of the two samples? ____

An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of 1.5 m. It is supported on a solid steel circular column of diameter 75 mm and total height (L) of 4m.Take, water density= $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and acceleration due to gravity = $10 \mathrm{m/s}^{2}$ . If elastic modulus (E) of steel is 200 GPa, ignoring self-weight of the tank, for the supporting steel column to remain unbuckled, the maximum depth (h) of the water permissible (in m, round off to one decimal place) is _____________

A granular soil has a saturated unit weight of 20 $kN/m^3$ and an effective angle of shearing resistance of 30 $^{\circ}$ . The unit weight of water is 9.81 $kN/m^3$ . A slope is to be made on this soil deposit in which the seepage occurs parallel to the slope up to the free surface. Under this seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1 decimal place) would be _____

A flownet below a dam consists of 24 equipotential drops and 7 flow channels. The difference between the upstream and downstream water levels is 6 m. The length of the flow line adjacent to the toe of the dam at exit is 1 m. The specific gravity and void ratio of the soil below the dam are 2.70 and 0.70, respectively. The factor of safety against piping is

A sheet pile has an embedment depth of 12 m in a homogeneous soil stratum. The coefficient of permeability of soil is $10^{-6}\, m/s$ . Difference in the water levels between the two sides of the sheet pile is 4 m. The flow net is constructed with five number of flow lines and eleven number of equipotential lines. The quantity of seepage (in $\frac{cm^{3}}{s}$ per m, up to one decimal place) under the sheet pile is________

The seepage occurring through an earthen dam is represented by a flow net comprising of 10 equipotential drops and 20 flow channels. The coefficient of permeability of the soil is 3 mm/min and the head loss is 5 m. The rate of seepage (expressed in $cm^{3}/s$ per m length of the dam) through the earthen dam is ___.

The relationship between the specific gravity of sand (G) and the hydraulic gradient (i) to initiate quick condition in the sand layer having porosity of 30% is

Which of the following statement is TRUE for the relation between discharge velocity and seepage velocity?

The flow net constructed for the dam is shown in the figure below. Taking the coefficient ofpermeability as $3.8\times 10^{-6}m/s$ , the quantity of flow (in $cm^{3}/s$ ) under the dam per meter of dam is______________

Water is flowing at a steady rate through a homogeneous and saturated horizontal soil strip of 10 m length. The strip is being subjected to a constant water head(H) of 5 m at the beginning and 1 m at the end. If the governing equation of flow in the soil strip is $\frac{d^{2}H}{dx^2}=0$ (where x is the distance along the soil strip), the value of H (in m) at the middle of the strip is ________.

The ratio $N_f/N_d$ is known as shape factor, where $N_f$ is the number of flow lines and $N_d$ is the number of equipotential drops. Flow net is always drawn with a constant b/a ratio, where b and a are distances between two consecutive flow lines and equipotential lines, respectively. Assuming that b/a ratio remains the same, the shape factor of a flow net will change if the

Laplace equation for water flow in soils is given below. $\frac{\partial^2 H}{\partial x^2}+\frac{\partial^2 H}{\partial y^2}+\frac{\partial^2 H}{\partial z^2}=0$ Head H does not vary in y and z directions. Boundary conditions are: at x = 0, H = 5; and $\frac{dH}{dx}=-1$ . What is the value of $H$ at $x = 1.2$ ? __________

The flow net around a sheet pile wall is shown in the sketch. The properties of the soil are: permeability coefficient = 0.09 m/day (isotropic), specific gravity = 2.70 and void ratio = 0.85. The sheet pile wall and the bottom of the soil are impermeable. The factor of safety against the occurrence of piping failure is

Steady state seepage is taking place through a soil element at Q, 2 m below the ground surface immediately downstream of the toe of an earthen dam as shown in the sketch. The water level in a piezometer installed at P, 500 mm above Q, is at the ground surface. The water level in a piezometer installed at R, 500 mm below Q, is 100 mm above the ground surface. The bulk saturated unit weight of the soil is 18 kN/ $m^3$ and the unit weight of water is 9.81 kN/ $m^3$ . The vertical effective stress (in kPa) at Q is

For a saturated sand deposit, the void ratio and the specific gravity of solids are 0.70 and 2.67, respectively. The critical (upward) hydraulic gradient for the deposit would be

Quick sand condition occurs when

To provide safety against piping failure, with a factor of safety of 5, what should be the maximum permissible exit gradient for soil with specific gravity of 2.5 and porosity of 0.35 ?