Homework # 4 - Solutions Fluid Flow (5 problems) 1. An open-ended cylindrical standpipe contains a soil specimen as shown below. The soil is saturated with void ratio = 0.75 and specific gravity = 2.7. Assuming both water levels are held at constant elevations and using the lower water level as the datum, determine the total head (ht), elevation head (he), and pressure head (hp) at points A, B, C, and D in the soil specimen. If the hydraulic conductivity of the soil is 10-5 cm/s, how long (min) after red dye is introduced in the influent reservoir will dye appear in the effluent?
2. A vertical permeameter containing a silty-clay is shown below. Determine the total head, pressure head, and pore pressure at the midpoint between standpipes A and B.
3. A cylindrical sample of soil measures 10 cm in diameter and 20 cm in length. The axis of the cylindrical sample lies in a horizontal plane. The hydraulic head at the left end of the specimen is controlled by a reservoir; the water surface in the reservoir is exactly 100 cm above the horizontal axis of the cylindrical soil sample and remains at 100 cm through a system that automatically adds water to the reservoir if any flows out of the reservoir. The other (right) end of the soil specimen drains through a tube with a valve. When the valve is closed, there is no flow of water. When the valve is open, water can flow through the soil. The tube and valve are located along the projection of the central axis of the sample. When the valve is open, water drips out of the tube such that the water is at atmospheric pressure at the elevation of the central axis. a. Sketch and label the test setup. b. When the valve is closed, what is (1) the hydraulic gradient across the sample, (2) the pressure head at the geometric centroid of the soil sample, and (3) the pore water pressure at the centroid of the sample? c. When the valve is open, what is (1) the hydraulic gradient across the sample, (2) the pressure head at the geometric centroid of the soil sample, and (3) the pore water pressure at the centroid of the sample? d. The soil has a hydraulic conductivity of 0.001 cm/sec. With the valve open, how much water (ml) will flow through the soil sample in 5 minutes?
4. A cap is constructed over sludge lagoons at the Madison Wastewater Treatment Plant as shown in Fig. 1. The sludge is fine-grained organic material with a water content of 300% and specific gravity of 1.85. The cap consists of a soil and woodchip mixture that has a moist unit weight of 12 kn/m 3. A filter layer separates the cap from the underlying sludge; the cap and filter layer are considered infinitely permeable. A peat layer underlies the sludge and has a water content of 510% and specific gravity of 1.41. The hydraulic conductivity of the sludge is 8.5x10-6 cm/s and for the peat is 7.8x10-4 cm/s. A piezometer is installed with the porous tip at the base of the peat layer and two different water levels are recorded at the base of the peat. The water table is at the interface between the cap and sludge; however, during the spring, the water level in the piezometer rises to 0.5 m above the cap. a. Using the bottom of the peat as the datum, what are the total, pressure, and elevation heads at the cap-sludge interface, the sludge-peat interface, and at the base of the peat for normal water level conditions? b. During the spring, what are the direction and rate of flow per unit area through the sludge and peat? c. Compute the pore water pressure at the middle of the sludge layer and middle of the peat layer for normal groundwater conditions. d. Compute the following for spring conditions: Total head and pressure head at the middle of the sludge layer and middle of the peat layer (set datum at base of peat).
(Note the solution below also contains additional solutions for computing effective stress)
5. Complete the following for the impermeable dam shown in Fig. 2: a. Identify a datum b. Indicate the first and last equipotential lines c. Indicate the first and last flow lines d. Draw the flow net e. Determine the flow under the dam f. Calculate the pore water pressure at points A, B, and C g. Estimate the uplift force under the concrete dam.