During a constant head permeability test on a sample of sand, 150 cu.cm. of water were collected in 2 minutes. The sample had a length of 10 cm. and a diameter of 5.08 cm. The head was maintained at 20 cm.
a) Compute the coefficient of permeability
b) What type of soil is this?
c) Compute the seepage velocity if the porosity of soil 0.30.
2 Problem: From the constant head permeability test arrangement shown, the following values are given: Void ratio of specimen ........ 0.46 Length of soil sample ........... 450 mm Constant head difference .......700 mm Water collected in a period of 3 min = 0.000354 m3 Cross sectional area of soil sample = 0.00226 m2
a) Determine the coefficient of permeability.
b) Compute the discharge velocity in m/min.
c) Compute the seepage velocity in m/min.
3 Problem: The MMDA in its previous study for a proposed sanitary land fill site in Cavite is planning to use a clay liner for the landfill. Tests were performed on a sample clay from a borrow site. It was deemed necessary to have a minimum clay liner thickness of 0.30 m. The following results were obtained in the laboratory test. Initial water level in standpipe … 96 cm. Final water level in standpipe …. 56 cm. Diameter of standpipe ... 12 mm. Height of soil sample ................. 10.2 cm. Diameter of soil sample .............. 5.4 cm. Duration of test .......................... 12 hours.
The project manager would like to determine the effectiveness of using
on-site day soils for the lining material if it is a favorable. Tests were also performed on the on-site clay and the following results were obtained.
Height of soil sample ............... 8 cm.
Diameter of soil sample ...........5 cm. Volume of water collected .......75600 cm3 Constant head .......................... 60 cm. Duration of test ....................... 1050 hours
a) Compute the permeability of the borrow clay in cm/sec.
b) Compute the permeability of the on- site clay in cm/sec.
c) Compute the thickness of the on- site clay which is equivalent to
0.3 m. of the borrow day.
4 Problem:
A soil sample 10 cm. In diameter is place in tube 1.2 m. long. A constant
supply of water is allowed to flow into one end of the soil at A and the outflow at B is collected by a beaker. The average amount of water collected is 2 cm3 for every 10 seconds.
a) Determine the hydraulic gradient.
b.) Determine the seepage velocity if the void ratio is 0.60 in cm/s. c.) Determine the coefficient of permeability cm/s. 5 Problem:
The coefficient of permeability of a sand at a void ratio of 0.62 is 0.03 cm/sec. Estimate the coefficient of permeability at a void ratio of 0.48.
a) Using Casagrande equation
b) Using Kozeny-Carman equation.
c) Find the difference in the rate of
flow using the results of “a” and “b” if i = 0.70 and A = 0.6 m2.
6 Problem: The max, dry unit weight determined in the laboratory for a quart sand is 102 lb/ft3. In the field, the relative compaction is 90%. Specific gravity of sand is 2.70.
a) Determine the void ratio at the max. dry unit weight condition.
b) Determine the void ratio of the sand in the field condition.
c) Determine the hydraulic conductivity of the sand in the field condition if the hydraulic conductivity of sand at the max. dry unit weight condition is 0.03 cm/sec. Using Kozeny-Carman equation
7 Problem:
A permeable soil layer is underlain by an impervious layer as shown. For
permeable layer K = 4.8 x 10-3 cm/sec. if H = 3 m. and a = 5’. a) Determine the hydraulic gradient
b) Determine the cross sectional area of the permeable soil layer.
c) Determine the rate of seepage in cm3/hr/meter.
8 Problem: The figure shows the layers of soil in a tube that is 100 mm x 100 mm in a cross section. When supplied to maintain a constant head difference of 300 mm across the sample. The hydraulic conductivity of the soils in the direction of flow to them are as follows: Soil K(cm/sec.) A 2 x 10-2 B 3 x 10-3 C 4 x 10-4
a) Find the equivalent hydraulic conductivity.
b) Find the hydraulic gradient.
c) Find the rate of water supply in cm3/hr.
9 Problem:
The figure shows layers of soil in a tube that is 100 mm x 100 mm in cross section water is applied to maintain a constant head difference of 300 mm. across the sample. The hydraulic conductivities of the soils in the direction of flow through them are as follows. Soil K(cm/sec.) A 10-2 - B 3 x 10-3 C 4.9 x 10-4
a) Find the rate of water supply in cm3/hour.
b) Find the value of hA
c) Find the value of hB
10 CE Board Nov. 2006
A confined aquifer has a source of recharge as shown in the figure. The
hydraulic conductivity of the aquifer is 40 m/day and its porosity is 0.25. The piezometric head in the two wells 1325 m. apart is 65 m. and 60 m. respectively from a common data. The average thickness of the aquifer is 25 m. and the average width is 4 km.
a) Compute the rate of flow through the aquifer in m3/day.
b) Compute the seepage velocity.
c) Compute the time of travel from the head of the aquifer to a point 4 km. downstream in days. 11 Problem: A channel runs almost parallel to a river as shown on the figure. The water level in the river has an elevation of 36 m. and the elevation of the channel is 33 m. The river and channel are 600 m. apart and a pervious formation of average thickness of 9 m. and hydraulic conductivity of 0.08 m/hr join them together.
a) Compute the hydraulic gradient.
b) Compute the rate of seepage flow from the river to the channel per meter width in liters per day.
c) If the seepage velocity is 0.048 m/day, compute the void ratio of the pervious medium. 12 Problem:
Three piezometers have been installed in the confined aquifer having a uniform thickness of 4.6 m. and a hydraulic conductivity of 2 x 10-4 m/s.
a) Compute the hydraulic gredient.
b) Compute the transmissivity in m2/day.
c) Compute the flow rate per unit width of the aquifer in liters/day. 13 Problem:
An aquifer having a thickness of 4 m. has a hydraulic conductivity of 2 x 10-4
m/s. Two piezometers have been installed at points A and B at a distance of 850 m. apart horizontally. Elevation of the water surfaces at A and B are at elevations 120.32 m. and 122.64 m. respectively.
a) Compute the hydraulic gredient.
b) Compute the transmissivity in m2/day.
c) Compute the flow rate in the aquifer per unit width in liters/day.
14 Problem: A 300 mm diameter test well penetrates 24 m. below the static water table. After 24 hours of pumping at 69 liters per second, the water level in an observation well at a distance of 96 m. from the test well is lowered by 0.60 . and the other observation well at a distance of 34 m. from the test well, the drawdown is 1.2m.
A.) Compute the coefficient of permeability of the unconfined aquifer in m/day.
B.) Compute the transmissivity of the unconfined aquifer in m2/day. C.) Compute the transmissivity if there is a confined aquifer of 8 m. thick below the unconfined aquifer in m2/day.
15 Problem:
For a constant laboratory permeability test on a fine sand, the following data are given: Length of specimen……………………….…16cm. Diameter of specimen…………………….9.6cm. Constant Head difference……………….50cm. Volume of water collected in 4min….420cc. Void ratio of the soil specimen……….0.55 a) Determine the coefficient of k permeability of the soil in cm/sec. b) Determine the discharge velocity in cm/sec. c) Determine the seepage velocity in cm/sec.
