Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN: 9781305635180
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
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Question
Chapter 7, Problem 7.2P
(a)
To determine
Find the flow rate beneath the dam (q).
(b)
To determine
Find the rise of water level.
(c)
To determine
Find the pore water pressure at the tip of the sheet pile.
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Nf : 5
Nd=16
25 m
Question 4
Seepage take place beneath a concrete dam as shown in Figure 2. The soil beneath the dam is a
fine silty sand with hydraulic conductivity of 4.2 x 10“cm/s and saturated unit weight of 19.5
kN/m³.
6 m
1.75 m:
1) Find the rate of seepage beneath the dam in m³/day/m
2) If a standpipe piezometer is installed at the tip of the sheet pile, how high will the water
rise?
Impervious stratum
EXAMPLE 8.2
A flow net for flow around a single row of sheet piles in a permeable soil layer is
shown in Figure 8.7. Given that k, = k = k = 5 x 10-³ cm/s, determine
a. How high (above the ground surface) the water will rise if piezometers are
placed at points a and b
b. The total rate of seepage through the permeable layer per unit length
c. The approximate average hydraulic gradient at c
Water level
Ground surface
Scale
5 m
5.6 m
2.2 m
Water table
Flow channel 1
Flow channel 2
Flow channel 3
Impervious layer
FIGURE 8.7 Flow net for seepage around a single row of sheet piles
b
1/
b
= 1
= 1
1 1
T
0.38
For the figure shown below, if the area of the tank is 0.5 m² and hydraulic
conductivity of sand is 0.1 cm/sec.
a. What is the magnitude and direction of the rate of seepage?
b. If the value of h=1.2m, will boiling occur? Why?
c. What should be the value of "h" to cause boiling?
Outflow
Inflow
1m
2m
A
B
h = 1.2m
e = 0.55
G=2.68
Valve (open)
Chapter 7 Solutions
Fundamentals of Geotechnical Engineering (MindTap Course List)
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- Water flows at the rate of 4 x 10-2 cm³/s through a cylindrical sand sample with a diameter of 10 cm and a coefficient of permeability of 8 x 10-4 cm/s. In Case I, the flow is in upward direction, as shown in Figure 3a. In Case II, the flow is in downward direction, as shown in Figure 3b. For each case: a). The total head loss through the sand. b). The total stress, the effective stress and the PWP at points A, B and C if the soil has a saturated unit weight of 19 kN/m³. a). Case I 9 cm 12 cm 12 cm ▼ C B A D = 10 cm 9 cm 12 cm 12 cm b). Case II Figure 3. Seepage through soil ▼ с B A ? D = 10 cmarrow_forward(b) Seepage takes place beneath a concrete dam as shown in Figure Q3. The soil beneath the dam is fine silty sand with hydraulic conductivity (permeability) of 4.2 x 10- cm/sec and saturated unit weight of 19.5 kN/m³. i. Calculate the rate of seepage beneath the dam in m/day/m. ii. If a standpipe (piezometer) is installed at point A, how high will the water rise? i. Calculate the pore water pressure at point A. R1.75m Impervious stratum Figure Q3arrow_forwardRefer to Figure 7.24. The following data were collected during the field permeability measurement of a confined aquifer using a pumping test. Determine the hydraulic conductivity of the permeable layer. Use Eq. (7.49). Thickness of the aquifer, H = 4.5 m Piezometric level and radial distance of the first observation well: h1 = 2.9 m; r1 = 17.8 m Piezometric level and radial distance of the second observation well: h2 = 1.8 m; r2 = 8.1 m Rate of discharge from pumping, q = 0.5 m3/minarrow_forward
- Q.1. The figure below shows the flow net for seepage under a concrete dam. The is silty sand with coefficient of permeability of 4X104 cm/sec, a void ratio of 0.6 and specific gravity of 2.7. The height of water upstream is H=( 6+) (a) Determine the flow rate under the dam in m/day per m length of the dam. (b) Determine the water pressure distribution at the base of the dam. (Select 3 points under the base. Comment on your results. m (where X is your group number). (c) From (b), calculate the resultant uplift force and its location from the upstream face of the dam. Also, calculate the weight of the dam to prevent uplift using a factor of safety of 5. (d) What is the factor of safety against piping? Is the dam safe? (e) Calculate the total vertical overburden stress, pore water pressure and the effective vertical overburden stress at Points A and B. Comment on your results. H 17.5 m 1.25 m x B 4 m Impervious clayarrow_forwardA pump well is dug through a confined aquifer having a thickness of 32 meters. The piezometric surface of the aquifer is 18 meters measured from the top impermeable layer. The first observation well is 75 feet directly west of the pump well and the second observation well is 75 feet directly north of the first observation well. Determine the hydraulic conductivity of the aquifer if it supplies a discharge of 10 liters per second and the drawdown of the observation wells are 13 feet and 23 feet.arrow_forward2):(A): Derive the basic differential equation of Terzaghi's one dimensional consolidation theory for saturated soils. (B): For the concrete dam shown in figure below. The water heads are 16 m on the upstream side and 2 m on the downstream side. 1- Calculate the seepage loss through the subsoil per unit length if the average value of the hydraulic conductivity is (6x10³ cm/sec) horizontally and (3x10 cm/sec) vertically. 2- Calculate the exit gradient if the average length of the last square is 0.9 m. XXX Impervious Dam Permeable Xxxxxarrow_forward
- 2.8 A 500 m long levee made of compacted clay impounds water in a reservoir as shown in Figure P2.8. There is a 1 m thick (measured in the direction perpendicular to the seam) sand seam continuing along the entire length of the levee, at 10° inclination to the horizontal, which connects the reser- voir and the ditch. The hydraulic conductivity of the sand is 2.6 × 10-³ cm/s. Determine the volume of water that flows into the ditch every day.arrow_forwardj: A dam shown in Figure 1 retains 10 m of water. A sheet pile wall (cutoff curtain) on the upstream side, which is used to reduce seepage under the dam, penetrates 7 m into a 20.3 m-thick silty sand stratum. Below the silty sand, there is a thick deposit of practically impervious clay. The average hydraulic conductivity of the silty sand is 2x10 cm/s. Assume that the silty sand is homogeneous and isotropic. a) Draw the flow net under the dam. b) Calculate the flow rate, q. c) Determine the hydraulic gradient at exit path ED. 10 m A 20.3 m B 2.4 mt C 30.6 m -Sheet pile wall E k = 2 x 10 cm/s Clay (impervious) Harrow_forwardProblem 3 A sand layer of the cross-sectional area shown in the figure has been determined to exist for a 500 m. length of the levee. The hydraulic conductivity of the sand layer is 3 m/day. Determine the quantity of water which flows into the ditch in m³/min. W.S. EL=160 Levee Impervious ·layer' W.S. El.=150 Sand Impervious layer 125 m 10 m 2 m Ditcharrow_forward
- A dam shown in Figure 1 retains 10 m of water. A sheet pile wall (cutoff curtain) on the upstream side, which is used to reduce seepage under the dam, penetrates 7 m into a 20.3 m-thick silty sand stratum. Below the silty sand, there is a thick deposit of practically impervious clay. The average hydraulic conductivity of the silty sand is 2x10 cm/s. Assume that the silty sand is homogeneous and isotropic. a) Draw the flow net under the dam. b) Calculate the flow rate, q. c) Determine the hydraulic gradient at exit path ED. 10 m A 20.3 m 2.4 mt C 7m 30.6 m- -Sheet pile wall Clay (impervious) Figure No. 1 E k = 2 x 104 cm/s Harrow_forward3 Seepage is occurring through the sandy layer underneath the concrete dam as shown in Figure 7.30. Concrete dam H₁ Seepage H₂ H₂ Sandy layer Impervious rock PXSXX2X L Figure 7.30 Given: upstream water level, H₁ = 16 m; downstream water level, H₂ = 2.3 m; thickness of the sandy layer, H, = 0.75 m; hydraulic conductivity of the sandy layer, k = 0.009 cm/sec; void ratio of sand, e = 0.8; and L = 45 m. Determine: a. Rate of seepage per unit length of the dam (in m³/hr/m) b. Seepage velocity c. Quantity of seepage per day if the dam is 350 m longarrow_forwardA dam, shown in Figure 5 retains IO m of water. A sheet pile wall (cutoff curtain) on theupstream side, which is used to reduce seepage under the dam, penetrates 7 m into a 20 mthick silty sand stratum. Below the silty sand is a thick deposit of clay. The averagecoefficient of permeability of the silty sand is 2.0 x 10-4 cm/sec. Assume that the siltysand is homogeneous and isotropic.(i) Draw the flow net under the dam.(ii) Calculate the seepage rate, q per meter length of the sheet pile.arrow_forward
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