Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN: 9781305635180
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
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Chapter 6, Problem 6.3P
To determine
Find the flow rate in
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Problem 1
Find the flow rate in m³/hr/m length (at right angles to the
cross-section shown) through the permeable soil layer
shown.
H = 3 m
H₁ = 1.07 m
h = 1.4 m
Ø = 14°
K = 0.000488 m/s
L = 36.58 m
Direction
of flow
h=1.4 m
impervious
layer
impervious layer
0=14°
L'
L=36.58 m
H=3 m
7.5 A pervious soil layer is sandwiched between two impervious layers as shown
in Figure 7.31. Find the rate of flow in m³/sec/m (at right angles to the cross
section) through the pervious soil layer. Given: H = 3.5 m, H, = 1.75 m,
h = 2.5 m, S = 28 m, a = 12°, and k = 0.055 cm/sec.
Direction
of flow
Impervious layer
Figure 7.31
Impervious layer
S
Problem 1: An unconfined aquifer underlies a confined aquifer as shown in the figure:
44 m
K1 - 40
m/day
55 m
47 m
36 m
K2 = 35 m/day
2,000 m
1. What is the equivalent coefficient of permeability for flow in the horizontal direction in meter per day?
2. What is the hydraulic gradient?
3. What is the rate of flow from one stream to another per meter width?
Chapter 6 Solutions
Fundamentals of Geotechnical Engineering (MindTap Course List)
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- 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_forwardNf : 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 stratumarrow_forwardFind the rate of flow in m^3/sec/m (at right angles to the cross-section shown in Figure 7.33) through the permeable soil layer. Given: H 4 m, H1 2 m, h 2.75 m, S 30 m, a 14°, and k 0.075 cm/sec.arrow_forward
- Two soils, soil A and soil B are arranged in the manner shown in Figs. 6.27 (a) and 6.27 (b) in two tubes. Determine the quantity of flow in each case and show the distribution of total head with respect to elevation. El. (m) 4.5 3.0- 1.5 0 Soil A k = 0.1 cm/s Soil B k = 0.01 cm/s K 1.5 m (a) 4.5 4.09 0 1.5 3.0 4.5 Total head (m) (b) El. (m) 4.5 3.0 0 Soil A Soil B k= 0.1 k = 0.01 cm/s cm/s 0.75 m 0.75 m +14 (c) 4.5 m 4.5 otal head (m) (d)arrow_forwardFind the rate of flow in m3/sec/m through the permeable soil layer. Given: H = 5.5 m, H1 = 2 m, h = 3.5 m, S = 40 m, a = 17°, and k = 0.085 cm/sec.arrow_forward01:For the apparatus shown in Fig.1. Determine: a) the pressure, elevation, and total head at points A-E. b) the average or discharge velocity of flow through the soil (the soil is located between points B and D), where the coefficient of permeability for the soil is estimated to be (k = 0.05 cm/s). 20 15 5.0 cm Ah =5 cm Head (cm) 5.0 cm 10 2.0 cm soil 5 5.0 cm 2.5 cm 1.5 cm Datum Fig.1 centerlinearrow_forward
- Question 2 Refer to Figure 2 below. If the water surface elevation in reservoir B is 110 m, what must be the water surface elevation in reservoir A if a flow of 0.06 m³/s is to occur in the cast-iron pipe (ks = 0.26 mm)? The kinematic viscosity of water at 10°C = 1.3x10-6 m²/s. Ignore all minor headlosses. Elevation = ? Water T= 10°C Elevation = 110 m B L= 150 m D = 15 cm Cast-iron pipe L=100 m, D = 20 cm, cast-iron pipe Figure 2arrow_forward11. A channel runs almost parallel to a river as shown in 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 previous formation of the average thickness of 9 m and hydraulic conductivity of 0.80 m/hr joints them together. Compute the hydraulic gradient Compute the rate of seepage flow from the river to the channel per meter width in liters per day. If the seepage velocity is 0.048 m/day, compute the void ratio of the previous medium.arrow_forward* The cross-section of an earth dam is shown in figure below. Assuming that the water level remains constant at 35m, determine the seepage loss through the dam. The width of the dam is 300m, and the soil is anisotropic with k=8.3*107 m/s and k, =3.2 10“ m/s. determine the seepage loss through the dam? 50m 35 m Filler Som 20m 20 m 30 m (a) The problem (bị Fiow netarrow_forward
- 5.4 The figure shows the cross-section of a levee that is 500 m long and is underlain by a 2-m-thick permeable sand layer. It was observed that the quantity of water flowing through the sand layer into the collection ditch is 250 m³/day. What is the hydraulic conductivity of the sand layer. Ans. k = 3.125 m/day Elv. 160 m Levee Elv. 150 m 2 m Ditch 125 m Impervious Sandarrow_forwardSoil layers are shown as the right figure. Given: H₁ = 2 m, k₁ = 10-4 cm/sec H₂ = 3 m, K₂ = 3.2 x 10-² cm/sec H₂ = 4 m, K₂ = 4.1 x 10-5 cm/sec Estimate the ratio of horizontal equivalent hydraulic conductivity and vertical equivalent hydraulic conductivity, i.e., k./k₂ T * H₂ H₂ a. 152 Ob. 270 O c. 140 O d. 225 k₁ k₂ k3arrow_forwardExample 2: A soil sample with 10 cm in diameter is placed in a tube 1 m long. A constant supply of water is allowed to flow into one end of the soil at A and flow out at B is collected by beaker. The average amount of water collected is 1 cm3 for every 10 seconds. The tube is inclined as shown in the figure. Determine: a. Hydraulic gradient b. Flow rate lisiya im University of Al- c. Average velocity d. Seepage velocity if e = 0.6 Of e Engine I m e. The hydraulic conductivity Soil 1 m 0.8 marrow_forward
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