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This document contains 4 problems from a homework assignment on permeability and hydraulic conductivity testing of soils. Problem 7.5 involves calculating flow rate through a layered soil system. Problem 7.6 gives results from a constant head test and calculates hydraulic conductivity and seepage velocity. Problem 7.8 involves a falling head test to determine hydraulic conductivity. Problem 7.10 uses a levee cross-section and flow rate to calculate hydraulic conductivity of the permeable layer.

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1K views2 pages

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This document contains 4 problems from a homework assignment on permeability and hydraulic conductivity testing of soils. Problem 7.5 involves calculating flow rate through a layered soil system. Problem 7.6 gives results from a constant head test and calculates hydraulic conductivity and seepage velocity. Problem 7.8 involves a falling head test to determine hydraulic conductivity. Problem 7.10 uses a levee cross-section and flow rate to calculate hydraulic conductivity of the permeable layer.

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imran5705074
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CE 3540

Homework #6

Problem 7.5
The pervious soil layer is sandwiched between two impervious layers as shown in Figure
7.31. Find the rate of flow in m^3/sec/m (all right angles to the cross section) through the
pervious soil layer. Given: H = 3.5 m, H1 = 1.75 m, h = 2.5 m, S = 28 m, a = 12o, and k =
0.055 cm/sec.
q = kia
h
q = k ( S/cosa ) (H1 × cosa)
q = (0.0555 cm/sec) ( 28 m2.5/ cos12
m
) (1.75 m × cos12)
q = 0.000075 m3 /sec/m

Problem 7.6
The results of a constant-head permeability test for a fine sand sample having a diameter of
70 mm and a length of 140 mm are as follows (refer to Figure 7.5):
- Constant-head difference = 550 mm
- Water collected in 7 min = 450 cm^3
- Void ratio of sand = 0.8
VL (450) (40×10−1 )
a.) Hydraulic conductivity, k (cm/sec): k = Aηt = = 0.121 cm/min
π
4
(72 ) (55) (7)
e 0.8
actual velocity
b.) Seepage velocity: VS = porosity (η) = 1+e
discharge = 1+0.8
450 = 1.7 cm/sec
area (7) (38) (48)
CE 3540
Homework #6

Problem 7.8
The following data are for a falling-head permeability test:
- Length of soil sample = 140 mm
- Diameter of soil sample = 70 mm
- Area of the standpipe = 19.6 mm^2
- At time t=0, head difference = 500 mm
- At time t=7 min, head difference = 350 mm
a.) Determine the hydraulic conductivity of the soil (cm/sec)
aL h1 (19.6 mm2 ) (140 mm) (500 mm)
k = At ln( h2 ) = ( π4 ×70mm2 ) (7 min × 60 min
sec
)
ln ( (350 mm) ) = 0.0006055 mm/sec = 0.00006055 cm/sec

b.) What was the head difference at t = 5 min


aL h1
k = At ln h2 → solved f or h2 using "k" value above → h2 = 387.84 mm

Problem 7.10
Figure 7.32 shows the cross section of a levee which is 650 m long and is underlain by a
2-5-m-thick permeable sand layer. It was observed that the quantity of water flowing
through the sand layer into the collection ditch is 13.5 m^3/hr. What is the hydraulic
conductivity of the sand layer?
q = kia
q
k = ia
(13.5 m3 /hr)
k = ( 175 m − 158 m
)
(650 m × 2.5 m)
= 0.10262 m/hr
210 m

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