   Chapter 7, Problem 7.9P Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939

Solutions

Chapter
Section Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

The following data are for a falling-head permeability test:• Length of the soil sample = 400 mm• Area of the soil sample = 7854 mm2• Diameter of the standpipe = 11 mm• At time t = 0, head difference = 450 mm• At time t = 8 min, head difference = 200 mmIf the test was conducted at 20°C at which γw = 9.789 kN/m3 and η = 1.005 × 10−3 N · s/m2,a. Determine the absolute permeability of the soil (cm/sec).b. What was the head difference at t = 4 min?

(a)

To determine

Find the absolute permeability of the soil.

Explanation

Given information:

The length of the soil sample L is 400 mm.

The area of the sample A is 7,854mm2.

The diameter of the standpipe (d) is 11 mm.

The head difference (h1) at t=0 is 450 mm.

The head difference  (h2) at t=8min is 200 mm.

The unit weight of water (γw) is 9.789kN/m3.

The dynamic viscosity of water (η) is 1.005×103Ns/m2.

Calculation:

Determine the area of the standpipe a using the relation.

a=πd24

Substitute 11 mm for d.

a=π(11)24=95.03mm2

Determine the hydraulic conductivity k using the relation.

k=2.303(aLAt)log10(h1h2)

Substitute 95.03mm2 for a, 400 mm for L, 7,854mm2 for A, 8 min for t, 450 mm for h1, and 200 mm for h2.

k=2.303(95.03×4007,854×8min×60sec1min)log10(450200)=8

(b)

To determine

Find the head difference at 4 min time duration.

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