Chapter 7, Problem 7.1CTP

### Principles of Geotechnical Enginee...

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

Chapter
Section

### Principles of Geotechnical Enginee...

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

(a)

To determine

Find the quantity of water flowing through the sample per hour.

Explanation

Given information:

The length of each soil layer (H1,H2,H3) is 200 mm.

The total length of the soil layer H is 600 mm.

The diameter of the cylindrical tube d is 150 mm.

The constant head difference Δh is 470 mm.

The porosity of the soil layer I (n1) is 0.5.

The porosity of the soil layer II (n2) is 0.6.

The porosity of the soil layer III (n3) is 0.33.

The hydraulic conductivity of soil layer I (k1) is 5×103cm/sec.

The hydraulic conductivity of soil layer II (k2) is 4.2×102cm/sec.

The hydraulic conductivity of soil layer III (k3) is 3.9×104cm/sec.

Calculation:

Determine the hydraulic conductivity in the vertical direction using the relation.

kV(eq)=HH1k1+H2k2+H3k3

Substitute 600 mm for H, 200 mm for H1, 5×103cm/sec for k1, 200 mm for H2, 4.2×102cm/sec for k2, 200 mm for H3, and 3.9×104cm/sec for k3.

kV(eq)=600mm×1cm10mm200mm×1cm10mm5×103+200mm×1cm10mm4

(b)

To determine

Find the elevation head (Z), pressure head (u/γw), and the total head (h) at the entrance and exit of the each soil layer.

(c)

To determine

Plot the variation of the elevation head, pressure head, and the total head with the horizontal distance along the sample axis (X–X).

(d)

To determine

Plot the variation of the discharge velocity and the seepage velocity along the sample axis (X–X).

(e)

To determine

Find the height of the vertical columns of water inside piezometers A and B installed on the sample axis.

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