Chapter 7, Problem 7.21P

### 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 layered soil is shown in Figure 7.33. Given:• H1 = 1.5 m k1 = 9 × 104 cm/sec• H2 = 2.5 m k2 = 7.8 × 10−3 cm/sec• H3 = 3.5 m k3 = 4.5 × 10−5 cm/secEstimate the ratio of equivalent permeability, kH(eq)/kV(eq).Figure 7.33

To determine

Find the ratio of equivalent permeability kH(eq)kV(eq).

Explanation

Given information:

The depth of first layer H1 is 1.5 cm.

The hydraulic conductivity for first layer (k1) is 9×104cm/sec.

The depth of second layer H2 is 2.5 cm.

The hydraulic conductivity (k2) second layer is 7.8×103cm/sec.

The depth of third layer H3 is 3.5 cm.

The hydraulic conductivity (k3) third layer is 4.5×105cm/sec.

Calculation:

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

kH(eq)=1H(k1H1+k2H2+k3H3)

Here, H is the total depth of the soil layer.

Substitute 7.5 cm for H, 9×104cm/sec for k1, 1.5 cm for H1, 7.8×103cm/sec for k2, 2.5 cm for H2, 3.5 cm for H3, and 4.5×105cm/sec for k1.

kH(eq)=17.5(9×104×1.5+7.8×103×2.5+4.5×105×3.5)=17.5(0.00135+0.0195+0.0001575)=2.801×103cm/sec

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

kV(eq)=HH1k1+H2k2+H3k3

Substitute 7

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