Principles of Geotechnical Engineering (MindTap Course List)
Principles of Geotechnical Engineering (MindTap Course List)
9th Edition
ISBN: 9781305970939
Author: Braja M. Das, Khaled Sobhan
Publisher: Cengage Learning
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Chapter 7, Problem 7.1P
To determine

Find the rate of seepage through the permeable layer.

Expert Solution & Answer
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Answer to Problem 7.1P

The rate of seepage through the permeable layer is 14.1×102m2/hr/m_.

Explanation of Solution

Given information:

The hydraulic conductivity of the permeable soil layer k is 6×103cm/sec.

The height of the layer H is 5.4 m.

The angle value α is 7°.

Calculation:

Draw the free body diagram of the permeable layer as in Figure (1).

Principles of Geotechnical Engineering (MindTap Course List), Chapter 7, Problem 7.1P

Refer Figure (1).

Determine the hydraulic gradient using the relation.

i=ΔhL=StanαScosα=sinαcosα×cosα=sinα (1)

Here, Δh is the head loss and L is the horizontal length of the layer.

Substitute 7° for α in Equation (1).

i=sin7°=0.122

Determine the rate of seepage through the permeable layer using the relation.

q=kiA=ki(Hcosα×1)

Here, A is the area of the permeable layer.

Substitute 6×103cm/sec for k, 0.122 for i, 5.4 m for H, and 7° for α.

q=6×103cm/sec×(1m100m)×3,600sec1hr×0.122×5.4×cos7°×1=14.1×102m3/hr/m

Therefore, the rate of seepage through the permeable layer is 14.1×102m2/hr/m_.

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