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Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
Publisher: Cengage Learning
ISBN: 9781305970939
BuyFind

Principles of Geotechnical Enginee...

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

Solutions

Chapter
Section
Chapter 7, Problem 7.1P
Textbook Problem

A permeable soil layer is underlain by an impervious layer as shown in Figure 7.29. Knowing that k = 6 × 10−3 cm/sec for the permeable layer, calculate the rate of seepage through this layer in m3/hr/m width. Given: H = 5.4 m and α = 7°.

Chapter 7, Problem 7.1P, A permeable soil layer is underlain by an impervious layer as shown in Figure 7.29. Knowing that k =

Figure 7.29

Expert Solution
To determine

Find the rate of seepage through the permeable layer.

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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