   Chapter 7, Problem 7.2P 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

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°. Figure 7.29Redo Problem 7.1 for α = 5° and α = 9°. All other site conditions remaining the same, what impact does the slope angle have on the rate of seepage?

To determine

Find the rate of seepage through the permeable layer at α=5°and9° and the impact on the rate of seepage due to the slope angle.

Explanation

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 5° and 9°.

Calculation:

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

Refer Figure (1).

Determine the hydraulic gradient at α is 5° 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 5° for α in Equation (1).

i=sin5°=0.087

Determine the rate of seepage through the permeable layer at α is 5° using the relation.

q=kiA=ki(Hcosα×1) (2)

Here, A is the area of the permeable layer.

Substitute 6×103cm/sec for k, 0.087 for i, 5.4 m for H, and 5° for α in Equation (2).

q=6×103cm/sec×1m100m×3,600sec1hr×0.087×5.4×cos7°×1=10.1×102m3/hr/m

Therefore, the rate of seepage through the permeable layer at α=5° is 10

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