   Chapter 7, Problem 7.1P 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 7.29

To determine

Find the rate of seepage through the permeable layer.

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

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 7°.

Calculation:

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