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Principles of Geotechnical Enginee...

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

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BuyFindarrow_forward

Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

An earth embankment is shown in Figure 10.44. Determine the stress increase at point A due to the embankment load. Given: β = 25°, γ = 119 lb/ft3, x = 55 ft, y = 28 ft, and z = 20 ft.

images

Figure 10.44

To determine

Calculate the increase in vertical stress at point A due to the embankment load.

Explanation

Given information:

The angle of slope of the embankment (β) is 25°.

The unit weight of the embankment soil (γ) is 119lb/ft3.

The height of the embankment (y) is 28ft.

The depth of the stress from ground surface (z) is 20ft.

The top width of the embankment (x) is 55ft.

Calculation:

Consider the width of rectangular loading of the embankment as B1 and the width of triangular loading of the embankment as B2 in the cross sections.

Calculate the embankment loading (qo) as shown below.

qo=γy

Substitute 119lb/ft3 for γ and 28ft for y.

qo=119×28=3,332lb/ft2

Calculate the bottom width of the triangular loading of the embankment (B2) as shown below.

B2=ytanβ

Substitute 28ft for y and 25° for β.

B2=28tan25°=60ft

Sketch the cross section of the loading diagram along point A as shown in Figure 1.

Refer to Figure 1.

Consider the left side of the cross section.

The width of rectangular loading of the embankment (B1) is 0.

The width of triangular loading of the embankment (B2) is 60ft.

Calculate the ratio B1z as shown below.

Substitute 0 for B1 and 20ft for z.

B1z=020=0

Calculate the ratio B2z as shown below.

Substitute 60ft for B2 and 20ft for z.

B2z=6020=3

Calculate the increase in vertical stress (Δσz) using the relation as follows.

Δσz=qoI2 (1)

  Here, I2 is the influence factor and as a function of B1z and B2z.

Refer Figure 10.19 “Osterberg’s chart for determination of vertical stress due to embankment loading” in the textbook.

Take the value of I2 as 0.39, for the values B1z of 0 and B2z of 3.

Calculate the increase in vertical stress for left side cross section ((Δσz)L) as shown below.

Substitute 3,332lb/ft2 for qo and 0

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