Chapter 10, Problem 10.15P

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9th Edition

Braja M. Das + 1 other

ISBN: 9781305970939

Textbook Problem

For the embankment shown in Figure 10.45, determine the vertical stress increases at points *A*, *B*, and *C*.

**Figure 10.45**

To determine

Calculate the increase in vertical stress at points *A*, *B*, and *C*.

Explanation

**Given information:**

The unit weight of the embankment soil

The height of the embankment

The depth of the stress from ground surface

The top width of the embankment

The relation of horizontal to vertical is

**Calculation:**

Consider the width of rectangular loading of the embankment as

Calculate the embankment loading

Substitute *H*.

Calculate the bottom width of the triangular loading of the embankment

Substitute *H*.

Calculate the increase in vertical stress

Here,

Stress increase at *A*:

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

Refer to Figure 1.

The left and right side of the cross sections are equal.

Consider the left side of the cross section.

The width of rectangular loading of the embankment

The width of triangular loading of the embankment

Calculate the ratio

Substitute *z*.

Calculate the ratio

Substitute *z*.

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

Take the value of

Hence, the value of

Calculate the increase in vertical stress *A* due to the embankment load as shown below.

Substitute

Hence, the increase in vertical stress at point *A* is

Stress increase at *B*:

Sketch the cross section of the loading diagram along point *B* as shown in Figure 2.

Refer to Figure 2.

Consider the left side of the cross section.

The width of rectangular loading of the embankment

The width of triangular loading of the embankment

Calculate the ratio

Substitute *z*.

Calculate the ratio

Substitute *z*.

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

Take the value of

Consider the right side of the cross section.

The width of rectangular loading of the embankment

The width of triangular loading of the embankment

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