Chapter 9, Problem 9.1P

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9th Edition

Braja M. Das + 1 other

ISBN: 9781305970939

Textbook Problem

**9.1 Through 9.3** A soil profile consisting of three layers is shown in Figure 9.25. Calculate the values of *σ*, *u*, and *σ*′ at points *A*, *B*, *C*, and *D* for the following cases. In each case, plot the variations of *σ*, *u*, and *σ*′ with depth. Characteristics of layers 1, 2, and 3 for each case are given below:

**Figure 9.25**

To determine

Find the total stress *A*, *B*, *C*, and *D* and plot the variations of total stress, pore water pressure, and effective stress.

Answer

The total stress at point *A* is

The pore water pressure at point *A* is

The effective stress at point *A* is

The total stress at point *B* is

The pore water pressure at point *B* is

The effective stress at point *B* is

The total stress at point *C* is

The pore water pressure at point *C* is

The effective stress at point *C* is

The total stress at point *D* is

The pore water pressure at point *D* is

The effective stress at point *D* is

Explanation

Given information:

The thickness

The thickness

The thickness

The dry unit weight

The saturated unit weight

The saturated unit weight

Calculation:

Calculate the total stress at point *A* (0 ft).

Thus, the total stress at point *A* is

Calculate the pore water pressure at point *A* (0 ft).

Thus, pore water pressure at point *A* is

Calculate the effective stress at point *A* (0 ft) using the relation.

Substitute 0 for *u*.

Thus, effective stress at point *A* is

Calculate the total stress at point *B* (7 ft) using the relation.

Substitute

Thus, total stress at point *B* is

Calculate the pore water at point *B* (7 ft) using the relation.

Thus, the pore water pressure at point *B* is

Calculate the effective stress at point *B* (7 ft) using the relation.

Substitute *u*.

Thus, the effective stress at point *B* is

Calculate the total stress at point *C* (19 ft) using the relation.

Substitute

Thus, the total stress at point *C* is

Calculate the pore water pressure at point *C* (19 ft) using the relation.

Here,

Take the unit weight of the water as

Substitute

Thus, the pore water pressure at point *C* is

Calculate the effective stress at point *C* (19 ft) using the relation.

Substitute *u*.

Thus, the effective stress at point *C* is

Calculate the total stress at point *D* (25 ft) using the relation.

Substitute

Thus, the total stress at point *D* is

Calculate the pore water pressure at point *D* (25 ft) using the relation.

Substitute

Thus, the pore water pressure at point *D* is

Calculate the effective stress at point *D* (25 ft) using the relation.

Substitute *u*.

Thus, the effective stress at point *D* is

Show the plot between depth and total stress as in Figure 1.

Show the plot between depth and pore water pressure as in Figure 2.

Show the plot between depth and effective stress as in Figure 3.

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