Chapter 9, Problem 9.3P

### Principles of Geotechnical Enginee...

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

Chapter
Section

### Principles of Geotechnical Enginee...

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 σ , pore water pressure u , and effective stress σ at points A, B, C, and D and plot the variations of total stress, pore water pressure, and effective stress.

Explanation

Given information:

The thickness H1 of soil layer 1 is 3 m.

The thickness H2 of soil layer 2 is 6 m.

The thickness H3 of soil layer 3 is 2.5 m.

The dry unit weight γd of soil in the first layer is 16kN/m3.

The saturated unit weight γsat of soil in the second layer is 18kN/m3.

The saturated unit weight γsat of soil in the third layer is 17kN/m3.

Calculation:

Calculate the total stress at point A (0 m).

σ=0

Thus, the total stress at point A is zero_.

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

u=0

Thus, the pore water pressure at point A is zero_.

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

σ=σu

Substitute 0 for σ and 0 for u.

σ=00=0

Thus, the effective stress at point A is zero_.

Calculate the total stress at point B (3 m) using the relation.

σ=γd×H1

Substitute 16kN/m3 for γd and 3 m for H1.

σ=16×3.0=48kN/m2

Thus, the total stress at point B is 48kN/m2_.

Calculate the pore water at point B (3 m).

u=0

Thus, the pore water pressure at point B is zero_.

Calculate the effective stress at point B (3 m) using the relation.

σ=σu

Substitute 48kN/m2 for σ and 0 for u.

σ=480=48kN/m2

Thus, the effective stress at point B is 48kN/m2_.

Calculate the total stress at point C (9 m) using the relation.

σ=γd×H1+γsat×H2

Substitute 16kN/m3 for γd, 3.0 m for H1, 18kN/m3 for γsat, and 6.0 m for H2.

σ=16×3.0+18×6.0=156kN/m2

Thus, the total stress at point C is 156kN/m2_.

Calculate the pore water pressure at point C (9 m) using the relation.

u=γw×H2

Here, γw is the unit weight of the water.

Take the unit weight of the water as 9.81kN/m3.

Substitute 9.81kN/m3 for γw and 6 m for H2

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