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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

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:

images

Figure 9.25

images

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 5 m.

The thickness H2 of soil layer 2 is 8 m.

The thickness H3 of soil layer 3 is 3 m.

The void ratio (e) of soil in the first layer is 0.7.

The specific gravity Gs of the soil in the first layer is 2.69.

The void ratio (e) of soil in the second layer is 0.55.

The specific gravity Gs of the soil in the second layer is 2.7.

The water content (w) of the soil in the third layer is 38 %.

The void ratio (e) of the soil in the third layer is 1.2.

Calculation:

Determine the dry unit weight γd of the soil in the first layer using the relation.

γd=Gsγw1+e

Here, γw is the unit weight of the water.

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

Substitute 2.69 for Gs, 9.81kN/m3 for γw, and 0.7 for e.

γd=2.69×9.811+0.7=15.52kN/m3

Determine the saturated unit weight γsat of the soil in the second layer using the relation.

γsat=γw(Gs+e)1+e

Substitute 9.81kN/m3 for γw, 2.7 for Gs, and 0.55 for e.

γsat=9.81(2.7+0.55)1+0.55=20.57kN/m3

Determine the saturated unit weight γsat of the soil in the third layer using the relation.

γsat=γw(Gs+e)1+eγsat=γw(ew+e)1+e

Substitute 9.81kN/m3 for γw, 1.2 for e, and 38 % for w.

γsat=9.81(1.2(38100)+1.2)1+1.2=19.43kN/m3

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 (5 m) using the relation.

σ=γd×H1

Substitute 15.52kN/m3 for γd and 5 m for H1.

σ=15.52×5.0=77.6kN/m2

Thus, the total stress at point B is 77.6kN/m2_.

Calculate the pore water pressure at point B (5 m) using the relation.

u=0

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

Calculate the effective stress at point B (5 m) using the relation.

σ=σu

Substitute 77.6kN/m2 for σ and 0 for u.

σ=77.60=77.6kN/m2

Thus, the effective stress at point B is 77.6kN/m2_

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