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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

Consider the soil profile shown in Figure 9.26:

a. Calculate the variations of σ, u, and σ′ at points A, B, and C.

b. How high should the groundwater table rise so that the effective stress at C is 111 kN/m2?

images

Figure 9.26

a)

To determine

Find the variation of total stress σ, pore water pressure (u), and the effective stress σ at point A, B, and C.

Explanation

Given information:

The thickness H1 of dry sand layer 1 is 4.0 m.

The specific gravity Gs of the dry sand is 2.66.

The void ratio (e) of the dry sand is 0.61.

The thickness H2 of saturated sand layer 2 is 5.0 m.

The specific gravity Gs of the saturated sand is 2.67.

The void ratio (e) of the saturated sand is 0.48.

Calculation:

Determine the dry unit weight γd of the sand 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 2.66 for Gs, 9.81kN/m3 for γw, and 0.61 for e.

γd=2.66×9.811+0.61=16.2kN/m3

Determine the saturated unit weight γsat(layer2) of the saturated sand in the second layer using the relation.

γsat(layer2)=(Gs+e)γw1+e

Substitute 2.67 for Gs, 9.81kN/m3 for γw, and 0.48 for e.

γsat(layer2)=(2.67+0.48)×9.811+0.48=20.88kN/m3

Calculate the total stress at point A using the relation.

σ=0

Thus, the total stress at point A is zero_.

Calculate the pore water pressure at point A using the relation.

u=0

Thus, pore water pressure at point A is zero_.

Calculate the effective stress at point A using the relation.

σ=σu

Substitute 0 for σ and 0 for u.

σ=00=0

Thus, effective stress at point A is zero_.

Calculate the total stress at point B using the relation.

σ=γd×H1

Substitute 16.2kN/m3 for γd and 4.0 m for H1.

σ=16.2×4.0=64

b)

To determine

Find the rise of water table to increase the effective stress at point C is equal to 111kN/m2

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