Principles of Geotechnical Engineering (MindTap Course List)
Principles of Geotechnical Engineering (MindTap Course List)
9th Edition
ISBN: 9781305970939
Author: Braja M. Das, Khaled Sobhan
Publisher: Cengage Learning
Question
100%
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Chapter 9, Problem 9.4P

(a)

To determine

Find the change in effective stress σ at point C when the water table drops by 2 m.

(a)

Expert Solution
Check Mark

Answer to Problem 9.4P

The change in effective stress at point C when the water table drops by 2 m is 12.64kN/m2_.

Explanation of Solution

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 depth (h) of water table drop is 2 m.

Calculation:

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

γd(layer1)=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(layer1)=2.69×9.811+0.7=15.52kN/m3

Determine the dry unit weight γd(layer2) of the soil in the second layer if the water table drops by 2 m using the relation.

γd(layer2)=Gsγw1+e

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

γd(layer2)=2.70×9.811+0.55=17.08kN/m3

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

γsat(layer2)=γw(Gs+e)1+e

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

γsat(layer2)=9.81(2.7+0.55)1+0.55=20.57kN/m3

Calculate the total stress at point C (13 m) using the relation.

σ=γd×H1+γsat×H2

Substitute 15.52kN/m3 for γd, 5 m for H1, 20.57kN/m3 for γsat, and 8.0 m for H2.

σ=15.52×5.0+20.57×8.0=242.16kN/m2

Calculate the pore water pressure at point C (13 m) using the relation.

u=γw×H2

Substitute 9.81kN/m3 for γw and 8 m for H2.

u=9.81×8=78.48kN/m2

Calculate the effective stress at point C (13 m) using the relation.

σ=σu

Substitute 242.16kN/m2 for σ and 78.48kN/m2 for u.

σ=242.1678.48=163.68kN/m2

Water table drops by 2 m:

Calculate the total stress at point C when the water level drops by 2 m using the relation.

σ=γd×H1+γd(layer2)×h+γsat×H2

Substitute 15.52kN/m3 for γd, 5 m for H1, 17.08kN/m3 for γd(layer2), 2 m for h, 20.57kN/m3 for γsat, and 6.0 m for H2.

σ=15.52×5.0+17.08×2.0+20.57×6.0=235.18kN/m2

Calculate the pore water pressure at point C when the water table drops by 2 m using the relation.

u=γw×(H2h)

Substitute 9.81kN/m3 for γw, 8 m for H2, and 2.0 m for h.

u=9.81×(82)=58.86kN/m2

Calculate the effective stress at point C when the water table drops by 2 m using the relation.

σ=σu

Substitute 235.18kN/m2 for σ and 58.86kN/m2 for u.

σ=235.1858.86=176.32kN/m2

Determine the change in effective stress when the water level drops by 2 m from the original position using the relation;

Changeineffectivestress=(EffectivestressatchangedwaterlevelEffectivestressatinitialwaterlevel)

Substitute 176.32kN/m2 for effective stress at changed water level and 163.68kN/m2 for effective stress at initial water level.

Changeineffectivestress=176.32163.68=12.64kN/m2

Thus, the change in effective stress at point C when the water table drops by 2 m is 12.64kN/m2_.

(b)

To determine

The change in effective stress σ at point C when the water rises to the surface up to point A.

(b)

Expert Solution
Check Mark

Answer to Problem 9.4P

The change in effective stress at point C rises to the surface up to point A is 28.85kN/m2_.

Explanation of Solution

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.

Calculation:

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

γsat(layer1)=γw(Gs+e)1+e

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

γsat(layer1)=9.81(2.69+0.7)1+0.7=19.56kN/m3

Calculate the total stress at point C (13 m) using the relation.

σ=γsat(layer1)×H1+γsat(layer2)×H2

Substitute 19.56kN/m3 for γsat(layer1), 5 m for H1, 20.57kN/m3 for γsat(layer2), and 8.0 m for H2.

σ=19.56×5.0+20.57×8.0=262.36kN/m2

Calculate the pore water pressure at point C (13 m) using the relation.

u=γw×(H1+H2)

Substitute 9.81kN/m3 for γw, 5 m for H1, and 8 m for H2.

u=9.81×(5+8)=127.53kN/m2

Calculate the effective stress at point C (13 m) using the relation.

σ=σu

Substitute 262.36kN/m2 for σ and 127.53kN/m2 for u.

σ=262.36127.53=134.83kN/m2

Water table rises to the surface up to point A:

Determine the change in effective stress when the water table rises to the surface up to point A using the relation;

Changeineffectivestress=(EffectivestressatinitialwaterlevelEffectivestressatpointC)

Substitute 163.68kN/m2 for effective stress at initial water level and 134.83kN/m2 for effective stress at point C.

Changeineffectivestress=163.68134.83=28.85kN/m2

Thus, the change in effective stress at point C rises to the surface up to point A is 28.85kN/m2_.

(c)

To determine

Find the change in effective stress σ at point C when the water level rises 3 m above point A due to flooding.

(c)

Expert Solution
Check Mark

Answer to Problem 9.4P

The change in effective stress at point C when the water level rises 3 m above point A due to flooding is 28.85kN/m2_.

Explanation of Solution

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 depth (h) of water rises above point A is 3.0 m.

Calculation:

Calculate the total stress at point C (16 m) using the relation.

σ=γw×h+γsat×H1+γsat×H2

Substitute 9.81kN/m3 for γw, 3.0 m for h, 19.56kN/m3 for γsat, 5 m for H1, 20.57kN/m3 for γsat, and 8.0 m for H2.

σ=9.81×3.0+19.56×5.0+20.57×8.0=291.79kN/m2

Calculate the pore water pressure at point C (16 m) using the relation.

u=γw×(h+H1+H2)

Substitute 9.81kN/m3 for γw, 3 m for h, 5 m for H1, and 8 m for H2.

u=9.81×(3+5+8)=156.96kN/m2

Calculate the effective stress at point C (16 m) using the relation.

σ=σu

Substitute 291.79kN/m2 for σ and 156.96kN/m2 for u.

σ=291.79156.96=134.83kN/m2

Water level rises 3 m above point A due to flooding:

Determine the change in effective stress when the water level rises 3 m above point A due to flooding using the relation;

Changeineffectivestress=(EffectivestressatinitialwaterlevelEffectivestressatpointC)

Substitute 163.68kN/m2 for effective stress at initial water level and 134.83kN/m2 for effective stress at point C.

Changeineffectivestress=163.68134.83=28.85kN/m2

Thus, the change in effective stress at point C when the water level rises 3 m above point A due to flooding is 28.85kN/m2_.

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