Fundamentals of Geotechnical Engineering (MindTap Course List)
Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN: 9781305635180
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
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Chapter 3, Problem 3.4P

(a)

To determine

Find the moist unit weight of the soil sample.

(a)

Expert Solution
Check Mark

Answer to Problem 3.4P

The moist unit weight of the soil sample is 18.07kN/m3_.

Explanation of Solution

Given information:

The volume of moist soil sample is V=5.66×103m3.

The moist weight of the soil is W=102.3×103kN.

The moisture content of the soil solid is w=11%.

The specific gravity of soil solids is Gs=2.7.

Calculation:

Find the moist unit weight (γ) using the equation:

γ=WV

Substitute 102.3×103kN for W and 5.66×103m3 for V.

γ=102.3×1035.66×103=18.07kN/m3

Therefore, the moist unit weight of the soil sample is 18.07kN/m3_.

(b)

To determine

Find the dry unit weight of the soil sample.

(b)

Expert Solution
Check Mark

Answer to Problem 3.4P

The dry unit weight of the soil sample is 16.28kN/m3_.

Explanation of Solution

Given information:

The volume of moist soil sample is V=5.66×103m3.

The moist weight of the soil is W=102.3×103kN.

The moisture content of the soil solid is w=11%.

The specific gravity of soil solids is Gs=2.7.

Calculation:

Refer part (a);

The moist unit weight of soil sample is γ=18.07kN/m3.

Find the dry unit weight (γd) using the equation:

γd=γ1+w

Substitute 18.07kN/m3 for γ and 11% for w.

γd=18.071+11100=16.28kN/m3

Therefore, the dry unit weight of the soil sample is 16.28kN/m3_.

(c)

To determine

Find the void ratio of the soil sample.

(c)

Expert Solution
Check Mark

Answer to Problem 3.4P

The void ratio of the soil sample is 0.626_.

Explanation of Solution

Given information:

The volume of moist soil sample is V=5.66×103m3.

The moist weight of the soil is W=102.3×103kN.

The moisture content of the soil solid is w=11%.

The specific gravity of soil solids is Gs=2.7.

Calculation:

Refer part (b);

The dry unit weight of soil sample is γd=16.28kN/m3.

Find the void ratio (e) using the equation:

γd=Gsγw1+e

Here, the specific gravity of soil solids is Gs.

Substitute 16.28kN/m3 for γd, 2.7 for Gs, and 9.81kN/m3 for γw.

16.28=2.7×9.811+e1+e=26.48716.28e=0.626

Therefore, the void ratio of the soil sample is 0.626_.

(d)

To determine

Find the porosity of the soil sample.

(d)

Expert Solution
Check Mark

Answer to Problem 3.4P

The porosity of the soil sample is 0.385_.

Explanation of Solution

Given information:

The volume of moist soil sample is V=5.66×103m3.

The moist weight of the soil is W=102.3×103kN.

The moisture content of the soil solid is w=11%.

The specific gravity of soil solids is Gs=2.7.

Calculation:

Refer part (c);

The void ratio of soil sample is e=0.626.

Find the porosity (n) using the equation:

n=e1+e

Substitute 0.626 for e.

n=0.6261+0.626=0.385

Therefore, the porosity of the soil sample is 0.385_.

(e)

To determine

Find the degree of saturation of the soil sample.

(e)

Expert Solution
Check Mark

Answer to Problem 3.4P

The degree of saturation of the soil sample is 47.4%_.

Explanation of Solution

Given information:

The volume of moist soil sample is V=5.66×103m3.

The moist weight of the soil is W=102.3×103kN.

The moisture content of the soil solid is w=11%.

The specific gravity of soil solids is Gs=2.7.

Calculation:

Refer part (c);

The void ratio of soil sample is e=0.626.

Find the degree of saturation (S) using the relation:

S=wGse×100%

Substitute 0.11 for w, 2.7 for Gs, and 0.626 for e.

S=0.11×2.70.626×100%=47.4%

Therefore, the degree of saturation of the soil sample is 47.4%_.

(f)

To determine

Find the volume occupied by water.

(f)

Expert Solution
Check Mark

Answer to Problem 3.4P

The volume occupied by water is 0.001m3_.

Explanation of Solution

Given information:

The volume of moist soil sample is V=5.66×103m3.

The moist weight of the soil is W=102.3×103kN.

The moisture content of the soil solid is w=11%.

The specific gravity of soil solids is Gs=2.7.

Calculation:

Find the weight of soil (Ws) solids using the equation:

Ws=W1+w

Substitute 102.3×103kN for W and 0.11 for w.

Ws=102.3×1031+0.11=92.16×103kN

Find the weight of water (Ww) using the relation:

Ww=WWs

Substitute 102.3×103kN for W and 92.16×103kN for Ws.

Ww=102.3×10392.16×103=10.14×103kN

Find the volume occupied by water (Vw) using the relation:

γw=WwVw

Substitute 9.81kN/m3 for γw and 10.14×103kN for Ws.

9.81=10.14×103VwVw=0.001m3

Therefore, the volume occupied by water is 0.001m3_.

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