EBK PRINCIPLES OF GEOTECHNICAL ENGINEER
EBK PRINCIPLES OF GEOTECHNICAL ENGINEER
9th Edition
ISBN: 9781337517218
Author: SOBHAN
Publisher: VST
Question
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Chapter 3, Problem 3.4P

(a)

To determine

Calculate the dry unit weight of the soil.

(a)

Expert Solution
Check Mark

Answer to Problem 3.4P

The dry unit weight of the soil is 108.22lb/ft3_.

Explanation of Solution

Given information:

The diameter of the cylindrical mold (d) is 4in..

The height of the cylindrical mold (h) is 4.58in..

The weight of the compacted soil (W) is 4lb.

The moisture content (w) is 12%.

The specific gravity of the soil solids (Gs) is 2.72.

Calculation:

Calculate the volume of the mold (V) using the relation.

V=14πd2h

Substitute 4in. for d and 4.58in. for h.

V=14π×42×4.58=57.554in.3×(1ft12in.)3=0.033ft3

Calculate the dry unit weight of the soil (γd) using the relation.

γd=WV(1+w)

Substitute 4 lb for W, 0.033ft3 for V, and 12% for w.

γd=40.033×(1+12100)=40.033×1.12=108.22lb/ft3

Hence, the dry unit weight of the soil is 108.22lb/ft3_.

(b)

To determine

Calculate the void ratio of the soil.

(b)

Expert Solution
Check Mark

Answer to Problem 3.4P

The void ratio of the soil is 0.568_.

Explanation of Solution

Given information:

The diameter of the cylindrical mold (d) is 4in..

The height of the cylindrical mold (h) is 4.58in..

The weight of the compacted soil (W) is 4lb.

The moisture content (w) is 12%.

The specific gravity of the soil solids (Gs) is 2.72.

Calculation:

Refer to part (a).

The dry unit weight of the soil (γd) is 108.22lb/ft3.

Consider the unit weight of water (γw) is 62.4lb/ft3.

Calculate the void ratio of the soil (e) using the relation.

e=Gsγwγd1

Substitute 2.72 for Gs, 108.22lb/ft3 for γd, and 62.4lb/ft3 for γw.

e=2.72×62.4108.221=169.728108.221=1.5681=0.568

Hence, the void ratio of the soil is 0.568_.

(c)

To determine

Calculate the degree of saturation of the soil.

(c)

Expert Solution
Check Mark

Answer to Problem 3.4P

The degree of saturation of the soil is 57.4%_.

Explanation of Solution

Given information:

The diameter of the cylindrical mold (d) is 4in..

The height of the cylindrical mold (h) is 4.58in..

The weight of the compacted soil (W) is 4lb.

The moisture content (w) is 12%.

The specific gravity of the soil solids (Gs) is 2.72.

Calculation:

Refer to part (b).

The void ratio of the soil is 0.568.

Consider the unit weight of water (γw) is 62.4lb/ft3.

Calculate the degree of saturation (S) using the relation.

S=wGse

Substitute 2.72 for Gs, 12% for w, and 0.568 for e.

S=12100×2.720.568=0.32640.568=0.574×100%=57.4

Hence, the degree of saturation of the soil is 57.4%_.

(d)

To determine

Calculate the additional water needed to achieve 100% saturation in the soil sample.

(d)

Expert Solution
Check Mark

Answer to Problem 3.4P

The required additional water to achieve 100% saturation in the soil sample is 0.316lb_.

Explanation of Solution

Given information:

The diameter of the cylindrical mold (d) is 4in..

The height of the cylindrical mold (h) is 4.58in..

The weight of the compacted soil (W) is 4lb.

The moisture content (w) is 12%.

The specific gravity of the soil solids (Gs) is 2.72.

Calculation:

Refer to part (b).

The void ratio of the soil is 0.568.

Consider the unit weight of water (γw) is 62.4lb/ft3.

Calculate the saturated unit weight of the soil (γsat) using the relation.

γsat=(Gs+e)γw1+e

Substitute 2.72 for Gs, 0.568 for e, and 62.4lb/ft3 for γw.

γsat=(2.72+0.568)×62.41+0.568=205.17121.568=130.8lb/ft3

Calculate the unit weight (γ) using the relation.

γd=WV

Substitute 4 lb for W and 0.033ft3 for V.

γ=40.033=121.21lb/ft3

Calculate the additional water needed to achieve 100% saturation using the relation.

Additional water needed=(γsatγ)V

Substitute 130.8lb/ft3 for γsat, 121.21lb/ft3 for γ, and 0.033ft3 for V.

Additional water needed=(130.8121.21)×0.033=9.59×0.033=0.316lb

Therefore, the additional water needed is 0.316lb_.

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