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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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CivilSoil Mechanics
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For a given soil mass, the void ratio is 0.60, water content is 18% and specific gravity of the soil particles is 2.6. The degree of saturation of the soil is

A

30 %

B

50 %

C

78 %

D

82.50 %

Correct Answer

⚙️ TE • Technical Direct FormulaCivilSoil Mechanics
Option C

78 %

Quick Summary:

Given: Void ratio e = 0.60, water content w = 18% (0.18), and specific gravity Gs = 2.6.

📐MAMath SolutionDirect Formula
📋 Given

Void ratio e = 0.60, water content w = 18% (0.18), and specific gravity Gs = 2.6.

🔢 Formula Used

S×e=w×GsS \times e = w \times G_sS×e=w×Gs​

🔢 Step-by-Step Solution
1

Identify given parameters

List the given geotechnical properties: void ratio e=0.60e = 0.60e=0.60, water content w=0.18w = 0.18w=0.18, and specific gravity of solids Gs=2.6G_s = 2.6Gs​=2.6.

e=0.60,w=0.18,Gs=2.6e = 0.60, w = 0.18, G_s = 2.6e=0.60,w=0.18,Gs​=2.6

2

Select the governing relation

Use the fundamental phase relationship in soil mechanics that links saturation, void ratio, water content, and specific gravity.

S×e=w×GsS \times e = w \times G_sS×e=w×Gs​

3

Substitute values

Substitute the known values into the equation to solve for the degree of saturation SSS.

S×0.60=0.18×2.6S \times 0.60 = 0.18 \times 2.6S×0.60=0.18×2.6

4

Calculate the result

Perform the arithmetic: S=0.18×2.60.60=0.4680.60=0.78S = \frac{0.18 \times 2.6}{0.60} = \frac{0.468}{0.60} = 0.78S=0.600.18×2.6​=0.600.468​=0.78. Convert the decimal to percentage by multiplying by 100.

S=0.78×100=78%S = 0.78 \times 100 = 78\%S=0.78×100=78%

✅

C is correct because the degree of saturation calculated using the relation Se=wGsSe = wG_sSe=wGs​ results in 78%.

Core Concepts Used
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Phase relationships Void ratio Degree of saturation Water content
💡 EXAM TIP

This relationship Se=wGsSe = wG_sSe=wGs​ is the most critical equation in soil mechanics; it is frequently used to determine the dry unit weight of soil when combined with the bulk unit weight formula.

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