Chapter 3, Problem 3.3P

### Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939

Chapter
Section

### Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

# Refer to Problem 3.2. For a unit volume of the soil, determine the various quantities of the phase diagram shown in Figure 3.13.Figure 3.133.2 The moist unit weight of a soil is 17.8 kN/m3 and the moisture content is 14%. If the specific gravity of the soil solids is 2.69, calculate the following:a. Dry unit weightb. Void ratioc. Degree of saturation

To determine

Calculate the weight and volume of the soil quantities.

Explanation

Given information:

The moist unit weight of soil (γ) is 17.8kN/m3.

The moisture content (w) is 14%.

The specific gravity of the soil solids (Gs) is 2.69.

Calculation:

Consider the total volume of the soil (V) is 1m3.

Consider the unit weight of water (γw) is 9.81kN/m3.

Calculate the dry unit weight of the soil (γd) as shown below.

γd=γ1+w

Substitute 17.8kN/m3 for γ and 14% for w.

γd=17.81+14100=17.81.14=15.6kN/m3

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

e=Gsγwγd1

Substitute 2.69 for Gs, 9.81kN/m3 for γw, and 15.6kN/m3 for γd.

e=2.69×9.8115.61=26.388915.61=1.691=0.69

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

S=wGse

Substitute 14% for w, 2.69 for Gs, and 0.69 for e.

S=(14100)×2.690.69=0.37660.69=0.545×100%=54.5%

Calculate the weight of soil solids (Ws) using the relation.

γd=WsV

Substitute 1m3 for V and 15.6kN/m3 for γd.

15.6=Ws1Ws=15.6kN

Hence, the weight of soil solids (Ws) is 15.6kN_.

Calculate the weight of water (Ws) using the relation

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