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 2, Problem 2.15CTP

In concrete work, Fuller and Thompson (1907) suggested that a dense packing of grains can be achieved if the percent finer (p) and grain size (D) are related by the following equation, where n is a constant varying in the range of 0.3-0.6. Dmax is the size of the largest grain within the soil.

p = ( D D max ) n × 100

This equation is sometimes used in roadwork for selecting the aggregates.

  1. a. For n = 0.5, show that the soil is well graded.
  2. b. If n = 0.5 and Dmax = 19.0 mm, find the percentages of gravel, sand, and fines within the soil. Use the Unified Soil Classification System.

(a)

Expert Solution
Check Mark
To determine

Show that the soil is well graded for constant as 0.5.

Answer to Problem 2.15CTP

The soil is well graded for n=0.5.

Explanation of Solution

Given information:

The range of the constant (n) is 0.30.6.

The constant value (n) is 0.5.

Calculation:

Show the equation of percent finer as follows.

p=(DDmax)n×100 (1)

Here, D is the grain size and Dmax is the size of the largest grain within the soil.

For 10% finer:

Substitute 30% for p and 0.5 for n in Equation (1).

10=(D10Dmax)0.5×100 (2)

For 30% finer:

Substitute 30% for p and 0.5 for n in Equation (1).

30=(D30Dmax)0.5×100 (3)

For 60% finer:

Substitute 60% for p and 0.5 for n in Equation (1).

60=(D60Dmax)0.5×100 (4)

Calculate the uniformity coefficient (Cu).

Divide Equation (4) by Equation (2).

6010=(D60Dmax)0.5×100(D10Dmax)0.5×1006=(D60D10)0.5D60D10=36Cu=36

Calculate the coefficient of gradation (Cc).

Apply (Equation(3))2Equation(2)×Equation(4).

30260×10=((D30Dmax)0.5×100)2(D60Dmax)0.5×100×(D10Dmax)0.5×10096=D30D600.5×D100.51.5=D30D600.5×D100.5D302D60×D10=2.25

Cc=2.25

The value of uniformity coefficient is greater than 6 (Cu>6) and the coefficient of gradation (Cc=2.25) lies between 1 and 3. Hence, the soil is termed as well graded soil.

Hence, the soil is well graded.

(b)

Expert Solution
Check Mark
To determine

Calculate the percentages of gravels, sands, and fines in the soils based on the Unified Soil Classification System.

Answer to Problem 2.15CTP

The soil contains 43.7%ofgravel,50%ofsand,and6.3%offines_.

Explanation of Solution

Given information:

The range of the constant (n) is 0.30.6.

The constant value (n) is 0.5.

The size of the largest grain within the soil (Dmax) is 19mm.

Calculation:

For percentage of fines the grain size (D) is 0.075mm.

For percentage of sand and fines the grain size (D) is 4.75mm.

Calculate the percentage of fines in the soil.

Substitute 0.075mm for D, 19mm for Dmax, and 0.5 for n in Equation (1).

p=(0.07519)0.5×100=0.0628×100=6.3%

Hence, the percentage of fines is 6.3%_.

Calculate the percentage of sand and fines in the soil.

Substitute 4.75mm for D, 19mm for Dmax, and 0.5 for n in Equation (1).

p=(4.7519)0.5×100=0.5×100=50%

Hence, the percentage of sand and fines is 50%_.

Calculate the percentage of gravel in the soil.

Gravel=100%ofsandandfines%offines=100506.3=43.7%

Therefore, the percentage of gravel is 43.7%_.

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