   Chapter 17, Problem 17.3P Principles of Geotechnical Enginee...

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

Solutions

Chapter
Section Principles of Geotechnical Enginee...

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

The following are the results of a standard penetration test in sand. Determine the corrected standard penetration numbers, (N1)60, at the various depths given. Note that the water table was not found during the boring operation. Assume that the average unit weight of sand is 18.7 kN/m3. Use Liao and Whitman’s relationship [Eq. (17.10)]. Assume pa ≈ 100 kN/m2. To determine

Find the corrected standard penetration numbers (N1)60 at the various depth.

Explanation

Given information:

Show the depth and number of blows shown in table:

 Depth,(m) N60 1 10 2.5 12 4 14 5.5 15 7 17

Assume the average unit weight (γ) of sand is 18.7kN/m3.

The atmospheric pressure is (pa) 100kN/m2.

Calculation:

Calculate the overburden pressure (σo) at depth 1m using the relation:

(σo)=γ×depth (1)

Substitute 1m for depth and 18.7kN/m3 for (γ) in Equation (1).

(σo)=18.7×1=18.7kN/m2

Find the correction factor (CN) at depth 1m using Liao and Whiteman’s relation:

CN=[1(σopa)]0.5 (2)

Here, (σo) is overburden pressure.

Substitute 18.7kN/m2 for σo and 100kN/m2 for pa in Equation (2).

CN=[1(18.7100)]0.5=[5.3475]0.5=2.31

Find the corrected standard penetration numbers (N1)60 at 1m depth.

(N1)60=CNN60 (3)

Here, (CN) is correction factor and N60 is standard penetration number.

Substitute 2.31 for CN and 10 for N60 in Equation (3).

(N1)60=2.31×10=23.123

Thus, the corrected standard penetration numbers at the depth 1m is 23.

Calculate the overburden pressure (σo) at depth 2.5m using the relation:

Substitute 2.5m for depth and 18.7kN/m3 for (γ) in Equation (1).

(σo)=18.7×2.5=46.75kN/m2

Find the correction factor (CN) at depth 2.5m using Liao and Whiteman’s relation:

Substitute 46.75kN/m2 for σo and 100kN/m2 for pa in Equation (2).

CN=[1(46.75100)]0.5=[2.1390]0.5=1.462

Find the corrected standard penetration numbers (N1)60 at 2.5m depth.

Substitute 1.462 for CN and 12 for N60 in Equation (3).

(N1)60=1.462×12=17.5418

Thus, the corrected standard penetration numbers at the depth 2.5m is 18.

Calculate the overburden pressure (σo) at depth 4m using the relation:

Substitute 4m for depth and 18.7kN/m3 for (γ) in Equation (1)

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