   Chapter 17, Problem 17.5P 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

Following are the results of a standard penetration test in fine dry sand. For the sand deposit, assume the mean grain size, D50, to be 1 mm and the unit weight of sand to be 18.5 kN/m3. Estimate the variation of relative density with depth using the correlation developed by Cubrinovski and Ishihara [Eq. (17.18)]. Assume pa ≈ 100 kN/m2.

To determine

Find the variation of relative density with depth using the correlation developed by Cubrinovski and Ishihara.

Explanation

Given information:

Show the depth and number of blows shown in table:

 Depth,(m) N60 0.5 6 2.0 9 3.5 12 5.0 14 6.5 17

Assume the average unit weight (γ) of sand is 18.5kN/m3.

The mean grain size (D50) is 1mm.

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

Calculation:

Calculate the overburden pressure (σo) at depth 0.5m using the relation:

(σo)=γ×z (1)

Here, z is depth.

Substitute 0.5m for depth and 18.5kN/m3 for (γ) in Equation (1).

(σo)=18.5×0.5=9.25kN/m2

Show the expression to find correlation of relative density by using Cubrinovski and Ishihara.

Dr(%)=[N60(0.23+0.06D50)1.79(paσo)]0.5100 (2)

Substitute 9.25kN/m2 for (σo), 100kN/m2 for (pa), 1mm for (D50), and 6 for N60 in Equation (2).

Dr(%)=[6(0.23+0.061)1.79(1009.25)]0.5100=[0.08128×10.8108]0.5×100=93.794%

Thus, the variation of relative density at the depth 0.5m is 94%.

Calculate the overburden pressure (σo) at depth 2m using the relation:

Substitute 2m for depth and 18.5kN/m3 for (γ) in Equation (1).

(σo)=18.5×2=37kN/m2

Find correlation of relative density by using Cubrinovski and Ishihara at the depth 2.0m

Substitute 37kN/m2 for (σo), 100kN/m2 for (pa), 1mm for (D50), and 9 for N60 in Equation (2).

Dr(%)=[9(0.23+0.061)1.79(10037)]0.5100=[0.121920×2.70270]0.5×100=0.574×10057%

Thus, the variation of relative density at the depth 2.0m is 57%.

Calculate the overburden pressure (σo) at depth 3.5m using the relation:

Substitute 3.5m for depth and 18.5kN/m3 for (γ) in Equation (1)

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