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Chapter 12, Problem 12.9P
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### Principles of Geotechnical Enginee...

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

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Principles of Geotechnical Enginee...

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

# The relationship between the relative density Dr and the angle of friction ϕ ′ of a sand can be given as ϕ ′ = 28 + 0.18 D r (Dr in %). A drained triaxial test was conducted on the same sand with a chamber-confining pressure of 250 kN/m2. The sand sample was prepared at a relative density of 88%. Calculate the major principal stress at failure.

To determine

Find the major principal stress (σ1) at failure.

Explanation

Given information:

The relative density (Dr) is 88%.

The confining pressure σ3 is 250kN/m2.

Calculation:

Determine the effective angle of friction (ϕ) using the relation:

ϕ=28+0.18Dr

Substitute 88% for (Dr).

ϕ=28+0.18(88)=43.84°

Show the expression of major effective principal stress as shown below:

σ1=σ3tan2(45+ϕ2)+2c(45+ϕ2)

Here, σ3 and σ1 minor and major effective principal stress and c is cohesion

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