   Chapter 12, Problem 12.21P 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

A consolidated-undrained triaxial test was conducted on a dense sand with a chamber-confining pressure of 14 lb/in.2. Results showed that ϕ ′ = 27 ° and ϕ = 33 ° . Determine the deviator stress and the pore water pressure at failure. If it were a loose sand, what would have been the expected behavior? Explain.

To determine

Find the deviator stress and pore water pressure at failure and write about the behavior of loose sand.

Explanation

Given information:

The chamber confining pressure (σ3) is 14lb/in2.

The undrained angle of friction ϕ is 33°.

The drained angle of friction ϕ is 27°.

Calculation:

Find the total stress (σ1) at failure using the Equation:

σ1=σ3tan2(45+ϕ2) (1)

Substitute 14lb/in2 for σ3 and 33° for ϕ in Equation (1).

σ1=14tan2(45+332)=14tan2(61.5)=14×3.392=47.4896lb/in2

Find the deviator stress [(Δσd)f] at failure using the relation as follows:

(Δσd)f=σ1σ3 (2)

Substitute 47.4896lb/in2 for σ1 and 14lb/in2 for (σ3) in Equation (2).

(Δσd)f=47.8414=33.48lb/in2

Thus, the deviator stress at failure is 33.48lb/in2_.

Show the equation of the major effective principal stress (σ1) as follows

σ1=σ1(Δud)f

Here, (Δud)f is the pore water pressure developed in the specimen at failure.

Show the equation of the minor effective principal stress (σ3) as follows

σ3=σ3(Δud)f

Find the major effective principal stress (σ1) as follows:

Modify Equation (1).

σ1=σ3tan2(45+ϕ2)σ1σ3=tan2(45+ϕ2)

Substitute σ1(Δud)f for σ1 and σ3(Δud)f for σ3

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