   Chapter 12, Problem 12.13P 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

Refer to the consolidated-undrained triaxial test in Problem 12.12. Determine the Skempton’s pore pressure parameter, A ¯ f .12.12 Consider the clay sample in Problem 12.11. A consolidated-undrained triaxial test was conducted on the same clay with a chamber pressure of 10 lb/in.2. The pore pressure at failure was (Δud)f = 4.2 lb/in.2. What would be the major effective principal stress, σ ′ 1 , at failure?

To determine

Find the Skempton’s pore pressure parameter, A¯f.

Explanation

Given information:

The pore pressure at failure (Δud)f is 4.2lb/in2.

The chamber pressure (σ3) is 10lb/in2.

Calculation:

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

σ1=σ3tan2(45+ϕ2)+2c(45+ϕ2) (1)

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

For normally consolidated clay, cohesion is equal to zero.

Substitute 0 for c in Equation (1)

σ1=σ3tan2(45+ϕ2)+2(0)(45+ϕ2)=σ3tan2(45+ϕ2) (2)

Substitute (σ3Δud(f)) for σ3 and 23° for ϕ in Equation (2).

σ1=(σ3Δud(f))tan2(45+232)=(σ3Δud(f))tan2(56.5) (3)

Substitute 10lb/in2 for σ3 and 4.2lb/in2 for Δud(f) in Equation (3).

σ1=(104.2)tan2(56.5)=5.8×2.2801=13.24lb/in2

Find the deviator stress at failure using the relation as follows:

Δσd(failure)=σ1σ3 (4)

Here, σ3 and σ1 minor and major effective principal stress at failure

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