Chapter 12, Problem 12.15P

### Principles of Geotechnical Enginee...

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

Chapter
Section

### Principles of Geotechnical Enginee...

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

# A consolidated-drained triaxial test was conducted on a normally consolidated clay with a chamber pressure of σ3 = 35 lb/in.2. The deviator stress at failure of (Δσd)f = 42 lb/in.2.a. Determine the angle of friction, ϕ ′ .b. Determine the angle θ that the failure plane makes with the major principal plane.c. Calculate the normal stress, σ ′ f , and the shear stress, τ f , on the failure plane.

(a)

To determine

Find the angle of friction ϕ.

Explanation

Given information:

The chamber pressure σ3 is 35lb/in2.

The deviator stress (Δσd)f at failure is 42lb/in2.

Calculation:

Show the expression of major principal effective stress at failure to find the angle of friction using the formula.

σ1=σ3tan2(45+ϕ2) (1)

Modify Equation (1).

σ1=σ3tan2(45+ϕ2)σ3+(Δσd)f=σ3tan2(45+ϕ2) (2)

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

Substitute 35lb/in2 for σ3 and 42lb/in2 for (Δσd)f in Equation (2)

(b)

To determine

Find the angle such that failure plane makes with the major principal plane.

(c)

To determine

Find the normal stress (σf) at failure and the shear stress (τf) at failure.

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