   Chapter 15, Problem 15.27P 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 slope with steady-state seepage has the following characteristics: H = 30 m, β = 18.43° (3:1 slope), γ' = 18 kN/m3, ϕ' = 23°, c' = 27 kN/m2, and ru = 0.5. Use Bishop and Morgenstern’s method to determine the minimum factor of safety.

To determine

Find the minimum factor of safety Fs using the Bishop and Morgenstern’s method.

Explanation

Given information:

The height (H) of the slope is 30 m.

The inclination β of a slope (3:1slope) is 18.43°.

The unit weight γ is 18kN/m3.

The angle of friction ϕ is 23°.

The cohesion c is 27kN/m2.

The value non-dimensional quantity ru is 0.5.

Calculation:

Determine the minimum factor of safety Fs from Table (15.5), using the procedure as follows:

• Step 1. Obtain the values of angle of friction, inclination of a slope, and the value of cγH
• Step 2. Obtain the value of nondimensional quantity.
• Step 3. Refer Table (15.5) “Values of m and n for cγH=0” in the text book. Obtain the values of m and n for D=1,1.25,and1.5.
• Step 4. calculate the factor of safety value, using the values of m and n for each value of D.
• Finally, the required value of factor of safety is the smallest one obtained in step 4.

Trial 1:

Determine the value of cγH.

Substitute 27kN/m2 for c, 18kN/m3 for γ, and 30 m for H.

cγH=2718(30)=0.05

Refer Table (15.5d) “Stability coefficients m and n for cγH=0.05 and D=1.00” in the text book.

Take the stability coefficient m as 2.014 when the angle of friction ϕ is 22.5°.

Take the stability coefficient m as 2.193 when the angle of friction ϕ is 25°.

Determine the stability coefficient m when the angle of friction ϕ is 23° using the interpolation.

m=(2322.5)(2.1932.014)(2522.5)+2.014=2.049

Take the stability coefficient n as 1.568 when the angle of friction ϕ is 22.5°.

Take the stability coefficient n as 1.757 when the angle of friction ϕ is 25°.

Calculate the stability coefficient n when the angle of friction ϕ is 23° using the interpolation.

n=(2322.5)(1.7571.568)(2522.5)+1.568=1.606

Calculate the factor of safety using the formula.

Fs=mnru

Substitute 2.049 for m, 1.606 for n, and 0.5 for ru.

Fs=2.0491.606(0.5)=1.25

Trial 2:

Refer Table (15.5e) “Stability coefficients m and n for cγH=0.05 and D=1.25” in the text book

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