   Chapter 15, Problem 15.28P 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

Determine the minimum factor of safety of a slope with the following parameters: H = 90 ft, β = 26.56° (2:1 slope), γ = 122.5 lb/ft3, ϕ' = 30°, c' = 568 lb/ft2, and ru = 0.5. Use Bishop and Morgenstern’s method.

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 90 ft.

The inclination β of a slope (2:1slope) is 26.56°.

The unit weight γ is 122.5lb/ft3.

The angle of friction ϕ is 30°.

The cohesion c is 568lb/ft2.

The value non-dimensional quantity ru is 0.5.

Calculation:

To determine the minimum factor of safety Fs from Table (15.5), the following procedure must be followed.

• 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. Then 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.

Determine the value of cγH.

Substitute 568lb/ft2 for c, 122.5lb/ft3 for γ, and 90 ft for H.

cγH=568122.5(90)=0.05

Determine the factor of safety using the formula.

Fs=mnru (1)

Consider D=1m:

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 1.888 when the angle of friction ϕ is 30°

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