Chapter 15, Problem 15.12P

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

Refer to Figure 15.50. Given that β = 55°, γ = 121 lb/ft3, ϕ' = 17°, c' = 1200 lb/ft2, and H = 45 ft, determine the factor of safety with respect to sliding. Assume that the critical sliding surface is a plane.

To determine

Find the factor of safety Fs with respect to sliding.

Explanation

Given information:

The slope with an inclination β is 55°.

The unit weight γ of the soil is 121lb/ft3.

The angle of friction ϕ is 17°.

The cohesion c is 1,200lb/ft2.

The height (H) of the retaining wall is 45 ft.

Calculation:

Trial 1:

Consider the factor of safety as 2.

Determine the cohesion cd develop along the potential failure surface using the relation.

cd=cFs

Substitute 1,200lb/ft2 for c and 2.0 for Fs.

cd=1,2002.0=600lb/ft2

Determine the angle ϕd of friction that develops along the potential failure surface using the relation.

ϕd=tan1(tanϕFs)

Substitute 17° for ϕ and 2.0 for Fs.

ϕd=tan1(tan17°2.0)=tan1(0.153)=8.69°

Determine height of the slope that will have a factor of safety of 2.0 against sliding using the formula.

Hcr=4cdγ[sinβcosϕd1cos(βϕd)]

Substitute 600lb/ft2 for cd, 121lb/ft3 for γ, 55° for β, and 8.69° for ϕd.

Hcr=4(600)121[sin55°cos8.69°1cos(55°8.69°)]=19.835(0.810.31)=51.83ft

The height of the retaining wall is not equal to the calculated height of the wall.

51.83ft45ft

Hence, the assumption is incorrect.

Trial 2:

Consider the factor of safety as 2.5.

Determine the cohesion cd develop along the potential failure surface using the relation.

cd=cFs

Substitute 1,200lb/ft2 for c and 2.5 for Fs.

cd=1,2002.5=480lb/ft2

Determine the angle ϕd of friction that develops along the potential failure surface using the relation.

ϕd=tan1(tanϕFs)

Substitute 17° for ϕ and 2.5 for Fs.

ϕd=tan1(tan17°2.5)=tan1(0

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