Principles of Geotechnical Enginee...

9th Edition

Braja M. Das + 1 other

ISBN: 9781305970939

Textbook Problem

The inclination of a finite slope is 1 vertical to 1 horizontal. Determine the slope height, H, that will have a factor of safety of 2.8 against sliding. Given: ρ = 1950 kg/m³, ϕ ′ = 23 ° , and c′ = 40 kN/m². Assume that the critical sliding surface is a plane.

To determine

Find the height (H) of the slope that will have a factor of safety of 2.8 against sliding.

Explanation

Given information:

The density ρ is 1,950 kg/m3.

The angle of friction ϕ′ is 23°.

The cohesion c′ is 40 kN/m2.

The factor of safety Fs is 2.8.

The inclination β of a finite slope is 1 vertical to 1 horizontal.

Calculation:

Determine the inclination angle β using the relation.

β=tan−1(11)=45°

Determine the unit weight γ using the relation.

γ=ρg1,000

Here, g is the acceleration due to gravity.

Take the acceleration due to gravity as 9.81 m/s2.

Substitute 1,950 kg/m3 for ρ and 9.81 m/s2 for g.

γ=(1,950)(9.81)1,000=19.12 kN/m3

Determine the cohesion c′d develop along the potential failure surface using the relation.

c′d=c′Fs

Substitute 40 kN/m2 for c′ and 2.8 for Fs.

c′d=402.8=14.28 kN/m2

Determine the angle ϕ′d of friction that develops along the potential failure surface using the relation.

ϕ′d=tan−1(tanϕ′Fs)

Substitute 23° for ϕ′ and 2

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The inclination of a finite slope is 1 vertical to 1 horizontal. Determine the slope height, H, that will have a factor of safety of 2.8 against sliding. Given: ρ = 1950 kg/m³, ϕ ′ = 23 ° , and c′ = 40 kN/m². Assume that the critical sliding surface is a plane.

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The inclination of a finite slope is 1 vertical to 1 horizontal. Determine the slope height, H, that will have a factor of safety of 2.8 against sliding. Given: ρ = 1950 kg/m3, ϕ ′ = 23 ° , and c′ = 40 kN/m2. Assume that the critical sliding surface is a plane.

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The inclination of a finite slope is 1 vertical to 1 horizontal. Determine the slope height, H, that will have a factor of safety of 2.8 against sliding. Given: ρ = 1950 kg/m³, ϕ ′ = 23 ° , and c′ = 40 kN/m². Assume that the critical sliding surface is a plane.