A cut is to be made in a soil having γ = 105 lb/ft³, c′ = 600 lb/ft², and Φ′ = 15°. The side of the cut slope will make an angle of 45° with the horizontal. What should be the depth of the cut slope that will have a factor of safety (Fs) of 3?

Question

A cut is to be made in a soil having γ = 105 lb/ft³, c′ = 600 lb/ft², and [latex]\phi ^\prime [/latex] = 15°. The side of the cut slope will make an angle of 45° with the horizontal. What should be the depth of the cut slope that will have a factor of safety ([latex]F_s[/latex]) of 3?

Accepted Answer

Given: [latex]\phi ^\prime [/latex] = 15°; c′ = 600 lb/ft². If [latex]F_s[/latex] = 3, then [latex]F_{c^\prime}[/latex] and [latex]F_{\phi^\prime}[/latex] should both be equal to 3.
[latex]F_{c^\prime}=\frac{c^\prime}{c^\prime_d}[/latex]
or
[latex]c^\prime_d=\frac{c^\prime}{F_{c^\prime}}=\frac{c^\prime}{F_s}=\frac{600}{3}=200[/latex] lb/ft²
Similarly,
[latex]F_{\phi^\prime}=\frac{ an \phi^\prime}{ an \phi^\prime_d}\ an \phi^\prime_d=\frac{ an \phi^\prime}{F_{\phi^\prime}}=\frac{ an \phi^\prime}{F_s}=\frac{ an 15}{3}[/latex]
or
[latex]\phi^\prime_d= an^{-1}\left[\frac{ an 15}{3} ight]=[/latex] 5.1°
Substituting the preceding values of [latex]c^\prime_d[/latex] and [latex]\phi^\prime_d[/latex] in Eq. (15.29)
[latex]H=\frac{4c^\prime_d}{\gamma}\left[\frac{\sin \beta \cdot \cos \phi^\prime_d}{1-\cos(\beta-\phi^\prime_d)} ight]\=\frac{4 imes 200}{105}\left[\frac{\sin 45 \cdot \cos 5.1}{1-\cos(45-5.1)} ight]\=[/latex] 23.05 ft

Question 15.2: A cut is to be made in a soil having γ = 105 lb/ft³, c′ = 60...

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