The critical height of infinite slope in c- - soil having slope angle i is - is unit weight of slope material and i - -

FOS for infinite slope in c ϕ soil FOS = c+γ z cos^2 i tanϕγ z cos i sin i For critical height , FOS = 1 γ z_c cos i sin i = c + γ z_c cos ^2 i tanϕ z_c = ...

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Standard VII

Physics

Elasticity

The critical ...

Question

The critical height of infinite slope in $c - ϕ$ soil having slope angle i is :
$γ$ is unit weight of slope material and $i > ϕ$

\frac{c}{γ (tan i - tan ϕ) {sin}^{2} i}

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\frac{c}{γ (tan i - tan ϕ) {cos}^{2} ϕ}

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\frac{c}{γ (tan i - tan ϕ) {cos}^{2} i}

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\frac{c}{γ (tan i - tan ϕ) {sin}^{2} ϕ}

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Solution

The correct option is C $\frac{c}{γ (tan i - tan ϕ) {cos}^{2} i}$
FOS for infinite slope in $c - ϕ$ soil

$F O S = \frac{c + γ z {cos}^{2} i tan ϕ}{γ z cos i sin i}$

For critical height , FOS = 1

$γ z_{c} cos i sin i = c + γ z_{c} {cos}^{2} i tan ϕ$

$z_{c} = \frac{c}{γ cos i (sin i - cos i tan ϕ)}$

$= \frac{c}{γ {cos}^{2} i (tan i - tan ϕ)}$

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The critical height of infinite slope in c−ϕ soil having slope angle i is : γ is unit weight of slope material and i>ϕ

The correct option is C cγ(tani−tanϕ)cos2iFOS for infinite slope in c−ϕ soil FOS=c+γzcos2itanϕγzcosisini For critical height , FOS = 1 γzccosisini=c+γzccos2itanϕ zc=cγcosi(sini−cositanϕ) =cγcos2i(tani−tanϕ)

The critical height of infinite slope in $c - ϕ$ soil having slope angle i is :
$γ$ is unit weight of slope material and $i > ϕ$