Given data### Given

• Slope angle $B = 25^\circ$
• Height of soil layer $h = 12 \text{ feet}$
• Moist unit weight $\gamma_m = 115 \text{ pcf}$
• Saturated unit weight $\gamma_s = 125 \text{ pcf}$
• Water table depth from the bedrock = $4 \text{ feet}$
• Cohesion $c = 200 \text{ psf}$ for part (b), and no cohesion for part (a).

Part (a): Friction angle at failure with no cohesion

We'll use infinite slope stability analysis for a purely frictional soil (i.e., with no cohesion):

The factor of safety $F_s$ for an infinite slope with no cohesion is given by:

$F_s = \frac{\tan \phi}{\tan B}$

Where:

• $\phi$ = friction angle of the soil
• $B$ = slope angle = $25^\circ$

For failure, the factor of safety $F_s = 1$, so:

$1 = \frac{\tan \phi}{\tan 25^\circ}$

Solving for $\phi$:

$\phi = \tan^{-1} (\tan 25^\circ)$

Thus,

$\phi = 25^\circ$

So, the friction angle at failure with no cohesion is 25 degrees.

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Part (b): Friction angle with cohesion equal to 200 psf

For the case with cohesion, the factor of safety is given by:

$F_s = \frac{c + (\gamma_m - \gamma_w h_w) h \cos^2 B \tan \phi}{\gamma_m h \sin B \cos B}$

Where:

• $\gamma_m$ = moist unit weight = $115 \, \text{pcf}$
• $\gamma_w$ = unit weight of water = $62.4 \, \text{pcf}$
• $h_w$ = height of water table = $4 \, \text{ft}$
• $h$ = total height of soil = $12 \, \text{ft}$
• $B$ = slope angle = $25^\circ$
• $c$ = cohesion = $200 \, \text{psf}$

Let me compute the required friction angle $\phi$ when cohesion is involved.The friction angle $\phi$ with cohesion equal to 200 psf is approximately 54.8 degrees.

Summary:

• (a) The friction angle at failure with no cohesion is 25 degrees.
• (b) The friction angle at failure with cohesion of 200 psf is approximately 54.8 degrees.

Would you like further details on these calculations, or do you have any specific questions?

Here are 5 related questions you could explore:

1. How does the depth of the water table influence the stability of slopes?
2. What happens to the friction angle if the slope angle is increased?
3. How does adding cohesion affect slope stability?
4. Can you explain the concept of "infinite slope" in soil mechanics?
5. How would the presence of pore pressure influence the analysis?

Tip: When cohesion is present, it significantly increases the soil's ability to resist shear failure, especially on steeper slopes.