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Soil Mechanics and Foundation Engineering - Engineering

Q1:

The active earth pressure of a soil is proportional to (where φ is the angle of friction of the soil)

A tan (45° - φ)

B tan2 (45° + φ/2)

C tan2 (45° - φ/2)

D tan (45° + φ)

ANS:C - tan2 (45° - φ/2)

Ka = (1-sin¢)/(1+sin ¢)
= Cot^2 (Alpha) = Cot^2 (45+¢/2)
=Cot^2 [90-(45-¢/2)]
={Cot [90-(45-¢/2)]}^2
= {tan(45-¢/2)}^2
= tan^2 (45-¢/2)

Kp = (1+sin¢) / (1-sin¢)
= tan^2 (Alpha) = tan^2 (45+¢/2)

=>In active earth pressure failure plane make angle of 45+¢/2 with horizontal .

=>In the Passive earth pressure, failure plane makes an angle of 45-¢/2 with horizontal.

=> Remember that angles are not indicated of Alpha.
In the above formulas, Alpha is the Critical Angle.