Civil Engineering - Soil Mechanics and Foundation Engineering - Discussion

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.

Active earth pressure is directly proportional to cot2 (45° + φ/2) or tan2 (45° - φ/2).

Hers, cot^2(45 +B÷2 ) or by converting cot into tan^2 (90 -45 - B÷2) = tan^2 (45 - B÷2).

Active earth pressure = ka*y*h where ka = (1-sinφ)/(1+sinφ) = tan2(45° - φ/2)

Active earth pressure = 1/(tan2 (45° + π/2)) = tan2 (45° + π/2)
ka = 1/ kp.

ka=1/tan^2(45°+Φ/2).
=tan^2(45°+Φ/2).
=flow value.

What will be for passive earth pressure of soil? Please explain.

The value. Tan^2 (45 +φ/2) is for passive earth pressure.

According to me, Pa is proportional to cot^2(45+π/2).

@Tanupa. Passive earth pressure = Tan^2(45+ angle\2).