## Thursday, September 5, 2013

### Rankine's Earth Pressure Theory

Rankine's earth pressure theory is widely used in analyzing the lateral pressure exerted by earth to a vertical wall (e.g. Retaining Wall) as long as it meets certain assumptions used in this theory.
Assumptions are the wall should be vertical and the friction resistance between the wall and the soil is neglected and the soil should be granular.

Pressures acting on the soil consists of three types; active, passive and at rest.

Rankine's coefficients are Ka for active, Kp for passive and Ko for at rest.

Applications:

1. Active pressure - assumed as horizontal neglecting the friction between soil and wall. This friction force gives a stabilizing
effect on the wall and is normally ignored for added factor of safety. Active pressure happens when the wall permits a certain amount of movement due to earths lateral pressure and has a formula of Pa = (1-sin A) / (1+sin A) x Y x H
where:  Y = effective unit weight of soil (bouyant unit weight for saturated soils)
H = Height of wall
A = angle of internal friction of soil

2. Passive pressure - when the wall is pushing onto the soil and develops a larger compression on the soil.
Pp =  (1+sin A) / (1-sin A) x Y x H
where:  Y = effective unit weight of soil (bouyant unit weight for saturated soils)
H = Height of wall
A = angle of internal friction of soil

3. At rest pressure - when the structure is not permitted to move, thus developing a higher stress than the active pressure. This is due to the overburden pressure of the soil that is being resisted by the restrained structure.
Po =  (1-sin A) x Y x H
where:  Y = effective unit weight of soil (bouyant unit weight for saturated soils)
H = Height of wall
A = angle of internal friction of soil

These pressures acts at the depth 'H' from the soil whichever is applicable. Total lateral load would be F = P x H / 2 acting at H/3 from the bottom assuming there is no inclination on the embankment behind the wall.