Lateral Earth Pressure - Part 02

Cohesion less Back fills

For Cohesion less back fills,
(1) Active state,
(2) Passive state,

Without water table - as usual method (please go through part 01)
With water table - Need to draw horizontal pressure distribution and water pressure diagrams. sum of those two diagrams equal to the final diagram. (using final diagram we can find final force and the line of action)

If there is a surcharge, on top of the ground it is also need to draw diagram for that and add up all diagrams to get the final.

If there is a surcharge, due to that this diagram need to add,

 

Cohesive Back fills

Due to cohesive back fills cracks appear on top of the ground surface [Tension (-) , Compression (+)] consider a cohesive horizontal back fill under active state, the active lateral pressure is given by,

The horizontal stress (sigma a') is zero at depth Z0
 

0 = sigma v' Ka - 2 c' (Ka)^1/2
0 = z0 gamma Ka - 2 C' (Ka)^1/2


where,
Z0 = Depth of the crack
gamma = unit weight of soil

Sloping Back fills

This is a new chapter before we talked about active and passive cases for horizontal ground condition. from this we will talk about sloping back fills,

Sloping back fills

(1)Cohesion less
 - Active
 - Passive

(2)Cohesive back fills
- Active
- Passive 
for cohesive back fills there are 3 methods to determine active and passive earth pressures
                     1. Extended ranking theory
                     2. Coulomb theory
                     3. Culman's graphical method

 

Sloping back fills - Cohesion less

(1) Active case

                        
 Pressure distribution and resultant force acting parallel to the slope (alpha)

or we can use below table to obtain Ka values, according to alpha values and phi values,

Therefore final equation is,

(2) Passive case

 Pressure distribution and resultant force acting parallel to the slope (alpha)



or we can use below table to obtain Kp values, according to alpha values and phi values,

Therefore final equation is,