Lateral Earth Pressure
2. Lateral strain condition
3. Pore water pressure
4. State of Equilibrium of soil
5. Wall and ground surface shape
a) Drainage conditions
b) Interaction between soil and wall
Soil state of Equilibrium
When a small change in stress produces a corresponding small change in strain.
b) State of Plastic Equilibrium
When irreversible strain takes place at a constant stress.
The strain state relating to earth pressure calculation fall into three categories:
a) At Rest State:
It is the case when state of elastic Equilibrium with no lateral displacement occurs (Figure 1 ).
b) Active state:
It is the case when plastic equilibrium with lateral expansion takes place (wall moves outward from the soil). ( Figure 2 ).
c) Passive state:
Plastic equilibrium with lateral contraction takes place (wall moves toward the soil). ( Figure 2 )
(1) Earth Pressure at rest (ko condition )
lateral strain , εh = 0
ko = coefficient of lateral earth presser at rest.
ko depends on :
§ Soil type ( sand, silt, clay)
§ Loading –Unloading history
§ Relative density of soil
For over consolidated soil (O.C.)
where OCR is the over consolidated ratio
and in general
where is Poisson ratio
In this case ,the mohre circle is below the shear envelope of this soil (Figure 3).
(2) Active Earth pressure (Rankine’s Active state )
between soil and wall .
when the wall moves outward from the
soil , the lateral earth pressure starts to
be reduced until it reaches its , minimum Figure 3
where , ka = coefficient of active earth pressure. (Figure 3)
And in this case , the failure plane makes ( 45 – Ø/2 ) with the direction of the major
principal plane ( usually horizontal axes ) .
(3) Rankin Passive State
If the wall moved toward the soil , the passive condition will take place.
The passive pressure will increase until it reaches its maximum value of:
and in this case , the failure place makes ( 45 + Ø/2 ) with the direction of the major principal plane.
Earth pressure Distribution for Sand
In general, the active earth pressure distribution in sand will be:
where γ = soil unit weight
H = wall height
However the distribution and value of passive earth pressure in sand is, Figure(5)
(b) For clay
The value of active earth pressure is (Figure 6)
where , c = soil cohesion
The passive pressure values are (Figure 7)
Effect of Ground Water Table
a) Static water table
For static water table the water pressure should be treated
separately from soil lateral pressure as shown in Figure(8)
where γsub = submerged unit weight of soil
= γsat - γw
b) Moving Water Table
In this case , the flow net and equipotential lines should be
drawn for the wall , Then the pore pressure against the wall can
be determined, ( Figure 9)
Figure (9 )
and the resultant in this case will be parallel to the ground surface,
Coulomb's Theory for Rough Walls
δ = angle of wall friction
for concrete wall
Strutted Trench sheeting
The location of struts affects the values and distributions of lateral earth pressures