### How to estimate the earth pressure on abutment

Earth pressure coefficient magnitude will vary depending on the degree of restraint provided by abutment.  for cantilever abutment with a possibility of small relieve movement to occur, for this type of abutments, active pressure shall be adopted. for abutments with piles foundation, this type of abutment is rigid and supported by piles. therefore it is fully restrained and difficult to move to relieve earth pressure, for this case, at-rest earth pressure is used.
AASHTO table C3.11.1-1 provides an approximate value of minimum movement to consider the pressure acting on an abutment at rest, active or passive

where
Δ is the movement at top of wall or abutment required to reach minimum active pressure or maximum passive pressure by tilting or lateral translation movement in (mm or ft)
H is the hight of wall or abutment in (mm, ft).

Figure 1

AASHTO LRFD  3.11.1 pointing some factors should be considered in calculating earth pressure:
• Type and unit weight of the earth
• water content
• soil creep characteristics
• degree of compaction
• location of the groundwater table
• earth-structure interaction
• amount of surcharge
• earthquake effects
• back slope angle and wall inclination

lateral earth pressure shall be calculated using this equation(AASHTO3.11.5.1):

p = k γs z(us units)
P=k γz*10^-3(Si units)

where
P is the lateral earth pressure(Ksf), (Mpa)
K is the coefficient of lateral earth pressure. taken as Ko (at-rest earth pressure coefficient where abutment doesn't move). and Ka if sufficient movement occurs in abutment as explained before.
γs is the unit weight of soil (Kcf),(Kn/m3)
Z is the depth below the surface of the earth (ft), (m)

the resultant lateral earth load due to the weight of backfilling is assumed to act at H/3 from the base of abutment of the wall. where is H is the hight of wall or abutment

At rest coefficient earth pressure for normally consolidated soil, vertical wall and level ground can be calculated using the following equation [AASHTO 3.11.5.2]

Ko=1-sin ɸ'f

where
ɸ'f is the effective angle of friction for soil

for overconsolidated soil the at rest coefficient earth pressure will vary as a function overconsolidated ratio or stress history

Ko=(1-sin ɸ'f)(OCR)^sin ɸ'f

Active earth pressure may calculated using the following equation [AASHTO 3.11.5.3]

where
δ is the angle of friction between fill and wall
β is the angle of fill with the horizontal as shown in figure 2
θ = angle of back face of wall to the horizontal as shown in Figure 3
ɸ'f = effective angle of internal friction

Figure 2

silt and lean clay shall not be used as backfill materials. in the events of using silt and clay as a backfill material, special design and construction procedure shall be followed to consider their presence effects. the force developed from pore water pressure shall be considered in the calculation of lateral earth pressure.