3523
Technical Committee 203 /
Comité technique 203
The total seismic earth pressure,
!!
, was obtained by
integrating the horizontal stress distributions as shown in the
xy-
graph of Figure 2 a). By subtracting the total at-rest earth
pressure, the total increment of seismic earth pressure,
∆
!!
,
was then calculated. Figure 3 shows the normalized
∆
!!
versus
seismic coefficient for internal frictional angles varying from 30
to 38 degrees for Case 3. It can be seen that the effect of shear
strength of the retained soil to the normalized
∆
!!
is
insignificant.
Figure 3. The relationship of normalized total increment of seismic
earth pressure versus seismic coefficient for various strength parameters
Figure 4 shows the normalized
∆
!!
versus seismic
coefficient for all of the three cases. For each case, the multiple
points at the same seismic coefficient indicate the results of
different strength parameters. It is clear that although based on
different approaches, the results for the case of a restrained rigid
wall connected to a rigid base are consistent with those obtained
by Wood (1973). However, if the rigid wall and its retained soil
are supported on a non-rigid base, the seismic earth pressure
increment will be approximately 15 to 17% higher. Considering
the anticipated real movement of the wall system during an
earthquake, it is recommended to calculate the seismic earth
pressure increment using the following equation:
∆!
!!
!"
!
= 1.15
!
(1)
Figure 4. The relationship of normalized total increment of seismic
earth pressure versus seismic coefficient for various conditions.
2.3
Thrust point
To design the stem of the wall, the distribution of earth pressure
is important. Several studies were intended to provide such a
distribution (Wu and Finn, 1999; Ostadan, 2004; Maleki and
Mahjoubi, 2010). However, in routine practice, a total force and
its thrust point are easier to handle and calculate.
The equivalent thrust point was calculated based on the
calculated earth pressure distributions such as shown in the
xy
-
graph of Figure 2 a). Figure 5 shows the normalized thrust point
of the total earth pressure (including static and seismic) as a
function of the seismic coefficient. The thrust point moves
upward with the increase in seismic coefficient and can be
conservatively approximated by the following equation.
= 0.55(
!
+ 0.1)
!.!
(2)
Figure 5. The relationship of normalized thrust point of total earth
pressure versus seismic coefficient
3
SEISMIC COEFFICIENT
Due to its irregularity, direct use of the acceleration time history
of an earthquake is usually difficult. Researchers typically use
equivalent approaches to deal with the problem. For example, a
harmonic wave is utilized in the laboratory for cyclic shear tests
and an equivalent uniform value equal to 65% of peak cyclic
stress is used in simplified liquefaction analysis procedures. In
the case of seismic earth pressure, a pseudostatic seismic
coefficient (
!
) is usually utilized. However, significant
variations exists in
!
, varying from 1/3 PGA (Kramer, 1996)
to as high as 100% of PGA (FEMA, 2003; HCHRP, 2008).
Yi (2011) proposed a method to establish the relationship
between
!
and PGA based on momentum equivalent: that is,
the total momentum created by irregular acceleration,
( )
, to a
soil mass,
m
, should be equivalent to that created by the seismic
coefficient,
!
:
∆ =
!
∆
(3)
At any time
t=T
, Equation (3) can be rewritten as
! !
= ∆ /
(4)
Figure 6 shows the normalized equivalent
!
for 35
acceleration time history records from 14 earthquakes where
PGA is varying from 0.04g to 1.15g. The results indicate that,
except for the El Centro Earthquake record (EW), the
equivalent
!
is generally less than 0.25 PGA.
Based on the results of centrifuge model tests, Al Atik and
Sitar (2010) obtained a relationship between dynamic earth
pressure coefficients,
!"
, and PGA, as shown in Figure 7, by
back-calculations. By introducing Equation (1), this relationship
could be modified to a relationship with
!
as shown on the
second
y
-axis in Figure 7. A line for
!
= 0.25
is also
plotted in this figure. It can be seen that even taking 25% of
PGA, it may still be conservative. This is consistent with Figure
6, that 0.25 is generally the maximum value for most
acceleration records.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
0.1
0.2
0.3
0.4
0.5
ΔP
0E
/γH
2
Pseudostatic Seismic Coefficient, k
H
Non-‐Rigid Base, Rigid Wall
φ=30⁰
φ=33⁰
φ=35⁰
φ=38⁰
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
0.1
0.2
0.3
0.4
0.5
0.6
ΔP
0E
/γH
2
Pseudostatic Seismic Coefficient, k
H
Rigid base, restrained rigid wall
Non-‐rigid base, restrained rigid wall
Non-‐rigid base, rigid wall
Wood (1973)
0
0.1
0.2
0.3
0.4
0.5
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
Thrust Point , z/H
Pseudostatic Seismic Coefficient, k
H
Rigid base, restrained rigid wall
Non-‐rigid base, restrained rigid wall
Non-‐rigid base, rigid wall
