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during the tilting tests and the sinusoidal shaking tests are also shown. The
P
a
-values are evaluated by integrating normal stresses measured with
loadcells along the depth of the facing, which include initial values measured
before the start of shaking or tilting. For each irregular or sinusoidal shaking
step, the P
a
-value was defined under three different conditions; i.e., when
either one of P
a
-values itself, the wall top displacement d
top
or base acceleration (on
the negative side, inducing outward inertia force) becomes respective peak state. The
k
h
-values are evaluated based on Eqs. (1) and (2). Note that for the tilting tests,
the measured values of the normal stresses at tilted conditions were corrected for the
effects of the sand box inclination by a factor of 1/(cosu), where uis the tilting angle.
In
Fig. 19a-c
,
theoretical relationships based on the Mononobe-Okabe
method are shown, while in Fig. 19d-f, those based on limit-equilibrium stability
analysis assuming the two-wedge failure mechanism, as shown in
Fig. 8
,
are
presented. In obtaining these relationships, similarly to the case with
Fig. 10,
the
shear resistance angle f of the backfill was set equal to f
peak
(
) and the
frictional angle d at the interface between the backfill and the wall facing with
sandpaper was set equal to 3/4f
peak
. For comparison, the residual condition of
f
¼
51
8
¼
¼
8
¼
3/4f
res
was also employed in the calculation.
For the cantilever-type RW, the resultant forces measured at the backface
of the wall cannot be directly compared to the calculated values, because the
calculated resultant forces are those acting on the vertical failure plane in the
backfill, which was actually observed to develop from the heel of the wall base
estimated from the measured values of the normal force P
a1
acting on the
backface of the facing and the shear force T acting on the top of the wall base
from the backfill as
f
res
(
43
) and d
P
a
¼
P
a1
þ
T
2
k
h1
£
W
ð
3
Þ
where k
h1
£
W is the horizontal inertia of the soil block located above the wall base
and separated by the vertical failure plane from the remaining part of the backfill
(i.e., W is the weight of this soil block, and k
h1
is the measured horizontal response
acceleration a
b
of this soil block divided by the gravitational acceleration g for the
shaking table tests); T and k
h1
£
W are defined positive when they act in the
direction toward the facing (i.e., at the active state). In this case, theoretical
relationships with f
f
res
are added to the figure, since
the frictional angle dat the vertical failure plane can be assumed equal to f.
It can be seen from Fig. 19 that, in general, the P
a
-values measured in the
tilting tests were larger than those measured in the sinusoidal or irregular shaking
tests. In a broad sense, the results from tilting tests were comparable with the
theoretical ones, except for the leaning-type RW. It should be noted, however,
that the direct comparison of the measured values with those calculated by the
Mononobe-Okabe or its equivalent method is valid at the active failure state in
¼
d
¼
f
peak
and f
¼
d
¼
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