To predict the failure plane, it was assumed that δw = 3/4φ. The failure planes observed
for the cantilever-type, gravity-type, and reinforced soil, Type 1 model walls in
the shaking table tests, and the failure planes for the reinforced soil, Type 1 model walls
with a surcharge of 1.0 kN/m2 in the tilt table tests were steeper than the predicted failure
planes. For the shaking table tests, the difference was greater for the reinforced soil,
Type 1 model wall than for the cantilever- and gravity-type model walls. Also, for the
tilt table tests on the reinforced soil, Type 1 model wall with a larger surcharge, the observed
failure plane was steeper than the predicted failure plane, although the difference
is marginal.
It should be noted that the predicted failure plane angle decreases as the seismic coefficient
increases (Figure 16). On the other hand, the shaking acceleration or the tilting
angle could be increased further, even after slight movement of the wall, without causing
an abrupt ultimate failure. The failure plane developed further during the increase of
shaking acceleration/tilting angle, as typically seen from Figure 5 forthe reinforced soil,
Type 1 model wall. It is important to note, however, that no multiple failure planes in the
backfill were observed in the models, except for the reinforced soil, Type 2 model wall.
The active earth pressure coefficient, Ka , was calculated for δw = 3/4φ by the trial
wedge method assuming a vertical interface between the backfill and the wall. In Figure
17, the results are plotted versus the angle of the direction of the bottom failure plane
of the trial wedge, ζ. For simplicity, the seismic coefficient kh was set to 0, 0.2, and 0.4
in Cases 1, 2, and 3, respectively. In these cases, the shear resistance angle φ was set
to 51_, which corresponds to the peak resistance of the backfill, as was the case with
the aforementioned prediction of wall stability (Section 3). On the other hand, for Case
4, the value of φ was reduced to 34_, which approximately corresponds to the residual
angle of friction, φres , while keeping kh = 0.4. Similarly, the value of δ for Cases 3 and
4 was reduced to 29_ by assuming the residual condition for this interface friction angle ([φss]res = arctan{sin[φss]}). The range of failure plane angles observed for the cantilever-type,
gravity-type, and reinforced soil, Type 1 model walls during shaking are also
shown in Figure 17. Based on Figure 17, the formation of a single failure plane during
shaking may be outlined in the following steps: