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where k hy is the yield value of the coefficient of horizontal acceleration. In
addition to the angle of friction, the magnitude and direction of vertical
acceleration also affect the yield coefficient. If k v acts downward, the yield
coefficient of horizontal acceleration is expressed as
6 0 Þ
k hy ¼ð
1
þ
k v Þ
tan f
ð
If the earthquake acceleration exceeds the yield acceleration, sliding
occurs. The equation of motion is double integrated to give displacement:
ZZ
x
¼
ð
k h 2
k hy Þ
g·dt
ð
7
Þ
where x is horizontal displacement and g is earth gravity.
Figure 3a shows typical vertical and horizontal accelerations for a block
having an interface friction angle f b ¼
when subject to Kobe earthquake
records. The peak horizontal and vertical accelerations of the earthquake are
k ho ¼
20
8
364
when the vertical acceleration is neglected. Figure 3b shows the relationships
between velocity and displacement for the rigid block where there are a few
spikes of earthquake acceleration that exceeded the yield value. Motion was
induced and the permanent displacement was calculated as 8.1 cm.
For different peak values of Kobe earthquake records and yield value of
acceleration,
0
:
63 and k vo ¼
0
:
34
;
respectively. The block has a yield value k hy ¼
0
:
the relationships between displacement x and k ho 2
k hy were
determined numerically and are presented in Fig. 4 . In design, for a given peak
acceleration of the earthquake and knowing the yield acceleration of the block,
the permanent displacement can be determined graphically from Fig. 4.
3 REINFORCED SOIL RETAINING WALL
The design of reinforced soil retaining walls encompasses several different
components, such as the internal stability that gives the length and strength of
geosynthetic layers against rupture and pullout, and the external stability against
direct sliding and overturning (Leshchinsky and Boedeker, 1989; Leshchinsky
et al., 1995). The procedure of internal stability analysis can be conducted using
Rankine/Coloumb analysis or a rigorous log-spiral analysis (Fig. 5) . The direct
sliding is determined by a two-part wedge analysis (Fig. 6) . Note that the most
critical acceleration for tieback and direct sliding acts in the downward and
upward directions, respectively.
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