Environmental Engineering Reference
In-Depth Information
Number of Cycles, N
c
1
10
100
1000
0.4
0.3
D
r
90%
0.2
82%
68%
54%
0.1
0.0
Figure 12.12.
Stress ratio
versus number of cycles to initial liquefaction from tests on a shaking
table (De Alba et al., 1976; USNRC, 1985, reproduced with permission of ASCE).
/
o
Table 12.3.
Representative number of cyles of ground motion versus
earthquake magnitude (adapted from Seed and DeAlba,
1986).
Earthquake magnitude
Number of representative cycles at 0.65
max
8.5
26
7.5
15
6.75
10
6.0
5-6
5.25
2-3
Table 12.3 shows that the number of cycles of ground motion are related to earthquake
magnitude, which can be related qualitatively to the effects shown in Figure 12.12 to
show that only large magnitude earthquakes will have sufficient cycles or large enough
cyclic stress ratio to liquefy medium dense to dense soils.
12.4.1.2.3 Post earthquake behaviour
As shown in
Figure 12.13
, the effect of cyclic loading is also to induce strain. If, as shown
in Figure 12.13(a), the soil is strain weakening, the strain may be sufficient to take the soil
to the condition that the static gravitational stresses
ST
exceed the available strength, so
straining will continue under gravity loads without further cycling by the earthquake.
This is the flow liquefaction condition and large, relatively rapid deformations of the
slope will occur. For a strain hardening soil, as shown in Figure 12.13(b) the cyclic load-
ing causes deformations during the cycling, but the static gravitational stresses are less
than the steady state undrained strength, S
us
, so the slope will be stable after the cyclic
loading ceases.
For slopes partly of strain softening and partly of strain hardening soil overall instability
will occur after the cyclic stresses cease only if after stress redistribution in the strain soft-
ening soil, the remaining soil cannot support the gravitational shear stress. Robertson and
Wride (1997) suggest a flow slide can only occur if a kinematically admissible mechanism
can develop. Whether a flow slide would occur would also depend on the factor of safety
