Environmental Engineering Reference
In-Depth Information
10
M~8
1
/
4
1
M~7
1
/
2
0.1
0.01
M~6
1
/
2
0.001
0.0001
0
0.2
0.4
0.6
0.8
1.0
k
y
/k
max
Figure 12.38.
Variation of yield acceleration with normalized permanent displacement (Makdisi and
Seed, 1978, reproduced with permission of ASCE).
It should be noted that an important step in determination of k
max
in step (d) is to estab-
lish the dynamic properties of the material forming the embankment and the foundation.
This can be achieved by:
-Triaxial compression tests, simple shear tests or torsional shear tests conducted under
cyclic loading conditions;
- Resonant column testing;
- Field measurement of shear wave velocities, either by downhole or crosshole techniques;
- Back calculation using finite element techniques, modelling measured responses to
earthquake events;
- Empirical relationships, such as those given by Hardin and Drenerich (1972) and Seed
et al. (1986).
Given that the laboratory and field based methods are expensive, it is recommended
that the values of k
max
be initially calculated using a range of G
max
values obtained from
the empirical relationships. Should the results of the analysis be marginal then a more
elaborate program of laboratory and/or field testing may be warranted.
It should be noted that relating satisfactory dam performance to earthquake induced
deformation is very subjective and generally depends on dam specific criteria about the
allowable loss of freeboard or the tolerable extent of horizontal displacements.
The Makdisi and Seed approach is widely used and accepted among practicing engi-
neers. However, like Newmark's approach, it is limited in application to dams not sus-
ceptible to liquefaction or strain weakening in the embankment or its foundations.
