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6
Design Earthquake Estimates:
Methods and Critique
The occurrence of an earthquake is a physical process which, in principle,
is completely understandable and, if enough data were available, would be
predictable. Strains and stresses are being built up in certain regions of the
earth's crust, and when the strength of the material is exceeded, a stress
failure occurs. The sudden release of stress that is triggered by the failure
generates stress waves that propagate in all directions and produce earth-
quake shaking at the surface of the ground. The stress failures that produce
destructive shaking are initiated at depths of a few miles or a few tens of
miles, and at these depths the weight of the superposed rock produces large
compressive stresses and, as a result, only shearing stress failures can occur.
Over the past millions of years many stress failures have occurred with
relative displacement across the failure surface, and these surfaces can be
identified by geologists when seen on the surface of the ground and at depth
by geophysical prospecting methods. Geologists have named these old stress
failure surfaces "faults." Such faults are surfaces of weaknesses, and present-
day stress failures invariably occur on existing faults, such as those shown in
Figure 6-1 for the state of California. Thus, earthquakes could be predicted
if we had knowledge of the locations and geometry of faults, the existing
stress distribution over the surface of the fault, the strain rates in the earth's
crust, the value of the failing stress on the fault, and the requisite physical
properties of the rock in the region of the fault being studied. However,
because of the difficulty of obtaining the necessary data, such information is
not sufficiently well known to make a scientific determination of the loca-
tion, time of occurrence, and magnitude of earthquakes.
61
OCR for page 62
62
SAFETY OF DAMS
(1865) (
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FIGURE 6-1 This diagram shows the prominent faults in California. The maximum capable
earthquake on a fault is sometimes taken to be that event generated by slip traversing three-
fourths of the length of the fault. Thus, great earthquakes can be expected on large faults. Small
earthquakes can be expected on both long and short faults. The dates within parentheses
indicate the locations of major earthquakes.
An additional difficulty in estimating the nature of ground shaking is that
as the seismic waves travel away from the fault, they traverse heterogeneous
earth and are affected by reflections and refractions at the heterogeneities.
Therefore, the shaking at a point on the surface of the ground depends not
only on the details of the source mechanism but also on the details of the
travel path, neither of which are well known. To circumvent this lack of
knowledge, data have been collected on historical earthquakes, including
OCR for page 63
Design Earthquake Estimates
location, ciate, magnitude, intensity, etc. In addition, data are collected on
the prehistory of earthquakes, including identification of faults, estimates of
most recent fault displacements, and crustal plate movements, which can
throw light on seismic activity. The historical data and the prehistorical data
(over geologic time) provide the bases for estimations of seismic hazard.
At present, to estimate seismic hazard, either statistical analyses of motion
characteristics must be used, or near upper bounds must be specified. If the
magnitude is taken to be that of the largest possible earthquake that can be
expected to occur along the fault, the event is called the maximum credible
earthquake (MCE). The motion at the dam site resulting from such an
earthquake is called the maximum credible earthquake motion, or some-
times simply, maximum credible earthquake. For example, along the south-
ern portion of the San Andreas fault in California the average return period
for earthquakes of magnitude 8-plus is estimated to be approximately 150
years.
At places where the historical record of earthquakes is short in comparison
with the recurrence time of the MCE, the MCE may be larger than the
largest historical earthquake. For such cases, different investigators employ
different empirical relations to estimate the magnitude of the MCE. These
methods usually take into account, either objectively or subjectively, the
notion of a "reasonable" return period based upon the present tectonic re-
gime; that is, the MCE is not taken to be the earthquake that will not be
exceecled in some extremely long period of time, such as 100 million years.
When adequate information is available, deterministic methods are used
for estimating design earthquake motion for clams when loss of a reservoir
would result in loss of human life anchor substantial economic loss, ant] these
methods are used most often for other critical facilities whose catastrophic
failure would produce similar kinds of losses. But, increasing attention is
being devotee] to the application of probabilistic-risk analysis methods for
earthquake-resistant design criteria for nuclear reactor facilities. Such
methods are also used, in some cases, to provi~le background information on
seismic hazards of major dams.
63
DETERMINISTIC-STATISTICAL METHOD
The cleterministic-statistical method requires certain basic information:
earthquake magnitude, smallest distance from the fault or the earthquake
source zone to the dam site, equations or curves relating magnitude and
distance to peak ground acceleration, peak ground velocity and duration of
strong ground shaking, and sometimes a site correction for the soil layer
above the bedrock at the dam site.
Uncertainty is associated with each phase or step of the deterministic
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64
SAFETY OF DAMS
estimation of strong ground motion at the site. Empirical equations or
curves, such as shown in Figure 6-2, that relate fault rupture length to
earthquake magnitude often are user] for estimating the MCE. However,
there is appreciable scatter in the data that are used to determine the fault
rupture length versus magnitude relation, because of variations in some of
the other physical characteristics of the earthquake source. Thus, a statisti-
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FIGURE 6-2 Idealized curve showing the approximate relation between the magnitude of the
earthquake and the length of the fault rupture. For example, for the M 8.25 San Francisco
earthquake of 1906, the graph gives approximately 250 miles for the length of fault slip, and this
agrees with the observed length. For the M 6.5 San Fernando earthquake of 1971, the graph
gives 10 miles, which is in good agreement with the length inferred after the earthquake. The
graph is based on the assumption that for magnitudes equal or less than M 6 the slipped fault area
is approximately circular in shape, although this is sometimes not true for real earthquakes. For
large magnitudes in California the length of fault slip is large but the vertical dimension of fault
slip is assumed not to exceed approximately 10 miles. Source: Housner and Jennings (1982).
OCR for page 65
Design Earthquake Estimates 65
cat value of earthquake magnitude must be selected from the data. To com-
plicate matters, the faults that produce many of the earthquakes in the
United States have not been iclentified, therefore, this method cannot be
used in such cases.
Seismographs were invented as recently as the late nineteenth century,
and the first magnitude scale was proposed by Richter in 1935. Therefore,
magnitudes based on instrumental data can be assigned only to relatively
recent earthquakes. However, the effects of earthquakes on people, struc-
tures, and land can be expressed in terms of earthquake intensity. (As noted
in Chapter 3, in the United States the Modified Mercalli intensity scale is
used for this purpose). For an individual earthquake the maximum value of
intensity usually occurs near the epicenter and, thus, is called the epicentral
intensity. Various empirical relations between epicentral intensity and the
different kinds of magnitudes (e.g., local, body-wave, and surface-wave
magnitudes) have been proposed. These relations show a dependence on
geographical location, as well as on the strength of the earthquake.
For cleterministic-statistical studies the distance from the earthquake to
the dam site is taken as the minimum distance from the fault to the site.
Because the actual earthquake may occur anywhere along the fault or in the
source zone, this assumption can lead to overestimation of the ground mo-
tion at the dam site from any single event occurring on the fault. Over a
sufficiently long period of time, motions associated with energy release on
the nearest part of the fault can be expected to occur.
There are many proposed "attenuation relations," relations in the form of
equations or curves that give an estimate of the strong ground motion if the
magnitude, or epicentral intensity, and distance to the site are known. Ex-
amples for the western United States are shown in Figure 6-3. Because the
fall-off of ground motion with distance varies geographically, different rela-
tions should be used for different regions. Thus, for any given region the data
must be interpreted statistically, as is shown in Figure 6-4. For example, the
attenuation is appreciably smaller east of the Rocky Mountains than to the
west, resultingin larger felt and damage areas for eastern U.S. earthquakes.
Most of the strong-motion data come from western U.S. earthquakes, for
which empirical attenuation relations can be established. For the east,
which is deficient in such data, various techniques that require additional
assumptions must be used, which adds to the uncertainty of ground-motion
estimates.
Finally, the variability of soil and poorly consolidated rock layers above
competent bedrock can have an appreciable effect on ground-motion esti-
mates. Sometimes a mathematical-physical model consisting of vertically
propagating shear waves is used to estimate the local site effects. Although
such a model is a gross simplification of actual conditions, it may provide
useful insights into local site efforts. Alternatively, empirical correlations of
OCR for page 66
66
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SAFETY OF DAMS
r
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FIGURE 6-3 Peak ground acceleration curves for stiff soils (Ms = 7.5~. Source: Seed and Idriss
(1982~.
ground motion for different soil conditions may be used, such as shown in
Figure 6-5.
When all the uncertainties that appear in this method of estimation of
peak ground motion are combined, the mean plus one standard deviation
value may be almost twice the mean value.
SEISMOTECTONIC (SEMIPROBABILISTIC) METHOD
With few exceptions, earthquakes in the United States east of the Rocky
Mountains cannot be associated with mapped faults. Although these earth-
quakes occur in the upper 25 kilometers of the earth's crust, the rupture
planes do not extend to the free surface. As a consequence, fault rupture
length cannot be determined from field evidence but rather must be inferred
from characteristics of the earthquake wave spectrum near the source. This
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Design Earthquake Estimates
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67
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CLOSEST HORIZONTAL DISTANCE FROM ZONE
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FIGURE 6-4 Regression analysis of the peak accelerations recorded during the October 15,
1979, Imperial Valley earthquake. Source: Seed and Idriss (1982).
adds further uncertainty into the relation between fault rupture length and
earthquake magnitude, over and above that due to typical scatter of obser-
vational data.
When earthquakes cannot be associated with identifiable faults, the spec-
ification of distance from the earthquake to the dam site, as required for
deterministic-statistical studies, takes on a significant amount of uncer-
tainty. Accordingly, in the seismotectonic method the country or a portion of
the country is divided into regions with similar geological and seismological
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68
SAFETY OF DAMS
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MAXIMUM ACCELERATION ON ROCK, 9
FIGURE 6-5 Approximate relationships between maximum accelerations on rock and other
local site conditions. Source: Seed and Idriss (1982).
characteristics, and it is assumed that the spatial density of historical earth-
quakes is more or less uniform in each of these regions. Each such region is
caller] a seismotectonic province or region.
An MCE must then be determined for each relevant seismotectonic prov-
ince. Because usually the recurrence interval of earthquakes of that magni-
tude is much longer than the record of historic seismicity, the magnitude of
the largest historical earthquake will be less than that of the MCE, which
requires that probabilistic procedures be employed to arrive at an estimate
of the magnitude of the MCE. Beyond this stage, the analysis proceeds as for
the deterministic-statistical method, except that the distance from the earth-
quake source to the dam site is considered to be the smallest distance from
any point in the seismotectonic province to the site, if the site lies outside the
province. When the dam site lies within the seismotectonic province, the
epicentral distance would become zero if the above criterion were applied,
and the only attenuation of the strong ground motion would be due to the
vertical travel path from the earthquake focus to the epicenter. This would
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Design Earthquake Estimates
69
result in unrealistically large estimates of the ground motion at the dam site,
because the likelihood that the epicenter of the MCE would occur at the dam
site is extremely small. Typically seismotectonic provinces in the eastern
United States have dimensions of at least several hundred kilometers. There-
fore, if the dam site lies within a seismotectonic region, it is normally consid-
ered to be sufficiently conservative to assume that the epicentral distance to
the dam site is some small portion of the province dimension so that the
probability of an epicenter being closer is sufficiently small.
PROBABILISTIC-RISK ANALYSIS
The deterministic-statistical and seismotectonic methods clo not take into
account the frequency of occurrence of earthquakes. Therefore, for areas
where the MCE has a very long return period, deterministic-statistical esti-
mates may lead to overly conservative estimates of the ground motions for
structures that have lifetimes considerably less than the recurrence period of
the MCE. In general, eastern U.S. earthquakes of any given magnitude have
longer recurrence times than western earthquakes of the same magnitude,
the difference being as great as 5-10 times. One of the principal purposes of
applying risk analysis methods is to take account of the frequency of earth-
quake occurrence in hazard assessment. Also, the uncertainties in the vari-
ous stages of calculation can, in a formal sense, be treated more readily in
probabilistic methods. This latter advantage, however, may have little or no
influence on the final selection of earthquake motions for which the safety of
the dam is evaluated.
Similar to the deterministic-statistical and seismotectonic methods, the
risk analysis method requires a knowledge of the location and extent of active
faults or earthquake source zones, of the MCE associated with each, of the
attenuation relations for peak ground acceleration and ground velocity, and
of the site correction for soils and unconsolidated rock. In addition, the
recurrence times for earthquakes of various magnitudes are required; often-
times this relation is assumed to satisfy a simple mathematical form. Finally,
possible variations in these parameters must be known. For example, it has
been customary to assume that the earthquake occurrences are distributed
randomly in time, resulting in a so-called Poisson distribution; however,
physical reasoning suggests that this is not likely for the large-magnitude
earthquakes that relieve most of the accumulated strain energy. Recently,
other time distributions that take account of this phenomenon have been
proposed and applied to a limited number of earthquake hazard calcula-
tions.
Rather than give a single estimate of the peak ground] motion (e.g., accel-
eration) at a site, as is clone with deterministic and seismotectonic methods,
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70
SAFETY OF DAMS
the risk analysis method gives a distribution of peak acceleration and veloc-
ity values at the site for various values of annual probability of exceedance.
The smaller the probability value, the larger the values of peak ground
acceleration and velocity. Alternatively, maps can be constructed that
present the peak acceleration or velocity values that have a selected proba-
bility of occurrence in a selected number of years, e.g., a 10 percent proba-
bility of being exceeded in a SO-year time interval. The acceleration or
velocity values on such maps can be contoured, as was done in those pre-
pared by the Applied Technology Council (1978) and by AIgermissen and
Perkins (1976) and Algermissen et al. (1982) for the United States.
In the probabilistic method the uncertainties must be estimated for each
step of the calculations and combined to give a mean ground-motion value
and its standard deviation for each annual probability of exceedance. In
general, the standard deviation increases significantly as the annual proba-
bility of exceedance decreases, particularly as the latter becomes less than
about 0.001 or 10-3. This is, in part, a result of the fact that the seismicity data
base is known only for a few hundred years, at most, in the United States.
If the MCE motion at a dam site is to be determined solely by probabilis-
tic-risk analysis methods in the future, there must be a decision as to an
acceptable value of the annual probability of exceedance. That is, the ac-
ceptable amount of risk must be decided, with the realization that the stan-
dard deviation of peak ground acceleration and peak ground velocity values
increases substantially as the annual probability of exceedance becomes less
than 10-3 to 10-4 range.
OTHER EARTHQUAKE PARAMETERS
The foregoing discussion of deterministic-statistical, seismotectonic
(semiprobabilistic), and probabilistic methods principally was concerned
with the estimation of the maximum credible ground acceleration and veloc-
ity and their uncertainties. Because permanent displacement or failure of an
embankment dam due to earthquake shaking may be the result of incremen-
tal slope failures or the consequence of liquefaction of the soil material
comprising or supporting the dam, and because those effects are influenced
by the number of cycles of strong ground shaking, the time duration of the
maximum credible ground motion also must be estimated. Also, propaga-
tion of cracks in concrete dams is affected by the numbers of cycles of such
shaking.
The time duration of strong ground shaking near the fault is largely a
function of the length of fault rupture, with the duration time increasing as
the rupture length increases. At large distances from the fault, attenuation
results in a reduction of the amplitude of the strong ground motion. In
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Design Earthquake Estimates
71
addition, there is an effect, called dispersion, which causes the wave train to
spread out in time as the distance from the earthquake source increases.
Because of these complications, it is necessary to determine the duration of
strong shaking by empirical means.
Different investigators use different definitions of duration time, so that a
numerical value (usually given in seconds of time) is by itself meaningless
unless the definition also is provided. To avoid this problem, a time history of
ground acceleration for the maximum credible ground motion can be pro-
vided. Such a time history usually is an actual recording of ground motion,
selected from a set of such recordings. Wherever possible, the selection of a
time history is done on the basis of similarity of earthquake magnitude,
distance to the site, and rock or soil conditions at the site.
One or more time histories of ground acceleration representative of the
maximum credible ground motion can be provided for analysis. An acce-
lerogram can be converted into a response spectrum, or a set of response
spectra with different amounts of damping. Response spectra, after smooth-
ing, can be used by the engineer for design proposes. Figure 6-6 shows an
example of a design accelerogram (time history) and design spectra for Ca-
manche Dam.
RESERVOIR-INDUCED EARTHQUAKES
The reservoir behind the 300-foot-high Koyna gravity dam in India
started filling in 1962, and in 1963 a number of small-magnitude earth-
quakes occurred in the vicinity of the dam. As the depth of water in the
reservoir increased in following years, the frequency of occurrence and the
magnitudes of these local shocks increased. In 1967, six earthquakes of M
5.5-6.2 occurred, and on December 12, 1967, a damagingM6.5 earthquake
occurred within 3 kilometers of the dam. The strong shaking causer] horizon-
tal cracks at about two-thirds the height with slight traces of water leakage
visible on the downstream face of the dam. The dam was located in a region
of low historical seismicity (Zone O on the Indian seismic zoning map), so
that the correlation of frequency of occurrence and magnitude with reser-
voir filling indicated a cause and effect relationship: filling of the reservoir
presumably triggered stress failures (earthquakes) in a prestressed body of
rock. Such presumed reservoir-induced earthquakes have been observed at
the six dams listed in Table 6-1 and, in addition, smaller events have been
observed at other dams. The Hsingfengkiang Dam, a concrete buttress struc-
ture, was cracked by the ground shaking in a 1962 earthquake. The dams
listed in Table 6-1 were all high dams with deep reservoirs.
The occurrence of reservoir-induced earthquakes is a peculiar circum-
stance in which the building of the dam leads to the triggering of local
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72
0.40
0.20
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-
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o
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TIME, s
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MOD I F I ED CASTA I C N69W
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FIGURE 6-6 Design accelerogram and spectrum for Camanche Dam. Source: Seed and Idriss
(1982).
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Design Earthquake Estimates
TABLE 6-1 Dams at Which Apparent Reservoir-
Induced Earthquakes Have Been Observed
Earthquake
Dam Location Height (m) Magnitude
Koyna India 103 6.5
Kremasta Greece 165 6.3
Hsingfengkiang China 105 6.1
Kariba Rhodesia 128 5.8
Hoover United States 221 5.0
Marathon Greece 63 S.O
73
earthquakes of potentially damaging intensity. The first five dams listed in
Table 6-1 were all located in regions of relatively low historical seismicity.
The possibility of reservoir-induced earthquakes should therefore be given
consideration when setting design criteria for new high dams, particularly in
regions of low historical seismicity where the seismotectonic province
method indicates a low intensity of shaking. At present, the committee is
unable to assess confidently the likelihood of a reservoir-induced earthquake
occurring at a proposed dam site.
Representative terms from entire chapter:
ground motion
