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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

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62 SAFETY OF DAMS (1865) ( (19094\ \> ( 1922 ) `\l ~ O R OV I L L E \ I (1898)~: ~1 YC<~ SA N F R A N C: (1906) ~` PACIFIC OCEAN (181 2) FAULT MAP OF CALIFORNIA (1940) = Major Earthquake o 50 100 \ ~ PARKFIELD ~~) A New Zip ~\ (1927)~1 FIR Ml LES \ i) _ O tm ~ ~ \ D :~ \ SANTA BARBARA \~1971,. CALTECH ( (1925)~ ~` EL CENTRO (1940) 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

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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- 500 100 . _ I Ad UJ ~ _ ~ C A: LL 50 1 .0 0.5 0.1 1600 800 160 80 ~ At J 1000 ~ I I I I ~ I I I I I l! / /1 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 MAGN ITUDE 16 ~ ILL 1.6 0.8 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).

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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

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66 0.9 ~ 0.8 of o - UJ LL Cal J it o N I 0.7 0.6 0.5 0.4 y ~ 0.2 LU Cal 0.1 SAFETY OF DAMS r ' 1 ' ' I "1"""'111 1 1 , I I I 1~1111111l' Joyner and Boore (1981 ) \ / ldriss et al. (1981) , Campbell (1981) 1 , , ~ . 1 , ,,,,,,'t1 ~ Seed and / Schnabel ~>,~,,/ (1980) ma\ lo\\ at\ W`\_ 1 , ,,,, 1, 1 111~111 20 ~ 5 10 CLOSEST HO R I ZONTAL D ISTANCE F ROM ZON E OF ENERGY RELEASE, km 50 100 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 3 1 is o - <: 0.3 LL Cat J 0.1 if o N to O 0.03 By LU 0.01 0.003 67 I I 1-1 1111 1 1. 1 1 1 11111 . - Median - 1 (J 1979 Imperial Valley Ms = 6~8, ML = 6~6 I I I I 11111 1 1 1 1 11111 1 ~. if; `2 ~ ~ ed fan + 1 CJ `. ~ \ Median .\ \\ 2~.i\2 2\\ \ \\\ \N 3 10 30 100 CLOSEST HORIZONTAL DISTANCE FROM ZONE OF ENERGY RELEASE, km 300 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 0.6 A' 0.5 O ~ 0.4 Al at: 0.3 :E 0.1 1 1 Rock I I- , - Stiff Soils ~ / Deep Cohesion less Soils \ c 1 - 'Soft to Medium Stiff Clay and Sand 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 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 an on - J o -O.40 3.5 3.o to 2 5 cow Lo J 2.0 1.5 J a: 1.0 0.5 o 0 2 4 6 8 10 12 14 16 TIME, s A,,.`,, ,1 ~ .,, ~ l \ \ . ~ ~ \ MEAN ROCK - MSD MOD I F I ED CASTA I C N69W - -1 1 0 0.5 1.0 1.5 2.0 2.5 3.0 PER I OD, s 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.