Earthquake Engineering for Concrete Dams Design, Performance, and Research Needs (1990) / Chapter Skim
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2. Earthquake Input
2. Earthquake Input
Pages 16-35
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From page 16... ...
It is not surprising, therefore, that the earliest method of defining earthquake input to concrete dams was merely to apply a distributed horizontal force amounting to a uniform specified fraction (typically 10 percent) of the weight of the dam body.
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From page 17... ...
However, as the methods of response analysis improved, it became apparent that the rigid base earthquake input no longer was appropriate. Because of the great extent of the dam, and recognizing the wave propagation mechanisms by which earthquake motions are propagated through the foundation rock, it is important to account for spatial variation of the earthquake motions at the dam-foundation interface; these spatial variations also may result from "scattering" of the propagating earthquake waves by the topography near the dam site.
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From page 18... ...
'MED SUPPORTED APPROPRI ATE LY FOR EACH EARTHQUAKE CO M PO N E N T ~\\~",' / i: CANYON _' WALL DEFO RMA B L E FOU NDATI O N ROC K DECONVOLVED RIGID BASE MOTION LIMIT OF FLEXIBLE WON i._. ~ 1 At' ~ \ \: ~ CANYON INPUT AT CAM I~TF~FArF /~/~/ L' FIGURE 2-1 Proposed seismic input models for concrete dams (2-2)
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From page 19... ...
these seismic input models are discussed in the context of arch dam analysis, but they are equally applicable for gravity dams when the foundation topography warrants a three-dimensional analysis. If the dam is relatively long and uniform, so that its response may be considered to be two-dimensional, the canyon scattering effect need not be considered, but the seismic input still may vary spatially due to travelingwave effects.
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From page 20... ...
The same problem also has been solved using a different integral equation formulation (2-9~; in this approach the free boundary condition at the canyon wall is satisfied in the least squares sense. An integral equation approach that imposes an approximately satisfied boundary condition also has been used in the solution of problems involving P and SV waves (2-10)
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From page 21... ...
The free-field motions at V-shaped and close-to-V-shaped canyons also have been studied using a combination of finite and infinite elements in a model with finite depth that extends to infinity horizontally (2-24~. In this case earthquake motions prescribed at the rigid base of the foundation are taken as input to the system.
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From page 22... ...
For the more irregular geometry of a real canyon, a calculated relative motion ratio as high as 6 was reported for Pacoima Dam, California (2-~. The relative phase of motions along the canyon walls has been reported for the case of SH waves incident to a semicircular canyon (2-6~.
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From page 23... ...
4 ~ 3 id LL ~ 2 LL a: CO 1 4: 3 2 1 o 1 2 3 6 7 8 7= 30 . - - ~ mar \4 5/ SH / / ;~ 0~ 0 1 2 3 5 1 2 3 6 7 8 ' ' 1 ~ I- ' ' SH \4 5J \/ ~ ~ =60 _ A 1 ~ 0 1 2 3 FIGURE 2-3 Calculated amplification of incident plane SH waves by a semicylindrical canyon surface (2-6)
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From page 24... ...
, although results are given only for a hemispherical cavity with a vertically incident P wave. Perhaps the most relevant solution for three-dimensional canyon topography is that obtained by finite element analysis of Pacoima Dam and its adjacent canyon (2-28)
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From page 25... ...
Random field theory (2-30, 2-31) is quite relevant to the problem of spatial variation of earthquake input motion.
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From page 26... ...
was about 1.75, but the frequency-domain ratio, as measured by the pseudorelative velocity spectra, was as high as 30 at a frequency of about 2 Hz. A correlation study on ground motion intensity and site elevation was carried out for the general area of Kagel Mountain and Pacoima Dam using the San Fernando earthquake data (242~.
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From page 27... ...
This arch dam is 180 m high, and the canyon width is about 250 m at crest level. The peak acceleration recorded at the center of the crest in the upstreamdownstream direction was 0.170 g.
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From page 28... ...
An amplification factor of between 2 and 3 was observed for abutment motion at the crest level relative to motion at the bottom of the canyon. Predicted Response to Spatially Varying Input Dynamic Excitation Direct application of measured earthquake motions to predict dam response has been reported for the Ambiesta (arch)
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From page 29... ...
In a separate study the effects of traveling waves on arch dams were examined using a finite element approach (2-54~. The model was similar to the free-field input model described above, but the free-field motion was taken as a prescribed traveling earthquake wave.
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From page 30... ...
These free-field motions were applied to a three-dimensional finite element model containing the dam, a massless foundation region, and an infinite reservoir of compressible water. Frequency-domain responses were converted into the time domain in the form of standard deviations of the response to a random input with an earthquakelike frequency content.
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From page 31... ...
Results for the particular case studied indicated that the dam did not crack as a result of fault displacement but partially separated from the foundation. It was recommended that the combined effect of fault displacement and vibratory seismic input could be accounted for in preliminary studies by performing a dynamic-response analysis with a linear finite element model, using a softened foundation.
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From page 33... ...
Even though the measuring of free-field and interface input motion has been recognized to be as important as that of the dam response (2-70) , current strong-motion instrumentation for concrete dams in the United States is inadequate for the purpose of defining seismic input.
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From page 34... ...
It is clear, therefore, that an improved instrumentation program for observation of earthquake motions at sites of existing or proposed dams is needed. Similarly, further theoretical work is needed on the deterministic and stochastic modeling of input motion to provide the basis for realistically modeling seismic input to concrete dams.
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From page 35... ...
7. Effects of Fault Displacement Further studies should be carried out focusing on the effects of fault displacements on the safety of concrete dams, using both numerical simulation procedures and physical model testing.
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