Earthquake Engineering for Concrete Dams Design, Performance, and Research Needs (1990) / Chapter Skim
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3. Analysis of Linear Response
3. Analysis of Linear Response
Pages 36-60
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From page 36... ...
2. The response of a dam is influenced to a significant degree by the interaction of the motions of the dam with the impounded water and the foundation rock; thus, the deformability of the foundation and the earthquakeinduced response of the reservoir water must be considered.
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From page 37... ...
Generally, interaction between the dam and the foundation rock was not considered in evaluating the aforementioned earthquake forces, but in the seismic stress analysis of arch dams the flexibility of the foundation rock sometimes was recognized through the use of Vogt coefficients (3-1~. Stresses in gravity dams with ungrouted construction joints were usually determined by treating the concrete
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From page 38... ...
In the design of gravity dams it was generally believed that stress levels were not a controlling factor, so the designer was concerned mostly with satisfying criteria for overturning and sliding stability. Earthquake Performance of Koyna Dam As mentioned in Chapter 1, Koyna Dam in India is one of two concrete dams that have suffered significant earthquake damage (3-5, 3-6~.
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From page 39... ...
The typical design seismic coefficients, 0.05 to 0.10, used in designing concrete dams are much smaller in the typical period range for such dams than are the ordinates of the pseudoacceleration response spectra for intense earthquake motions, as shown in Figure 3-3. It is of interest to note that the seismic coefficients used for dams are similar to the base shear coefficients specified for buildings.
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From page 40... ...
resist moderate levels of earthquake ground motion without structural damage, but possibly some nonstructural damage; and 3. resist major levels of earthquake ground motion .
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From page 41... ...
. In linear analyses the effective modal earthquake forces may be expressed as the product of a seismic coefficient (which depends on the earthquake pseudoacceleration response spectrum and the vibration period of the mode, and varies according to the shape of the mode)
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From page 42... ...
, the crest mass may cause a dramatic increase in the dynamic stresses approximately doubling them in the earthquake response of Pine Flat Dam, as shown in Figure 3-7. An interesting consequence of this type of unfavorable response mechanism was seen in monolith 18 of Koyna Dam, which suffered the worst damage during the earthquake; it is believed that this exaggerated damage resulted from an elevator tower that extended 50 ft above the top of the block and therefore was subjected to greatly increased inertial forces.
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From page 43... ...
. ~ 7 / FUNDAMENTAL SYMMETRIC VIBRATION MODE 7 / 7 \ / 7 / FUNDAMENTAL ANTISYMMETRIC VIBRATION MODE FIGURE 3-5 Variation of seismic coefficient over face of arch dams (3-12)
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From page 45... ...
. Traditional design earthquake loading for concrete dams includes seismic water pressures in addition to hydrostatic pressure, as specified by various formulas (3-2, 3-9~.
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From page 46... ...
Finally, it is evident that the static overturning and sliding stability criteria that have been used in traditional gravity dam design procedures have little meaning in the context of the oscillatory responses produced in dams by earthquake motions. DYNAMIC ANALYSIS Arch Dam Analysis Forerunner Recognizing the limitations of the static seismic coefficient method, design and research engineers became interested in dynamic analysis procedures to reliably predict the earthquake response of dams.
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From page 47... ...
Clearly, the earthquake motions at depth in the foundation rock will not be the same as the free-field motions recorded at the ground surface; hence, the dynamic analysis procedure should be formulated to use some different specification of the seismic input, as described in Chapter 2. Ideally, the earthquake input should be specified as spatially varying motion at the dam-foundation rock interface, but this has usually
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From page 48... ...
, the impounded water affects the dam response essentially as an incompressible fluid. However, this frequency ratio usually is less than 2 for dams with realistic values for the elastic modulus of concrete; hence, water compressibility is expected to be important in the earthquake response of both arch dams (as
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From page 49... ...
It is apparent from these figures that these wave absorption effects can be significant in the response of arch dams and are particularly important in the response to the vertical component of the earthquake motions. PRESENT KNOWLEDGE AND CAPABILITIES Conclusions About Interaction Effects The extensive research that has been devoted during the past 20 years to evaluating hydrodynamic and foundation interaction effects has led to greatly increased understanding of these phenomena.
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From page 50... ...
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From page 51... ...
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From page 52... ...
TV ~50 Compressible water, = 0.9 two \/ J an ~ Compressible water, = 0.5 FIGURE 3-10 Calculated effects of water compressibility and reservoir boundary absorption on upstream face maximum envelope stress contours for Monticello Dam subjected to Morgan Hill earthquake record (3-26)
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From page 53... ...
~ CROSS-STREAM COMPONENT Full Reservoir Rigid Reservoir Boundary,a= 1 Cantilever Stress Arch Stress Cantilever Stress Arch Stress 100 ~25 \ \50\ \ 7511 ~JI ~0 / FIGURE 3-11 Calculated effects of reservoir boundary absorption on upstream face maximum envelope stress contours for Morrow Point Dam due to Taft earthquake record (3-11)
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From page 54... ...
Because arch dams resist the reservoir water pressures and the thermal and earthquake forces, at least in part, by transmitting them by arch action to the canyon walls, dam-foundation rock interaction also is likely to be significant in the earthquake response of arch dams, possibly more so than in the case of gravity dams. The preceding observations lead to the conclusion that dam-reservoir water interaction, including water compressibility and pressure wave absorption at the reservoir boundaries, and dam-foundation rock interaction all should be considered in the earthquake response analysis of concrete dams.
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From page 55... ...
ADAP (2-5) , the first widely available program developed specifically for dynamic analysis of arch dams, also uses a mesh of finite elements to model the foundation rock.
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From page 56... ...
has been directed toward modeling of arch dam-foundation rock interaction, but it has not yet advanced sufficiently to be of use in practical arch dam earthquake response analyses. Both EACD-3D and ADAP can be used to perform a complete dynamic analysis of a concrete arch dam subjected to the simultaneous action of upstream, vertical, and cross-stream components of the free-field motion specified at the interface between dam and foundation rock.
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From page 57... ...
In response to this need a simplified procedure was developed in 1978 for the analysis of gravity dams in which the maximum response due to the fundamental mode of vibration was represented by equivalent lateral forces computed directly from the earthquake design spectrum (3-29~. Recently, this simplified two-dimensional analysis of the fundamental mode response has been extended to include the effects of dam-foundation rock interaction and wave absorption at the reservoir bottom (3-30)
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From page 58... ...
i .. FIGURE 3-12 Littlerock Multiple Arch Dam, Califomia, completed in 1924 for use in irrigation, has a maximum height of 168 ft and length of 800 ft.
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From page 59... ...
4. Improvement of Arch Dam Analysis The methods used for input of the earthquake motions in present methods of earthquake analysis of arch dams urgently need improvement.
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From page 60... ...
6. Evaluation of Dynamic Sliding and Rocking Response of Gravity Dams Analysis procedures should be developed to determine the dynamic sliding and rocking response of gravity dam monoliths.
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