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Experimental and Observational Evidence EARTHQUAKE EXPERIENCE Cases with Strongest Shaking It was noted earlier that no concrete dam has ever failed as a result of an earthquake; however, as far as can be determined, neither has a large concrete dam with full reservoir been subjected to very strong ground shaking. The closest to such an event was the previously mentioned 1967 experience at the 103-m-high Koyna (gravity) Dam (Figure 3-1) with the reservoir nearly full (3-5, 3-6~. Recorded ground motions at the dam from a nearby earthquake of magnitude 6.5, probably reservoir induced, peaked at 0.49 g in the stream direction and continued strongly for 4 sec. As stated in Chapter 3, significant horizontal cracking occurred through a number of nonoverflow monoliths at a level 36 m below the crest where the downstream face changed slope, but gravitational stability prevailed, even though the water level was 25 m above the crack (Figure 5-1~. Spalling of the concrete in many of the contraction joints and damage to the joint seals provided some evidence that the monoliths vibrated individually rather than as a single block. A similar experience had occurred in 1962 at the 105-m-high Hsinfengkiang (buttress) Dam (5- 1~. Cracking at a level 16 m below the crest and 3 m below the water surface resulted from a magnitude 6.1 earthquake, again probably reservoir induced. Ground motions were not recorded, but with the epicenter in close proximity they probably reached significant intensity. Perhaps the strongest shaking experienced by a concrete dam to date was that which acted on Lower Crystal Springs Dam, a curved gravity structure with the modest height of 42 m (shown in Figure 5-2), during the magnitude 8.3 San Francisco earthquake of 1906 (5-2, 5-3~. The dam incurred no 80

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81 338 ft elevations 48 ft 218 ft elevation ,1 O ft elevation ~ 1. r me\ \ ~ \ \7 Water level during 1 967 earthquake (301 ft elevation) ) Regions where major crack) ng was observed 231 ft - 1 FIGURE 5-1 Cross section of Koyna Dam showing waterlevel during 1967 earthquake and regions where principal face cracking was observed (3-6). damage, even though it stood with its reservoir nearly full within 350 m of the fault trace at a point where the slip reached 2.4 m. However, the stability of this structure exceeds that of typical gravity dams due to its curved plan and a cross section that was designed thicker than normal in anticipation of future heightening, which was never completed. Another example of a concrete dam subjected to strong shaking is the 103-m-high Pacoima (arch) Dam, shown in Figure 2-4. During the 1971 magnitude 6.6 San Fernando earthquake (5-4, 5-5), an accelerograph located on the left abutment ridge 15 m above the dam crest recorded peak accelerations of 1.2 g in both horizontal components and 0.7 g vertical with a duration of strong shaking of 8 sec. Even though amplification of this motion occurred at the recorder location, the excitation to the dam's boundaries must have been severe. However, the only visible damage was a slight opening of the contraction joint on the left thrust block, a crack in this thrust block, and slumping of an area on the left abutment; the first two effects may have been caused by the latter. The good performance of the dam can be attributed partly to the low water level, 45 m below the crest at the time of the earthquake. Moderate shaking, on the order of 0.3 g in a horizontal component as recorded on the abutment, failed to damage Ambiesta (arch) Dam (59 m high) during the magnitude 6.5 Friuli earthquake of 1976 (2-51, 5-6), and motion of similar intensity affected only some appurtenant structures at Rapel Dam (arch, 110 m high) during the strong (magnitude 7.8) 1985

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82 FIGURE 5-2 Lower Crystal Springs Dam, California; the San Andreas fault lies under the reservoir (5-3). Photo courtesy of San Francisco Public Utilities Commission.

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83 Chilean earthquake (5-7~. At Rapel cracking occurred on the inner walls of the spillway intakes, and the power intakes, which had been designed as vertical cantilevers, suffered some minor damage. In another instance the magnitude 6.3 Santa Barbara earthquake in 1925 caused no damage to Gibraltar Dam (arch, 50 m high), even though the shaking was so strong that a workman on the dam reportedly had difficulty standing up (5-8~. For these cases the reservoir condition was mentioned in the references only for Rapel Dam, and it was stated to be full. Thus, although the experience outlined above (which represents the most significant earthquake events that have acted on concrete dams) is impressive, it falls short of providing complete confidence that large concrete dams with full reservoirs are safe against strong seismic shaking. Cases with Recorded Responses Actual recorded time histories of the response of concrete dams during earthquakes are scarce for events causing other than very small shaking. What is believed to be the largest recorded peak acceleration measured on a concrete dam was the 0.6 g value obtained on the crest of Hsinfengkiang Dam during a magnitude 4.5 shock in 1972 (5-9~. Peak crest accelerations recorded at other dams have been much smaller and include 0.25 g at Nagawado (arch) Darn (247), shown in Figure 5-3, 0.20 g at Hoover (gravity-arch) Dam (5-10), 0.17 g at Techi (arch) Dam (2-46), 0.15 g at Yuda (gravity- arch) Dam (5-11) and at Big Dalton (multiple arch) Dam (2-45), and 0.12 g at Kurobe (arch) Dam (2-39~. Among all these events, the maximum recorded foundation acceleration was 0.08 g at Hoover. Large amplification of motion from foundation to crest was detected often, indicating small damping. Such evidence exists at Ambiesta (2-43), Hsinfengkiang (5-9), Kurobe (2-39), Nagawado (2-47), Shintoyone (arch) Dam (5-12), Tagokura (gravity) Dam (5-12), Talvacchia (gravity-arch) Dam (5-13), Techi (2-46), Tonoyama (arch) Dam (5-14, 2-37), and Yuda (5-11~. None of these data are from strong shaking, when the material component of the damping would be higher. A number of measurements of motion at the dam-foundation interface during small to very small shaking have been obtained by instrument arrays located at Ambiesta (2~3), Kurobe (2-39), Nagawado (2-47), Pacoima (2- 45), Tagokura (5-12), Talvacchia (5-13), Tonoyama (5-14, 2-37), and Techi (2-46~; the maximum recorded interface motions were 0.04 g at Nagawado and Techi. In general, the motion varied significantly around the canyon, often showing considerable amplification in the upper abutments over that at the toe. Some of these data were for distant earthquakes and may not characterize the strong motions expected from nearby earthquakes. Nonuniformities can be present in the free-field motions and can also arise from the interaction between the dam and foundation; relative proportions

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84 G A B D _ ~ 0 1 55 m H o Froc t u re 0 /P Zone //Jo / Q /°R ° o`_, 0 M N Station I Peak accelerations (9) A I 0.035 (R) B 1 0.247 (R) C i, 0.049 (R) D 0.196 (R) E 0.074 (R) F I 0.036 (R) G 0.021 (S), 0.027 (C). 0.013 (V) H I 0.027 (S), 0.031 (C) 1 ! 0 037 (a) J ~ 0.021 (S), 0.019 (C) K j 0.029 (S), 0.021 (C) L ! 0.020 (O) M N o p Q R 0.017 (C) 0.029 (S) 0.016 (S), 0.027 (C) 0.025 (S), 0.022 (C) 0.020 (S), 0.023 (C) Orientation R = radial S = stream C = cross-stream V = vertical 0 = other horizontal FIGURE 5-3 Nagawado Dam face, showing locations of accelerograph stations; peak accelerations during the 1984 magnitude 6.8 Naganokan Seibu earthquake are tabulated (2-47). of these two effects in the measured motions are unknown. Some data from Hsinfengkiang Dam, where peak accelerations at a free-field site were reduced by a third at the base of the dam, suggest that dam-foundation interaction effects can be significant (5-9~. The subject of seismic input is one on which much more needs to be learned, as discussed in Chapter 2. However, in the United States only Lower Crystal Springs and Pacoima dams are well enough instrumented to record motions at both the abutments and the toe (2-69, S-1S), and it may be that the three accelerographs used on the dam- foundation interface at each of these sites are not sufficient to define the spatial distribution of earthquake motions. Only for Tagokura Dam have dynamic pressures in the reservoir been measured during seismic shaking (2-36, 2-38, 5-16~. The events for which pressures were recorded included two small earthquakes and the larger Niigata earthquake; however, time histories from the latter were unintelligible. From records of the two smaller earthquakes, investigators noted that the dynamic pressure and crest acceleration of the dam responded nearly in phase and

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85 concluded that, since the predominant period of response appeared to be close to what was thought to be the resonant frequency of the water, compressibility effects of the water were absent, because they would be expected to cause a phase difference. However, it is possible that the response frequency was somewhat below the resonant frequency of the water, and without an analytical investigation to indicate the expected phase difference, the conclusion seems premature. In the United States, only the 219-m-high Dworshak (gravity) Dam is equipped with dynamic pressure transducers, five on the center monolith at various depths (5-17), but no records have been obtained. Analyses to Reproduce Earthquake Response A number of analyses have been performed on concrete dams that have received earthquake shaking with the aim of reproducing some features of their response. Analyses of Lower Crystal Springs Dam (5-2, 5-3) for the 1906 San Francisco earthquake and of Pacoima Dam (5-4) and Big Tujunga (arch) Dam (5-18, 5-19) for the 1971 San Fernando earthquake were carried out under a State of California program on the seismic safety of dams. Finite element models of the dam and foundation region (the latter assumed massless and truncated at a far boundary) with the reservoir water (assumed incompressible) represented by lumped added masses were subjected to uniform excitations at the foundation boundary. Damping at 5 percent of critical was included in the system modes. For Lower Crystal Springs Dam (Figure 5-2) an artificial accelerogram with a 0.60-g peak acceleration represented the 1906 ground motion and was applied in the stream direction. Computed tensile stresses exceeded the tensile strength of concrete only over a small region at the upper part of one abutment, indicating that some separation would have occurred, since the foundation rock was highly fractured. Thus, the computations are not at odds with the lack of observed damage from the 1906 earthquake. Ground accelerations employed in the Pacoima analysis were those measured on the ridge reduced by a third in an approximate attempt to represent the motions that actually excited the dam. Computed arch tensile stresses indicated that some openings of the contraction joints should have taken place, but no evidence of opening and closing was noted in the postearthquake inspection. However, such openings may have left little evidence, or perhaps the assumption of uniform base input motion exaggerated the predicted response. A recent nonlinear analysis (4-38) of Pacoima Dam using the above ground motion produced significant contraction joint openings, but the same comments apply. At Big Tujunga, where the water was at an intermediate level during the earthquake, input accelerations were constructed from a seismoscope trace obtained on one abutment, resulting in peak input accelerations of 0.2

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86 g in both horizontal components. The computations led to a comparison between a seismoscope trace recorded on the crest at the center of the dam and a computed trace at the same location; reasonable correlation was seen. The cracking that occurred at Koyna Dam and the availability of recorded ground motions at Mat site have stimulated a number of analytical investigations. Two-dimensional representations have been employed on the assumption that the monoliths vibrated independently. Linearly elastic finite element analysis (3-6) in which dam-water interaction effects were approximately included showed that net tensile stresses near the point of slope change on the downstream face and at a similar elevation on the upstream face significantly exceeded the tensile strength of concrete when the recorded ground motion was used as input. Several nonlinear analyses of Koyna Dam have attempted to include cracking, as mentioned in Chapter 4. In one of these analyses (5- 20) a horizontal preexisting crack was assumed at the elevation of slope change, and the portion of the dam above the crack was treated as a rigid body with only a single rotational degree of freedom. Water was included statically as a pressure on the upstream face of the dam and in the crack and also was included dynamically through an added mass. Although the dam was shown to be Cinematically stable under the ground motions recorded during the earthquake, the analysis appeared to incorrectly reverse the angular velocity upon impact. Another study (4-26) employed the finite element method and smeared cracking, with stress release once the tensile stress reached a critical value that was a function of strain rate. The effect of water was neglected. With the measured ground motion as input, cracks on both faces occurred near the elevation of slope change, but the crack penetration was not very deep. A recent finite element study (4-31) attempted to model the formation and propagation of discrete cracks through mesh adaptation using a maximum tensile stress criterion. The results appeared to exhibit unstable branching of cracks, and different crack patterns were produced by mesh refinement. In an analysis of Koyna Dam using a ground motion weaker than the recorded one, cracks issued from the point of slope change and quickly reached the upstream face. Again, the effects of water, both as added mass and in crack penetration, were neglected. Based on these studies, it is evident that considerable improvement in nonlinear mathematical models of concrete dams is still needed and that the data from Koyna Dam are the most complete set from which to evaluate the performance of these models. Analyses of Hsinfengkiang Dam were stimulated by the 1962 earthquake experience in which cracking occurred and by a valuable set of records obtained on the dam during the magnitude 4.5 shock in 1972 after the dam had been greatly strengthened and stiffened. Nonlinear analyses (5-21) have been performed to examine the rocking and sliding stability of the top portion of the dam treated as a rigid body and separated from the flexible structure below by a preexisting crack. The water at a level 8 m above the

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87 crack was included statically as an applied force and dynamically as an added mass. Separate analyses were performed for rocking and sliding, but the two mechanisms were not allowed to occur simultaneously. With these assumptions the top portion of the dam was shown to remain Cinematically stable for reasonable ranges of friction coefficients, rotational impact assumptions, and ground motions. For the magnitude 4.5 shock, using the recorded base motion as input, linearly elastic finite element analysis (5-9) of an individual buttress idealized as two-dimensional successfully reproduced the time history recorded on the crest of the dam. Although the reservoir was partially full during the earthquake, it was omitted from the analysis. The computed vibration profile agreed with the measured one; both showed very large amplification of motion in the upper part of the dam, which probably was the cause of the cracking that occurred in 1962. Other reported analyses include two performed for the 90-m-high Yuda Dam (5-11) for magnitude 5.9 and 7.4 earthquakes in 1976 and 1978, respectively, and one analysis of Ambiesta Dam (2-43) for an aftershock of the 1976 Friuli earthquakes. The linearly elastic analyses of Yuda Dam employed a two-dimensional finite element model of a 67-m-high monolith with reservoir water included; this monolith was chosen because its resonant frequency matched the observed predominant frequency of response of the three-dimensional darn. With modal damping taken to be 3 percent of critical and using accelerations recorded on one abutment during the two earthquakes as input, the computed response time histories of the crest showed similarities to those recorded on the crest of the 90-m-high monolith. However, because controlling both the predominant frequency of vibration by selecting which monolith to analyze and the response amplitude level by selection of the value of damping is enough to guarantee a reasonable match, the conclusions to be drawn from this study are limited. Water compressibility was both included and neglected in the comparisons and was found to be unimportant. However, because only a short monolith was analyzed, the effect of water compressibility was limited by the reduced water depth. The finite element model of Ambiesta was subjected to nonuniform excitations as recorded by seismographs at five locations on the foundation interface. Although reservoir water was present during the aftershock, none was included during the analysis. Nevertheless, the computed profile of maximum response of the dam crest agreed with that measured on the crest, but few details were provided. Presumably, a uniform foundation input produced poorer results. A recent investigation of the response of Nagawado Dam (arch, 155 m high) to the magnitude 6.8 Naganoken Seibu earthquake of 1984 in Japan made use of a number of accelerograms obtained on the dam and foundation rock and employed a sophisticated finite element model that included nonuniform ground motion, dam-foundation interaction, and water compressibility (2- 48~. The foundation rock was represented by springs and dashpots defined

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88 from two-dimensional solutions for a strip footing on an elastic half space. Modes of the dam-foundation system (dashpots omitted) were employed as generalized coordinates and were assigned damping values equal to 2 percent of critical. To represent the water, the analysis used a velocity potential formulation with compressibility included along with an approximate transmitting boundary to represent an infinite reservoir and a 33 percent pressure wave absorption condition on the reservoir floor and sides. The elastic moduli of the dam and foundation were adjusted to match measured resonant frequencies from previous forced-vibration field tests. The solution procedure defined seismic input in terms of free-field motions at the foundation interface; these motions, which were applied to both dam and reservoir, were taken as those recorded on the foundation rock a short distance from the dam at both abutments at crest level and at the canyon bottom. Interpolation was used to obtain the motions at intermediate levels. The analysis sought to reproduce the time histories recorded on the dam crest, but satisfactory results were not achieved. The major discrepancy was underestimation of the strong antisymmetric response of the dam as evidenced by a sizable record from the left quarter point on the crest. Other results using a finite element model of the foundation failed to enhance the relative amount of antisymmetnc response. A number of potential sources of error existed. Those associated with definition of the free-field input included siting the accelerographs off the dam-foundation interface and the absence of records at intermediate levels and along the reservoir (the latter for use as input to the reservoir water). Siting the accelerographs off the interface was intended to reduce the contamination from the dam response, but it introduced other errors. In summary, analyses of concrete dams that were intended to reproduce features of their observed earthquake response have in some cases been successful, although many of the studies reported used crude mathematical models such as a lumped-added-mass representation of incompressible water or spatially uniform excitations. It is possible that adjustments in the analyses were made until correlation was obtained. The study of Nagawado Dam reveals the complexity of the seismic response of a concrete dam arising from nonuniform excitations and suggests that accurately capturing free- field motions at the foundation interface of the dam and reservoir water is difficult. Certainly, more earthquake data and study are needed regarding seismic input, as well as for dam-water interaction and nonlinear response. Important data sets obtained recently at Techi Dam (2-46) and Pacoima Dam (2-45) provide other opportunities for postearthquake analysis. FIELD VIBRATION TESTS: FORCED AND AMBIENT The literature contains a large amount of data from forced-vibration tests and ambient measurements from actual dams, some of which should be

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89 regarded with caution. For example, modal damping values ranging from 1 to over 12 percent of critical have been reported from forced-vibration tests. Much of the high damping data (e.g., Baitings [gravity] [5-22], Upper Glendevon [gravity] [5-23l, Naramata [arch] [5-24], and Tsukabaru [gravity] [5-251) is probably not accurate due to excessive modal interference in the dam response or, perhaps for some of the older data, inadequate frequency control on the shaking machines. When these problems are absent, low damping values in the range of 1 to 3 or 4 percent of critical usually result. Examples of lightly damped gravity or gravity arch dams include Fengshuba (5-26), Fiastra (2-51, 5-27), Pine Flat (5-28, 5-29), Place-Moulin (2-51), Talvacchia (5- 13), and Xiang Hong Dian (5-30, 5-31), while lightly damped arch dam examples are Ambiesta (2~3), Emosson (5-32), Hengshan (5-33), Kolnbrein (5-34), Kops (5-35), Kurobe (2-39), Liuxihe (5-33), Lumiei (2-51, 5-27), Monticello (5-36), Morrow Point (5-37, 5-38, 5-39), Quan Shui (540), Sakamoto (5-41), Sazanamigawa (5-42), Schlegeis (5-35), and Yugoslavia No. 1 and No. 2 (543~. No clear trends between the amount of damping and resonance number have appeared. It is very interesting that with the large potential for radiation of energy that exists with a concrete dam, being fully embedded in foundation rock that often has material properties similar to concrete, and with the impounded water completely covering one face, so little damping is present. Of course. during strong shaking the material component of the ~ , A, %, damping would be expected to increase. Contraction joints that can accommodate differential movements in gravity or buttress dams, if present, would complicate their behavior during forced- vibration tests, and data from Pine Flat Dam (5-28, 5-29) and Wimbleball (buttress) Dam (5-22, 5-44) indicate that some relative motion can occur across a joint. However, some of the complex behavior observed for such dams, as at Wimbleball (5-22, 5-44) and Upper Glendevon (5-23), which has been attributed to movements across joints, may actually be due to excessive modal interference arising from shaking a long structure with a single shaker. Some odd behavior observed at Pine Flat Dam (5-28, 5-29) between winter and summer forced-vibration tests at different water levels may have been due to changes in joint contact resulting from variations in temperature or water load. It should be mentioned that if only frictional forces exist across the joints (i.e., unkeyed), the friction may be overcome during the response to strong shaking, resulting in primarily individual vibrations of the monoliths or buttresses. In this case forced-vibration or ambient data would not be entirely relevant. Contraction joints may also affect the forced- vibration behavior of arch dams, as at Talvacchia Dam (5-13), where differences in resonant frequencies were observed between different tests at the same water level. In this case temperature was again suspected of playing a role. The presence of reservoir water lowers the resonant frequencies of the system because of the added mass effect. Data on the amount of reduction

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9o comes from forced-vibration field tests or ambient measurements carried out at significantly different water depths (Alpe Gera [gravity] [545], Ambiesta [2-43l, Big Tujunga [5-18], Fiastra [5-27], Kamishiiba [arch] t5-14, 5-42], Kolnbrein [5-34], Kops [5-35], Morrow Point [5-37, 5-38, 5-39], Pine Flat [5-28, 5-291, Talvacchia [5-13], Techi [5-46, 5-47], Tonoyama [2-37, 5-14], Sazanamigawa [5-42], Stramentizzo [arch] [5-48], Val d'Auna [gravity-arch] [5-48l, Wimbleball [5-22, 5-44], Yahagi [arch] [5-49], and Yugoslavia No. 2 [5-431~. The amount of reduction in resonant frequencies depended on the amount of increase in water depth, the initial depth, the resonance number, and the type of dam. The largest reductions occurred in the lower resonances and for thinner dams and reached 20 percent in either the fundamental symmetric or antisymmetric resonance at Ambiesta, Morrow Point, and Sazanamigawa dams for increases in the water level by 22, 32, and 33 per- cent of the dam heights, respectively, that filled the reservoirs. Modal damping as a percentage of critical tended to remain the same or increase slightly with an increase in water depth, possibly indicating some extra energy loss due to radiation. A number of analytical studies have been carried out in conjunction with forced vibration field tests or ambient measurements. The most thorough studies were performed on Xiang Hong Dian (5-30, 5-31), Quan Shui (5- 40), Techi (5-46), Monticello (3-26), and Morrow Point (5-39) dams, all by U.S. investigators; the layout of Xiang Hong Dian Dam is shown in Figure 54. Finite element models of the dam-foundation-water system were employed in all of these analyses, assuming the foundation to be massless; water compressibility was included only for Morrow Point Dam and in a few results for Monticello Dam. Parameters of the finite element models adjusted for best fit to the data included the elastic moduli of the dam and foundation, and the damping values. In the studies of Xiang Hong Dian (gravity-arch, 88 m high) and Quan Shui (arch, 80 m high) dams, comparisons of the computed results with those measured during forced-vibration field tests were made for resonant frequencies; for resonating shapes and amplitudes of the dam, including those at the foundation interface; for frequency-response curves of the dam crest near the resonant frequencies; and for profiles and amplitudes of the dynamic water pressure at the resonant frequencies. The agreement obtained for Xiang Hong Dian Dam, in all comparisons, was quite remarkable and represents a significant step forward in understanding the dynamic behavior of concrete dams; the mode shape comparison is shown in Figure 5-5. Agreement for Quan Shui Dam, although good in some aspects, was not as consistent as that obtained for Xiang Hong Dian Dam. Possible reasons include the more complicated geometry of Quan Shui Dam, making it more difficult to model, a greater nonsymmetry that increased the interference between the

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93 results demonstrate the desirability of evaluating a numerical model with data obtained at different water depths. Comparisons between computed and measured results at Monticello Dam (arch, 93 m high) were good for resonant frequencies, resonating shapes of the dam crest, and frequency-response curves of the dam crest near the resonant frequencies. However, less-than-satisfactory agreement was obtained for amplitudes of the dynamic water pressures, including a too-rapid decay with distance from the dam in the numerical results. A repeat of the water pressure calculations with water compressibility included produced only slight differences from the results obtained with incompressible water. An attempt to isolate a resonance of the water domain by normalizing a measured dynamic-pressure-frequency response with a nearby acceleration frequency response of the dam was inconclusive. From the studies performed on Xiang Hong Dian, Quan Shut, Techi, and Monticello dams, no obvious evidence emerged to suggest that the omission of foundation mass and the neglect of water compressibility in the analyses prevented adequate fits to the field data from being obtained. Regarding water compressibility, some effects may have been present in the measured data, especially for Techi Dam (5-501. Perhaps in the fit of the mathematical results to the data, neglecting water compressibility was compensated for in the adjustment of the values of elastic moduli and modal damping. It should be pointed out that successfully calibrating a mathematical model that uses incompressible water to forced-vibration or ambient data does not necessarily imply that neglecting water compressibility is appropriate for earthquake analysis. Because of the greater extent of the earthquake excitation over the boundaries of the water domain, water compressibility effects may be more important for earthquakes than under forced-vibration or ambient conditions. The forced vibration correlation study of Morrow Point Dam (Figure 5-6, arch, 142 m high) was performed with and without consideration of water compressibility, using mostly recent data obtained with full reservoir. Measurement stations at the face of the dam are shown in Figure 5-6. From this study it was concluded, in contrast to all previous experimental studies, that water compressibility can strongly influence the dynamic response of a dam. The presence of near-perfect symmetry, which eliminated interference between symmetric and antisymmetric responses, permitted calibration of the finite element model on the antisymmetric response, which, unlike the symmetric response, was little affected by water compressibility in the frequency range examined. Good matches were obtained to antisymmetric resonating shapes and frequency-response curves for both the dam accelerations and water pressure (Figure 5-7), whether or not water compressibility was included. Reasonable agreement was also achieved with some older data (5-37) for antisymmetric response at a significantly lower water level. However, use

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94 - 1 00 f t 200 ft 3 00 f t A A a a A A A A A '~1 A A A A A A A ~ 1~ UPSTREAM EL EVATION . Et 7165 EL 7025 E L 6906 ~ L 6 785 E L 6 7 0 0 FIGURE 5-6 Measurement stations at the face of Morrow Point Dam where accelerations (A) and dynamic pressures (P) were recorded (5-39). (PS and PA indicate syrnmetncal-only or aniisymmetncal-only tests.) of the calibrated finite element model to predict the symmetric response data was not satisfactory, although it was somewhat better when water compressibility was included. Possibly water compressibility made the symmetric responses sensitive to the geometry and/or boundary conditions of the reservoir, which may not have been modeled accurately. Water compressibility effects were exhibited in the forced vibration data through larger measured damping ratios for the symmetric resonances and by the presence of a "cantilever" crossover in the dynamic water pressures at the second symmetric resonance, where the resonating shape of the dam, with only a slight cantilever crossover, closely resembled the shape at the first resonance. An attempt to isolate the fundamental symmetric resonance of the reservoir water domain apparently succeeded by extracting the frequency-dependent amplitude of the water mode from the measured pressure data and normalizing it with the corresponding frequency-dependent measured motion of the dam. The isolated water resonance revealed a different behavior from that of the finite element compressible- water model. The work at Morrow Point Dam should be continued to determine if a numerical water model with response features similar to those of the actual reservoir water domain can be developed and if this will lead to better agreement between observed and computed darn responses. It should also be mentioned, as was pointed out in reference 5-39, that water compressibility effects at Morrow Point Dam may be more pronounced than

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9s - 1 _ I _ Q CO o o CO CO X 11 o I~ ~ ,~. · . · Z ~ ~ = 0 , . ,. o LL C) ~C~ CL ~ ., Lr) .~< co I o o X CO Lt) 11 m. ~ ~ lL I C~ C~ Q y - cn C~ o X CD CO I~ -m I C~ CO 11 a' LL o c, CL ~ Y _ cn cv) o X U~ CO ~ ln CO C~ 11 a' LL C) C) o U3 C) C~ .e - C) ;- ._ Ct - ._ ~: - ._ a5 - ._ o P" 3 o o ~: o C~ C, - C' U' U. C) C) ._ Ct' - Cd - - C~ oo C~ a~ o ~: o .= Ct o _

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96 for an "average" concrete dam because the ratio of the fundamental frequencies of the water and dam, which varies inversely with the importance of water compressibility, is lower for Morrow Point than the average. As mentioned previously, a good test for a mathematical model is its ability to predict forced-vibration or ambient data at significantly different water depths, as was attempted at Techi (5-46) and Morrow Point (5-39) dams. For the dams listed previously for which such data are available, other analytical studies have been reported for Big Tujunga (5-18), Yugoslavia No. 2 (5-43), Pine Flat (5-28, 5-29), Wimbleball (5-22), and Kolnbrein (5- 34~. Analyses of Big Tujunga and Yugoslavia No. 2 dams were not very satisfactory, which may have been partially due to use of the lumped-added- mass representation of incompressible water. Studies of Pine Flat and Wimbleball dams considered only the fundamental resonance of a single monolith or buttress, and indications were that both sets of data were affected by variations in joint conditions. Remarkable analyses of Kolnbrein Dam for an empty to near-full reservoir employed a variation of the lumped-added-mass representation of incompressible water in which the added masses were adjusted for each resonance depending on the shape of vibration (distances between nodes of radial motion), so the significance of this study is not clear. Certainly, further work is needed in evaluating mathematical models using experimental data for significantly different reservoir water depths. Another approach for evaluating a mathematical model is to compare resonant frequencies computed using experimentally determined values of elastic moguls ot the dam and foundation, either by in situ geophysical means or from core tests, with those derived from forced-vibration field tests or ambient measurements. This is possible for a few dams in the United States: Pacoima (5-4), Big Tujunga (5-18), Lower Crystal Springs (5-2, 5-3), and Morrow Point (5-39~. Satisfactory results were obtained only for Lower Crystal Springs and Morrow Point. Of course, problems may lie with either the mathematical models, the measured elastic moduli, or both. The redundant data obtained at Lower Crystal Springs and at . .. . .. ~ . Pacoima dams indicate that elastic moduli cannot be determined precisely. A number of other analyses of forced-vibration data have been carried out in which data on elastic moduli were available only for the dam (5-50~. MODEL TESTS Dynamic tests on linearly elastic models have been used in a number of countries to determine the resonant frequencies and mode shapes of proposed or existing dams. One advantage of linear modeling is that it is possible to scale water compressibility effects properly. However, of the tests on models of actual darns that have been reported in some detail (Bai-Shan Egravity- arch] [5-51], Hendrik Verwoerd [gravity-arch] [3-14, 5-52], North Fork

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97 [arch] [5-53, 5-54], Pine Flat [5-55], and Victoria [arch] [5-56]), only the test of the Pine Flat model was in the range where water compressibility effects would be important (5-50~. Analytical studies were performed for all of these model tests using data obtained under conditions of full and empty reservoir, and the agreement between computed and measured resonant frequencies and shapes ranged from poor to good. Some of this variation can be attributed to differences in the quality of the mathematical models. Best results were obtained for Bai-Shan and Hendrik Verwoerd using a finite element model of the dam and reservoir water; good agreement with measured dynamic water pressure distributions also was obtained at Bai- Shan. A recent experiment was designed to demonstrate water compressibility effects by employing a steel arch for the dam and was accompanied by numerical analysis that included water compressibility (5-57~. However, insufficient published results prevent definite conclusions from being drawn. Two special small-scale experiments (5-58, 5-59), not involving dams but intended to indicate the importance of water compressibility effects in the earthquake response of concrete dams, gave inconclusive results; moreover, a number of objections have been raised regarding the validity of the experiments (5-50, 5-60~. Two recent shaking-table experiments conducted at very small scale (2- 50) of a canyon, with or without a dam, and a large expanse of foundation rock sought to determine the degree of amplification of the earthquake motion in the upper portions of the abutments compared with that at the canyon bottom. Amplifications at the level of the crest equaled about 3 in one case where the abutments leveled off at crest level and about 2 in another case where the abutments extended higher than the crest. Reasonable agreement was obtained with both finite element calculations and ambient- field measurements. The presence of the dam had little effect on the rock motions. In contrast, results of a similar study employing incident waves (2-49) showed a strong effect from the presence of the dam, with maximum amplifications occurring at about midheight of the dam. Concerns regarding such model tests include boundary effects and inability to represent possible nonlinear behavior, which may occur in the actual rock mass. Model tests are perhaps most useful when used to investigate nonlinear aspects of dam response (cracking, joint opening, sliding behavior under high compression, and cavitation in the water) and require special materials and usually a shaking table. The main difficulty with the model materials is that when the experiment is conducted under normal gravity, the strength and stiffness of the model materials compared with those of the prototype must be reduced by the product of the density and length ratios. Since the density ratio cannot practically be increased above about 2, the reduction required in strength and stiffness of model materials is large. Nevertheless, approximate small-scale versions of concrete have been developed that are

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98 typically plaster based with a high water content and lead powder added to increase density (4-3, 5-41, 5-45, 5-61 to 5-65~. Water generally is used as the model liquid, but the use of a liquid having higher density can offset some of the reduction required in strength and stiffness of the model materials (5-45, 5-61~. Use of a centrifuge produces the same effect to a greater degree, as has been reported once (2-49~. Note that with nonlinear scaling, compressibility of water does not scale; neither does cavitation. However, separating the dam and fluid by a membrane with air access between the dam and membrane approximately accounts for cavitation at the upstream face of the dam (4-3~. Such a membrane is actually necessary to prevent leakage of the fluid around the model if only the central part of the dam is being modeled and to prevent water contact with the plaster-based model material and consequent deterioration. Although nonlinear model tests are common in Japan (5-16, 5-41, 5-62), the Soviet Union (2-49, 5-63, 5-64, 5-66), at ISMES in Italy (5-45, 5-61, 5- 67 to 5-70), and at LNEC in Portugal (5-71, 5-72), very little detailed information from these sources is available in the earthquake engineering literature. What there is, though, indicates that nonlinear behavior is a very important feature in the response of concrete darns to strong ground shaking and that a dam undergoing nonlinear behavior can retain considerable stability. A recent experiment at LNEC, which was reported in some detail (2-62), described a test of a special system of joints in an arch dam designed to accommodate slip on a fault passing under the dam. Relative motions were applied pseudostatically to the perimeter of the dam, while dead and water loads were applied hydraulically. The model withstood prototype fault displacements of several meters without collapse; however, the test could not alleviate all concerns regarding water tightness. A recent shaking-table test in Yugoslavia (5-73) investigated the effect of opening of the contraction joints on the earthquake response of arch dams. The model consisted of the central cantilever and halves of the adjacent ones and thus included two vertical joints; steel springs represented the arch support provided by the remainder of the dam. Horizontal cracks caused by the shaking initiated an overturning failure in the upper third of the central cantilever, where bending stresses had increased significantly following openings of the joints and loss of arch support. Keys were not included in the joints, so the effect of such features on the failure mechanism was not determined. Only a few nonlinear model tests with valid scaling have been performed in the United States. A shaking-table test of a single monolith of Koyna Dam (4-3) produced a single crack extending all the way through the neck portion (Figure 5-8~. The top block rocked back and forth but remained stable and continued to withstand the water load, even under intense excitations. Noticeable separations between the dam and a membrane supporting the

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....-~--~9~ CRACKED FIGURE 5-8 Model of single monolith of Koyna Dam; crack resulted from shaking-table test, including two-dimensional reservoir model (4-3).

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100 FIGURE 5-9 Segmented arch dam section model scaled to simulate effects of hydrostatic pressure and earthquake response Enema during horizontal and veridical shak~ng-table tests; it subsequently collapsed during severe shaking (4-30). water (i.e., cavitation) played a role in the response of the system. In another shaking-table test, using a jointed arch (4-3) to represent a horizontal cross section of an arch dam (shown in Figure 5-9), it was confirmed that opening of the contraction joints is an important response mechanism. Intense excitations were required to cause collapse of the arch, which was initiated by a compression failure at an abutment over the reduced contact area in a partially open joint. Both of these experiments confirmed the possible existence of continued stability in the nonlinear realm. A series of shaking-table tests on three models of a single monolith of Pine Flat Dam (Figure 5-10) with full reservoir has recently been completed (5-65~. Each model cracked all the way through the neck region, but no failures occurred, even during subsequent tests on the cracked models that employed severe table motions. The models remained stable because the crack profiles that developed were favorable: a V shape in one case and a dip in the upstream direction in the other two cases (Figure 5-11~. Details of the cracking patterns were quite different among the models, even though the experiments were roughly similar. This suggests that cracking patterns in prototype dams may be sensitive to parameters describing the existing state of the dam and the excitation, which implies that reliable cracking

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101 FIGURE 5-10 Setup for shaking-table test of scaled model of Pine Flat Dam monolith, including two-dimensional reservoir (5-65). FIGURE 5-11 Model of Figure 5-10 shown after testing; the sliding displacement visible along the crack is equivalent to 2 ft of prototype movement (5-65).

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102 analyses may be difficult to perform. Although the three models exhibited excellent stability during and after cracking, the possibility of developing an unfavorable crack profile, such as one that dips in the downstream direction, could not be ruled out. Certainly, much more experimental work is needed on nonlinear models, including three-dimensional ones. This is an area where a glaring deficiency now exists in the United States. One potentially important feature of the earthquake response of concrete dams that has not been examined is water intrusion into cracks on the upstream face of a dam, especially as facilitated by crack opening. It is noted that such an occurrence was prevented in the experiment mentioned above by the use of a membrane between the dam model and the liquid. Slip along a rough crack dilates the crack (as occurred for the model shown in Figure 5-10) and would greatly facilitate water intrusion. The combination of an unfavorable crack profile with water intrusion would be an event of considerable concern. Another issue regarding such model studies is a lack of knowledge about the fracture mechanics of the plaster-based model materials; that is, how well does the critical stress intensity factor (a material property that governs crack propagation) scale? RESEARCH NEEDS 1. Data Collection from Actual Earthquakes The collection of data from actual earthquakes should be accelerated through increased instrumentation because of the current sparsity of records from dams and their foundation rock for moderate and intense shaking. Such records can provide a general understanding of the dam response; they are the only reliable source of information on the spatial variations of rock motions that occur in complicated site geometries and it is critical to include such variations in analyses. Also, the motion of the reservoir bottom upstream of the dam, which provides seismic excitation to the water, must be measured. Records of dynamic water pressure response would be very useful; practically none exist. Consideration should also be given to measuring movements associated with contraction joints, such as joint openings for arch and gravity dams and relative tangential motions across unkeyed joints in gravity and buttress dams. Accurate earthquake data are essential for guiding development of appropriate mathematical models. 2. Forced-Vibration Field Tests Forced-vibration field tests, carefully carried out, are the preferable means for investigating dam-reservoir water interaction and water compressibility effects. Important work has been accomplished in this area, but in many

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103 cases correlations with analytical results have been poor. Field tests must be planned to obtain data for significantly different water levels and should include measurements of dynamic water pressure against the dam and also upstream from the dam face. Dam-foundation interaction can also be studied via forced-vibration tests and should include measurements of the rock motion at the dam-foundation interface and beyond. 3. Nonlinear Phenomena Nonlinear phenomena play an important role in the response to strong shaking of a large concrete dam with full reservoir. A major concentrated effort is needed in this area, about which little quantitative information is available, using small-scale model tests on shaking tables. A high-frequency capability is necessary for the shaking table because of the very small scales that must be used. Difficulties associated with carrying out such experiments in a valid way (e.g., in reproducing joint keys and in allowing intrusion by the liquid into cracks) should not be underestimated. Attempts should be made to learn as much as possible from the experiences of laboratories in other countries, and cooperative research programs should be planned to take advantage of foreign facilities that have no counterparts in this country— such as large-capacity shaking tables with high-frequency capabilities.