seismic response

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2009; 38:307–329Published online 1 September 2008 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.851

Seismic response of intake towers includingdam–tower interaction

M. A. Millan∗,†,‡, Y. L. Young§ and J. H. Prevost¶

Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, U.S.A.

SUMMARY

The seismic response of the intake–outlet towers has been widely analyzed in recent years. The usualmodels consider the hydrodynamic effects produced by the surrounding water and the interior water,characterizing the dynamic response of the tower–water–foundation–soil system. As a result of these works,simplified added mass models have been developed. However, in all previous models, the surroundingwater is assumed to be of uniform depth and to have infinite extension. Consequently, the consideredadded mass is associated with only the pressures created by the displacements of the tower itself. For a realsystem, the intake tower is usually located in proximity to the dam and the dam pressures may influencethe equivalent added mass. The objective of this paper is to investigate how the response of the tower isaffected by the presence of the dam. A coupled three-dimensional boundary element-finite element modelin the frequency domain is employed to analyze the tower–dam–reservoir interaction problem. In all cases,the system response is assumed to be linear, and the effect of the internal fluid and the soil–structureinteraction effects are not considered. The results suggest that unexpected resonance amplifications canoccur due to changes in the added mass for the tower as a result of the tower–dam–reservoir interaction.Copyright � 2008 John Wiley & Sons, Ltd.

Received 3 August 2007; Revised 21 July 2008; Accepted 22 July 2008

KEY WORDS: CE database subject headings: intake structures; seismic analysis; dams; hydrodynamicpressures; fluid–structure interaction; structural dynamics

1. INTRODUCTION

The safety of the intake–outlet towers after an earthquake is of great importance because it isrelated to the continuity of the water supply. In some cases, these towers are freestanding and arefounded on an enlarged base on the reservoir bottom, whereas in other cases they are structurally

∗Correspondence to: M. A. Millan, Dep. Estructuras, Escuela Superior de Ingenieros, Camino de los Descubrimientoss/n, Isla de la Cartuja, 41092 Sevilla, Spain.

†E-mail: [email protected], [email protected]‡Visiting researcher.§Assistant Professor.¶Professor.

Copyright � 2008 John Wiley & Sons, Ltd.

308 M. A. MILLAN, Y. L. YOUNG AND J. H. PREVOST

water

tower

Infinitereservoir

Infinitereservoir

Towerexcitation

Figure 1. Tower–water system in typical models. The surrounding water is assumed to be of uniformdepth and to have an infinite extension.

reservoir

damIntake-outlet tower

Plane of symmetry

x y

z

Figure 2. Symmetric dam–tower–reservoir model considered in this paper.

connected to the surrounding land or to the upstream concrete dam. It is recognized that theresponse of the tower can be significantly influenced by the fluid structure interaction effects.There are several solutions for earthquake-induced hydrodynamic pressures on flexible, submerged,cylindrical structures surrounded by a compressible fluid as described hereafter.

The most extended procedure [1–4] accounts in the calculation the effects of added mass due tothe internal and external water, as well as the influence of fluid compressibility and hydrodynamicradiation damping. In a series of publications, Goyal and Chopra [1–4] presented frequencyfunctions and earthquake responses, as well as simplified procedures, to determine the maximumseismic forces and the added mass due to the presence of the interior and exterior fluid.

In all previous models, the surrounding water is assumed to be of uniform depth and to have aninfinite extent (see Figure 1). Consequently, the added mass effect is associated with the pressures

Copyright � 2008 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2009; 38:307–329DOI: 10.1002/eqe

SEISMIC RESPONSE OF INTAKE TOWERS 309

Figure 3. Dam–tower–reservoir BEM model. Upper part: concrete dam; bottom part: earth dam.

created by the displacements of the tower only. However, for a real system, the intake tower islocated in proximity to the dam, where wave reflections from the dam may change the resultantadded mass, which in turn may change the natural frequencies and the seismic response of thetower. The objective of this paper is to investigate the influence of the dam on the tower duringan earthquake.

Two simplified problems are considered: (1) a concrete intake tower in the presence of a concretedam and (2) an earth dam. A schematic representation of the problem is presented in Figure 2.A coupled three-dimensional boundary element-finite element method in frequency domain isemployed to analyze the dynamic dam–water–tower interaction problem. The boundary elementmethod (BEM) model used in this research has been described earlier in [5–7]. The BEM modelsfor the concrete dam and earth dam are shown in Figure 3. In all cases, symmetry about the x–zplane is exploited.



The effects of the interior fluid and the soil–structure interaction are not considered in order tofocus on the influence of the dam–tower interaction.

2. BASIC THEORETICAL ANALYSIS OF THE PROBLEM

As explained before, the main difference between the real behavior of the system and that of thetypical models is the presence of the dam. A simplified analysis of the problem can be done bydecomposing the coupled system as a sum of simpler models as discussed hereafter.

As represented in Figure 4, the complex behavior of the coupled dam–tower–water systemsubject to bottom seismic excitation can be decomposed as the sum of two simpler cases ofexcitation. Case 1 includes the excitation of the dam base but not of the tower base. Case 2includes the excitation of the tower base but not of the dam base. Both the dam and the towerare flexible in all cases and may be excited by pressure waves propagating through the reservoirwater.

From a very simple analysis of the two problems, some important conclusions can be obtainedabout the behavior of the coupled model. For the first simplified case with dam excitation only,the main component of the pressure field is due to the dam oscillation, which creates a prop-agating wave from the dam to the infinite reservoir. This wave will produce resonance of thetower if the excitation frequency is close to the tower natural frequencies, or if the excitationis related to the natural frequency of the dam–reservoir system (even if this frequency doesnot correspond to the tower natural frequency). As a consequence of this behavior, the pressurefield effect on the tower cannot be represented simply as an added mass to the tower mass.For the second simplified case with tower excitation only, the pressure field is created by thetower vibration and thus can be properly represented by an added mass. When the distancebetween the tower and the dam is large, the results obtained from Case 2 are almost identicalto those obtained from the analysis of a tower reservoir model without the dam, as described inFigure 1.

Dam excitation

Fixed base

Tower excitation

Fixed base

Tower excitation

Dam excitation

CASE 2

CASE 1

Figure 4. Dam–tower–water system subject to bottom seismic excitation can be decomposed as the sumof two simpler cases of excitation. Case 1 includes the excitation of the dam base but not of the tower

base. Case 2 includes the excitation of the tower base but not of the dam base.



3. CONCRETE DAM MODEL

3.1. Description of the BEM model

The dam is idealized as a triangle with a vertical upstream face and a downstream face with aslope of 0.8:1. The transversal dimension of the dam is assumed to be equal to the reservoir width,which is 300m. Free slip boundary conditions are applied at the ends of the dam on the lateral faceof the block, and zero displacement condition is applied in the transversal direction. The waterdepth H at the upstream face of the dam is the same as the dam and the tower height, which is100m. The dam is assumed to be symmetric about the x–z plane. The half width of the dam isb=150m (the full width is 2b=300m). The intake tower is assumed to be a cylinder with uniformcross section. The outside diameter is taken to be 2R=13.6m and the wall thickness is taken tobe 0.2R. To simplify the mesh, the tower is modeled as a solid cylinder without the hollowedcore. The effect of the hollowed core is considered by changing the material properties (Young’smodulus and solid density) of the solid cylindrical tower to match the natural frequencies of thehollowed cylindrical tower.

The reservoir is discretized to a distance of 600m. At this point, a transmitting boundary ofthe Robin type [8] is used to simulate an infinite channel of constant rectangular shape. Quadraticrectangular and triangular boundary elements are used to model the dam, the tower and the reservoir.The reservoir lateral boundaries are assumed to be rigid.

The assumed parameter values for the dam are: modulus of elasticity E=3.45×1010N/m2,Poisson’s ratio �=0.17, density �=2480.0kg/m3, damping ratio �=0.05. The water wave velocityc=1440m/s, water density �w=1000kg/m3 and reservoir depth H=100m. For the selectedvalues, the natural frequency of the reservoir is �r=�c/(2H)=22.6rad/s=3.6Hz.

The material properties of the actual hollowed core tower are assumed to be the same as thedam. To allow the tower to be simplified as a solid cylinder, the tower modulus of elasticity isET=2.0×1010N/m2 and the tower density is �T=893.5kg/m3, which gives the same fundamentalfrequency (5.7 rad/s or 0.91Hz) as the actual hollowed core concrete tower.

Two different models have been defined in order to analyze the effect of the dam–tower sepa-ration. A separation distance S=50m is used in the first model and S=100m in the secondmodel.

The wave reflection at the bottom boundary of the reservoir, accounting for the flexibility ofthe bottom rock and of the possible bottom sediments, is represented in a simplified way using abottom absorption coefficient � (�=0 implies a non-reflective boundary and �=1 implies a fullyreflective boundary). It is defined as (see [9] for details)

�= 1−qc

1+qc(1)

where c is the water wave velocity and q=�w/�rCr. �r and �w are the soil and water densities,respectively. Cr=

√Er/�r is the transversal wave velocity in the soil. Er is Young’s modulus for

the soil. An absorption coefficient of �=0.75 has been considered in the model with the 50m.separation distance between the dam and the tower.

In order to study the dam–tower interaction effects, the results are compared with those obtainedusing a model without the dam, which are obtained by applying transmitting boundary conditionsat the two axial extremes of the reservoir. One of the BEM models is shown in Figure 3 (upperpart). In all cases, symmetry about the x–z plane is exploited.



Figure 5. Natural modes of vibration and associated displacement and pressure distributions of the intaketower. Horizontal excitation. The pressures have been normalized by the corresponding peak pressure for

the first mode of the tower (without the dam), p1.

3.2. Frequency-domain seismic response

Results for the models with and without the dam subject to horizontal and vertical seismic exci-tations are presented in this section. The first two mode shapes and pressure distributions for thecoupled dam–tower case (100m separation) are presented in Figure 5. The results correspond tothe first and second resonance frequencies. The pressures p are normalized by the peak pressurefor the first modal response of the tower (without the dam) under horizontal excitation, p1. Asshown in the figure, for the first mode, the results with the dam (tower+dam+reservoir) aresimilar to the results without the dam (tower+reservoir). However, a significant amplification ofthe mode 2 pressures can be observed for the case with the dam.



Table I. Peak frequencies for different elements of thesystem (dam–tower distance=100m).

Element Mode � (rad/s) �/�1

Tower only First 5.70 1.000Second 35.75 6.267

Dam+reservoir First 21.50 3.769Reservoir only 22.62 3.965Tower+infinite reservoir First 4.25 0.745

Second 25.25 4.426Tower+reservoir+dam First 4.25 0.745

New peak 21.50 3.769Second 25.50 4.470

To understand the significant amplifications in the mode 2 response, the natural frequencies ofthe different elements in the system are compared in Table I.

As expected, the second natural frequency of the tower in the presence of the dam (tower+reservoir+dam) is slightly higher than the natural frequencies of the tower without the presenceof the dam (tower+reservoir) due to the decrease in added mass effect, since the reservoir isblocked in the downstream end by the dam. More interestingly, as shown in Table I, the presenceof the dam introduces a new resonance peak at 21.50 rad/s, which is the same as the fundamentalfrequency of the dam with the effect of the added mass due to the reservoir, 21.50 rad/s, and is nearthe fundamental frequency of the reservoir itself, 22.62 rad/s. Hence, it can be concluded that thisnew additional peak on the tower response is caused by the dam–reservoir system resonance. Theresults imply a potentially dangerous situation of simultaneous tower, dam, reservoir resonanceif the excitation frequency is between 21.5 and 25.5 rad/s, which explains the difference in thepressure response of the tower with and without the dam for the second mode.

The predicted displacements at the top of the tower and the dam due to horizontal and verticalseismic excitations at the base are shown in Figures 6 and 10, respectively. The displacements, u, inboth the figures are normalized by the peak displacement in the first modal response of the tower+reservoir without the presence of the dam under horizontal excitation, u1. The circular frequency,�, is normalized with the first natural frequency of the tower alone without the reservoir, �1.

For the case of horizontal excitation, there is a small decrease in the displacement amplitude ofthe tower+dam+reservoir case, but no change in frequency at the first resonance peak (�/�1=0.745). However, compared with the case of the tower without the presence of the dam (i.e.tower+reservoir), a noticeable increase can be observed in the displacement at the second resonancepeak, along with a slight shift in frequency. More importantly, a new peak can be observed betweenthe first and the second resonance peaks in the tower+dam+reservoir case. The frequency of thisnew peak corresponds to the fundamental frequency of the dam–reservoir system (�/�1=3.77),and is near the fundamental frequency of the reservoir (�/�1=3.96), as well as the secondnatural frequency of the tower with added mass due to the reservoir in the presence of the dam,�/�1=4.47. Thus, it can be concluded that the new additional peak is due to resonance as a resultof tower–dam–reservoir interactions, which significantly modified the global response of the towerin the presence of the dam.

A noticeable influence of the dam–tower distance is observed in Figure 6 where the new peakdisplacement amplification (�/�1=3.96) changes from 1.75 for the 50m distance case to 1.27 for



Figure 6. Top of the tower displacement response for the coupled dam–tower–reservoir case.Concrete dam. Horizontal excitation.

the 100m distance case. Considering that this new peak is related to the reservoir resonance, whichappears to be due to the presence of the dam, the decrease can be expected since the water pressureis reduced when the dam–tower distance is increased. However, the first peak (�/�1=0.745) isincreased from 0.71 for the S=50m case to 0.89 for the S=100m case and the second peak(�/�1=4.470) is increased from 1.0 for the S=50m case to 1.21 for the S=100m case. Thiscontradictory behavior is explained in the following using the two simple case decompositionsdescribed in Section 2.

The resonance at the natural frequencies of the tower is determined by the addition of thetower responses for Case 1 (dam excitation only) and Case 2 (tower excitation only) described inSection 2. As explained before, the influence of the dam on the tower response for large separationdistance between the dam and the tower for Case 2 is negligible. Thus, the changes in the peakshould be explained using Case 1. When the dam is excited with the tower base fixed, the resultantpressure field does not vary uniformly with distance, as represented in Figure 7. The response ofthe tower for this case depends on the dam–tower distance and may or may not increase the globalresponse of the tower, depending on the value and phase of the pressure wave. In Figure 8, thereal and imaginary components of the frequency displacement response at the top of the tower forCase 1 and Case 2 are represented. The displacements at the first natural frequency of the towerfor Case 1 are in opposite phase with the displacements for the tower+reservoir case (Case 2 inSection 2). Since in Case 1 the pressures decrease with distance away from the dam, but not inthe Case 2 pressures, and since the two pressure responses are in opposite phase, its total valueincreases when the separation distance increases from 50 to 100m. Similarly, the displacements atthe second natural frequency for Case 1 change when the dam–tower distance increases (due to thechange in the pressure field with distance) and present a small shift in frequency. This producesan increase in the final tower displacement at this frequency.

A similar consideration can be applied to the analysis of the change in the new resonance peak.From Figure 8, the displacements corresponding to case 1 are reduced with distance away from



Figure 7. Real and imaginary part of the water pressure distributions for Case 1 described in Section 2.Second tower natural frequency. Concrete dam. Horizontal excitation.

the dam and those corresponding to Case 2 (tower+reservoir) do not change. Thus, a reductionin the final displacements of the tower is expected when the distance changes from 50 to 100m.

The natural modes of vibration and the associated water pressure distribution for differentdam–tower distances are shown in Figure 9.

A very important change can also be observed for the vertical excitation case shown in Figure 10.For the tower without the dam, when an infinite reservoir is considered, there is no horizontaldisplacement due to the geometric symmetry, and hence it is not shown in Figure 10. When thepresence of the dam is considered, however, a vertical excitation produces waves propagatingfrom the dam to the infinite, which leads to an unexpected vibration of the tower around the new



Figure 8. Real and imaginary part of the horizontal displacement of the top of the tower for Cases 1and 2 in Section 2. Second tower natural frequency. Concrete dam. Horizontal excitation. As shown,

the pressure field varies with distance.



Figure 9. Natural modes of vibration and associated water pressure distribution for different dam–towerdistances. Horizontal excitation.

Figure 10. Top of the tower displacement response for the coupled dam–tower–reservoir case.Concrete dam. Vertical excitation.

resonance mode (�/�1=3.77) and the second resonance mode (�/�1=4.47), which resulted intwo closely spaced peaks in the displacement response.

When the dam–tower distance increases, the vertical tower response decreases at both thepeaks. As pressures propagating from the dam are the main cause of this resonance, an increased



Figure 11. Reservoir bottom absorption influence. Horizontal and vertical excitation. The displacements,u, are normalized by the maximum first peak displacement of the tower with reservoir (Case 2) with the

corresponding � coefficient, u (Case 2,�).



dam–tower distance results in a decreased displacement response (as for the horizontal excitationcase).

Similar conclusions can be obtained by analyzing pressure results but they are not included inthe present paper due to length limitations.

The influence of the reservoir bottom absorption is analyzed in Figure 11 for horizontal andvertical excitations. The displacements, u, are normalized for this case by the maximum first modedisplacement of the tower with the reservoir (Case 2) with the corresponding � coefficient, u(Case2,�). For example, the displacement for the tower placed 50m from the dam with �=0.75 (denotedby tower S=50m, �=0.75) is normalized by the displacement for the tower in an infinite reservoirwith �=0.75, u(Case 2, �=0.75) The wave reflection at the bottom boundary is represented bythe absorption coefficient �, which can vary from 0 to 1. �=0 implies a non-reflective boundaryand �=1 implies a fully reflective boundary. In this paper, an �=0.75 is assumed for the bottomabsorption case and �=1 for the non-absorptive bottom case. A similar analysis considering thesimple cases in Section 2 is used to explain the behavior of the system. In Figure 12, the real andthe imaginary part of the displacement responses are compared for the cases with and without thebottom absorption.

A small amplification of the first resonance peak is observed for the horizontal excitation casewhen � changes from 1 to 0.75. As shown in Figure 12, the Case 1 pressures remain almostunchanged with � except for the higher frequencies, but the tower response for the tower+reservoircase is reduced from �=1 to �=0.75, as can be expected. Since they are in opposite phase, the finalpeak is increased for the �=0.75 case. The most important change due to the bottom absorptionis that the peak related to the reservoir resonance is significantly reduced, as shown in Figure 11.However, the second resonance peak of the tower increases for the horizontal excitation case whenthe bottom absorption is considered. For the tower+reservoir case (Case 2 in Section 2) a clearreduction in both the real and the imaginary part of the displacement response can be observedfor all the frequency ranges. For Case 1, very close results for majority of the frequency range canbe observed for �=1 and �=0.75 cases, except a small increase in the response for �=0.75 anda small shift in frequency around the second natural frequency of the tower. This case 1 behaviorcan be explained by considering the change in the pressure field caused by the reservoir bottomabsorption. Both the effects lead to a higher second-peak response.

The contrary takes place for the vertical excitation case because, for this case, the resonanceis related mainly to the water pressures created by the dam vertical excitation, which are reducedwhen the bottom absorption is considered.

The results suggest that dangerous simultaneous resonance of the tower, dam, reservoir canoccur for the selected configuration due to tower–dam–reservoir interaction. This effect cannot berealized with the previous analysis method due to the assumption of the infinite reservoir withoutthe dam.

3.3. Time-domain seismic response

Due to the drastic differences observed in the frequency-domain response, the time-domain responseof the tower with and without the presence of the dam is analyzed in this section.

The time-domain seismic response is obtained from the frequency-domain response using theinverse FFT. The earthquake data used in the analysis correspond to the El Centro earthquake(1940) and the Taft earthquake (1952). The selected earthquake has some fixed characteristics thatcan heavily influence the final response. To examine the sensitivity to the frequency content, the



Figure 12. Real and imaginary part of the horizontal displacement of the top of the tower forCases 1 and 2 in Section 2. Second tower natural frequency. Concrete dam. Reservoir bottom

absorption �=0.75. Horizontal excitation.



original earthquake spectrum is shifted slightly to determine how the final response can changefor a similar earthquake with a slightly different frequency content.

The influence of the frequency shift on the final time-domain horizontal displacements at thetop of the tower with and without the presence of the dam is compared in Figure 13 consideringboth the horizontal and vertical seismic inputs. The displacement amplifications shown in thefigures are relatives to the horizontal displacement in the tower+reservoir (without dam) caseunder horizontal excitation only. Three different lines are presented in the figures, correspondingto the tower+dam+reservoir case under horizontal excitation only, the tower+dam+reservoircase under vertical excitation only, and the tower+dam+reservoir case under horizontal andvertical excitation combined. The last one is obtained by adding the two previous responses, sincethe analysis is linear. The responses for horizontal excitation only and vertical excitation onlyconsidering the dam are clearly lower than the response for horizontal excitation without the dam,since the first natural mode dominates the response and there is no first mode resonance for thevertical excitation case or its peak is reduced for the horizontal excitation case. However, when thehorizontal and vertical excitations are considered simultaneously, the addition of both responsesmay produce a final response higher than the horizontal excitation case without the dam (usualmodels).

For example, consider the case of the response of the concrete dam–tower–reservoir system tothe El Centro earthquake. Figure 13 (upper part) shows that for zero frequency shift and horizontalexcitation, the displacement at the tower top is roughly 27% less than that produced in the towerwithout the dam under horizontal excitation. For vertical excitation and no frequency shift, thedisplacement at the top of the tower in the dam–tower–reservoir system is roughly 25% less thanthat produced in the tower without the dam under horizontal excitation. Assuming the followingvalues for the response:

• Tower displacement in the tower–reservoir system under horizontal excitation=100%• Tower displacement in the tower–dam–reservoir system under horizontal excitation=73%• Tower displacement in the tower–dam–reservoir system under vertical excitation=75%

Then, for the case of combined horizontal and vertical excitations, we can add the time-domainresponses for the horizontal excitation case and the vertical excitation case. If the maximumamplifications for the horizontal case and the vertical case occur at the same time, then themaximum tower displacement for the tower–dam–reservoir system for the above example wouldbe 148 or 48% greater than the response for the case with tower without the dam. However,the maximum tower displacement would probably be less than 148%, since the maximumamplifications for the horizontal case and the vertical case would occur at different times (infact, for this particular example, the maximum tower displacement of the tower–dam–reservoirsystem subject to combined horizontal and vertical excitations is 110%). Nevertheless, for thecombined horizontal and vertical excitation case, the maximum response of the tower–dam–reservoir system is still likely to be significantly higher than that for the case of the tower withoutthe dam.

The implication, for this particular example, is that under a realistic excitation, which hascontributions from a broad range of frequencies, the presence of the dam in fact leads to a reduction(not amplification) in the response if the excitation is purely horizontal. However, under verticalexcitation, which would not produce any response in the tower–reservoir system, the presence ofthe dam causes significant amplification in the response to be produced.



Figure 13. Concrete dam. Horizontal displacement amplification at the top of the tower in the time domainfor the dam–tower coupled case relative to the tower+reservoir case. El Centro and Taft earthquakes.Dam–tower distance 50m. Dam–tower H: horizontal excitation only; dam–tower V: vertical excitation

only; dam–tower H+V: horizontal and vertical excitation combined.



Figure 14. Concrete dam. Reservoir bottom absorption �=0.75. Horizontal displacement amplification atthe top of the tower in the time domain for the dam–tower coupled case relative to the tower+reservoircase. El Centro and Taft earthquakes. Dam–tower distance 50m. Dam–tower H: horizontal excitation only;dam–tower V: vertical excitation only; dam–tower H+V: horizontal and vertical excitation combined.



The same analysis is made for the reservoir bottom absorption case and is presented in Figure 14,showing increased amplifications compared with the non-absorptive case. This result is expectedsince the first resonance, which dominates the final response, is increased when the bottom absorp-tion is considered.

4. EARTH DAM MODEL

4.1. Description of the BEM model

Although the dynamic behavior of earth dams is known to be nonlinear, linear behavior is assumedin this work in order to analyze the influence of the dam presence on the dynamic response of thetower. This assumption can be accepted considering small amplitude vibrations and taking intoaccount that the dam response is not the main objective of the research so there is no need to dothe analysis with a more complicated model.

The earth dam is idealized as a triangle with an upstream and a downstream face with a slopeof 1.5H:1V. The transversal dimension of the dam is assumed to be equal to the reservoir width,which is 300m. Free slip boundary conditions are applied at the ends of the dam on the lateral faceof the block, and zero displacement condition is applied in the transversal direction. The waterdepth H at the upstream face of the dam is the same as the dam and the tower height, is 100m.The dam is assumed to be symmetric about the x–z plane. The half width of the dam is b=150m(the full width is 2b=300m).

The BEM model for the earth dam and intake tower is shown in Figure 3 (bottom part). As forthe concrete dam case, symmetry about the x–z plane is exploited.

Others parameters like reservoir discretization length, transmitting boundary and intake towerrepresentation are assumed to be identical to those considered for the concrete dam analysis. Inthis case, the dam–tower distance is assumed to be 50m at the ground level.

The assumed parameter values for the dam are: dam modulus of elasticity E=150×106N/m2,dam Poisson’s ratio �=0.364, dam density �=2000.0kg/m3, dam damping ratio �=0.05, waterwave velocity c=1440m/s, water density �w=1000kg/m3 and reservoir depth H=100m.

4.2. Frequency-domain seismic response

Results for the models with and without the dam subject to horizontal and vertical seismic excita-tions are presented in Figure 15, where the displacements, u, are normalized for this case by themaximum first mode displacement of the tower with the reservoir (Case 2) with the corresponding� coefficient, u (Case 2,�). As expected, the dam resonance is less clear than for the concretedam case, since it is a massive structure and it is much more flexible than the concrete dam. Thisproduces a minor influence of the reservoir resonance on the tower response. This behavior canbe observed in Figure 15 (upper part) for horizontal excitation, where the tower response showslittle difference with or without the dam. However, the dam influence on the tower behavior issignificant for the vertical excitation case, as shown in Figure 15 (bottom part). Due to the dampresence, the vertical excitation produces horizontal pressure waves that excite the dam’s secondmode response since it is very close to the reservoir resonance frequency. As for the concretedam case, there is also a small shift in frequency for the second tower mode. The influence ofbottom absorption can also be observed in Figure 15. For the horizontal excitation case, a small



Figure 15. Top of the tower displacement response for the coupled dam–tower–reservoir case. Earthdam. Horizontal and vertical excitation. The displacements, u, are normalized by the maximum first peakdisplacement of the tower with reservoir (Case 2) with the corresponding � coefficient, u (Case 2, �).



amplification on the first and second peaks is shown, similar to the concrete dam case. For thevertical excitation case, a reduction in the resonance peak from 1.64 (�=1 case) to 1.09 (�=0.75case) is observed.

4.3. Time-domain seismic response

Similar to the concrete dam case, the time-domain response of the tower with and without thepresence of the earth dam is analyzed in this section, using the same earthquake data, consideringboth the horizontal and the vertical seismic inputs.

The influence of the frequency shift on the final time-domain displacements at the top ofthe tower with and without the presence of dam is compared in Figure 16 considering both thehorizontal and the vertical seismic inputs. The resultant behavior is very similar to that observed forthe concrete dam case. Similar analysis was also conducted to study the influence of the reservoirbottom absorption. Figure 17 shows increased amplifications for �=0.75 compared with �=1, asexpected, since the first resonance, which controls the final response, is increased when the bottomabsorption is considered.

5. CONCLUSIONS

In all previous tower–dam–reservoir fluid–structure interaction models, the surrounding water isassumed to be of uniform depth and to have an infinite extension. Hence, the added mass effect ofthe external fluid is associated with the pressures created by the displacements of the tower only.However, for a real system, the intake tower is usually located in proximity to the dam, wherewave reflections from the dam may change the resultant added mass, which will in turn changethe natural frequencies and seismic response of the tower.

In this work, the influence of the dam on the seismic response of the tower is analyzed using a3D BEM numerical model, which lead to the following conclusions:

(i) For the selected configuration, the presence of the dam leads to the introduction of a newresonance mode near the tower’s second resonance frequency due to the dam–reservoirexcitations. Consequently, a potential amplification of the response under the horizontalexcitation may be produced due to the tower–dam–reservoir interaction if the excitationfrequency is near the fundamental frequency of the dam and the reservoir. As time-domainresults show, this amplification is usually less than 10–20% in most cases (and there is noamplification for many of the cases).

(ii) When the dam presence is considered, the tower under vertical excitation does not presentsymmetry, which leads to resonances that could not be captured using conventional toweranalysis methods due to the assumption of an infinite reservoir around the tower.

(iii) The results show that when considering simultaneous horizontal and vertical excitation,the tower displacements and pressures can be significantly amplified due to tower–dam–reservoir interactions. This behavior is more significant for a concrete dam than for an earthdam.

(iv) Additional research is needed to analyze the influence of other important parameters inthe response: e.g. flexibility of the dam and tower, variations in water depth, soil–structureinteractions, spatial variability of the excitation, etc.



Figure 16. Earth dam. Horizontal displacement amplification at the top of the tower in the time domainfor the dam–tower coupled case relative to the tower+reservoir case. El Centro and Taft earthquakes.Dam–tower H: horizontal excitation only; dam–tower V: vertical excitation only; dam–tower H+V:

horizontal and vertical excitation combined.



Figure 17. Earth dam. Reservoir bottom absorption �=0.75. Horizontal displacement amplification at thetop of the tower in the time domain for the dam–tower coupled case relative to the tower+reservoircase. El Centro and Taft earthquakes. Dam–tower H: horizontal excitation only; dam–tower V: vertical

excitation only; dam–tower H+V: horizontal and vertical excitation combined.



It should be noted that the models analyzed do not include the effects of the interior waterand the soil–structure interaction. Future work will address these effects to enhance the predictivecapabilities of the current model.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the use of the 3D Boundary Element software developed byJ. Dominguez (University of Seville, Spain), O. Maeso and J.J. Aznarez (University of Las Palmas deGran Canaria, Spain).

REFERENCES

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2. Goyal A, Chopra AK. Hydrodynamic and foundation interaction effects in dynamic of intake towers: earthquakeresponses. Journal of Structural Engineering 1989; 115(6):1386–1395.

3. Goyal A, Chopra AK. Simplified evaluation of added hydrodynamic mass for intake towers. Journal of EngineeringMechanics 1989; 115(7):1393–1412.

4. Goyal A, Chopra AK. Simplified evaluation of added hydrodynamic mass for intake towers. Journal of EngineeringMechanics 1989; 115(7):1413–1433.

5. Maeso O, Aznarez JJ, Dominguez J. Effects of space distribution of excitation on seismic response of arch dams.Journal of Engineering Mechanics 2002; 128(7):759–768.

6. Maeso O, Aznarez JJ, Dominguez J. Three-dimensional models of reservoir sediment and effects on the seismicresponse of arch dams. Earthquake Engineering and Structural Dynamics 2004; 33:1103–1123.

7. Millan MA, Young YL, Prevost JH. The effects of reservoir geometry on the seismic response of gravity dams.Earthquake Engineering and Structural Dynamics 2007; 36:1441–1459.

8. Brebbia CA, Dominguez J. Boundary Elements, An Introductory Course. Computational Mechanics. McGraw-HillBook Co.: Southampton, Boston, New York, 1992.

9. Fenves G, Chopra AK. Effects of reservoir bottom absorption on earthquake response of concrete gravity dams.Earthquake Engineering and Structural Dynamics 1983; 11:809–829.


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