document1

KSCE Journal of Civil Engineering (2015) 19(1):142-150

Copyright ⓒ2015 Korean Society of Civil Engineers

DOI 10.1007/s12205-014-1221-8

− 142 −

pISSN 1226-7988, eISSN 1976-3808

www.springer.com/12205

Structural Engineering

An Experimental Study on Shaking Table Tests on Models of

a Concrete Gravity Dam

Bupavech Phansri*, Sumetee Charoenwongmit**, Ekkachai Yooprasertchai***, Kyung-Ho Park****,

Pennung Warnitchai*****, and Dong-Hun Shin******

Received August 27, 2010/Revised June 9, 2013/Accepted January 11, 2014/Published Online July 7, 2014

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Abstract

This study deals with the shaking table tests for two small-scale models (Model #1 and Model #2) of a concrete gravity dam, whichhas been planned for the construction with the recommendation of the peak ground acceleration of the maximum credible earthquakeof 0.42 g. The development of bentonite-concrete mixture material, which matches the similitude requirements between theprototype and the model, is discussed. Two types of excitation, resonance test and ambient test, were conducted to investigate theresonant frequency, the maximum failure acceleration and the crack initiation/propagation. In both models, large amplification wasobserved at around 24-28 Hz. The crack initiated at the slope changing point and then propagated around the neck area. The crackfailures were occurred at the base acceleration of 0.55 g-0.65 g.

Keywords: concrete gravity dam, shaking table model test, bentonite-concrete mixture, crack

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1. Introduction

While concrete dams have been designed to withstand both

static and seismic loading, some concrete dams have been

damaged due to the strong ground motion, for example Koyna

Dam, India, 1967; Hsingfengkiang Dam, China, 1962; Sefid Rud

Dam, Iran, 1990.

For concrete gravity dams designed according to current design

criteria, the static and earthquake compressive stresses are

generally much less than the compressive strength of the concrete.

However, linear dynamic analyses of gravity dams show that the

earthquake ground motion can produce tensile stresses that

exceed the tensile strength of the mass concrete (Wieland, 2003;

Wieland et al., 2003). Therefore, the nonlinear tensile cracking

must be considered in the seismic response of concrete gravity

dams.

Shaking table model tests have been used to investigate the

nonlinear response effected by earthquake such as cracking, joint

opening, sliding behavior under high compression, and cavity in

the water (Bakhtin and Dumenko, 1979; Niwa and Clough,

1980; Donlon, 1989; Hall, 1989; Donlop and Hall, 1991; Lin et

al., 1993; Zadnik and Paskalov, 1992; Zadnik, 1994; Mir and

Taylor, 1995,1996; Ghobarah and Ghaemina, 1998; Harris et al.,

2000; Tinawi et al., 2000; Li et al., 2005; Ghaemmaghami and

Ghaemian, 2008). One of the main difficulties in the shaking

table tests is to development the model material which matches

the similitude requirements between the prototype and the model

by reducing the reduced strength and stiffness by the product of

the density and length scale. Table 1 summarizes previous

studies in terms of model materials and length scale used to

satisfy the similitude requirements. It can be seen from Table 1

that different materials, such as plaster, polymer, barite powder,

bentonite, as well as concrete, were used with the length scale of

1:30-1:150. Of particular interest is the tensile behaviour of the

material, such as ultimate tensile strength and elastic modulus.

Although some previous researches reported the success in the

development of the proper material, the behaviour of bentonite-

concrete mixture material, used for small scale concrete dam

models in shaking table tests, has not been adequately addressed

in the literature, especially for the similitude requirements of

properties, such as tensile strength and elastic modulus.

The other important issue is the initiation of crack and its

propagation for the evaluation of seismic response of dams.

From the comparison of the crack patterns in the previous tests

TECHNICAL NOTE

*Lecturer, Civil Engineering Dept., Faculty of Engineer, Rajamangala University of Technology Lanna, Chiang Mai 50000, Thailand (E-mail: bupavech

@rmutl.ac.th)

**Engineer, Provincial Waterworks Authority Region 10, Bangkok 10210, Thailand (E-mail: [email protected])

***Doctoral Student, School of Engineering & Technology, Asian Institute of Technology, Pathumthani 12120, Thailand (E-mail: [email protected])

****Member, Engineer, Bon E&C Co. Ltd., Korea (Corresponding Author, E-mail: [email protected])

*****Associated Professor, School of Engineering & Technology, Asian Institute of Technology, Pathumthani 12120, Thailand (E-mail: [email protected])

******Member, Head Researcher, K-water Institute, Korea Water Resources Corporation, Daejeon 305-730, Korea (E-mail: [email protected])

An Experimental Study on Shaking Table Tests on Models of a Concrete Gravity Dam

Vol. 19, No. 1 / January 2015 − 143 −

using the sinusoidal excitation, artificial and actual earthquake

records, the cracking initiated near neck region or at the base of

model, and then propagates from one side to the other.

This study deals with shaking table tests of two small-scale

models for a concrete gravity dam (the peak ground accelerations

of the design base earthquake and the maximum credible

earthquake in the dam site are recommended as 0.25 g and 0.42 g,

respectively). Considering the size of shaking table (1.2 m × 1.0 m)

and the similitude requirements between the prototype and the

model, the bentonite-concrete mixture material is developed. The

material preparation and behavior are discussed in details. Two

types of excitation, resonance and ambient testing, are applied to

investigate the natural frequency of the model, the maximum

failure acceleration and the crack initiation/propagation.

It is noted that the reservoir and foundation effects are neglected

due to the experimental limitations and the tests conducted under

the period action of horizontal sinusoidal loading. Thus, the

interpreting of the results should be done with regard to these

discrepancies.

2. Development of Model Material

2.1 Similitude Requirements

In order to simulate the nonlinear behavior of its prototype, or

full-scale structure, the small-scale model must follow certain

laws of similitude, which are determined by a dimensional analysis

of the problem under investigation and are relationship among

the dimensionless ratios formed by corresponding parameters of

the prototype and the model. Using the scale factor definitions,

Fp/Fm=SF, Tp/Tm=ST, Mp/Mm=SM, Lp/Lm=SL, γp/γm=Sγ, and σp/σm=

Ep/Em=Sσ, the relationships between model and prototype are

given by:

(1)

(2)

(3)

where F, T, M, L, γ, σ, and E are force, time, mass, length, unit

weight, stress and elastic modulus, respectively, and subscripts p

and m represent prototype and model.

If the unit weight ratio is set to be unity (Sγ=1), the scales for

strength and elastic modulus of the model material are equal to

the length scale, that is Sσ (=SMSL−1ST

−2=SγSL) = SL (Donlon, 1989;

Donlon and Hall, 1991). A summary of the similitude require-

ments established for this investigation is presented in Table 2.

Considering the size of the shaking table (1.2 m×1.0 m) used

in this study and the prototype, the length scale is set to be 1:100.

Then the properties of model are estimated from those of the

prototype to match the similitude requirement, as summarized in

Table 3.

2.2 Development of Bentonite-concrete Mixture Material

Following the estimation of the properties of model, the material

having the corresponding strength and elastic modulus must be

developed. As mentioned earlier, different materials, for example

plaster, polymer, barite powder or bentonite, were used to reduce

strength and elastic modulus. The shrinkage cracking is the

serious problem when using plaster-based material. Recently,

Harris et al. (2000) and Ghaemmaghami and Ghaemian (2008)

showed the good performance of the bentonite-concrete mixture

material. In this study, the bentonite-concrete mixture is consi-

dered to reduce the values of strength and elastic modulus.

In order to find the suitable mixture proportions, the trial mix

was separated into two phases. In the first phase, seven mixtures

were proportioned with zero (control mixture)-31% bentonite by

SF

Fp

Fm

------=MpLpTp

2–

MmLmTm2–

---------------------=⎝ ⎠⎛ ⎞ SMSL

ST2

-----------=

Sσ

σp

σm

------=FpLp

2–

FmLm2–

-------------SF

SL2

-----SMSL

ST2SL

2-----------= = =⎝ ⎠

⎛ ⎞ SM

SLST2

----------=

Sγ

γp

γm

-----=FpLp

3–

FmLm3–

-------------SF

SL3

-----SMSL

ST2SL

3-----------= = =⎝ ⎠

⎛ ⎞ SM

SL2ST

2----------=

Table 1. Summary of Previous Researches

Researchers Prototype dam Length scale Model material

Niwa & Clough (1980)

Koyna Dam 1:150 Plaster-celite-sand

Donlon (1989) Pine Flat Dam 1:115 Plaster, polymer

Mir & Taylor (1995)

Typical Concrete Dam

1:30Plaster-based-

material

Mir & Taylor (1996)

Typical Concrete Dam

1:30 Concrete

Harris et al. (2000)

Koyna Dam 1: 50Bentonite-concretev

Li et al. (2005)Three Gorges

Dam1:100 Barite powderv

Ghaemmaghami & Ghaemian

(2008)Sefid-rud Dam 1:30

Bentonite-concrete mixture

This studyTypical concrete

dam1 : 100

Bentonite-concrete mixture

Table 2. Scale Factors for Nonlinear Seismic Response Analysis

Physical & mechanical quantities Notation Dimensions Scale factor

Acceleration due to gravity g LT−2 1

Linear dimension L L SL

Modulus of elasticity E FL−2Sσ

Stress σ FL−2Sσ

Strain ε - 1

Poisson's ratio υ - 1

Ultimate strength σcu, σtu FL−2Sσ

Time T T

Frequency f T-1

Unit weight γ FL−3 1

Table 3. Estimation of Model Material Properties

Physical property Unit Prototype Scale factor Model

Ealastic modulus, E MPa 18,200 100 182

Ultimate strength

- compressive, f 'c MPa 10-15 100 0.1-0.15

- tensile, ft MPa 2.5 100 0.025

Density kg/m3 2,400 1 2,400

Ultimate strain

- compressive, εc - 0.003 1 0.003

- tensile, εt - 0.00012 1 0.00012

SL

1 SL⁄

Bupavech Phansri, Sumetee Charoenwongmit, Ekkachai Yooprasertchai, Kyung-Ho Park, Pennung Warnitchai, and Dong-Hun Shin

− 144 − KSCE Journal of Civil Engineering

mass of cement plus bentonite. The binder (cement+bentonite)

content was reduced from 178 kg/m3 to around 119 kg/m3 for

Mix 5, 6, and 7 (Table 4). Cement, bentonite and aggregates were

obtained from local commercial suppliers.

The trial mixes were made in the laboratory. Standard 10 cm×20 cm cylinders were made from each batch to identify required

properties. Elastic modulus and Poisson's ratio are determined

from two strain gages (vertical and horizontal direction) at 7 and

28 day's age. They are calculated from stress-strain values

corresponding to an initial strain of 50×10−6 mm/mm and the

strain at 40 % of the ultimate compressive strength.

The influence of w/c ratio and % bentonite on material is

shown in Fig. 1. The percentage of bentonite largely effects on

the properties of material. Elastic modulus and strength decrease

with increasing w/c ratio. In order to match the requirements,

such as E = 182 MPa, ft = 0.025 MPa and fc' = 0.1-0.15 MPa,

about 31% of bentonite is needed. It is noted that 20-25% of

bentonite was used in the previous studies (Harris et al., 2000;

Ghaemmaghami and Ghaemian, 2008).

Based on these results, the second concrete mixture proportions

were prepared for small-scale dam models by varying other

components, for example, content of fine or coarse aggregate.

The mixture components are summarized in Table 5.

In this study, two dam models (Model #1 and Model #2) were

constructed. Three batches were mixed in each model and nine

standard 10cm×20cm cylinders were collected from each batch

to identify the physical properties and the stress-strain curves.

Compressive strength was obtained from compression test at 28

days after casting. Ultimate tensile strength of specimens was

obtained using two different methods: direct tensile method and

splitting tensile method. Stress-strain curves of tensile and com-

pressive tests are shown in Figs. 2 and 3, respectively. The

physical properties of the mixture are summarized in Table 6,

and Table 7 shows the comparison of relative errors of physical

properties in the previous studies and this study. In Table 6, the

values of the modulus of elasticity for tensile test were estimated

from the stress-strain curves of Specimen-1 and -2 in Fig. 2.

Of particular interest is the tensile behavior of the bentonite-

concrete mixture material. In Fig. 2, the stress-strain curves from

tensile tests show different behavior between plastic and brittle

behavior. Model #1 shows the behavior between softening-

plastic and brittle, while in Model #2 the strength suddenly drops

after the peak value. Although the value of ultimate tensile

strength is close to the target value, the values of ultimate tensile

Table 4. Bentonite-concrete Mixture Proportions

Mix 1 (kg/m3)

(Control)

Mix2 (kg/m3)

Mix3 (kg/m3)

Mix4 (kg/m3)

Mix5 (kg/m3)

Mix6 (kg/m3)

Mix7 (kg/m3)

Water 258 309 314 332 332 319 366

Cement 178 160 151 142 95 91.5 81.3

Bentonite 0 18 27 36 24 27.5 36.5

Bentonite(%)

0% 10% 15% 20% 20% 23% 31%

FineAggregate

866 798 797 773 810 811 1057

CoarseAggregate

873 806 804 780 820 820 1060

w/c 1.45 1.93 2.08 2.34 3.49 3.49 4.5

w/b 1.45 1.74 1.76 1.87 2.79 2.68 3.11

Weight (kg) 2175 2091 2093 2063 2081 2069 2601

Fig. 1. Influence of w/c Ratio and % Bentonite on Material (Trial

Mix): (a) Ultimate Compressive Strength and w/c Ratio, (b)

Ultimate Tensile Strength and w/c Ratio, (c) Modulus of Elas-

ticity and w/c Ratio

Table 5. Bentonite-concrete Mixture of Dam Models

Component

Actual model mix

Model mix(kg/m3)

Volume in mixper 0.065 m3 batch

Water 404.46 26

Cement 81.23 5.28

Bentonite 36.46 2.37

Fine Aggregate 1,056.92 68.70

Coarse Aggregate (No.4-3/8''): wet 1,060.00 68.90

w/c 4.98

w/b 3.44

Weight (kg) 2,639.08 171.54


Vol. 19, No. 1 / January 2015 − 145 −

strain and the modulus of elasticity are different. The modulus of

elasticity obtained from the compressive tests is 65-136 times

higher than that obtained from the tensile tests. These values of

modulus of elasticity show larger relative error than those in the

previous studies, as shown in Table 7. It can be described that

satisfying all the similitude requirements is quite difficult.

3. Experiment Set-up and Procedure

The small-scale model was constructed on the floor, mounted

on a shake table and excited in a single axis corresponding to a

horizontal motion along the upstream-downstream axis. The

shaking table was calibrated to determine the actual response

with the frequency range of 2-30 Hz. A sinusoidal excitation was

selected for practical reasons associated with the shaking table.

Fig. 4 shows the dam model mounted on the shaking table. The

base of model was fixed on the shaking table by using steel plate

connected with nut and steel bar. Instrumentation was designed

to measure displacements, strains and accelerations on the model

and from the input actuator. The locations of accelerometer,

strain guage and LVDT for two models are shown in Fig. 5.

The geometry and the mixture proportion for both Model #1

and Model #2 are same, while their tensile behaviors are

different as mentioned in the previous section. In Model #2, the

locations of strain gauges (STR) are changed near the neck

region to observe the cracking.

The test program consisted of two phases: (1) resonance test

Fig. 2. Stress-strain Curves from Tensile Tests: (a) Model #1, (b)

Model #2

Fig. 3. Stress-strain Curves from Compressive Tests: (a) Model

#1, (b) Model #2

Table 6. Properties of Dam Models

Physical & mechanical properties

UnitTargetValue

Actual modelmix at 28 days

Model 1 Model 2

Ultimate compressive strength, f 'c

MPa 0.1-0.15 0.317 0.399

Ultimate tensile strength, ft MPa 0.025

- Direct tensile 0.029 0.054

- Splitting tensile 0.0135 0.0103

Elastic modulus, E MPa 182

- Ec : Compressive test 1,798 906

- Et : Tensile test 13 14

Mass density, ρ kg/m3 2,400 1,907 1,937

Ultimate compressive strain, εc 0.003 0.00139 0.00262

Ultimate tensile strain, εt 0.00012 0.00495 0.00429

Poisson ratio - - 0.203 0.193

Table 7. Relative Error in Physical Properties

Physical & mechanical properties

Relative error (%)*

Harris et al. (2000)

Ghaemmaghami& Ghaemain

(2008)

This study

Model1

Model2

Ultimate compressive strength, f'c

90.1 34.5 153.6 219.2

Ultimate tensile strength, ft

- Direct tensile 16.0 116.0

- Splitting tensile 146.9 -47.7 -46.0 -58.8

Elastic modulus, E

- Ec : Compressive test -32.2 -26.5 887.7 397.7

- Et : Tensile test -92.8 -92.2

Mass density, ρ -10.0 -20.5 -19.3

Ultimate compressive strain, εc

100.0 -53.7 -12.7

Ultimate tensile strain, εt 4,025 3,475

*Relative error (%) = (actual value – target value)/(target value) × 100



and (2) ambient test. First, the resonance test was conducted to

determine the resonant frequency. The model response was

recorded at even frequencies from 2 to 30 Hz with a constant

input acceleration of 0.05 g. Second, the ambient test was con-

ducted to determine the maximum acceleration for the failure

and investigate the crack initiation/propagation. The model was

shaken up to the failure at the lowest resonant frequency, increas-

ing the acceleration amplitude from 0.05 g to failure. In each

step, the acceleration amplitude was increased by 0.0125 g and

held 5 seconds.

4. Test Results

4.1 Resonance Test: Fundamental Mode

The acceleration and normalized relative displacement at the

top of the model along the excitation axis at even frequencies

from 10 to 30 Hz are shown in Figs. 6 and 7, respectively. The

normalized relative displacement (NRD) is defined as:

(4)

In Model #1, the first amplification of acceleration and normalized

relative displacement is noticed around 14-16 Hz and the second

large amplification around 24-28 Hz. In Model #2, the amplifica-

tion is noticed from 14 Hz and large amplification is observed

around 24-28 Hz. This range of amplification can be expected

because of the different mode shapes, for example the same

direction of excitation or out of plane. Harris et al. (2000) showed

the different mode shapes, such as 14 Hz with out of plane and

28 Hz with the same direction of excitation, through the

numerical analysis. They conducted the shaking table test with

the fundamental mode of out of plane, 14 Hz (approximately 2

Hz frequency for the Koyna event).

Based on the resonance tests, two different sinusoidal motions

were chosen for ambient test: 14 Hz for Model #1 and 28 Hz for

NRD %( )

Disp. at the top LVDT 4–( ) Disp. at the bottom LVDT 1–( )–{ }

Disp. at the bottom LVDT 1–( )------------------------------------------------------------------------------------------------------------------------------------------------------ 100×=

Fig. 4. Model Mounted on the Shaking Table

Fig. 5. Instrumentation Locations (unit: m): (a) Model #1, (b) Model

#2

Fig. 6. Resonance Test: Horizontal Acceleration: (a) Model #1, (b)

Model #2


Vol. 19, No. 1 / January 2015 − 147 −

Model #2. Those are scaled to 1.4 Hz and 2.8 Hz frequency events.

In order to investigate the effect of different values of elastic

modulus on the mode shape and frequency, frequency extraction

analysis is conducted by using the finite element software

ABAQUS (2004). The results of mode shape and frequency are

summarized in Table 8. In Table 8, Prototype indicates the results

with real dam size and E=18,200 MPa, while Prototype(scale),

Model #1, and Model #2 indicate the results with the small scale

size and E=182, 13, and 14 MPa, respectively. The mode shapes

are very similar because of the same shape of each model. As

expected from similitude requirements, the frequency of Prototype

is less than ten times than that of Prototype(scale). For Model #1

and Model #2 the frequencies of the first and second modes are

7.55-7.77 Hz and 18.94-19.53 Hz, while 25.06 Hz and 62.84 Hz

for Prototype(scale). It is noted that the frequency of 28 Hz, used

for ambient test of Model #2, is very close to that of the first

mode in Prototype(scale). The frequency of 14 Hz, used for

ambient test of Model #1, is within the range of the frequencies

of the first and second modes in Model #1 and Model #2.

4.2 Ambient Test: Maximum Failure Acceleration and Crack

Initiation/Propagation

4.2.1 Model #1

Two typical acceleration plots at the base accelerations of 0.05

g and 0.0875 g are shown in Fig. 8. It can be seen that the base

acceleration is amplified at the top of the model. Unfortunately,

because of the set up error in measurement limit of the accelero-

meter, the maximum acceleration of the model could not be

observed until the failure. However, the maximum acceleration

at the base of model was anticipated from the input data which

showed about 0.55 g-0.60 g. Fig. 9 shows the crack pattern. The

crack initiated at the slope changing point and propagated around

Fig. 7. Resonance Test: Normalized Displacement at the Top of

Model: (a) Model #1, (b) Model #2

Table 8. Mode Shape and Frequency

ModeModeShape

Frequency (Hz)

Prototype(E=18,200

MPa)(ρ=2,400kg/m3)

Prototype(scale)(E=182 MPa)(ρ=2,400 kg/

m3)

Model #1(E=13 MPa)

(ρ=1,907kg/m3)

Model #2(E=14 MPa)

(ρ=1,937kg/m3)

1a 2.5057 25.057 7.5458 7.7732

2b 6.2837 62.837 18.938 19.530

3 7.2568 72.568 21.904 22.552

4 11.622 116.22 35.037 36.139

Note : ( )a,( )b show in the direction of acceleration load

Fig. 8. Amplification of Acceleration (Model #1): (a) Base Acceler-

ation of 0.05 g, (b) Base Acceleration of 0.0875 g



the neck of model.

4.2.2 Model #2

Model #2 was also tested up to failure using the same method

as Model #1. Two typical acceleration plots at the base accelera-

tion of 0.05 g and 0.625 g are shown in Fig. 10. The crack failure

occurred at the base acceleration of 0.625 g. The acceleration at

the top is about 0.06 g for the base acceleration of 0.05 g, which

shows an amplification factor of 1.2 from the base to the top of

the model. For the base acceleration of 0.625 g, the amplification

factor is 1.3.

Figure 11 shows the variations of acceleration and relative dis-

placement during the testing. It can be seen that the acceleration

at the top was amplified up to 0.8 g and relative displacement is

increased up to 0.9 mm. At the base acceleration of 0.625 g, the

crack was observed at the slope changing point of the model.

The crack propagated around the neck of model as shown in Fig.

12, same as the case of Model #1. Although the different

resonant frequencies were applied to the models (14 Hz for

Model #1 and 28 Hz for Model #2), the crack patterns in both

models were very similar.

4.3 Discussion on Stability of the Prototype Dam

Since tests conducted under the harmonic excitations without

the consideration of reservoir and foundation effects, the inter-

preting of the results for the seismic safety of the prototype dam

should be made with regard to these discrepancies. The sinusoidal

excitations can be useful to estimate the crack initiation and

Fig. 9. Crack Propagation (Model #1): (a) Front View, (b) Side View

Fig. 10. Amplification of Acceleration (Model #2): (a) Base Acceler-

ation of 0.05 g, (b) Base Acceleration of 0.625 g

Fig. 11. Amplification During Testing (Model #2): (a) Horizontal Ac-

celeration at the Base, (b) Horizontal Acceleration at the Top,

(c) Horizontal Relative Displacement


Vol. 19, No. 1 / January 2015 − 149 −

failure.

Ghaemmaghami and Ghaemian (2008) observed the failure of

dam model with 1.67 times greater than the peak acceleration in

Manjil earthquake record. Li et al. (2000) observed fully destroy

of the dam model when the acceleration reached 0.87 g (the

estimated peak horizontal acceleration at the site = 0.1 g) using

the Three Gorges seismic accelerogram. In both tests, the effects

of reservoir and foundation flexibility were neglected.

In this study, the crack was initially occurred by 0.55 g of the

base acceleration for Model #1 and 0.625 g for Model #2. These

values are 1.31-1.49 times greater than the recommended peak

ground acceleration of the maximum credible earthquake of 0.42

g, and 2.2-2.5 times greater than the recommended peak ground

acceleration of the design base earthquake of 0.25 g. Considering

that the testing conducted under the first frequency condition,

those results may demonstrate the safety of dam body due to the

earthquake. Due to the experimental limitations in this study,

however further study on the stability of the proposed dam

including the effects of reservoir, foundation, and earthquake

motion can be recommended.

Considering the effects of reservoir, foundation, and earthquake

motion, many researches (Aidi and Hall, 1989; Loli and Fenves,

1989; Bhattacharjee and Leger, 1993, 1994; Cervera et al., 1995;

Ghrib and Tinawi, 1995; Mao and Taylor, 1997; Ghaemian and

Ghobarah, 1999; Calayir and Karaton, 2005a,b; Mirzabozorg

and Ghaemian, 2005) have attempted to simulate the earthquake

response of concrete dams by using numerical methods. The

most case study of the earthquake response of concrete gravity

dam was Koyna gravity dam which subjected to an earthquake

of magnitude 6.5 on the Richter scale on December 11, 1967.

Most cases have considered the effect of dam-reservoir and/or

dam-foundation interaction by using the finite and/or boundary

element methods. The nonlinear behaviour of the concrete has

been considered by using the discrete crack model, the smeared

crack model, the continuum damage mechanics model and the

plastic damage model.

5. Conclusions

Experimental shaking table tests have been conducted for two

small-scale dam models, which were constructed by using the

bentonite-concrete mixture material to match the similitude re-

quirements between the prototype and the model. The

resonance and ambient tests were conducted to investigate the

fundamental frequency, the maximum failure acceleration and

the crack initiation/propagation. The following conclusions can

be drawn:

1. The bentonite-concrete mixture material was developed to

reduce strength and elastic modulus and match the simili-

tude requirements. Although the value of ultimate tensile

strength is close to the target value, the values of ultimate

tensile strain and elastic modulus show larger relative errors

than those in the previous studies.

2. From the resonance test, different amplification frequencies

were noticed. In Model #1, the first amplification of acceler-

ation and normalized relative displacement was noticed

around 14-16 Hz and the second large amplification around

24-28 Hz. In Model #2, the amplification was noticed from

14 Hz and the large amplification was observed at around

24-28 Hz. These are scaled to 1.4-2.8 Hz frequency event.

3. The crack was initially occurred by 0.55 g of the base accel-

eration for Model #1 and 0.625 g for Model #2, which are

2.2-2.5 times and 1.31-1.49 times greater than the recom-

mended peak ground accelerations of the design base earth-

quake of 0.25 g and the maximum credible earthquake of

0.42 g, respectively.

4. Although the different resonant frequencies were applied

(14 Hz for Model 1 and 28 Hz for Model 2), the crack patterns

in both models were very similar. The crack initiated at the

slope changing point and then propagated around the neck

area.

It should be noted that in this study the effects of reservoir,

foundation, and earthquake motions are neglected due to the

experimental limitations. While the tests conducted under the

period action of horizontal sinusoidal loading, the results in this

Fig. 12. Crack Propagation (Model #2): (a) Side View, (b) Back

View



study can be useful to demonstrate the safety of a dam body and

assess numerical models.

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