paper 11
TRANSCRIPT
International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
Amplification and natural frequencies of Khanpur Dam Project
Dr. Irshad Ahmad1, Syed Kazim Mehdi2, Waseem Khan3, Zahid Shahzad4, M. Shakur5
1 Associate Professor, Department of Civil Engineering, University of Engineering and Technology Peshawar
Pakistan
([email protected], [email protected])
2Director, Seismic Studies, WAPDA, Tarbela Dam Project, Pakistan
3Research Associate, National Center of Excellence in Geology, University of Peshawar
4 Assistant Director (Seismology, WAPDA), Tarbela Dam Project
5Department of Civil Engineering, University of Engineering and Technology Peshawar Pakistan
Abstract
Earthquake records at crest and toe of Khanpur Dam are analyzed in this paper to find dam amplification
factors and first three natural frequencies of the dam. Beam shear model is also used to estimate the dam natural
frequencies. The earthquake data consists of fourteen events recorded from October 10, 2008 to November 15,
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
2010. The records are filtered to remove noise. Amplification factors along the dam x-section vary from 1.2 to
3.7. First three natural frequencies of the dam are found from the ratio of the Fourier amplitude of the crest and
toe. These frequencies are 2.5, 6.5, and 9.0 Hz. Dam natural frequencies are also found from Beam Shear Model
which are 2.6, 6.0, and 9.4 Hz. Natural frequencies from the observed records and analytical model match
closely. It is concluded that damage to dam does not only depend on the peak ground acceleration of the input
motion but also on its frequency content. Therefore frequency content must be considered while selecting time
histories for dynamic analysis of the dam. It is also concluded that the beam shear model can be used to estimate
the dynamic parameters of Khanpur dam.
Keywords: Dam; Amplification; Fourier Amplitude; natural frequency
1. Introduction
Khanpur Dam is located 334431N, 725609E on the Haro River near the town
of Khanpur, Khyber Pakhtunkhwa, Pakistan, about 25 miles (40 km) from Islamabad, Pakistan
(figure-1, and figure 2). It forms Khanpur Lake, a reservoir which supplies drinking water to
Islamabad and Rawalpindi and irrigation water to many of the agricultural and industrial areas
surrounding the cities. The dam was completed in 1983 after a 15 year construction period believed to
have cost Rs. 1,352 million. It is 167 feet (51 m) high and stores 110,000 acre feet (140,000,000 m³)
of water.
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
Figure 1 Arial View of Khanpur Dam
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
Figure 2 Khanpur Dam Reservoir
The x-section of the dam is shown in figure-3. The dam is built of core, filter material, and rocks fill.
Figure 3 Typical cross section of the dam
Khanpur dam lies in seismic zone 2b [1]. The dam is heavily instrumented. The accelerometers
and seismometers are installed on and around the dam. In this research paper strong motion records at
crest and toe of the dam are analyzed. The data consists of 14 records from different earthquakes. The
data contains noise and is, therefore, filtered in SeismoSignal, freely available software for strong
motion data processing. Dam amplification factors are found from the data recorded at crest and toe of
the dam. Fourier amplitudes are also evaluated using Fast Fourier Transform algorithm. First three
natural frequencies of the dam are then found both from the observed records and analytical method.
2. Data processing
The records contained noise. Unprocessed acceleration, velocity, and displacement time histories of
an earthquake recorded at the dam crest on 10/10/2010 are shown in figure 4. It can be seen that the
displacement record is unreasonable and contains permanent dam displacements after the earthquake.
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
Time [sec]242220181614121086420
Acc
eler
atio
n [g
]0.15
0.1
0.05
0
-0.05
-0.1
-0.15
Time [sec]242220181614121086420
Vel
ocity
[cm
/sec
]
4
2
0
-2
-4
Time [sec]24222018161412108642
Dis
plac
emen
t [cm
]
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
Figure 4 Unprocessed time histories
To process the records, a high pass filter of 0.1 Hz, and low pass filter of 25 Hz was selected for band-
pass filter. The frequencies of band pass filter are chosen on the visual inspection of displacement
time histories. The processed records are shown in figure 5.
Time [sec]242220181614121086420
Acc
eler
atio
n [g
]
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
Time [sec]242220181614121086420
Vel
ocity
[cm
/sec
]
4
2
0
-2
-4
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
Time [sec]24222018161412108642
Dis
plac
emen
t [cm
]0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
Figure 5 processed records
It can be seen in figure 5 that the displacement at crest of the dam comes back to zero after the
earthquake is ended. A summary of peak ground accelerations, velocities and displacements recorded
at crest along the dam cross-section are given in table-1.
Table 1 ground motion parameters from processed and unprocessed records
Ground motion parameter Unprocessed Processed
Peak ground acceleration 0.170 g 0.173 g
Peak ground velocity 4.887 cm/sec 4.577 cm/sec
Peak ground displacement 0.511 cm 0.440 cm
All the fourteen records are likewise processed.
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
3. Dam Amplification Factors from records
The dam amplification factor is defined as the ratio between peak ground acceleration (PGA)
recorded at crest of the dam and peak
ground acceleration recorded at toe of
the dam for the same earthquake i.e.
(1)
Amplification factors calculated from all records are listed in table-2. It can be seen that the dam
amplification factors vary from 1.2 to 3.7 depending upon the frequency content of the input motion
(toe records). It can also be noticed from the table-2 that the predominant frequencies of the toe
records vary from 2.6 to 10.0.
Table 2 Earthquake records and dam amplification factors
S.N
O
date of
Earthquake
PGA(g) Dam
AmplificationToe Predominant frequency
(Hz)Toe Crest
1 22/10/2008 0.003 0.008 2.7 10.0
2 4/1/2009 0.004 0.012 3.0 3.3
3 20/2/2009 0.003 0.011 3.7 7.1
4 3/4/2009 0.001 0.001 1.5 5.6
5 6/4/2009 0.001 0.003 2.8 3.3
6 9/4/2009 0.001 0.002 2.1 3.1
7 13/7/2009 0.001 0.002 1.5 5.6
8 27/7/2009 0.003 0.006 1.8 5.0
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
9 29/10/2009 0.003 0.009 2.6 5.6
10 17/9/2010 0.001 0.002 2.2 8.3
11 9/10/2010 0.003 0.003 1.2 8.3
12 10/10/2010 0.077 0.173 2.2 6.3
13 7/11/2010 0.001 0.002 2.0 10.0
14 15/11/2010 0.002 0.006 2.6 2.6
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
4. Natural frequencies of dam from observed records
Natural frequencies of the Khanpur dam are calculated from Fourier amplitude spectra of the
observed records. Natural frequencies from the observed records have been determined by
various researchers [2, 3]. Fast Fourier transformation is used to find Fourier amplitudes. Ratio of
the Fourier amplitudes of the crest and toe records are calculated for each earthquake. The peaks
ordinates correspond to the natural frequencies of the dam. Only four graphs are shown in figure-
6 for four earthquakes.
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
Figure 6 Peaks corresponds to natural frequencies of the dam
Average ordinates of the ratio of Fourier amplitudes for all the fourteen records are shown in
figure 7. As indicated the first three natural frequencies deduced from the figure 7 are f1=2.5 Hz,
f2=6.5 Hz, and f3=9.0 Hz.
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
Figure 7 Average of Fourier amplitude ratios of all 14 records.
5. Analytical Model
Shear beam approach to model the two dimensional response of the dam is used. This model
requires the dam to be triangular in x-section and homogenous [4]. Strictly speaking the shear beam
model is not applicable to Khanpur dam. However, since the dam is only 10.5 m wide at crest, which
is closed to a triangle and the core is larger compared to other components in the dam x-section, the
method can loosely be applied to Khanpur dam. The advantage is simplicity of the method.
To apply the method, we need to estimate the average shear wave velocity of the dam. Shear
wave velocity (Vs) proposed by Swada et al. 1975 [5] are given in table-3. The Vs-profile is plotted in
figure-8. However use of lower bound is recommended [6].
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f1=2.5 Hz
f1=6.5 Hz
f1=9.0 Hz
International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
Table 3 Shear wave velocity equations for dam
Depth (m) Shear Wave Velocity Profiles in Core Zone
(m/sec)
Low Bound Upper Bound
0-5 Vs-210 m/s
5-30 Vs=140 Z0.34 Vs=180 Z0.34
30>
Figure 8 Shear wave velocity profile in the core zone
Using the figure 8 as guideline, shear wave velocity for Khanpur dam is estimated to be 350 m/s.
Idealized model of the dam on which the shear beam method is based is shown in figure 9.
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
Figure 9 Idealized model of the dam
The differential equation governing the free vibration response of dam is:
(2)
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
In the above equation, is the density and G is shear modulus of the dam, z is the depth below
tip, t is time, and u is the horizontal displacement of dam.
The solution of differential equation yields the natural frequencies of the dam
(3)
where j is the natural circular frequency of the dam in the jth mode and j are constants respectively
equal to 2.4, 5.52, and 8.65 for the first, second, and third mode.
Using equation-3, the first three natural frequencies of the dam are estimated to be:
f1=2.6 Hz, f2=6.0 Hz, and f3=9.4 Hz.
6. Conclusions
The following points are noted in this paper.
1. The amplification factors for dam vary from 1.2 to 3.7. This means that damage to dam does
not only depend on the peak ground acceleration of the input motion but also on its
frequency content. It is therefore strongly recommended to consider frequency content of the
input motion in the selection of time histories for dynamic analysis of dam.
2. The first three natural frequencies of the dam from the observed records are found to be 2.5,
6.5, and 9.0 Hz.
3. The first three natural frequencies of the dam from shear beam model are 2.6, 6.0, and 9.4
Hz.
4. The frequencies from the observed records and analytical method match closely. This means
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International Conference on Earthquake Engineering and Seismology (ICEES 2011), NUST, Islamabad, Pakistan
April 25-26, 2011
that the beam shear method can be employed to find the dynamic response of Khanpur dam.
References
[1] Building Code of Pakistan, Seismic Provisions, 2007.
[2] Ueda M., Toyoda Y., Shiojiri H., and Satou M., “Resonant frequency of concrete arch dam
evaluated from observational in-situ records and effects of contraction joints on these
features”, Proceedings Japan Society of Civil Engineering, 2000, issue 654, pp 207-222.
[3] Castro R.R., Mucciarelli M., Pacor F., Federici F., and Zaninetti A., “Determination of the
Characteristic frequency of two Dams located in the region of Calbria, Italy”, Bulletin of the
Seismological Society of America, Vol. 88, No. 2, pp. 503-511, April 1998.
[4] Kramer, S.L. “Geotechnical Earthquake Engineering”, Prentice Hall
[5] Sawada, Y. and Takahashi, T., “Study on the material properties and the earthquake
Behaviors of rockfill dam,” Proc. of 4th Japan Earthquake Engineering Symposium,
Pp.695-702, 1975.
[6] Ik So, H., and Byung-Hyum, O., “Applicability of the existing empirical method for
evaluating shear wave velocity in core zone to Korean dam sites”
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