Prediction of seismic motion at engineering
bedrock based on earthquake records andnumerical analysis
N Yasuda*, Z Cao† & Y Kobayashi‡

Abstract: In Japan, dam safety against large-scale earthquakes is verified by numericalanalysis. Seismic motion defined for verification of the seismic performance of a dam is set basedon the distance attenuation formula, which is obtained by statistical analysis of the earthquake
records of many dams, the empirical Green’s function method, and a method of adjusting
ground motion records to the stipulated lower-limit acceleration response spectrum.
Generally, the input seismic motion for earthquake response analysis is prepared by pullingthe seismic motion back to the engineering bedrock, hypothesized by a numerical analysis
method. However, lack of precise criteria for setting engineering bedrock for earthquake
response analysis, the appropriateness of the preparation method of the seismic motion, andof the prepared input seismic motion, are not necessarily clarified. This study predicts theseismic motion of deep bedrock using earthquake acceleration recordings from the Tokachi
offshore earthquake of 2003 (M. 8.0) inside bedrock at a depth of 57m below the bottom of
Satsunaigawa Dam, which is equipped with 8 seismographs. Based on the results from theresearch it was concluded that, in the case of concrete gravity dams, engineering bedrock should
be set at a depth equal to approximately 1.5 times the dam’s height, and where the shear
wave velocity of the bedrock should be no less than 2000m/sec. Then, a procedure forpreparing input seismic motion for earthquake response analysis is proposed.

Keywords: Concrete dam, engineering bedrock, earthquake records, seismic motion.

1. Introduction
Earthquake response analysis of a dam in order to verify its seismic performance is often carried out using the following flow: firstly, estimating the seismic motion of the bottom surfaceof the dam, or open bedrock, by applying either the empirical method[1], or semi-empiricalmethod[2,3,4], then predicting the seismic motion of the engineering bedrock, hypothesized bya pull-back calculation of the wave. Naturally, thepredicted seismic motion of the engineering bedrockis dependent on conditions of the analysis model,
and is nothing more than a numerical analysis. The
earthquake response of the foundation bedrock, theAuthor information: [*]Japan Dam Engineering
Center (JDEC), 2-9-7 Ikenohata, Taito-ku, Tokyo
110-0008, Japan, Email: yasuda@jdec.or.jp,
Webpage: www. jdec.or.jp; [†]JP Business Service
Corporation; [‡]Japan Dam Engineering Center

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surrounding natural ground, and the dam body, excited by the input seismic motion, are notnecessarily clarified. Furthermore, verification of the seismic performance of the dam, based on
the analysis results, has several matters to be resolved. Because, on the other hand, it is difficult
to directly measure seismic motion in deep bedrock, almost no effort has been made in thefield of dam engineering to verify the setting of seismic motion for engineering bedrock.
Satsunaigawa Dam is a concrete gravity dam with a height of 114m. Three-direction
component seismographs have been installed at the locations shown in Figure 1, and havecollected several sets of earthquake records since the dam was completed in 1996. The
seismograph placed at a depth of 57m beneath the bottom surface of the dam has, in particular,
obtained valuable records inside the bedrock. Seismographs are also installed inside the rimtunnels of both banks. The dynamic properties and dynamic behaviour of the dam were studied
based on numerical analysis using earthquake records[5]. This study aims to contribute tosetting the input seismic motion in order to verify future seismic performances of dams. Based onearthquake records obtained at multiple monitoring points at the Satsunaigawa Dam site, theseismic motion of the deep bedrock is predicted by a numerical analysis method. Simultaneously,
the criteria for setting engineering bedrock, and the preparation methods for inputting seismic
motion for earthquake response analyses of a dam are investigated.

Figure 1. Location of the seismographs at Satsunaigawa Dam (downstream side)

2. Investigation Method and Conditions
2.1 Investigation method
The following points must be considered when setting engineering bedrock:(1) Seismic motion in engineering bedrock is almost immune to the effects of the dynamic
behaviour of the upper ground structure and the dam, so seismic motion at any location on
the same elevation of the foundation bedrock is almost identical;

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EARTHQUAKE RECORDS AND NUMERICAL ANALYSIS(2) When there are earthquake records at multiple monitoring points, including natural
ground, it is possible to predict the seismic motion of engineering bedrock based on theserecords. Inversely, when the estimated seismic motion of engineering bedrock has been input,
the dynamic response at all monitoring points must be reproduced.
According to these premises, in this study the earthquake response analysis of a 3D damfoundation bedrock-reservoir system was performed in order to reproduce the behaviourof Satsunaigawa Dam and its foundation bedrock during the Tokachi offshore earthquake,
which occurred on 26th September 2003. Four items were considered concerning reproducibility,
i.e. maximum acceleration, accelerogram, Fourier spectrum, and transfer function. To improve
the reproducibility of the observed dynamic behaviour, the physical properties of the dam
and foundation bedrock were repeatedly adjusted. Through this process the seismic
motion of the engineering bedrock, which was assumed to be 171m below the bottom
surface of the dam, was sequentially estimated. Figure 2 shows the investigation flow. By
considering the seismic motion inside the bedrock when the earthquake record for eachmonitoring point was reproduced, setting the criteria and appropriate method for creating
seismic motion at the engineering bedrock in order to retrieve the earthquake response
analysis of a dam was proposed.

Figure 2. Investigation flow

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2.2 Investigation conditions(1) Earthquake record: During the earthquake acceleration records were obtained from eachseismograph (shown in Figure 1). The accelerations and Fourier spectra at the lower point of
the bedrock (F1) are shown in Figure 3 and Figure 4, respectively, as examples.
(2) Model used for the investigation: Figure 5 shows the model used for this study. The
geology and detailed topography of the foundation bedrock are taken into account in theanalysis model. Viscous boundaries[6] were set as the side and bottom surface boundaries ofthe foundation bedrock model, and the extent of ground spreading infinitely outside theanalysis range was considered.
(3) Physical properties: For the dam concrete, as a linear material, its elastic modulus anddamping coefficient were adjusted to most accurately reproduce the dam’s behaviour during
the earthquake. The damping coefficient was obtained by the half power method using theearthquake records[5], and the elastic modulus of the dam’s concrete was adjusted, startingwith the design value. Table 1 shows the physical properties of the dam concrete definedconclusively. Of these, the density and Poisson’s ratio are the results of quality control testing
during dam execution.

Table 1. Physical properties of the dam concrete

The foundation bedrock is also considered to be a linear material. Its physical properties
were obtained from seismic velocity (PS) logging and rock testing, but the damping coefficient
was finely adjusted so that it would be possible to accurately reproduce the behaviour of themonitoring points of the concerned foundation bedrock during the earthquake. Ultimately,
its physical properties were defined as shown in Table 2.

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Figure 3. Earthquake records below
the bedrock (F1)Figure 4. (F1) Fourier spectra bedrock

Figure 5. Model used for the study

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Table 2. Physical properties of the foundation bedrock(4) Input seismic motion: The input seismic motion at the bottom surface of the model(hypothesized engineering bedrock) was prepared based on the pull-back method[7,8] of the 3D
seismic motion using earthquake records from the lower points of the bedrock (F1), which isimmune to the effects of the vibration of the dam and surrounding natural ground. Figure 6
shows the procedure image, and a detailed description is given in references [7] and [8].

Figure 6. Preparing the input seismic motion

3. Results of Reproduction Analysis of Dynamic
Behaviour of the Dam and Foundation Bedrock
The earthquake motions at each monitoring point on the dam body and foundation bedrock
were successfully reproduced by numerical analysis with relatively good precision. The
maximum accelerations at each monitoring point are summarized in Table 3. As examples,
Figure 7 shows the acceleration response time histories at the dam crest (T) and upper pointof the bedrock (F2), and Figure 8 shows the Fourier spectra and transfer functions of theseacceleration responses.
The differences between the maximum acceleration responses and recorded accelerations at
the dam crest (T2) and upper point of the bedrock (F2) are scattered according to direction
but, as shown in Figure 7, the accelerograms generally coincide with each other. Figure 8

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shows that the Fourier spectra and transfer functions of the calculated acceleration response,
and the recorded accelerations at these two locations, are extremely close. The calculated
and recorded results for the left bank (T1) and right bank (T3) also closely conform and,from the results these generally reproduced, both the natural ground on the left bank (R1)
and the right bank (R2) were obtained. The reasons for good reproducibility of the analysis are
assumed to be the fact that the analysis model reflects detailed topographical and geologicalinformation, and the physical properties were precisely defined.

Table 3. Maximum accelerations at each monitoring point resulting from reproduction analysis
Note: *Error = (analysis value – observed value)/observed value

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Figure 7. Comparison of acceleration at dam crest and dam base during reproduction analysis

Figure 8. Comparison of Fourier spectra and transfer functions at dam crest and theupper point of bedrock (recorded and calculated)
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4. Seismic Motions Inside Bedrock and atEngineering Bedrock
4.1 Seismic motions inside bedrock
When the earthquake motions at all monitoring points on the dam body and inside thefoundation bedrock had been reproduced by numerical analysis, it was assumed that theearthquake response deep in the foundation bedrock model approximated the actual
seismic motion without the effects of the vibrations of the dam body and surrounding natural
ground. Accelerations at a total of 18 points on two horizontal planes, as shown in Figure 9a,
were calculated. The time histories and Fourier spectra of the calculated accelerations at
each location considered in the stream direction and axial direction (see Figure 9b) werecompared on each plane.

(a) Depth of the plane considered(b) Points on each plane considered

Figure 9. Locations of calculated accelerations inside the bedrock

In order to clearly compare the accelerograms at different locations, 10 seconds (20.01 to
30.0 seconds) of main motion were extracted from the total time history (length 81.92 seconds).
Figure 10 shows the main motions of three components at three locations on the F1 plane(depth of 57m from the bottom surface of the dam) of the dam axis section. Comparing withthe lower point of the bedrock (F1), the accelerations at both sides (L1 and R1) are slightly
larger in three directions, and the phase difference appeared partially in time histories. This
result is assumed to be the disturbance of the seismic motion in the bedrock of this depth by
the influence of the dynamic behaviour of the dam and natural ground on both sides.
Figure 11, on the other hand, shows the main motion at three locations on the bottom planeof the model (depth of 171m below the bottom surface of the dam). At this depth, the relative
error of the maximum acceleration at three locations was quite small, and its phases conformed
throughout almost the entire time history. For this reason, it is assumed that the depth of theengineering bedrock for analysis should be set at least 1.5 times the dam height (171m inthis model), and that the seismic motion at this location will be almost unaffected by the
behaviour of the dam and natural ground during the earthquake.

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4.2 Seismic motion at engineering bedrock
As stated in the previous section, seismic motion on the bottom surface of the model, at a
depth of 171m, is almost immune from the influence of the dynamic behaviour of the dam
or natural ground, so this depth (Figure 9a) can be set as the engineering bedrock. Figure 12
shows waves (E+ F waves) at the intra-layer at this location, obtained by reproduction analysis.
This is considered to be similar to the actual seismic motion generated in deep bedrock by
the Tokachi offshore earthquake. Figure 13 shows the outcrop waves (2E waves) on the
open bedrock surface (Figure 9a) at this location. It is possible to reproduce the dynamic
behaviour at each monitoring point on the dam body, and on the foundation bedrock, by
inputting this wave so it can be considered to be the seismic motion at the engineering bedrock.

Figure 10. Comparison of seismic motion on F1 plane

Figure 11. Comparison of seismic motion on bottom of model

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EARTHQUAKE RECORDS AND NUMERICAL ANALYSISThe hypocenter of the 2003 Tokachi offshore earthquake was 45km deep, at an epicentral
distance of 150km downstream of Satsunaigawa Dam. Figure 14 shows the relative locational relationship of the hypocenter and the dam. The vibration components of stream direction
and vertical direction at the dam site are based on a synthesis of P waves and SV waves of theseismic motion, and the axial direction is almost exactly parallel to the vibration direction of
the earthquake’s SH wave. Thus, as shown in Figure 12 and Figure 13, the main seismic
motion in the stream direction and vertical direction at Satsunaigawa Dam appear to havearrived a little earlier than the axial direction component. On the other hand, the amplitudeof the seismic motion in the axial direction or, in other words, of the SH wave component,
was a little larger than the other two components.
From the above it is assumed that at Satsunaigawa Dam the appropriate location of theengineering bedrock for earthquake response analysis is in deep bedrock, at a depth 1.5 times
the dam height, and where the shear wave velocity is about 2000m/sec. The preparation
method of the hypothesized seismic motion at the engineering bedrock is to identify the analysis
model by reproducing the earthquake records at multiple monitoring points following theinvestigation flow in Figure 2, then performing the pull-back calculation of the seismic motion
as explained in Section 2.2(4). Rightly, the analysis model used must reflect the geology andtopography of the foundation bedrock.

Figure 12. Seismic motion at intra-layer,
171m deep

Figure 13. Seismic motion at engineering
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N YASUDA, Z CAO & Y KOBAYASHIFor past analysis relating to the verification work of the seismic performance of a dam,the input seismic motion was prepared by a method of the dam distance attenuation formula,the empirical Green’s function method, or the method of adjusting an earthquake record to
the lower limit acceleration response spectrum for verification. Seismic motion at foundation
bedrock obtained through this study can contribute to the verification of these preparation
methods for input seismic motion.

Figure 14. Relationships of seismic motion directions and orientations of the dam

5. Summation
This study clarifies the following:(1) The physical properties of Satsunaigawa Dam were identified by preparing an analysis
model based on detailed topographical data and geological information in order to perform
reproduction analysis of the dam’s dynamic behaviour during the Tokachi offshore earthquakeof 2003. The analysis succeeded in precisely reproducing the earthquake records at multiple
monitoring points on the dam body and foundation bedrock, and predicting the seismic
motion in deep bedrock, particularly at engineering bedrock.
(2) As a criteria for setting the position of engineering bedrock, in the case of a concrete gravity
dam, engineering bedrock should be set at a depth equal to 1.5 times the dam height, andwhere the shear wave velocity is at least 2000m/sec.
(3) Seismic motion at engineering bedrock should be prepared using the pull-back calculation
method using an analysis model identified by the reproduction of the earthquake records at
multiple monitoring points.
(4) The seismic motion at engineering bedrock produced by this study can help verify seismic
motion preparation methods that have been widely-used for the verification of the seismic
performance of dams.

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Earthquake Engineering Symposium,
pp151-156 (1986).
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[4] Kamae, K, Irikura, K & Fukuchi, Y,‘Prediction of strong ground motion basedon scaling law of earthquake’, Journal of
Structural & Construction Engineering, No.
430, pp1-9 (1991).
[5] Yasuda, N, Shimamoto, K et al, ‘3Dseismic response analysis of concrete
gravity dam - Satsunaigawa dam analysis’,

Memorandum of National Institute forLand & Infrastructure Management, No.
429 (2007).
[6] Cao, Z & Saotome, A, ‘Analytic methodof method of 3D soil-structure system withthe viscous boundaries considering thevertical motion, Proceedings, 15th World
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No. 0598 (2012).
[7] Yasuda, N, Matsumoto, N & Cao, Z,‘Study on the mechanism of the peculiar
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[8] Cao, Z, Matsumoto, N, Tardieu, B, Fry,
J J, Bourdarot, E & Robbe, E, ‘Practicalguide for selection seismic parameters
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