cfrd dynamic analysis

8/9/2019 CFRD Dynamic Analysis

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21st Century Dam Design —

Advances and Adaptations

31st Annual USSD Conference

San Diego, California, April 11-15, 2011


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On the CoverArtist's rendition of San Vicente Dam after completion of the dam raise project to increase local storage and provide

a more flexible conveyance system for use during emergencies such as earthquakes that could curtail the region’s

imported water supplies. The existing 220-foot-high dam, owned by the City of San Diego, will be raised by 117

feet to increase reservoir storage capacity by 152,000 acre-feet. The project will be the tallest dam raise in the

United States and tallest roller compacted concrete dam raise in the world.

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advertising or promotional purposes and may not be construed as an endorsement of any product or

from by the United States Society on Dams. USSD accepts no responsibility for the statements made

or the opinions expressed in this publication.

Copyright © 2011 U.S. Society on Dams

Printed in the United States of America

Library of Congress Control Number: 2011924673ISBN 978-1-884575-52-5

U.S. Society on Dams

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Denver, CO 80202

Telephone: 303-628-5430

Fax: 303-628-5431

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To be the nation's leading organization of professionals dedicated to advancing the role of dams

for the benefit of society.

Mission — USSD is dedicated to:

• Advancing the knowledge of dam engineering, construction, planning, operation,

performance, rehabilitation, decommissioning, maintenance, security and safety;

• Fostering dam technology for socially, environmentally and financially sustainable water

resources systems;

• Providing public awareness of the role of dams in the management of the nation's water

resources;

• Enhancing practices to meet current and future challenges on dams; and

• Representing the United States as an active member of the International Commission onLarge Dams (ICOLD).


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Earthquake Response of Rockfill Dam 1451

EARTHQUAKE RESPONSE OF ROCKFILL DAM WITH ASYMMETRIC PLAN

GEOMETRY OF UPSTREAM AND DOWNSTREAM SLOPE WITH RESPECT

TO DAM AXIS

Ik-Soo, Ha1

ABSTRACT

Two-dimensional dynamic analysis for the maximum section of a dam cannot consider

the canyon effect, because it is carried out in the plane strain condition. Also, if the plan

geometry of upstream and downstream slope is not symmetrical with respect to the dam

axis, the results of 2-D analyses cannot accurately represent dynamic response of the dam

to earthquake. In this study, three-dimensional dynamic analyses for Miryang multi-

purpose dam (concrete-faced rockfill type) in South Korea, with asymmetric plan

geometry of upstream and downstream slope with respect to the dam axis, were carried

out and the response of the dam was analyzed. The results of 3-D dynamic analyses were

compared with those of 2-D plane strain dynamic analyses. It was found that themaximum settlement did not appear at the maximum cross-section and the magnitude of

maximum settlement obtained by 3-D analysis was different from that by 2-D analysis

for the maximum cross-section. Furthermore, it was found that the characteristics of

acceleration amplification obtained by 3-D analysis were different from those by 2-D

analysis. This study presents an insight in the earthquake response behaviors of a rockfill

dam with the asymmetric plan geometry of upstream and downstream slope with respect

to the dam axis. It can also be used as fundamental data for seismic stability and design

for rockfill dams with asymmetric plan geometry of upstream and downstream slope.

INTRODUCTION

According to the previous researches (Hatanaka, 1955; Ambraseys, 1960; Makdisi, 1976),

one of the canyon effects for dynamic response of a dam is to increase the stiffness of the

system. This effect can increase the fundamental frequency of the dam located at the

canyon compared to that of the dam under plane strain condition. Shown in Figure 1 is

the ratio between first or fundamental natural frequencies computed from 3-D and 2-D

models of the dams analyzed in the previous study (Ambraseys, 1960) as a function of

the crest to height ratio, L/H. The fundamental frequency of the dam with a crest length

to height ratio of more than 3 computed from 3-D model is 10 to 20 percent higher than

those computed from a plane strain analysis of the dam. The higher frequencies obtained

from the 3-D models are mostly the result of a stiffening effect of canyon geometry. Thus,

two-dimensional dynamic analysis for the maximum section of a dam cannot consider thecanyon effect, because it is conducted in the plane strain condition.

1Principal Researcher, Dam Safety Research Center, Korea Water Resources Corporation, Daejeon,

Republic of Korea, [email protected]


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21st Century Dam Design — Advances and Adaptations1452

0

1

2

3

4

1 2 3 4 5 6 7

Dam Length/Height

f 3 D

/ f 2

D

Figure 1. Comparison between Natural Frequencies Computed from 2-D and 3-DAnalyses of Dams in Rectangular Canyons

In this study, the meaning of a symmetric plan geometry of upstream and downstream

slope with respect to the dam axis is that the length of the toe line of the upstream slope is

almost the same as that of the downstream slope and the straight line connecting the

center of the upstream slope toe line and the downstream slope toe line is nearly

perpendicular to the dam axis. If the plan geometry of the upstream and downstream

slopes of a dam does not satisfy the above condition, it is regarded as a dam with

asymmetric plan geometry of the upstream and downstream slope with respect to the dam

axis, as shown in Figure 2. If the plan geometry of the upstream and downstream slopes

of a dam is not symmetrical with respect to the dam axis, the results of 2-D dynamic

analyses using the maximum section for the dam cannot accurately represent dynamic

response to earthquake.

In this study, three-dimensional dynamic analysis for Miryang multi-purpose dam in

South Korea, with asymmetric plan geometry of upstream and downstream slopes with

respect to the dam axis, was conducted and the response (such as the settlement of the

crest and acceleration with depth) was analyzed. The results of 3-D dynamic analysis

were compared with those of 2-D dynamic analysis. On the basis of this comparison,

points to be considered when evaluating the response of a dam by 2-D dynamic analysis

were discussed.


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Figure 2. Plan View of Miryang Dam with asymmetric plan geometry of upstream and

downstream slope with respect to the dam axis

SYNOPSIS OF NUMERICAL MODELING AND ANALYSIS

Dam Profile

The dimensions of Miryang dam are 89m in height and 394.3m in length, as shown in

Figure 2 (plan view) and Figure 3 (cross-section). Dam type is a concrete-faced rockfill

dam.

Figure 3. Maximum Cross-section of Miryang Dam


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Analysis Program and Boundary Condition

To conduct the 3-D and 2-D dynamic analysis, FLAC3D (ver.3.1, Itasca Consulting

Group) and FLAC2D (ver.4.0, Itasca Consulting Group) were used, respectively.

Numerical analysis of the seismic response of surface structures such as dams requires

the discretization of a region of the material adjacent to the foundation. The seismic inputis normally represented by plane waves propagating upward through the underlying

materials. The boundary conditions at the sides of the model must account for the free

field motion that would exist in the absence of the structure. The free field boundary

condition is to enforce the free-field motion in such a way that boundaries retain their

non-reflecting properties – i.e., outward waves originating from the structure are properly

absorbed. As shown in Figure 4, the lateral boundaries of the main grid are coupled to the

free-field-grid by viscous dashpots to simulate a quiet boundary.

Figure 4. Model for Seismic Analysis of Dam and Free-field Mesh

Input Motion

Due to the lack of earthquake data in South Korea, time history records from other

location (Tokachi-oki earthquake in Japan, 1968) were used for the analysis. This original

ground motion was modified by reducing the peak acceleration, 0.17g, to 0.154g in order

to match the Dam Earthquake Design Standard of South Korea. Figure 5 shows the input

earthquake time history records used in this study. The input motion was assumed to act

in the upstream-downstream direction of the dam (perpendicular to dam axis).


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Figure 5. Input Acceleration Time History used in This Study

Input Parameters

A Mohr-Coulomb failure criterion and constitutive model were used to simulate the

behavior of dam materials such as rockfill and bedrock. The parameters for static analysis

were obtained from the Design and Construction Report and are presented in Table 1.

After the completion of the static analysis and initialization of the displacement and

velocities, the dynamic analysis was carried out. The material properties of bedrock for

the dynamic analysis were obtained from Table 1, as for the static analysis.

Table 1. Input Parameters for Static Analysis (from Design and Construction Report)

Material Unit weight

(kN/m3)

Bulk modulus

(kN/m2)

Shear modulus

(kN/m2)

Friction

angle (°)

Cohesion

(kN/m2)

Rockfill zone 20 6.46E4 2.98E4 41 0

Bed rock 26 1.67E7 1.25E7 45 2000

For the purpose of obtaining the maximum shear modulus for rockfill material, a HWAW

(Harmonic Wavelet Analysis of Waves) survey was conducted, as shown in Figure 6. The

shear modulus for rockfill material was computed by the following relationship:

'1000max,2max mk G σ ⋅⋅= ( 'mσ in Pa) (Vrymoed, 1981) (1)

in which Gmax= the shear modulus, in Pa, at small shear strains (10-4

%), k 2,max = the shear

modulus parameter at small strains (10-4

%), and 'mσ = the mean effective confining

pressure, in Pa. The mean effective confining pressure was computed using the results

from the static numerical analysis.

In this study, for the purpose of evaluating the shear modulus of rockfill zone which must

reflect the effect of the confining pressure with depth, the repeated 2-D static numerical

analyses for the various k 2,max were carried out. After the completion of each static

analysis for a certain value of k 2,max, shear moduli of 2-D model elements with depth

were extracted, as shown in Figure 7. The extracted shear moduli were changed into

shear wave velocities using equation (2). From this procedure, shear wave velocity


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profiles with depth for each k 2,max can be obtained like Figure 8. From Figure 8, we can

find that the shear wave velocity profile obtained by HWAW survey is almost similar to

that obtained by static analysis using a k 2,max of 180. So, this value, 180, for k 2,max is

representative of the rockfill material for 3-D dynamic analyses.

ρ maxGv s = (2)

in which = density (= / g , =unit weight, g= acceleration of gravity).

Figure 6. HWAW Survey carried out at Miryang Dam Slope Surface and Dam Crest

Figure 7. Extraction of Shear Moduli by Static Numerical Analysis


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Figure 8. Shear Wave Velocity Profile with Depth Evaluated by HWAW Surveys and by

Repeated Dynamic Analyses

However, this value, 180, is not representative of rockfill material for 2-D dynamic

analysis. In order to approximate the actual three-dimensional behaviors of the dam by

two-dimensional techniques, the stiffness of the dam must be strengthened artificially

(Vrymoed, 1981). That is, the shear moduli in the rockfill zone must be artificiallymodified to satisfy the condition that the fundamental frequency computed by two-

dimensional dynamic analysis is the same as that by three-dimensional dynamic analysis.

Therefore, to determine the shear moduli of the rockfill zone for 2-D dynamic analysis, 2-

D dynamic analyses were repeated for various k 2,max values that were higher than 180.

Figure 9 shows the computed acceleration time history at the crest during free vibration

only by 3-D dynamic analysis using a k 2,max of 180 and by 2-D dynamic analysis using a

k 2,max of 280. Figure 10 shows the FFT (Fast Fourier Transform) results for acceleration

histories shown in Figure 9. From Figure 10, it can be found that the fundamental

frequency of the 3-D dynamic analysis using a k 2,max of 180 is 3.3Hz and the fundamental

frequency of 2-D dynamic analysis using a k 2,max of 280 is 2.7Hz. Also, it can be found

that the ratio of fundamental frequency computed from the 3-D model to that from the 2-D model is about 1.2. Therefore, we can regard this value of k 2,max as the representative

value of rockfill material for 2-D dynamic analysis.


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-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 16

tim e(sec)

a c c e

l e

r a t

i o n

( g

)

2D crest(max section)

3D crest(max section)

Figure 9. Acceleration Histories at the Crest of 2-D Maximum Section and 3-D

Maximum Section during Free Vibration Only

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 5 10 15 20

Frequency(Hz)

F o u r

i e r A m

p l i t u

d e

( g - s e

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0 5 10 15 20

Frequency(Hz)

F o u r

i e r A m

p l i t u

d e

( g - s e

(a) (b)

Figure 10. Fourier Amplitude Spectra for Computed Crest Free Vibration Motion: (a) by

2-D Dynamic Analysis, (b) by 3-D Dynamic Analysis

Three Dimensional and Two Dimensional Finite Difference Grid

Figure 11 and Figure 12 show the three-dimensional finite difference grid and the two-

dimensional finite difference grid of the Miryang dam, respectively.


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Figure 11. Finite Difference Grid for 3-D Dynamic Analysis of Miryang Dam

Figure 12. Finite Difference Grid for 2-D Dynamic Analysis of Miryang Dam

RESULTS AND DISSCUSSIONS

Settlement

Figure 13 shows settlement time histories computed by 2-D and 3-D dynamic analyses.

At the mid point of the crest of the dam at the maximum section, the settlement computed

by 3-D analysis is quite similar to that by 2-D analysis. It is very interesting that the

maximum settlement at crest midpoint of the dam did not occur at the maximum section,

Rather, the maximum settlement occurred at the section about 50m away from the

maximum section toward the left abutment or at the section about 50m away from the

maximum section toward the right abutment.

Figure 14 shows permanent settlement along the dam axis at the crest computed by 3-D

analysis and that at the crest midpoint by 2-D dynamic analysis. We can see the same

interesting point in Figure 14. The maximum settlement at crest midpoint occurred at thesection about ±50m away from the maximum section. Figure 15 shows the results of

Figure 14 three-dimensionally. From Figure 14 and Figure 15, it is found that the

settlement at the crest of a dam with asymmetric plan geometry of upstream and

downstream slope with respect to the dam axis occurred very asymmetrically.

From the results of Figure 11, Figure 12, and Figure 13, it is also important to note that

the settlement at the crest of a dam with asymmetric plan geometry of upstream and


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downstream slope with respect to the dam axis computed by 2-D dynamic analysis using

the maximum section might give engineers non-conservative results of the magnitude of

the maximum crest settlement.

Figure 13. Settlement Time Histories Computed by 2-D and 3-D Dynamic Analysis

Figure 14. Permanent Settlement along the Dam Axis at the Crest Computed by 3-D

Analysis and that at the crest by 2-D Analysis


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Figure 15. Distribution of Permanent Settlement at the Crest Computed by 3-D Analysis

Acceleration Response

Figure 16 shows acceleration time histories for crest midpoint at each section computed

by 3-D analyses and computed by 2-D analysis. Figure 17 shows acceleration

amplification along the dam elevation for each section computed by 3-D dynamic

analysis and that by 2-D dynamic analysis.

From Figure 16 and Figure 17, it is found that the patterns of acceleration amplification

for the dam with asymmetric plan geometry of upstream and downstream slopes with

respect to the dam axis are similar at each section of the 3-D model and at the maximum

section of the 2-D model but the extent of amplification is different at each section; the

maximum amplification occurred at the maximum section. Also, it is found that if 2-D

analysis is conducted by procedures described in this study, the characteristics of

acceleration amplification evaluated by 2-D analysis might approximate those by 3-D

analysis.


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Figure 16. Acceleration Time Histories for Crest Midpoint at Each Section Computed by

3-D Analyses and at the crest Computed by 2-D Analysis

Figure 17. Acceleration Amplification along the Dam Elevation for Each Section

Computed by 3-D Analyses and that by 2-D Analysis


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CONCLUSIONS

In this study, 3-D dynamic analysis for Miryang multi-purpose dam in South Korea, with

asymmetric plan geometry of upstream and downstream slope with respect to the dam

axis, was conducted and the response (such as the settlement of the crest and acceleration

with depth) was analyzed. The results of 3-D dynamic analysis were compared with thoseof 2-D dynamic analysis. From the results of this research, the following conclusions

were made:

1. The maximum settlement at crest midpoint of the dam did not occur at the maximum

section. Rather, the maximum settlement occurred at the section about 50m away

from the maximum section toward the left abutment or at the section about 50m away

from the maximum section toward the right abutment. The settlement at the crest of a

dam with asymmetric plan geometry of upstream and downstream slope with respect

to the dam axis occurs very asymmetrically. It is also important to note that the

settlement at the crest of a dam with asymmetric plan geometry of upstream and

downstream slope with respect to the dam axis computed by 2-D dynamic analysisusing the maximum section may give non-conservative results.

2. The patterns of acceleration amplification for the dam with asymmetric plangeometry of upstream and downstream slope with respect to the dam axis are similar

at each section along the dam axis of the 3-D model and at the maximum section of

the 2-D model, but the extent of amplification is different at each section; the

maximum amplification occurred at the maximum section. If two-dimensional

analysis is conducted by the procedures described in this study, the characteristics of

acceleration amplification evaluated by 2-D analysis might approximate those by 3-D

analysis.

ACKKNOWLEDGEMENT

This study was supported by a grant from the Construction Technology Innovation

Program (CTIP) funded by the Minister of Land, Transport, and Maritime Affairs

(MLTM) of the South Korean government. This financial assistance is gratefully

acknowledged. Special thanks are to John Stoessel and Tom Brown for their revisions and

helpful suggestions.

REFERENCES

Ambrasey, N.N., “On the shear response of a two dimensional wedge subjected to an

arbitrary disturbance,” Bulletin of the Seismological Society of America, Vol. 50, pp.45-

56, 1960.

Hatanaka, M., “Fundamental considerations on the earthquake resistant properties of the

earth dam,” Bulletin No. 11, Disaster Prevention Research Institute, Kyoto Univ., Japan,

1955.


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Itasca, “FLAC – Fast Lagrangian Analysis of Continua, Version 4.0, user’s guide,”

Itasca Consulting Group, Inc., Minneapolis, Minnesota, 2000.

Makdisi, F.I., “Performance and analysis of earth dams during strong earthquake,”

Thesis presented of the University of California at Berkeley, 1976.

Mejia, L.H. and Seed, H.B., “Three dimensional dynamic response analysis of earth

dams,” Report No. UCB/EERC-81/15, Univ. of California, Berkeley, California, 1981.

Vrymoed, J., “Dynamic FEM model of Oroville dam,” Journal of Geotechnical

Engineering, Vol. 107, No. 8, pp.1057-1077, 1981.

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