Earthquake Analysis, Design, and

Safety Evaluation of Concrete Gravity

Dams

Electricity Generating Authority of Thailand

Bangkok, Thailand

December 7-8, 2010

Anil K. Chopra

University of California, Berkeley

2

Earthquake Performance of Koyna

Dam

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3

Traditional Design Procedures

• Lateral

Earthquake

Forces

• Design Criteria–Factors of safety against

•Overturning

•Sliding

•Overstressing in compression

–At most small tension permitted•Cracking possibility not considered

• Stresses generally do not control design

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Koyna Dam

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Koyna Dam - Sections

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Koyna Dam – Plan and Elevation

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Accelerogram Recorded at Block 1-A of

Koyna Dam on Dec. 11, 1967

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Locations of Cracks in Koyna Dam Caused by Earthquake

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Koyna Dam: Downstream Face

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Koyna Dam: Construction of Butresses

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Koyna Dam After Adding Butresses

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Computed Stresses v’s Concrete

Strength in Koyna Dam

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Limitations of Traditional Design

Procedures

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Traditional Design Procedures

• Lateral

Earthquake

Forces

• Design Criteria–Factors of safety against

•Overturning

•Sliding

•Overstressing in compression

–At most small tension permitted•Cracking possibility not considered

• Stresses generally do not control designEGAT Thailand

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Traditional Procedures v’s Dynamic Response

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Traditional Procedures v’s Dynamic Response

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Uniform Seismic Coefficient: Undesirable ResultsDecreasing Concrete Strength with Increase in Elevation

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Envelope Tensile Stresses in Koyna Dam Due to

Koyna Earthquake

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Uniform Seismic Coefficient: Undesirable Results

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Structures on Dam Crest

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Traditional Design Procedures

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Hydrodynamic Effects

Upstream Ground Motion

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Analyses in Traditional Design

Procedures Do Not Recognize:

• Dynamic response of dam

• Hydrodynamic effects

• Earthquake ground motion properties

• Dam-foundation rock interaction

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Factors To Be Considered in

Dynamic Analysis

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Approximate Interaction Model

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Hydrodynamic and Reservoir Bottom

Absorption Effects

Upstream Ground Motion

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Hydrodynamic Effects

Upstream Ground Motion

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Reservoir Bottom Absorption Effects

Upstream Ground Motion

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Hydrodynamic and Reservoir Bottom

Absorption Effects

Vertical Ground Motion

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Water Compressibility Effects

Upstream Ground Motion

Es = 0.65 million psi

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Water Compressibility Effects

Upstream Ground Motion

Es = 4.0 million psi

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Foundation Interaction Effects

Upstream Ground Motion

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Dynamic Analysis Procedures

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Dam-Water-Foundation Rock System

• Factors to consider– Dynamics of system

– Dam-water interaction including water compressibility

– Reservoir bottom absorption

– Dam-foundation rock interaction

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Substructure Representation of Dam-Water-

Foundation Rock System

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Pine Flat Dam: Finite Element Model

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Taft Ground Motion, 1952

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Displacement Response

Pine Flat Dam – Taft Ground Motion

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Critical Stresses

Pine Flat Dam – Taft Ground Motion

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Pine Flat Dam

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Forced Vibration Generator

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Hydrodynamic Pressure Gauge

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Acceleration and Pressure Frequency Responses

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Reduction in Fundamental Frequency Due to Water

Analytical v’s Experimental Results

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Simplified Analysis Procedure

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Simplified Analysis Procedure

• Purpose: Preliminary design and safety

evaluation

• Objective: Maximum forces from earthquake

spectrum

• Concepts:

– Fundamental mode response (considering dam-

water-foundation rock interaction) from an

equivalent SDF system

– Higher mode response (neglecting both interaction

effects) by “static correction” method

– SRSS combination of the two responses

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Earthquake Design Spectrum

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Critical Stresses

Lateral Forcesstatic

analysisStresses

1f y

scf y

1r

scr

Dynamic Response

22

1d scr r r

Total Response

22

max 1st scr r r r

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Lateral Earthquake Forces

Fundamental Vibration Mode

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Fundamental Vibration Period and

Mode: Several Cross Sections

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Standard Fundamental Period and Mode Shape

of Vibration for Dam Design

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Lateral Earthquake Forces

Fundamental Vibration Mode

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Hydrodynamic Effects

Period Lengthening Ratio, Rr

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Lateral Earthquake Forces

Fundamental Vibration Mode

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Dam-Foundation Rock Interaction

Period Lengthening Ratio, Rf

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Lateral Earthquake Forces

Fundamental Vibration Mode

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Hydrodynamic Effects

Added Damping Ratio, r

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Dam-Foundation Rock Interaction

Added Damping Ratio, f

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Fundamental Vibration Mode

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Hydrodynamic Pressure Function, p(y)

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Lateral Earthquake Forces

Higher Vibration Modes

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Hydrodynamic Pressure Function, po(y)

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Critical Stresses

Lateral Forcesstatic

analysisStresses

1f y

scf y

1r

scr

Dynamic Response

22

1d scr r r

Total Response

22

max 1st scr r r r

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Pine Flat Dam: Tallest Non-Overflow Monolith

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Taft Ground Motion, 1952

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Response Spectrum – Taft Ground Motion

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Evaluation of Simplified Procedure

Flexible Foundation/Full Reservoir

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Seismic Design & Safety Evaluation

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Seismic Design and Safety Evaluation

• Selection of earthquake motion and design spectrum

• Linear analysis of dynamic response of dam– Stage 1: simplified analysis

– Stage 2: refined analysis

• Prediction of dam performance– tensile stresses < tensile concrete strength

• NO DAMAGE

– tensile stresses > tensile concrete strength• ESTIMATION OF DAMAGE

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Tensile Strength of Concrete

2 32.6 ctf f

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Koyna Dam

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Pacoima Dam

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Lower Crystal Springs Dam

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Application to Design of New Dams

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Richard B. Russel Dam, USA (1980s)170 ft high

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Balambano Dam, Indonesia (1997)

Roller-compacted concrete, 90 m high

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Olivenhain Dam, California (2003)

Roller-compacted concrete, 315 ft high

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San Vicente Dam, California (2009) Current height: 220 ft

Raised height: 337 ft

Roller-compacted concrete for dam raise

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Applications to Evaluation and

Remediation of Existing Dams

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Thermalito Diversion Dam, California, USA

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Folsom Dam, California340 ft high

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Old Aswan Dam, Egypt

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Seven Mile Dam, Canada215 ft high

Seismic remediation:

fifty-two 92-strand post-

tensioned anchors

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Gatun Spillway, Panama Canal

107 ft high

84EGAT Thailand

Madden Dam, Panama Canal

85EGAT Thailand