zeidan promotion -2014-revised

State of Art in

Design and Analysis of

Concrete Gravity Dams

Dr. Bakenaz A. Zeidan Faculty of Engineering

Tanta University, Egypt

[email protected]

1/24/2015 Dr. Bakenaz A. Zeidan

1

Faculty of Engineering – Tanta University

2014


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DESIGN AND ANALYSIS OF CONCRETE

GRAVITY DAMS

Presentation Outline

Introduction to Gravity Dams

About Concrete Gravity Dams

Cases of Loading on Gravity Dams

Theoretical Approach Gravity Dams

Modeling of Gravity Dam

Analysis of Gravity Dams

Safety Criteria for Gravity Dams

Recent Trends in Gravity Dams

Summing up


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INTRODUCTION

Many concrete gravity dams have been in service for over 50

years.

Older existing dams may fail to meet revised safety criteria

and structural rehabilitation.

The identified causes of failure, based on a study of over 1600

dams [1] are: foundation problems (40%), inadequate spillway

(23%), poor construction (12%), uneven settlement (10%),

and high pore pressure (5%), acts of war (3%), embankment

slips (2%), defective materials (2%), incorrect operation (2%),

and earthquakes (1%).


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INTRODUCTION


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Classification of Dams Worldwide

INTRODUCTION

STAGE I: PLANNING STUDIES

• Geography, geology, hydrology, construction materials,

STAGE II: Design

• Dam profile, loads determination, stability analysis, stress analysis, safety criteria

STAGE III:

Construction, operation, and maintenance

•Channel diversion, foundation treatment, concrete curing, construction joints, instrumentation, operation, maintenance

PLANNING STUDIES

5/13/2013

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DR. BAKENAZ ZEDAN

TOPOGRAPHIC SURVEYS

FOUNDATION STUDIES

MATERIALS AND CONSTRUCTION

FACILITIES

HYDROLOGIC STUDIES

RESERVOIR OPERAION

STUDY

INTRODUCTION

Choice of Dam Geometry &

Material Properties

• H, B, hu, hd, hs, γc, γw, γs, α ….

Determination of Acting

Loads

• W , P , P , c u d

W Ps, Ws H, w

V, Phd , …….

Stability & Stress Analysis

• FSo, FSs, σheel, σtoe ,

σ1. σ2, σmax.

σmin, qmax ,…

DESIGN

STAGES

INTRODUCTION

INTRODUCTION

STABILITY ANALYSIS

Allowable F.O.S. against overturning

Allowable F.O.S. against forward

sliding

STRESS ANALYSIS

σmax ≤ max. allowable compression stress

for dam concrete

σmax ≤ max. allowable bearing stress for

dam foundation

σmin ≥ 0 .0 no tension is allowed

qmax ≤ max. allowable shear stress for dam

concrete


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SAFETY CRITERIA

INTRODUCTION C

ON

ST

RU

CT

ION

Channel diversion,

Foundation Treatment

Concrete Curing,


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INTRODUCTION C

ON

ST

RU

CT

ION

Instrumentation

Operation

Maintenance


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CONCRETE GRAVITY DAMS


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Figure 1: Different types of concrete dams (2).

Types of gravity dams: Gravity dams

Buttress dams Arch dams


Basic Definitions

Length of the dam

Structural height of the dam

Max. base width of the dam

Toe and Heel

Hydraulic height of the dam


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Dam Concrete Static Properties (USBR)

• Strength

• Elastic Properties

• Thermal Properties

Dam Concrete Dynamic Properties

• Strength

• Elastic Properties

• Average Properties


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Average Properties (USBR)

Compressive strength- 3,000 to 5,000 Ibs/in2 (20.7 to 34.5 MPa)

Tensile strength- 5 to 6 % of the compressive strength

Shear strength: Cohesion-about 10% of the compressive strength

Coefficient of internal friction- 1.0

Poisson’s ratio- 0.2

Instantaneous modulus of elasticity- 5.0 x 106 lbs/in2 (34.5 GPa)

Sustained modulus of elasticity- 3.0 x 106 lbs/in2 (20.7 GPa)

Coefficient of thermal expansion- 5.0 x 10-6/“F (9.0 x l0-6PC)

Unit weight- 150 Ibs/ft3 (2402.8 kg/m3)


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Foundation Properties

• Deformation Modulus

• Shear Strength

• Pore Pressure and Permeability

• Treatment

• Compressive and Tensile Strength


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CONCRETE GRAVITY DAMS Criteria- Foundation data required for the analysis of a gravity dam (4):

The deformation modulus of each type of material

within the loaded area of the foundation.

The effects of joints, shears, and faults obtained by

direct (testing) or indirect (reduction factor) methods.

An effective deformation modulus.

The effective deformation moduli.


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GRAVITY DAM LOADS

Factors to be considered as contributing to the loading combinations for a gravity dam are: Reservoir & tail water loads Temperature Internal hydrostatic pressure Dead weight Wind Wave Ice Silt Earthquake


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GRAVITY DAM LOADS

Static Loads:

Dead weight

Reservoir hydrostatic pressure

Tail water hydrostatic pressure

Uplift pressure

Sand and silt


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GRAVITY DAM LOADS


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Reduced Uplift Extreme Uplift

GRAVITY DAM LOADS


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Seismic Loads

Dam Body

Horizontal Inertia/ Seismic Forces

Vertical Inertia/ Seismic Forces

Reservoir Body

Hydrodynamic Pressures

in Excess to Hydrostatic Pressures

GRAVITY DAM LOADS

Earthquake Excitation


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TAFT GROUND MOTION, 1952

GRAVITY DAM LOADS

Seismic Loads

Horizontal and vertical accelerations are generated due to earthquake excitations which are not equal, horizontal being of greater intensity than vertical.

Earthquake acceleration ϋg is usually designated as a fraction of the acceleration due to gravity g and is expressed as:

• ϋg = α⋅g

• where α is called the Seismic Coefficient and

αh :Horizontal seismic coefficient = 1.5 α

αv : Vertical seismic coefficient = 0.75 α

Seismic force = M. ϋg = M. α⋅g = W. α

Horizontal inertia force H= W. αh

Vertical inertia force V = W. αv


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GRAVITY DAM LOADS • Seismic Loads (Chopra 2012)


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Nonlinear α

Constant α

Linear α

Spectrum

approximate

simplified

GRAVITY DAM LOADS


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Seismic Loads

H

V

W

H

Inertia forces due to earthquakes

Horizontal inertia force H= W. αh

Vertical inertia force V = W. αv

GRAVITY DAM LOADS


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Hydrodynamic Pressure Westergard Equation (1933)

GRAVITY DAM LOADS

Hydrodynamic Pressure Westergard Equation (1933)

The hydrodynamic pressure generated due to the horizontal movement of the water body in the

reservoir during earthquakes may to be calculated by:

P= Cs. γw.α.h

where:

P: Hydrodynamic Pressure

in KN/m2 depth y below reservoir surface

Cs : is a shape factor

γw : unit weight of reservoir water in KN/m3

α : seismic coefficient

h: reservoir depth (m)


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GRAVITY DAM LOADS Load Combinations

1-Usual (Normal) 2-Unusual (Maximum) 3- Extreme ( Earthquake)


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Stresses in Koyna Dam (Thailand) due to

Earthquake

Principal Stresses in a concrete gravity Dam

GRAVITY DAM LOADS

▫ Stability Criteria Accounts for :

Sliding stability

Tension stress

Compressive stress

Displacement


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Figure 10: Simple dam model showing critical areas for compressive (blue), tensile (green) and sliding (red).

GRAVITY DAM LOADS

• Factors of Safety (USBR)

(1) Compressive stress.-

The maximum allowable compressive stress should in no case exceed:

” 1,500 lbs/in2 (10.3 MPa for “Usual Loading Combinations”.

“2,250 lbs/in2 (15.5 MPa) for “Unusual Loading Combinations”.

A safety factor greater than 1 for “Extreme Loading Combinations”.

Safety factors of 4.0, 2.7, and 1.3 should be used in determining

allowable compressive stresses in the foundation for “Usual,”

“Unusual,” and “Extreme Loading Combinations,”


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GRAVITY DAM LOADS

• Factors of Safety (USBR)

(2) Tensile stress

The minimum allowable compressive stress computed without internal

hydrostatic pressure should

σz = p. γ. h – (ft/s)

where:

σz = minimum allowable stress at the face

p = a reduction factor to account for drains

γ = unit weight of water

h = depth below water surface

ft = tensile strength of concrete at lift surfaces

s = safety factor.


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THEORETICAL APPROACH


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THEORETICAL APPROACH

Governing Equations The well-known Helmholtz equation governing the pressure p Zienkiewicz (2000) , Chopra (1967):


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Ω (1)

where P is the acoustic hydrodynamic pressure; t is time and ∂ is the two-dimensional Laplace operator and C is the speed of pressure wave given by:

where

THEORETICAL APPROACH Boundary Conditions Dam-Reservoir Boundary

Reservoir-Foundation Boundary

Reservoir-Far-End Boundary

Free-Surface Boundary

P(x, y, z, t) = 0


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MODELING OF CONCETE GRAVITY DAMS


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GRAVITY DAM MODELING

Mathematical Modeling

Analytical Modeling

Physical Modeling

Experimental setup

Numerical Modeling

Deterministic Modeling

Stochastic Modeling


ALALYTICAL MODELING

EXIMENTAL MODELING

NUMERICAL MODELING


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• FEM Deterministic Modeling

• Monte Carlo Simulation

Probabilistic Modeling


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FINITE ELEMENT MODELING


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FE Mesh

Once a dam has been modeled in FEM, it is possible to experiment and change details about it without the need to restart the whole process.

FINITE ELEMENT MODELING FEM Formulation: Zienkiewicz (2000)

The standard Galerkin’s Finite Element technique in which the structure displacement vector is discretized as:

u= Nu 𝒖 , …………………….p= Np 𝒑

where 𝒖 and 𝒑 are the nodal parameters of each field and Nu and Np are appropriate shape functions. The discrete equations of the structure dynamic response following Galerkin method reads

M 𝒖 + C 𝒖 +K 𝒖 – Q 𝒑 + f =0 (7) In which M, C, K and f refer to mass matrix, damping matrix, stiffness matrix of the structure and prescribed

force vector respectively, where 𝒖 , 𝒖 and 𝒖 are displacement, velocity and acceleration vectors respectively. Standard Galerkin’s discretization applied to the fluid Equation (1) and its boundary conditions leads to [7]

S 𝒑 + ξ 𝒑 + H 𝒑 + QT 𝒖 + q = 0 (9)

in which S, ξ, H and q are pseudo fluid mass matrix, pseudo fluid damping matrix, pseudo fluid stiffness matrix and prescribed flux vector respectively . Q is a transform matrix and 𝒑 , 𝒑 and 𝒑 are nodal pressure vector, the first and second order derivatives of nodal pressure vector with respect to time, respectively.


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FEM Formulation: Zienkiewicz (2000)

The coupled equation of the fluid-structure-foundation system based on Equations (7) and (9) subjected to earthquake ground motion can be presented as follows:

In which represents the nodal ground acceleration vector.


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+

(11)


• Dam - Reservoir –Foundation Coupling System


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Dam-Reservoir Coupling System


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Interface Elements

• Imposing Line elements between fluid and concrete elements

Coincide nodes

• Coupling coincide nodes on the interface


Dam - Foundation Coupling System


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Fixed Soil Foundation

Massless Soil Foundation

Mass soil Foundation


Assumptions:

Only the displacements in the direction normal to the interface are assumed to be compatible in the structure as well as the fluid.

The fluid is generally assumed to be linear-elastic, incompressible, irrotational and nonviscous.

2-D finite element model is implemented.

Absorption is considered at reservoir bottom.


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Assumptions:

A length of 2 to 3 times reservoir depth is recommended along with Summerfield boundary conditions.

The depth of foundation is taken about 1.5 the dam base width into account in the calculations.

The dam and foundation materials are assumed to be linear-elastic, homogeneous and isotropic.

The effect of foundation flexibility is considered as ratios i.e. modulus of elasticity of foundation to modulus of elasticity of dam Ef/Ec.


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Material Properties Sample

ANALYSIS OF CONCRETE GRAVITY DAMS Gravity Method 2-D rigid block dam. Linear base pressure distribution Simple dam geometry

FEM Method • 2-D, 3-D analysis • Complex dam geometry • Complex boundary conditions • linear/Nonlinear behaviour • Dam –reservoir interaction • Dam –foundation interaction • Crack analysis

Can be analyzed


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ANALYSIS OF CONCRETE GRAVITY DAMS

Modal Analysis and Natural Response

• The structural response of a material to different loads determines how it will be economically utilized in the design process.

• Earthquake is a major source of seismic forces that impinge on structures

• This necessitates the seismic analysis of concrete gravity dam


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Modal Analysis and Natural Response

Mode shapes for a gravity dam with empty reservoir

Mode shapes for a gravity dam with full reservoir


Dynamic Analysis

• Dynamic analysis refers to analysis of loads whose duration is short with the first period of vibration of the structure.

• Dynamic methods are appropriate to seismic loading

because of the oscillatory nature of earthquakes, and the subsequent structural responses.


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• Dynamic Analysis

The purpose of dynamic analysis is not to determine dam stability in a conventional sense, but rather to determine what damage will be caused during the earthquake, and then to determine if the dam can continue to resist the applied static loads in a damaged condition with possible loading changes due to increased uplift or silt liquefaction.


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TAFT GROUND MOTION, 1952

Dynamic Analysis

Dynamic Analysis

Factors to Be Considered in Dynamic Analysis:

1. Hydrodynamic and reservoir bottom absorption

effects upstream ground motion.

2. Hydrodynamic effects upstream ground motion.

3. Reservoir bottom absorption effects upstream ground

motion.

4. Hydrodynamic and reservoir bottom absorption effects

vertical ground motion.

5. Water compressibility effects upstream ground

motion.

6. Foundation interaction effects upstream ground motion.


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Dynamic Analysis


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Pseudo Dynamic Method (Quasi-static)

This procedure was developed by Pro. Anil Chopra as a hand calculated alternative to the more general analytical procedures which require computer programs

PINE FLAT DAM

Dynamic Analysis

• Pseudo Dynamic Method (Quasi-static)


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Stress distribution in Pin Plate Dam after Chopra (2010)

Dynamic Analysis

• Response Spectrum Analysis


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Dynamic Analysis Time History Analysis


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Dynamic Analysis

Time History Analysis


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DESIGN AND SAFETY CRITERIA

International Safety Regulation Codes United States Department of the Interior Bureau of Reclamation (USBR)

“Design Of Gravity Dams Design” Design Manual For Concrete Gravity

Dams, 1976

Federal Guidelines for Dam Safety-Earthquake Analyses and Design of

Dams-May 2005

US Army Corps of Engineers -Engineering And Design – Gravity Dam

Design – 2000

Dam Safety Code – 2008 -Australian Capital Territory

Egyptian Code for Hydraulic Structures (Part 7)


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STABILITY ANALYSIS

Allowable F.O.S. against overturning

Allowable F.O.S. against forward

sliding

STRESS ANALYSIS

σmax ≤ max. allowable compression stress for

dam concrete

σmax ≤ max. allowable bearing stress for dam

foundation

σmin ≥ 0 .0 no tension is allowed

qmax ≤ max. allowable shear stress for dam

concrete


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DESIGN AND SAFETY CRITERIA Recommended Minimum Sliding Stability Safety Factors

Dams having a high or significant hazard potential.

Loading Condition Factor of Safety Usual 3.0 Unusual 2.0 Post Earthquake 1.3

Dams having a low hazard potential.

Loading Condition Factor of Safety Usual 2.0 Unusual 1.25 Post Earthquake Greater than 1.0

Alternate Recommended Minimum Factors of Safety

Loading Condition Factor of Safety

Worst Static 1.5 Flood if Flood is PMF 1.3 Post Earthquake 1.3


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Sliding Stability Safety Factors

Overturning Stability Safety Factors

Cracked Base Criteria

Safety Factor Evaluation

Foundation Stability

Construction Materials


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Recent Analysis Aspects

Fracture Analysis

Thermal Stress Analysis

Breach Analysis

Risk Analysis


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Recent Analysis Trends

Fracture Analysis


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Thermal Stress Analysis


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Breach Analysis


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Risk Analysis


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RISK ANALYSIS OF CONCRETE GRAVITY DAMS

Risks under Normal Operations

Risks under Flood Loading

Risks under Earthquake Loading

Accounting for Uncertainty

Probabilistic Seismic Risk Assessment

•

•


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Relevant Case History

Austin (Bayless) Dam: 1911

Bouzey Dam: 1895

Koyna Dam: 1967


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SUMMING UP Gravity dams are very important structures.

The collapse of a gravity dam due to earthquake ground motion may cause an

extensive damage to property and life losses.

Therefore, the proper design of gravity dams is an important issue in dam

engineering.

An integral part of this procedure is to accurately estimate the dam earthquake

response.

The prediction of the actual response of a gravity dam subjected to earthquake is a

very complicated problem.

It depends on several factors such as dam-foundation interaction, dam-water

interaction, material model used and the analytical model employed.

In fluid-structure interaction one of the main problems is the identification of the

hydrodynamic pressure applied on the dam body during earthquake excitation.

The analysis of dam-reservoir system is complicated more than that of the dam

itself due to the difference between the characteristics of fluid and dam's concrete

on one side and the interaction between reservoir and dam on the other side.


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Main References USBR (1976) “Design Criteria For Concrete Arch And Gravity Dams”.

Westergard, H. M. (1933). Water pressure on dams during earthquakes.

TRANSACTIONS ASCE Vol.98.

Chopra A.K. (1967). Hydrodynamic Pressure on dams during earthquakes”

Proc .ASCE , EM6.

Chopra A.K . (1970). Earthquake response Analysis of concrete gravity dams.

Proc. ASCE, EM4.

Zienkiewicz, 0.C. and Taylor, R.L. (2000) “The Finite Element Method”; 5th Edition

McGraw-Hill.

Zeidan, B. A. (2014) "Seismic Analysis of Dam-Reservoir-Foundation

Interaction for Concrete Gravity Dams", International Symposium on Dams in

Environmental Global Challenges" ICOLD2014, Bali, Indonesia, June 1ST - 6TH, 2014


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Main References Fenves, G., And Chopra, A. K., (1985) “Effects Of Reservoir Bottom

Absorption And Dam-Water-Foundation Rock Interaction On

Frequency Response Functions For Concrete Gravity Dams”

Earthquake Engineering & Structural Dynamics, Vol. 13, 1985, Pp. 13-31.

Gaun F., Moore I.D. & Lin G. (1994) “Seismic Analysis of Reservoir-Dam-

Soil Systems in the Time Domain”, The 8th international conference on

Computer Methods and Advances in Geomechanics, Siriwardane & Zaman

(Eds), Vol. 2, 917-922.

Ghaemian M., Noorzad A. & Moghaddam R.M. (2005) “Foundation Effect

on Seismic Response of Arch Dams Including Dam-Reservoir

Interaction”, Europe Earthquake Engineering, 3, 49-57.


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Main References US. Army Corps of Engineers (USACE), (2003) “Time-History Dynamic Analysis of

Concrete Hydraulic Structures;” Chapter 2- Analytical Modeling of Concrete

Hydraulic Structures, Chapter 3-Time-History Numerical Solution Techniques”, EM 1110-

2-6051.

Lysmer J. & Kuhlemeyer R.L. (1969) “Finite Dynamic Model for Infinite Media”,

Journal of Engineering Mechanics Division, ASCE, 95 (EM4), 859-877.

Wilson E.L. (2000) “Three Dimensional Static and Dynamic Analysis of

Structures, A Physical Approach with Emphasis on Earthquake

Engineering”, 4th Ed., Computers and Structures Inc.

Wolf J. P. (1985) “Dynamic Soil-Structure Interaction”, Prentice Hall: Englewood

Cliffs, NJ.

Bakenaz A. Zeidan (2014) “Finite Element Modeling For Acoustic Reservoir-

Dam-Foundation Coupled System”, International Symposium on Dams in a Global

Environmental Challenges, ICOLD2014, Bali, Indonesia, 1-6 June, 2014.


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zeidan promotion -2014-revised

Documents

types of gravity dams

gravity dams recent

dam concrete max

dam foundation

older existing dams

dam toe

design dam profile

dam structural height