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
drbakenaz@yahoo.com
1/24/2015Dr. Bakenaz A. Zeidan
1
Faculty of Engineering – Tanta University
2014

2

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
3

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%).
4

INTRODUCTION
5
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
12
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
9
SAFETY CRITERIA

INTRODUCTION
CONSTRUCTION
Channel diversion,
Foundation Treatment
Concrete Curing,
10

INTRODUCTION
CONSTRUCTION
Instrumentation
Operation
Maintenance
11

CONCRETE GRAVITY DAMS
12

13
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
14

Dam Concrete Static Properties (USBR)
• Strength
• Elastic Properties
• Thermal Properties
Dam Concrete Dynamic Properties
• Strength
• Elastic Properties
• Average Properties
15

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)
16

Foundation Properties
• Deformation Modulus
• Shear Strength
• Pore Pressure and Permeability
• Treatment
• Compressive and Tensile Strength
17

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.
18

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
19

GRAVITY DAM LOADS
Static Loads:
Dead weight
Reservoir hydrostatic pressure
Tail water hydrostatic pressure
Uplift pressure
Sand and silt
20

GRAVITY DAM LOADS
21
Reduced Uplift Extreme Uplift

GRAVITY DAM LOADS
22
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
23
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
24

GRAVITY DAM LOADS
• Seismic Loads (Chopra 2012)
25
Nonlinear αConstant αLinear α
Spectrumapproximatesimplified

GRAVITY DAM LOADS
26
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
27
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)
28

GRAVITY DAM LOADS
Load Combinations
1-Usual (Normal) 2-Unusual (Maximum) 3- Extreme ( Earthquake)
29
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
30
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,”
31

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.
32

THEORETICAL APPROACH
33

Governing Equations
The well-known Helmholtz equation governing the pressure p
Zienkiewicz (2000) , Chopra (1967):
34
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

Boundary Conditions
Dam-Reservoir Boundary
Reservoir-Foundation Boundary
Reservoir-Far-End Boundary
Free-Surface Boundary
P(x, y, z, t) = 0
35

MODELING OF CONCETE GRAVITY DAMS
36
GRAVITY DAM
MODELING
Mathematical
Modeling
Analytical
Modeling
Physical
Modeling
Experimental
setup
Numerical
Modeling
Deterministic
Modeling
Stochastic
Modeling

ALALYTICAL MODELING
EXIMENTAL MODELING
NUMERICAL MODELING
37

• FEMDeterministic
Modeling
• Monte
Carlo
Simulation
Probabilistic
Modeling
38

FINITE ELEMENT MODELING
39
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.

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.
40

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.
41
+ (11)

• Dam - Reservoir –Foundation Coupling System
42

Dam-Reservoir Coupling System
43
Interface Elements
• Imposing Line elements between fluid and
concrete elements
Coincide nodes
• Coupling coincide nodes on the
interface

Dam - Foundation Coupling System
44
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.
45

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.
46

47
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
48

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
49

50
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.
51

• 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.
52

53
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.
54

Dynamic Analysis
55
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)
56
Stress distribution in Pin Plate Dam after Chopra (2010)

Dynamic Analysis
• Response Spectrum Analysis
57

Dynamic Analysis
Time History Analysis
58

Dynamic Analysis
Time History Analysis
59

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)
60

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
61

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.
 Usual 2.0
 Unusual 1.25
 Post Earthquake Greater than 1.0
Alternate Recommended Minimum Factors of Safety
 Worst Static 1.5
 Flood if Flood is PMF 1.3
 Post Earthquake 1.3
62

 Sliding Stability Safety Factors
 Overturning Stability Safety Factors
 Cracked Base Criteria
 Safety Factor Evaluation
 Foundation Stability
 Construction Materials
63

Recent Analysis Aspects
 Fracture Analysis
 Thermal Stress Analysis
 Breach Analysis
 Risk Analysis
64

Recent Analysis Trends
Fracture Analysis
65

Thermal Stress Analysis
66

Breach Analysis
67

Risk Analysis
68

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
•
•
69

Relevant Case History
 Austin (Bayless) Dam: 1911
 Bouzey Dam: 1895
 Koyna Dam: 1967
70

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.
71

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
72

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.
73

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.
74

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