SLIDE 1CS 362 Artificial Intelligence Hassan Najadat Jordan University of Science & Technology.
At Jordan University of Science and Technology
Transcript of At Jordan University of Science and Technology
Determination of Temperature Distributions and Thermal Stresses for RCC Dams Using Two Different
Finite Element Codes (Comparative Study)
By
Ehab Salem Shatnawi
At Jordan University of Science and Technology
January 2004
Determination of Temperature Distributions and Thermal Stresses for RCC Dams Using Two Different Finite
Element Codes (A Comparative Study)
By
Ehab Salem Shatnawi
A thesis submitted in partial fulfillment of the requirements of the degree of M.Sc. in Civil Engineering
At
The Faculty of Graduate Studies
Jordan University of Science and Technology
January 2004
Signature of Author ..................................................................., January 2004 Committee Members Date and Signature Prof. Abdallah I. Husein Malkawi, Advisor ...................................... Dr. Mousa Attum ......................................
Dr. Nezar A. Hammouri (Cognate, Hashemite University) ......................................
@ßbÔ¶bÉm@ @
@
{ ČiŠ@ÝÓëbàÜÇ@ïㆌ@ï }
{ @ê†bjÇ@åß@a@ó“²@b¹gŽõbàÜÈÛa }
@
@ׇ–âïÅÉÜa@a
I
Acknowledgements
\ ãÉâÄw Ä|~x àÉ xåÑÜxáá Åç á|ÇvxÜx zÜtà|àâwx àÉ cÜÉyxááÉÜ
TuwtÄÄt{ `tÄ~tã| yÉÜ {|á áâÑÑÉÜà? zâ|wtÇvx? tÇw yÜ|xÇwá{|ÑA
fÑxv|tÄ à{tÇ~á yÉÜ à{x vÉÅÅ|ààxx ÅxÅuxÜá? WÜA axétÜ
[tÅÅÉâÜ| tÇw WÜA `Éâát TààâÅA
\ ãÉâÄw Ä|~x àÉ à{tÇ~ Åç ÑtÜxÇàá? Åç uÜÉà{xÜá? tÇw Åç á|áàxÜá
yÉÜ à{x|Ü ÄÉä|Çz tÇw áâÑÑÉÜà wâÜ|Çz Åç áàâwçA
TÄáÉ? \ ãÉâÄw Ä|~x àÉ à{tÇ~ Åç yÜ|xÇwá yÉÜ à{x|Ü áâÑÑÉÜà
xáÑxv|tÄÄç XÇzA `É{:w ltÅ|Ç? XÇzA ^|yt{ Xã|átà? XÇzA
ftÅxxÜ TÄ@`Éâát? XÇzA `tÅÉâÇ f{tàÇtã|? XÇzA
`É{:w TÄ@ft~ÜtÇ? tÇw XÇzA fttw Táá|A
II
Dedication
To My Family
And
Friends
¶a@a@ì@ðÝèað÷bÔ‡–@ @
III
Table of Contents
ACKNOWLEDGEMENTS ............................................................................................... I
DEDICATION .................................................................................................................III
TABLE OF CONTENTS ................................................................................................ IV
LIST OF TABLES......................................................................................................... VII
LIST OF FIGURES......................................................................................................VIII
CHAPTER ONE................................................................................................................ 1
INTRODUCTION ............................................................................................................. 1
1.1 INTRODUCTION .................................................................................................... 1
1.2 CASE STUDY AL-WEHDAH RCC DAM ........................................................... 3
1.2.1 DESCRIPTION OF THE DAM ............................................................................... 3
1.2 LITERATURE REVIEW ........................................................................................ 6
1.4 OBJECTIVES........................................................................................................... 8
1.5 THESIS OUTLINE .................................................................................................. 9
CHAPTER TWO............................................................................................................. 10
BACKGROUND.............................................................................................................. 10
2.1 OVERVIEW ........................................................................................................... 10
2.2 ROLLER COMPACTED CONCRETE .............................................................. 10
2.2.1 PLACING AND COMPACTING RCC ................................................................. 10 ٢٫٢٫٢ RCC PROPORTIONS .................................................................................. 11
2.2.2.1 Portland Cement .................................................................................... 11 ٢٫٢٫٢٫٢ Pozzolanic Materials ...................................................................... 11 2.2.2.3 Flyash Materials .................................................................................... 12
2.2.3 STRUCTURAL RCC PROPERTIES .................................................................... 13 2.2.3.1 Density (ρ ). ............................................................................................ 13 2.2.3.2 Compressive and Tensile Strength (Fc, Ft). .......................................... 13 2.2.3.3 Modulus of Elasticity (E c)..................................................................... 14 2.2.3.4 Poisson's Ratio (υ) ................................................................................. 15
2.2.4 THERMAL RCC PROPERTIES ......................................................................... 15 2.2.4.1 Thermal Conductivity (k). ..................................................................... 15 2.2.4.2 Coefficient of Thermal Expansion (Cth) . ............................................. 16 2.2.4.3 Specific Heat (C).................................................................................... 16 2.2.4.4 Adiabatic Temperature Rise (Tab) ......................................................... 16 2.2.4.5 Heat of Hydration. ................................................................................. 17 2.2.4.6 Tensile Strain Capacity (ε tc ). ................................................................ 17
2.3 THE FINITE ELEMENT METHOD................................................................... 18
2.4 THERMAL ANALYSIS ........................................................................................ 18
IV
2.4.1 THERMAL ANALYSIS CONCEPT ....................................................................... 18 2.4.2 THERMAL ANALYSIS OBJECTIVES .................................................................. 20
2.5 TEMPERATURE CONTROL REQUIREMENTS............................................ 20
CHAPTER THREE......................................................................................................... 22
MODELING..................................................................................................................... 22
3.1 OVERVIEW ........................................................................................................... 22
3.2 MODELING METHODOLOGY ......................................................................... 22
3.3 PRINCIPAL ASSUMPTIONS .............................................................................. 23
3.4 MODEL PROPERTIES AND PARAMETERS.................................................. 24
3.4.1 CEMENTITIOUS MATERIALS........................................................................... 24 3.4.2 CONCRETE PLACEMENT TEMPERATURE ....................................................... 26 3.4.3 INITIAL TEMPERATURE OF ROCK FOUNDATION ........................................... 27 3.4.4 MATERIEL PROPERTIES AND ENVIRONMENTAL CONDITIONS ...................... 27 3.4.5 HEAT OF HYDRATION...................................................................................... 29
3.5 BOUNDARY AND INITIAL CONDITIONS...................................................... 32
CHAPTER FOUR ........................................................................................................... 34
COMPARATIVE STUDY BETWEEN COSMOS & ANSYS .................................... 34
4.1 OVERVIEW ........................................................................................................... 34
4.2 COSMOS/M SOFTWARE .................................................................................... 34
4.3 ANSYS SOFTWARE ............................................................................................. 37
4.4 MODEL ANALYSIS.............................................................................................. 39
4.4.1 TWO-DIMENSIONS MODEL ANALYSIS USING COSMOS............................... 39 4.4.2 THREE-DIMENSIONS MODEL ANALYSES USING COSMOS .......................... 39 4.4.3 TWO-DIMENSIONS MODEL ANALYSIS USING ANSYS................................... 40 4.4.4 THREE-DIMENSIONS MODEL ANALYSES USING ANSYS............................... 41
4.5 FINITE ELEMENT RESULTS ............................................................................ 45
4.5.1 FINITE ELEMENT RESULTS OF COSMOS ..................................................... 45 4.5.2 FINITE ELEMENT RESULTS OF ANSYS.......................................................... 50
4.6 SUMMARY AND DISCUSSION.......................................................................... 55
THERMAL AND STRESS ANALYSIS........................................................................ 60
5.1 OVERVIEW ........................................................................................................... 60
5.2 THERMAL ANALYSIS FOR RCC DAM........................................................... 61
5.2.1 EFFECT OF CONVECTION COEFFICIENTS....................................................... 61 5.2.2 EFFECT OF HEAT OF HYDRATION AND PLACEMENT TEMPERATURE............ 61 5.2.3 RESULTS AND DISCUSSION OF THERMAL ANALYSIS ...................................... 61
5.3 THERMAL STRESSES IN RCC DAM ............................................................... 80
5.3.1 THERMAL STRESS DUE TO TEMPERATURE DROP NEAR THE FOUNDATION. 80 5.3.2 THERMAL STRESSES DUE TO TEMPERATURE DEFERENCE BETWEEN THE SURFACE AND INTERIOR OF DAM. ................ 81
V
5.3.3 THERMAL STRESSES DUE TO RESTRAINT OF FOUNDATION.......................... 81 5.3.4 THERMAL STRESSES DUE TO VERTICAL TEMPERATURE DIFFERENCE........ 81 5.3.5 INFLUENCE OF GALLERY IN THE DAM BODY................................................. 82 5.3.6 RESULTS AND DISCUSSION OF STRUCTURAL ANALYSIS ................................ 82
5.4 CRACKING ANALYSIS....................................................................................... 95
5.4.1 INTRODUCTION................................................................................................ 95 5.4.2 TRANSVERSE CONTRACTION JOINTS. ............................................................ 96 5.4.3 CONSTRUCTION JOINT SPACING ASSESSMENT .............................................. 96
CHAPTER SIX.............................................................................................................. 100
CONCLUSIONS AND RECOMMENDATIONS ...................................................... 100
6.1 CONCLUSIONS................................................................................................... 100
6.2 RECOMMENDATIONS ..................................................................................... 102
REFERENCES .............................................................................................................. 103
APPENDIX A................................................................................................................. 105
VI
List of Tables
Table
Description Page
3.1 Predicted RCC Placement Temperatures …………………………… 27 3.2 Properties Adopted for Thermal Analysis …………………………... 28 4.1 Summary Results for COSMOS and ANSYS. ……………………… 57 5.1 Peak Temperature in the dam core at the end of heat of hydration. … 67 5.2 Maximum temperatures occurred during the construction process…. 68 5.3 Crack Analysis in Al Wehdah Dam for Different RCC Mix and
Placement Temperatures. …………………………………………… 99
VII
List of Figures
Figure
Description Page
1.1 Location of Al Wehdah Dam Site. …………………………………… 41.2 Longitudinal section of Al Wehdah Dam …………………………... 5 1.3 Typical Cross Section for Al Wehdah Dam ………………………... 51.4 Imaginary Overview for AL-Wehda Dam ………………………….. 62.1 Compressive strength test results for different pozzolanic materials
uses ………………………………………………………………….. 143.1 The Accumulative Heat of Hydration after 7 days for different
Percent of Different Pozzolanic Material …………………………… 253.2 The Percent of the Heat of Equivalent Cement calculated from
different Percent of Different Pozzolanic Material …………………. 253.3 The accumulative heat of hydration of the cement (OPC) …………. 293.4 Heat of Hydration for RCC mix (60 kg/m3 cement, and 30 kg/m3
South Africa fly ash), for Finite Element Analysis …………………. 303.5 Heat of Hydration for RCC mix (60 kg/m3 cement, and 30 kg/m3
Turkey fly ash), for Finite Element Analysis ……………………….. 303.6 Heat of Hydration for RCC mix (60 kg/m3 cement, and 30 kg/m3
Jordanian Pozzolan), for Finite Element Analysis ………………….. 313.7 Heat of Hydration for RCC mix (60 kg/m3 cement, and 30 kg/m3
Rock Flour), for Finite Element Analysis …………………………... 313.8 Thermal Boundary Conditions for Thermal Analysis ……………… 334.1 Time Curves Used in COSMOS/M for the 1st three layers ………… 364.2 Births and Death of Elements ………………………………………. 384.3 Element Types Used in COSMOS …………………………………… 424.4 Element Types Used in ANSYS ……………………………………... 424.5 Two Dimension Model Mesh in COSMOS ………………………… 434.6 Three Dimension Model Mesh in COSMOS ……………………….. 434.7 Two Dimension Model Mesh in ANSYS …………………………... 444.8 Three Dimension Model Mesh in ANSYS …………………………. 444.9 Temperature Contour after 100 days for (28°C) Placement
Temperature using COSMOS ………………………………………. 464.10 Temperature Contour at the End of Heat of Hydration, 410 days for
(28°c) Placement Temperature using COSMOS …….……………… 474.11 Predicted temperature history in the dam center at different heights .. 48
4.12
Predicted Temperature History at Different Nodal Point at 12m from the Base of the Dam …………………………………………………
494.13 Temperature Contour after 100 days using ANSYS ………………... 514.14 Temperature Contour at the End of Heat of Hydration, 410 days for
(28°c) Placement Temperature using ANSYS ……………………… 52
VIII
4.15 Predicted Temperature History in the Dam Center at Different Heights using ANSYS for 2D & 3D Analysis Respectively ……….. 53
4.16 Predicted Temperature History at Different Nodal Point at 12m from the Dam Base using ANSYS for 2D & 3D Analysis Respectively … 54
4.17 Comparative Predicted Temperature History using ANSYS and COSMOS at the Dam Center and 12 m from the Dam Base using 3D Analysis ……………………………………………………………... 58
4.18 Comparative Predicted Temperature History using ANSYS and COSMOS at 3m from Upstream and 12 m from the Dam Base using 2D Analysis …………………………………………………………. 58
4.19 Cross Section Temperature Distribution at 22 m from the Dam Base using ANSYS and COSMOS ……………………………………….. 59
4.20 Vertical Temperature Distribution at the Dam Center using ANSYS and COSMOS ………………………………………………………. 59
5.1 Temperature contour at the end of heat of hydration, 410 days for different placement temperature (20, 24, 28°C) for RCC mix of South Africa Fly ash ………………………………………………… 63
5.2 Temperature contour at the end of heat of hydration, 410 days for different placement temperature (20, 24 and 28 °C) for RCC mix of Turkey Flyash ……………………………………………………….. 64
5.3 Temperature contour at the end of heat of hydration, 410 days for different placement temperature (20, 24, 28 and 32 °C) For RCC mix of Jordanian Pozzolan ………………………………………….. 65
5.4 Temperature contour at the end of heat of hydration, 410 days for different placement temperature (20, 24, 28 and 32 °C) For RCC mix of Rock Flour …………………………………………………... 66
5.5 Predicted Temperature History in the Dam Center at 22 m from Base of Dam for Different Placement Temperatures for RCC Mix of South Africa Flyash …………………………………………………. 68
5.6 Predicted Temperature History in the Dam Center at 22 m from Base of Dam for Different Placement Temperatures for RCC Mix of Turkey Flyash ……………………………………………………….. 69
5.7 Predicted Temperature History in the Dam Center at 22 m from Base of Dam for Different Placement Temperatures for RCC Mix of Jordanian Pozzolan ………………………………………………….. 69
5.8 Predicted Temperature History in the Dam Center at 22 m from Base of Dam for Different Placement Temperatures for RCC Mix of Rock Flour …………………………………………………………...
70
5.9 Comparison 2D & 3D Analysis for Predicted Temperature History at Different Points at 12 m from Dam Base, Using 28°C Place_Temp for RCC Mix of South Africa Flyash …………………. 71
5.10 Comparison 2D & 3D Analysis for Predicted Temperature History at Different Points at 12 m from Dam Base, Using 28°C
IX
Place_Temp for RCC Mix of Turkey Flyash ……………………….. 725.11 Comparison 2D & 3D Analysis of Predicted Temperature History at
Different Points at 12 m from Dam Base, Using 28°C Place_Temp for RCC Mix of Jordanian Pozzolan ………………………………...
735.12 Comparison 2D & 3D Analysis for Predicted Temperature History
at Different Points at 12 m from Dam Base, Using 28°C Place_Temp for RCC Mix of Rock Flour …………………………... 73
5.13 Cross Section Temperature Distribution at 22 m from the Dam Base for Different Placement Temperatures for RCC Mix of South Africa Flyash ……………………………………………………………….. 75
5.14 Cross Section Temperature Distribution at 22 m from the Dam Base for Different Placement Temperatures for RCC Mix of Turkey Flyash ……………………………………………………………….. 75
5.15 Cross Section Temperature Distribution at 22 m from the Dam Base for Different Placement Temperatures for RCC Mix of Jordanian Pozzolan …………………………………………………………… 76
5.16 Cross Section Temperature Distribution at 22 m from the Dam Base for Different Placement Temperatures for RCC Mix of Rock Flour .. 76
5.17 Vertical Temperature Distribution at the Dam Center for Different Placement Temperatures for RCC Mix of South Africa Flyash ……. 77
5.18 Vertical Temperature Distribution at the Dam Center for Different Placement Temperatures for RCC Mix of Turkey Flyash ………….. 78
5.19 Vertical Temperature Distribution at the Dam Center for Different Placement Temperatures for RCC Mix of Jordanian Pozzolan …….. 78
5.20 Vertical Temperature Distribution at the Dam Center for Different Placement Temperatures for RCC Mix of Rock Flour ……………... 79
5.21 Summary for the Maximum Temperature Occurred in the Dam during the Construction Process …………………………………….. 80
5.22 Different Stress Contour (σx, σz, N/m2) at the End of Heat of Hydration using 2D Analysis ……………………………………….. 84
5.23 3D Stress Contour (X-direction, N/m2) at the End of Heat of Hydration ……………………………………………………………. 85
5.24 3D Principal Stress Contour (S1, N/m2) at the End of Heat of Hydration ……………………………………………………………. 85
5.25 3D Stress Contour (Z-direction, N/m2) at the End of Heat of Hydration …………………………………………………………….
86
5.26
Principal Stresses History at Different Nodal Points at 9m from the Dam Base Using 2D Analysis ……………………………………….
88
5.27 Cross Valley Stresses ( z-direction ) History at Different Nodal Points at 9m from the Dam Base Using 2D Analysis ………………. 88
5.28 Principal Stresses History at Different Nodal Points at 6m from the Dam Base Using 3D Analysis ………………………………………. 89
X
5.29 Cross Valley Stresses ( z-direction ) History at Different Nodal Points at 6m from the Dam Base Using 3D Analysis ………………. 89
5.30 Comparison Cross Valley Stresses ( z-direction ) History for 2D & 3D Analysis at 1.5 m from base of dam and 2.5 m from upstream ... 90
5.31 Principal stresses across dam section at different time period (9 m from the dam base) Using 2D Analysis …………………………….. 91
5.32 Comparison Principal stresses across dam section using 2D and 3D (9 m from the dam base) ……………………………………………. 91
5.33 Principal and Cross Valley Stresses Distribution at Vertical Section at the Dam Centre Using 2D Analysis ……………………………… 93
5.34 Principal and Cross Valley Stresses Distribution at Vertical Section at the Dam Centre Using 2D Analysis ……………………………… 93
5.35 Comparison between temperature and stresses in z-direction at 1.5 m from base of dam and 2.5 m from upstream Using 2D Analysis ... 94
5.36 Comparison between temperature and stresses in z-direction at 1.5 m from base of dam and 2.5 m from upstream using 3D Analysis …. 95
XI
Determination of Temperature Distributions and Thermal Stresses for RCC Dams Using Two Different Finite Element
Codes (Comparative Study)
By: Ehab Shatnawi Supervisor: Prof. Abdallah I. Husein Malkawi
Abstract
In this thesis, thermal and structural analyses are performed for Al-
Wehdah RCC dam in Jordan, using different finite element codes namely
ANSYS and COSMOS. Two and three-dimensional finite element methods
have been carried out in order to understand the thermal influence of several
elements and constituent materials of the dam. The effect of RCC heat of
hydration and placement conditions on the resulting temperature and stress
distribution has been studied.
ANSYS program was chosen to carry out parametric study to find the
placement temperature at which the block length between contraction joints
not to exceed 20 m. Different cementitious material (i.e. South Africa flyash,
Turkey flyash, Jordanian pozzolan, and rock flour) with different placement
temperatures (i.e. 20, 24, 28, and 32 °C) were used in this study. A design
chart to determine the RCC placement temperature was developed from this
parametric study.
A comparative study between the two finite element programs was done
using Jordanian pozzolan RCC mix with 28°C placement temperature. The
study demonstrated that the results of temperature computed using ANSYS
numerical model analysis is higher and more conservative than the COSMOS
results.
The same cementitious material (Jordanian pozzolan) with the same
placement temperature (28°C) was used to perform a structural analysis. The
locations of tensile cracks were determined as a result of this analysis.
XII
CHAPTER ONE
INTRODUCTION
1.1 Introduction
Roller-compacted concrete (RCC) is defined as "concrete compacted
by rolling compaction which, in its unhardened state, will support a roller
while being compacted" (American Concrete Institute ACI).
RCC dams consist of concrete placed at a lower water-to-cement ratio as
compared to conventional concrete with the aid of compaction equipment and
methodologies normally employed for earthfill placement. RCC has gained
worldwide acceptance as an alternative to conventional concrete in dam
construction due to the construction advantages and proved performance
(Luna, et al, 2000). When RCC was first introduced in dam construction, for
a time it was thought that there was no problem in the temperature control of
RCC because the amount of cement in RCC is much less than that in the
conventional concrete. But some time later, it was discovered after RCC still
has the problem of temperature control when it is used in dam construction
(Zhu, et al, 1999). Since less cement is used, the hydration heat produced by
RCC is much less than that produced by conventional concrete. Therefore,
the rate of hydration process is slower in RCC.
1
Mass concrete placement requires precautions to minimize cracking.
During the hydration process, cement liberates a substantial amount of heat
with a resulting rise of the concrete temperature. It is often reaches about 40-
70 °C (Ishikawa M, 1991), after the maximum temperature is reached inside
the RCC dam, the latter cools down slowly to a constant temperature. This
temperature variation can induce two kinds of problems. First, the heat
generated creates temperature gradients between the surface and the RCC
core. The resulting nonuniform temperature distribution generates undesired
stresses. Second, the reduction of the global concrete temperature to the final
equilibrium temperature induces volumetric changes that lead to additional
stresses if the mass concrete is externally restrained (Ayotte, et al., 1997).
These temperature gradients induce cracks in the structures, which harm their
integrity, permeability, and durability.
Crack control is achieved by constructing the concrete gravity dam in a
series of individually stable monoliths separated by transverse construction
joints filled with sand-blasting or polystyrene (Forbes and Williams, 1998).
The significance of obtaining an accurate computer model is to provide
the engineer with means of predicting excessive tensile stresses and strains,
which could indicate possible cracking, therefore, allowing the designer to
take appropriate measures to limit or control such potential cracks (Truman,
et al., 1991).
2
To find the optimum construction method to avoid thermal cracks
before the structure construction, numerical simulations with Finite Element
Method (i.e. FEM) can be carried out and it can be checked for cracking. In a
simulation, some parameters can be assumed, such as kind of cement, mixed
design of concrete, casting schedule, and curing method, etc (Ishikawa M,
1991). Many finite element software packages can be used to predict the heat
generated by the concrete, Such as ANSYS, COSMOS/M, ABAQUS and
ADINA.
The finite element methods are becoming an increasingly popular and
powerful tool for civil engineers to analyze practical problems. With rapid
developments in the fields of computational methods, software design and
high speed and low cost hardware, up to date commercial finite elements
codes are capable of dealing with highly complex problems involving staged
construction, complex geometries and material properties.
1.2 Case Study AL-Wehdah RCC Dam
AL-Wehdah dam, located at latitude 32.714 N Longitude 35.822 E, is
situated about 26 km east of the Jordan Rift Valley (see Figure 2.2).
The upstream face of the dam is vertical with a batter at 1:0.6 from El 65
to foundation level, the stepped downstream slope is at 0.8:1 (Figure 2.3).
1.2.1 Description of the Dam
AL-Wehdah dam will be built on the Yarmouk River near the Maqarin
Railroad Station. The dam will regulate the stream flow of the Yarmouk
3
River to provide enough water for irrigation in the Jordan Valley and for
municipal and industrial supplies to the Amman/Zarqa area. Al-Wehdah dam
will be built as a Roller Compacted Concrete (RCC) gravity dam of about
96m high with crest at elevation 110 m ASL. The total storage capacity is
about 110 MCM at elevation 110 m ASL, the normal maximum reservoir
level (see Figure 2.4 and 2.5).
Fig. 1.1 Location of Al Wehdah Dam Site.
4
Fig. 1.2 Typical Cross Section for Al Wehdah Dam
Fig. 1.3 Longitudinal section of Al Wehdah Dam
5
Fig. 1.4 Imaginary View for AL-Wehdah Dam
1.2 Literature Review
In the recent years many researchers conducted studies to determine the
RCC thermal properties.
Truman, et al. (1991) used the finite element program, ABAQUS, along
with user – developed subroutines and experimentally derived material
constants to analyze a pile – founded mass concrete lock and dam structure,
which is performed by an incremental construction analysis including
thermal load.
Ayotte, et al. (1997) presented details of an experimental and
numerical study of thermal strains and induced stresses in large – scale mass
6
concrete. Three large scale monoliths were built on a dam construction site in
the James Bay Territory to monitor the thermal behavior of mass concrete
subjected first to heat of hydration development and subsequent freeze and
thaw cycles. The modeling of one monolith was carried out with computer
program ADINA. Excellent agreement between measured and computed
temperature and stresses was obtained.
Malkawi, et al. (2002) determined the thermal and structural stresses and
temperature control requirements for the 60m high Tannur RCC dam in
Jordan. Also they study temperature distribution with time, concrete
placement temperature limits, and joint spacing requirements to minimize
cracking in the Tannur dam. The computer program ANSYS was used to
simulates the construction process of the Tannur dam. The actual temperature
distribution in the body of the dam also was measured by thermocouples and
was compared with that obtained by ANSYS, and generally a good
agreement was obtained.
Forbes and Williams (1998) discussed the thermal stress modeling,
using of high sand RCC mixes and in-situ modification for RCC construction
of the Candiangullong dam. They concluded that finite element thermal and
stress analysis using ANSYS provide a good understanding of the thermal
condition.
Crichton, et al. (1999) presented a thermal structural analysis using the
ANSYS computer program to assess the effect of heat of hydration in RCC
7
structural stresses. The effect of using simple linear elastic material
properties on the calculated stresses has been compared to a more complex
time variant material modulus and creep analysis. They concluded that the
simple models overestimate the initial stresses and underestimate or cannot
predict the long-term tensile stresses.
Nollet, et al. (1994) described the general aspect of design of the Lac
Robertson dam, its thermal characteristics, methodology and results of the
thermal analysis carried out. The analysis was performed using COSMOS/M
program and consisted of a series of consecutive analysis using the previous
temperature results as initial conditions.
The U.S. Army Corps of Engineers, Engineer Technical Letter (ETL)
1110-2-542(1997) provides guidance for performing thermal studies of mass
concrete structures (MCS) and provide methodology for the first two levels
of thermal studies. Background and examples for several levels of less
complex analysis are presented in this (ETL).
1.4 Objectives
The purpose of this work is to study the temperature distributions and
thermal stresses for RCC dams using two and three – dimensional unsteady
thermo – mechanical analysis. AL-Wehdah dam is presented and analyzed as
case study.
8
A parametric study to find the placement temperature at which the block
length between contraction joints not to exceed 20 m was done for different
cementitious material the have different heat of hydration.
The commercially available software ANSYS and COSMOS/M were
chosen to perform this analysis on a PC work station to model a 2D and 3D
section of the dam, these software are based on the Finite Elements Method
(FEM). Also, comparing the predicted temperatures resulted using ANSYS
program versus the temperature obtained from COSMOS/M program.
1.5 Thesis Outline
In this thesis, Chapter two presents a background about the roller
compacted concrete and its properties, and about the finite element method,
also, it contains a background about thermal analysis. The case study for this
work is described also in this chapter.
Chapter three describes the model characteristics that will be used to
perform the thermal and stress analysis of AL-Wehdah dam.
In Chapter four, a comparison and discussion of the results obtained
from both ANSYS and COSMOS.
A parametric study considering different RCC mixes and different
placement temperatures was presented in Chapter five; analysis and
discussion of the obtained results are also presented in this chapter.
Conclusions and recommendation for this study will be presented in
chapter six
9
CHAPTER TWO
BACKGROUND
2.1 Overview
Three major subjects can be seen from the title of this thesis; thermal
analysis; roller compacted concrete; and finite element method. In this
chapter these subjects will be discussed widely.
2.2 Roller Compacted Concrete
RCC is a concrete that differs from conventional concrete principally in
that it has a consistency that will support a vibratory roller and an aggregate
grading and fines content suitable for compaction by the roller. RCC offers
some substantial benefits over conventional materials for the construction of
major engineered structures such as dams and roads. The significant
advantages of RCC over conventional earth and rock fill construction
including time of construction and hence cost, as well as the lower cost of
materials.
2.2.1 Placing and Compacting RCC
RCC dams are built with a construction technology that uses a concrete
of no-slump consistency. This material is transported, placed and compacted
10
using earth and rockfill construction equipment with the same design
philosophy of conventional gravity dams (Andriolo, 1998).
2.2.2 RCC Proportions
The objective of RCC proportioning is to provide a dense and stable mass
that meets the strength, durability, and permeability requirements for its
application. Materials used for RCC include cementitious materials (Portland
cement and pozzolans such as fly ash), aggregates, water, and admixtures. A
wide range of materials has been used successfully to produce RCC mixtures.
RCC can be made with any of the basic types of cement or combination
of cement and pozzolanic material. Selection of cementitious materials to
resist to chemical attack of sulfate and potential alkali reactivity with certain
aggregates should follow the same standard procedures adopted for CVC.
2.2.2.1 Portland Cement
RCC can be made from any of the basic types of Portland cement. For
mass applications, cements with lower heat of generation are beneficial. They
include Type II (low heat), Type IP (Portland Pozzolanic cement), and Type
IS (Portland Blast Furnace slag cement). The blended cement can be
beneficial also. Pozzolanic Portland cement manufactured by the Jordan
Cement Factory was used in the mixes.
2.2.2.2 Pozzolanic Materials
The selection of pozzolanic material suitable for RCC should be based on
its conformance with applicable standards (ASTM C-618). This standard
11
defines pozzolan as “siliceous or siliceous and aluminous materials which in
themselves posses little or no cementitious value but will, in finely divided
from in the presence of moisture, chemically react with calcium hydroxide at
ordinary temperatures to form compounds possessing cementitious
properties”.
The type of pozzolanic material can include natural pozzolans;
diatomaceous earth; Industrial waste material as fly ash or silica fume.
The use of a pozzolanic material in RCC serves some purposes:
As a partial replacement for cement to reduce heat generation
To increase compressive strength at great ages, if the material
has high pozzolanic activity with cement.
To increase durability
To reduce cost.
As a mineral addition to the mixture to provide fines to improve
workability.
2.2.2.3 Flyash Materials
Flyash is residue of the combustion of the finely ground coal used in the
generation of electric power. The use of fly ash in a properly designed mix
should also help to produce a more homogenous and densely with better
surface finish and all these will tend to reduce the permeability.
The influence of flyash on fresh concrete, ordinary Portland cement
grains are prone to exhibit some coagulation or flocculation in fresh concrete,
12
which tends to produce an inhomogeneous and non-uniform hydrate structure.
The addition of flyash, or any ultra-fine powder, can physically disperse these
cement flows, thus freeing more paste to lubricate the aggregates and
improving workability.
2.2.3 Structural RCC Properties
The strength and elastic properties of RCC vary depending on the mix
components and mix proportions in much the same manner as that for
conventional mass concrete. Aggregate quality and water-cement ratio are the
principal factors affecting strength and elastic properties.
2.2.3.1 Density (ρ ).
Density is defined as mass per unit volume, typical values of density
for mass concrete range from 2240 to 2560 kg /m3 (U.S. Army Corps of
Engineers, 1997).
2.2.3.2 Compressive and Tensile Strength (Fc, Ft).
RCC strength depends upon the quality and grading of the aggregate,
mixture proportions, as well as degree of compaction. The significant
properties of conventionally placed concrete are also significant in Roller
Compacted Concrete. These are compressive strength, tensile strength, and
modulus of elasticity.
Compressive strength test results that shown in Figure 2.1 which done by
(Malkawi, et al. 2003) show that the average compressive strength for RCC is
a bout 10 MPa. The ratio of tensile strength to compressive strength for RCC
13
0
2
4
6
8
10
12
14
16
18
0 50 100 150 200 250 300
Age (day)
Com
pres
sive
Stre
ngth
, MP
a
FlyAsh
Pozzolan
60 kg cement
75 kg cement
100 kg cement
mixtures has typically varied depending on aggregate quality, age, cement
content and strength. Tensile strength of RCC can be determined by tests
either by measuring direct tension or splitting (indirect) tension. The splitting
tension test is also known as the Brazilian test. Data from 22 dams or testing
programs indicates that the average tensile strength of RCC is 10% to 15% of
its compressive strength (Andriolo, et al, 2002).
Figure 2.1 Compressive strength test results for different pozzolanic materials uses
2.2.3.3 Modulus of Elasticity (E c)
Principal factors affect the RCC modulus of elasticity are.
Age of test: the modulus increase with age up to maximum value.
Aggregate type: At large ages the RCC modulus could be similar to
that of the aggregate.
14
Water to cement ratio
2.2.3.4 Poisson's Ratio (υ)
It appears that values for RCC are similar to values reported for CVC
mixtures. A range from about 0.17-0.22 has occurred (U.S. Army Corps of
Engineers, 1997).
2.2.4 Thermal RCC Properties
The important properties for a thermal analysis of a mass-concrete
structure are: convection coefficients, ambient temperature of the air, lift
placement rate, adiabatic temperature rise, specific heat, and coefficient of
thermal expansion.
2.2.4.1 Thermal Conductivity (k).
The thermal conductivity of a material is the rate at which it transmits
heat and is defined as the ratio of the flux of heat to the temperature gradient.
Water content, density, and temperature significantly influence the thermal
conductivity of a specific concrete.
Typical values for thermal conductivity of mass concrete range from
1.73 to 3.46 W/m-k, while for foundation material may ranges from 4.15
W/m-k for clay, to 4.85 W/m-k for sand, to 5.19 W/m-k for gravels, and can
range from 1.73 to 6.23 W/m-k for rock (U.S. Army Corps of Engineers,
1997).
15
2.2.4.2 Coefficient of Thermal Expansion (Cth) .
The coefficient of thermal expansion can be defined as the change in
linear dimension per unit length divided by the temperature change. It is
usually considered constant for temperature varying between 0°C and 65° C
(Ayotte, et al. 1997).
2.2.4.3 Specific Heat (C).
Specific heat is the amount of heat required per unit mass to cause a unit
rise of temperature. It is affected by temperature changes but should be
assumed to be constant for the range of temperature in mass concrete
structure (MCS). For mass concrete mixtures, specific heat is not
substantially affected by age. Typical values for specific heat of mass
concrete range from 0.75 to 1.17 kJ/kg-k, while for soil foundation ranges
from 0.8 kJ/kg–k for sand, to 0.92 kJ/kg–k for clay. Specific heat for
foundation rock generally ranges from 0.8 to 1.0 kJ/kg–k (U.S. Army Corps
of Engineers, 1997).
2.2.4.4 Adiabatic Temperature Rise (Tab)
An adiabatic system is a system in which heat is neither allowed to enter
nor leave. Therefore, adiabatic temperature rise is the change in the
temperature of the concrete due to heat of hydration of the cement under
adiabatic conditions. It is the measure of the heat evolution of the concrete
mixture in a thermal analysis. In a very large mass of concrete, temperatures
near the center of the mass will be approximately equal to the sum of the
16
placement and adiabatic temperatures. However, near the surfaces, the
temperature will be close to the ambient air temperature. The magnitude of
the adiabatic temperature rise and the shape of the curve can vary
significantly for different concrete mixtures. Typical values for the adiabatic
temperature rise of the mass of concrete range from 11–19°C at five days to
17–25°C at 28 days.
2.2.4.5 Heat of Hydration.
The reaction of water with cement is exothermic and generates a
considerable amount of heat over an extended period of time. Heats of
hydration for various cements vary from 300 to 400 J/g at 28 days. The
higher the concrete temperature, the faster the rate of hydration and the more
rapid heat is generated in the concrete member, the higher the cement
content, the greater the potential temperature rises in the concrete.
2.2.4.6 Tensile Strain Capacity (ε ). tc
The strain capacity is considered as the ultimate deformation under
tension before the rupture. Strain is induced in concrete when a change in its
volume is restrained. When the volume change results in tensile strains that
exceed the capability of the material to absorb the strain, a crack occurs.
Design is based on maximum tensile strain. The modulus of rupture test
(CRD-C 16) is done on concrete beams tested to failure under third-point
loading. Tensile strain capacity is determined by dividing the modulus of
rupture by the modulus of elasticity. Typical values range from 50 to 200
17
millions depending on loading rate and type of concrete. Tensile strain
capacity of the RCC is 80µm (Dunstan, 1981)
2.3 The Finite Element Method
Early thermal analysis of mass concrete made use of very simple
concepts and various stepwise, hand calculation methods of determining
temperature changes. Later development of Finite Element (FE) techniques
made possible more accurate and realistic thermal analysis.
The finite element method is a numerical analysis technique for solving
differential equations or boundary value problems in science and engineering.
The differential equations, which govern the physical problem to be solved,
are assumed to exist in a certain domain. The domain then is divided into
smaller parts, which are termed finite elements, and the connected set of
finite elements is called a finite element mesh. The behavior of each element
is described by geometry, kinematics and proper constitutive relationships.
Finally, the elements are linked together to represent the whole domain, and
boundary conditions are applied.
2.4 Thermal analysis
2.4.1 Thermal analysis concept
Mass concrete is defined by ACI code as "any volume of concrete with
dimension large enough to require that measures be taken to cope with
generation of heat of hydration of the cement and attendant volume change to
minimize cracking." When Portland cement combines with water, the
18
ensuring exothermic (i.e. heat-releasing) chemical reaction causes a
temperature rise in concrete mass. The actual temperature rise in a mass
concrete structure (MCS) depends upon the heat generating characteristics of
the mass concrete mixture, the thermal properties, environment conditions,
geometry of MCS, and construction conditions. Usually, the peak
temperature is reached in a few days to weeks after placement, followed by a
slow reduction in temperature. Over period of several months to several
years, the mass eventually cools to some stable temperature, or a stable
temperature cycle for thinner structures. A change in volume occurs in the
MCS proportional to the temperature change and the coefficient of thermal
expansion of the concrete. If volume change is restrained during cooling of
the mass, by either the foundation, the previously placed concrete, of the
exterior surfaces, sufficient tensile strain can develop to cause cracking.
Cracking generally occur in main body or at the surface of the MCS. These
two cracking phenomenon are termed mass gradient and surface gradient
cracking, respectively. ACI 207.1R contains detailed in formation on heat
generation, volume change, restraint, and cracking in mass concrete.
The objectives of the thermal analysis were to define a procedure of
analysis that could be used in larger RCC projects. The intentions were not to
use the results of the analysis in the design process, but to take advantage of
the available information during the construction. The thermal characteristics
of the material, the thermal conditions and the modeling assumptions have
19
been studied to obtain a model giving a temperature distribution as close as
possible to the temperatures measured in the dam. The working model allows
predicting the temperature distribution in the dam at different time.
2.4.2 Thermal analysis Objectives
Thermal analysis is one of the most important analyses that must be
done for the design purposes; it provides a guide for formulation
advantageous design features, optimizing concrete mixture proportions, and
implementing necessary construction requirements. Also it provides cost
savings by revising the structural configuration, constriction sequence,
construction requirements for concrete placement temperature, mixture
proportions, placement rates, and insulation requirements. Cost savings may
be achieved through items such as eliminating unnecessary joints, allowing
increased placing temperatures, increased lift heights, and reduced insulation
requirements. In addition it is necessary to more accurately predict behavior
of unprecedented structures for which limited experience is available, such as
structure with unusual structural configuration, extreme loading, unusual
construction constraints, or severe operational requirements.
2.5 Temperature Control Requirements
Significant thermal induced stresses are developed as a result of the heat
of hydration of the cementitious materials in RCC dams. The temperature
distribution through the dam and its evolution with time depend on the
following:
20
RCC concrete properties,
Climatic factors,
Construction procedure,
lifts Thickness, and
Initial temperature of the lifts, and the Interval between their
placements.
These thermally induced stresses can be significant enough to induce
cracks in the RCC. Recent developments in sophisticated software based on
advanced numerical methods, together with the continually increasing power
of computers allow complex analyses for such thermal-structural problems.
The ANSYS and COSMOS/M computer programs based on the finite
element method were used to analyze the thermal behavior of AL-Wehdah
Dam. The desired outcome of the numerical analysis was
To determine the spatial distribution of temperature and its evolution
with time,
To determine the stress distribution during and following the dam
construction and at the time of reservoir filling,
To identify the appropriate joint spacing to minimize the development
of transverse cracking, and
To determine the concrete placement temperature limits.
21
CHAPTER THREE
MODELING
3.1 Overview
The numeric modeling of the 96 meter high AL Wehdah dam is based
on the information obtained from the literature and the field, that includes:
the daily ambient temperature, the temperature of the RCC in unsettled initial
stage, the adiabatic increment curve of temperature, thermal conductivity,
specific heat, density of the RCC, the bedding mix., and the placement
temperature of the concrete.
3.2 Modeling Methodology
Modeling thermal processes is essential for the analysis of many
structural problems. Obtaining good thermal and stress results is a complex
problem due to the uncertainties related to the prediction of spatial and
temporal variations of material properties and applied loading.
The thermo-mechanical analysis was modeled using an un-coupled
approach. The thermal behavior of the dam was firstly simulated using
incremental construction of the finite element mesh. The results of the
thermal model were then applied using direct super positioning to a structural
model, which also included the step-by-step construction process. The
22
analysis was time marching to closely model the construction of 3m RCC
"lifts" in 10 day intervals over the 320 day construction period.
3.3 Principal Assumptions
The analysis considered some simplifying assumptions related to factors
that should affect thermal variations and the stress distribution.
The first calibration of the thermal characteristics of the material as well
as the modeling assumptions were done on small models of the test section
and the spillway.
The model divided the RCC dam in to 32 layers, each layer was 3 m
high and constructed in 10 days, while according to the actual method of
construction, the layer is 30 cm high constructed each day. Placing lifts every
ten days results in higher temperatures since the new lift adds heat to the
previous lift before a significant amount of cooling can occur. The
temperature of the convective medium, the air, is the mean daily ambient
temperature that is a function of time and represents the project site
conditions. A mean daily temperature is used because of the difficulty in
predicting changes in the temperature variations throughout the day and to
alleviate the need for an excessive number of time steps.
The analysis was carried out considering plain strain linear elastic
behavior, simplified soil-structure interaction entailing elastic foundation and
a uniform, homogeneous foundation, a uniform placement temperature, and a
uniform convection coefficient to all layers.
23
Linear stress analysis was assumed in this study, that is; the relationship
between loads and the induced response is linear. If you double the
magnitude of loads, for example, the response of the model (displacements,
strains, and stresses), will also double. All real structures behave nonlinearly
in one way or another at some level of loading. In some cases, linear analysis
may be adequate. In many other cases, the linear solution can produce
erroneous results. In such cases, nonlinear analysis must be used.
3.4 Model Properties and Parameters
3.4.1 Cementitious Materials
The analysis is based on an RCC mixture containing 60 kg/m3 of
Portland cement and 30 kg/m3 of different pozzolanic material. As shown in
Figure 3.1 theses materials have different heat of hydration. They assumed to
produce different percent of the heat of equivalent cement shown in Figure
3.2, the percent of the heat of equivalent cement that calculated from the
average of (25,40%) was used in this model.
24
100
150
200
250
300
350
400
0% 10% 20% 30% 40% 50%
Pozzolanic Material %
Hea
t of h
ydra
tion
kJ/k
g
Flyash South Africa
Flyash Turkey
Pozzolan Jordan
Rock Flour
Fig. 3.1 The Accumulative Heat of Hydration after 7 days for different Percent of Different Pozzolanic Material
0
10
20
30
40
50
60
70
South Africa Turkey Pozzolana Rock Flour
Type of Pozzolanic Material
perc
ent o
f the
hea
t of e
quiv
alen
t cem
ent ,
% Avg(10,25,40%)
Avg(25,40%)
40%
Fig. 3.2 The Percent of the Heat of Equivalent Cement calculated from different Percent
of Different Pozzolanic Material
25
3.4.2 Concrete Placement Temperature
The temperature of concrete aggregate has the greatest influence on the
initial temperature of the fresh RCC. Due to the low volume of mix water and
the minor temperature difference of the water compared to the aggregate, the
water temperature has a much less significant effect on the overall
temperature. Table 3.1 provides the basis for estimating aggregate
temperature and approximating the RCC placing temperature used in the
analysis. Since aggregate production will be done concurrently with the RCC
placement, stockpile temperatures should closely parallel the average
monthly ambient temperatures. Some heat is added because of screening,
crushing, and transportation activities. In practice, that temperature may vary
from one layer to the other because of exposition to the sun (Nollet, 1994).
The average monthly ambient air temperature is shown in Table 3.1
RCC placement was assumed to take place in the cooler months of the year
i.e., from November to the end of April. Based on the average ambient air
temperature from November to April of 19.7o C, an average RCC placement
temperature of 20.o C was adopted., also the analysis was carried out for an
average RCC placement temperature of 24oC considering placing RCC all
over the year and limiting the RCC placement temperature to (28,32)oC
during the hot months .
26
3.4.3 Initial Temperature of Rock Foundation
Before calculating the temperature we must know the temperature
distribution in the rock ground just before the starting of the casting of the
concrete. It may be difficult to measure the temperature within the rock
foundation directly. Usually the temperature distribution within rock
foundation is obtained from calculation. As a method to calculate it, it is
assumed that the initial temperature for all nodes corresponding to the rock
foundation are the same changing in atmospheric temperature for two or
three years according to the observed data (Ishikawa, M., 1991).
Table 3.1 Predicted RCC Placement Temperatures Month Mean
Monthly Temp (oC)
Mean Annual
(oC)
Diff (oC)
2/3 Diff (oC)
Sub Total (oC)
Aggregate Crushing
Add (oC)
Aggregate Stocking
Temp (oC)
Mixing Add (oC)
Trans. Add (oC)
Final Temp (oC)
Jan. 12.3 21.2 -8.9 -5.93 15.27 1.2 16.47 1.2 -0.6 17.07 Feb. 12.8 21.2 -8.4 -5.60 15.60 1.2 16.80 1.2 0 18.00 Mar. 15.6 21.2 -5.6 -3.73 17.47 1.2 18.67 1.2 0.6 20.47 Apr. 20.6 21.2 -0.6 -0.40 20.80 1.2 22.00 1.2 0.6 23.80 May 24 21.2 2.8 1.87 23.07 1.2 24.27 1.2 1.1 26.57 Jun. 26.7 21.2 5.5 3.67 24.87 1.2 26.07 1.2 1.1 28.37 Jul. 28.4 21.2 7.2 4.80 26.00 1.2 27.20 1.2 1.7 30.10
Aug. 30.1 21.2 8.9 5.93 27.13 1.2 28.33 1.2 1.7 31.23 Sep. 27.8 21.2 6.6 4.40 25.60 1.2 26.80 1.2 1.1 29.10 Oct. 24.5 21.2 3.3 2.20 23.40 1.2 24.60 1.2 0.6 26.40 Nov. 19 21.2 -2.2 -1.47 19.73 1.2 20.93 1.2 0 22.13 Dec. 14 21.2 -7.2 -4.80 16.40 1.2 17.60 1.2 -0.6 18.20
Average 24.4
3.4.4 Materiel Properties and Environmental Conditions
The model properties used were assessed from available data and
typical RCC properties. The density, modulus, Poisson ratio, specific heat
27
and thermal conductivity are given in Table 3.2. A convection coefficient for
air was used, which is consistent with moderate wind speed.
The thermal behavior of the RCC dam was modeled by considering the
heat generated by the exothermic reaction of the cement paste during the
cure. The heat transfers by conduction in the concrete mass and the rock, as
well as the convection on the faces exposed to ambient temperature were
considered. The thermal expansion coefficient is another properties used in
analysis on thermal stress in concrete.
Table 3.2 Properties Adopted for Thermal Analysis
Roller Compacted Concrete Density 2450 kg/m3
Coeff. of Thermal Expansion 8.6 E-6 /deg C Specific Heat 920 J/kg deg C Thermal Conductivity 2.15 J/s m deg C Film (convection) Coefficient (air) 15 J/s m2
Heat Generation of RCC 405 J/g at 28 days Placement Temperature 20o, 24o, 28o and 32o C Modulus of Elasticity 10.0 GPa
Rock Foundation Density 2600 kg/m3
Coeff. of Thermal Expansion 6.0 E-6 /deg C Specific Heat 900 J/kg deg C Thermal Conductivity 2.15 J/s m deg C Foundation Rock Temperature 21.3o Modulus of Elasticity 4.9 GPa
28
0
50
100
150
200
250
300
350
400
450
500
0 50 100 150 200 250 300 350 400
Time (day)
H.H
. (J/
g)
3.4.5 Heat of hydration
During the hydration of cementations materials, numerous factors and
interaction are involved, some of which are currently not fully understood.
As part of this study, a different cementations materials and mixture
proportions that give a different heat of hydration are used.
Heat generation rates adopted for the 60 kg/m3 cement plus 30 kg/m3
pozzolanic material were based on the heat of hydration of the Jordanian
Ordinary Portland Cement (OPC) plus that of pozzolanic material as shown
in Figure 3.1. A heat of hydration of 405 J/g at 28 days was adopted and used
in the thermal analysis (Figure 3.3). Figures 3.4, 3.5, 3.6, and 3.7 show the
simulated heat of hydration for finite element analysis for the four pozzolanic
material.
Fig. 3.3 The accumulative heat of hydration of the cement (OPC)
29
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80 90 100
Time (day)
Rat
e of
H.H
. (J/
m3.
s)
Fig 3.4 Heat of Hydration for RCC mix (60 kg/m3 cement, and 30 kg/m3 South Africa
flyash), for Finite Element Analysis
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Time (day)
Rat
e of
H.H
. (J/
m3.
s)
Fig 3.5 Heat of Hydration for RCC mix (60 kg/m3 cement, and 30 kg/m3 Turkey flyash),
for Finite Element Analysis
30
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Time (day)
Rat
e of
H.H
. (J/
m3.
s)
Fig 3.6 Heat of Hydration for RCC mix (60 kg/m3 cement, and 30 kg/m3 Jordanian
pozzolan), for Finite Element Analysis
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Time (day)
Rat
e of
H.H
. (J/
m3.
s)
Fig 3.7 Heat of Hydration for RCC mix (60 kg/m3 cement, and 30 kg/m3 rock flour), for Finite Element Analysis
31
3.5 Boundary and Initial Conditions
Figure 3.8 shows the boundary and initial conditions for thermal and
structural analysis, which are:
1. All boundaries around the foundation rock satisfy the adiabatic
condition: 0.0=∂∂ nT (i.e., no change in temperature in the direction
normal to the planes. The dam and foundation that are exposed to the
atmosphere satisfy the following condition (as defined previously).
( ) ( )Bf TThnTK −−=∂∂ 3.1
Where T is the transient temperature, n the outer unit normal, K is the
thermal conductivity, hf is the film coefficient and TB is ambient temperature.
2. Initial condition. The initial temperature for all nodes of foundation is
assigned from rock temperature. The initial temperature of each layer of
the dam is set to be equal to the placement temperature.
3. Structural boundary conditions. The foundation rock is infinite, and no
horizontal movement is allowed; thus the foundation rock is restricted
in all horizontal direction (i.e., there are rollers on vertical boundaries
and pins at the bottom boundary). Therefore, the vertical direction
movement is restricted in the bottom boundary.
Appendix A shows more detail about the theories and the boundary
condition
32
Fig 3.8 Thermal and Structure Boundary Conditions for Thermal Analysis
33
CHAPTER FOUR
COMPARATIVE STUDY BETWEEN COSMOS & ANSYS
4.1 Overview
COSMOS and ANSYS are the two finite element based softeware
that are used to carry out the thermal analysis for the RCC AL-Wehdah
dam. The analysis was carried out for Jordanian Pozzolan RCC mix, with
placement temperature of 28°C. It is quite necessary to talk about these two
codes and what are the bases and theories that each code depends on, the
results after that will be presented and discussed.
4.2 COSMOS/M Software
COSMOS/M Thermal is a fast, robust, and accurate finite element
program for the analysis of linear static structural problems. The program
exploits a new technology developed at Structural Research for the solution
of large systems of simultaneous equations using sparse matrix technology
along with iterative methods combined with novel database management
techniques to substantially reduce solution time, disk space, and memory
requirements (Structural Research and Analysis Corporation , 1997).
COSMOS/M Thermal has been written from scratch using state of the
art techniques in FEA with two goals in mind: 1) to address basic design
34
needs, and 2) to use the most efficient possible solution algorithms without
sacrificing accuracy. The program is particularly suitable for the solution of
large models subjected to a variety of loading and boundary conditions
environments.
The program can analyze linear and nonlinear steady state and transient
heat conduction problems with convective and radiative type boundary
conditions in one, two, and three-dimensional geometries
Time curves facility is the most important option in the COSMOS
program. It enables the user to simulate any dependent time problems. For
example, many parameter in our model is time dependent; RCC casting, heat
generation due to the heat of hydration of RCC, and convection… etc. Killing
and living the elements are also done using the time curve option.
Figure 4.1 shows all the time curves that were used in model analysis.
For the first layer as shown, the heat generation started from time zero, while
for the next layer, zero values were given to the heat generation until the
placement time reached for this layer. The same thing done to apply the heat
convection on the layer surface, this convection continuing for ten days only,
so a time curves with zero values are made and a value of one (1) for 10 days
only is given to the time curve to alive the convection on this layer, the
convection on the outer surface will start when the layer placed but this
convection will continue, so the value (1) will extend from the placement to
the last time as shown.
35
0 10 20 30 40 50 60 70 80 90 100
Time (day)
Hea
t Gen
erat
ion
C
onve
ctio
n on
the
Laye
rs
C
onve
ctio
n on
Up
& D
ownS
tream
Fig 4.1 Time Curves Used in COSMOS/M for the 1st three layers
36
4.3 ANSYS Software
ANSYS is finite element analysis based software enables engineers to
perform the following tasks:
Build computer models or transfer CAD models of structures,
products, components, or systems.
Apply operating loads or other design performance conditions.
Study the physical responses, such as stress levels, temperature
distributions.
Optimize a design early in the development process to reduce
production costs.
The ANSYS program has a comprehensive graphical user interface
(GUI) that gives users easy, interactive access to program functions,
commands, and documentation and reference material. An interactive menu
system helps users to navigate through the ANSYS program. Users can input
data using a mouse, a keyboard, or a combination of both (Anonymous,
2002).
Birth and death of elements is also some of the effective facilities in
ANSYS program, it is used to simulate any dependent time problems. For
heat convection boundaries for instant, heat convection boundary condition
should be superimposed on the surface of conduction element. In the process
of adding the concrete, it should be given ‘birth’ to heat conduction elements
that correspond to the concrete. The heat convection boundary condition are
37
also given ‘birth’, which means apply convection on top of conduction
element at the same time, if the conduction elements include heat convection
boundaries as shown in Figure (3.7). However, the element which has
previously given the operation of ‘birth’’, should not given the ‘death’
operation in any of the following steps, only for convection boundary
condition, delete from the previous layer and apply to the next layer and so
on until the dam complete. Also for heat of hydration, as in Figure 4.2, which
shows from STEP, i to STEP i+1 is allowed. In this way, the analysis can be
done with a single computational mesh instead of several ones, one for each
stage of construction.
Convection
Conduction Conduction Conduction
Convection
Convection
Step i-1 Step i Step i+1
Birth
Death
Birth
Death
Figure 4.2 Births and Death of Elements
38
4.4 Model Analysis
4.4.1 Two-Dimensions Model Analysis using COSMOS
The dam was modeled as a two-dimensional transient heat transfer
model to simulate the real construction process of the dam. The time curve
option in the COSMOS/M Program that was discussed previously is used for
the heat of hydration and the heat convection effects to simulate the time lag
between the placements of the RCC layers. The dam is divided into 32 layers.
Each layer has thickness of 3 m constructed in 10 days. The total number of
elements and nodes are 2266 and 7074 respectively. Quadrilateral plane
element with eight nodes was used in the finite element analysis (Figure 4.3).
The element has one degree of freedom temperature at each node. This is a
high order element that has 8 nodes, is suitable for simulating irregular
shapes, and is applicable to the study of a two-dimension steady state or
transient thermal analysis. Figure 4.5 shows the finite element mesh of cross
section of dam.
4.4.2 Three-Dimensions Model Analyses using COSMOS
A 3-D analysis was also carried out for Al Wehdah RCC dam. The
length of the dam is divided into 16 blocks, each block 30 m long. Figure 4.6
shows the finite element mesh for 3D, the total number of elements and
nodes is 11330 and 14424 respectively. A solid element type was used for the
thermal analysis (see Fig 4.3). This element has 8 nodes with a single degree
of freedom temperature at each node.
39
4.4.3 Two-Dimensions Model Analysis using ANSYS
The dam was modeled as a two-dimensional transient heat transfer
model using a birth and death procedure (see Figure 4.2) to simulate the real
construction process of the dam. The dam is divided into 32 layers. Each
layer has thickness of 3 m constructed in 10 days; the rock foundation is
presented from 30 meters upstream, 30 meters downstream and 30 meters
under the dam. The rock elements simulate the heat dissipation through the
foundation. The total number of elements and nodes are 2266 and 7074
respectively. PLANE77 element type available in ANSYS element library
was used. The element has one degree of freedom temperature at each node
as shown in Figure 4.4. This element is a higher order element has 8 nodes
and it is suitable to simulate irregular shape and applicable to a two
dimension steady – state or transient thermal analysis. Also, the element can
be used to carry out structural analysis by replacing it by an equivalent
structural element called PLANE82, Figure 4.4. A plane strain model was
adopted for two-dimension analysis. Plane strain is the condition for which
the strains perpendicular to the plane of the analysis are maintain at zero.
Gravity loads due to self – weight of the rock foundation and the RCC and
thermal loads from thermal analysis were included in the structural analysis.
Figure 4.7 shows the finite element mesh of cross section of dam.
40
4.4.4 Three-Dimensions Model Analyses using ANSYS
A 3-D analysis was also carried out for Al Wehdah RCC dam. The
length of the dam is divided into 16 blocks, each block 30 m long. Figure 4.8
shows the finite element mesh for 3D analysis. A solid 70 element type was
used for the thermal analysis, Figure 4.4. This element has 8 nodes with a
single degree of freedom temperature at each node. A solid 65 element type
was used for the structural analysis. This element has three degrees of
freedom in each node, permitting movement in the x, y and z direction. Same
procedure in two dimensions was used for three dimensions to generate the
mesh. The total number of elements and nodes is 11330 and 14424
respectively. The step-by-step analysis of the construction simulation process
allows the determination of the temperature for each added lift.
41
Fig. 4.3 Element Types Used in COSMOS
Fig. 4.4 Element Types Used in ANSYS
42
Fig. 4.5 Two Dimension Model Mesh in COSMOS
Fig. 4.6 Three Dimension Model Mesh in COSMOS
43
Fig. 4.7 Two Dimension Model Mesh in ANSYS
Fig. 4.8 Three Dimension Model Mesh in ANSYS
44
4.5 Finite Element Results
4.5.1 Finite Element Results of COSMOS
Figure 4.9 shows the temperature contours in the dam body after 100
days for placement temperatures of 28°C and for RCC mix containing
Jordanian pozzolan using two and three dimensional analysis, it can be seen
that the maximum temperature in the dam core is 42.34 °C for 2D analysis
and 43.17 °C for 3D analysis. At the end of heat of hydration as shown in
figure 4.10 the temperature decreased to 42°C and 42.2°C for 2D and 3D
analysis respectively.
Figure 4.11 shows the predicted temperature history in the dam center at
different heights, this figure determines the elevation where the maximum
temperature was occurred. For 2D analysis as shown, 42.3 °C is the
maximum temperature that can occur in the dam during the construction; it is
at 12 m from the dam base. While in 3D analysis the peak temperature was
42.6 °C at the same elevation.
The temperature distribution shown in Figure.4.12 is for a specific
points located at a distance 12m from the dam base at different distance from
the dam upstream, once the RCC placed the temperature drop quickly to
23.2°C due to the convection on the layer surface then the temperature rise to
42.3°C for two dimensional analysis, the drop in 3D analysis was 23.1°C and
the maximum reached temperature was 42.6°C.
45
Fig 4.9 Temperature Contour after 100 days using COSMOS
46
Fig 4.10 Temperature Contour at the End of Heat of Hydration, 410 days using COSMOS
47
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0 50 100 150 200 250 300 350 400 450
Time (Day)
Tem
pera
ture
(Deg
C)
At the dam base12 m from the dam base22 m from the dam base34 m from the dam base45 m from the dam base60 m from the dam base
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0 50 100 150 200 250 300 350 400 450
Time (Day)
Tem
pera
ture
(Deg
C)
At the dam base12 m from the dam base22 m from the dam base34 m from the dam base45 m from the dam base60 m from the dam base
Fig 4.11 Predicted Temperature History in the Dam Center at Different Heights using COSMOS for 2D & 3D Analysis Respectively
48
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0 50 100 150 200 250 300 350 400
Time (Day)
Tem
pera
ture
(Deg
C)
3 m from UpstreamCenter of dam4 m from Downstream
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0 50 100 150 200 250 300 350 400 450
Time (Day)
Tem
pera
ture
(Deg
C)
3 m from UpstreamCenter of dam4 m from Downstream
Fig 4.12 Predicted Temperature History at Different Nodal Point at 12m from the Dam
Base using COSMOS for 2D & 3D Analysis Respectively
49
4.5.2 Finite Element Results of ANSYS
Figure 4.13 shows the temperature contours in the dam body after 100
days for placement temperatures of 28°C and for RCC mix containing
Jordanian Pozzolan using two and three dimensional analysis, it can be seen
that the maximum temperature in the dam core is 43.6 °C for 2D analysis and
43.6 °C for 3D analysis. At the end of heat of hydration as shown in figure
4.14 the temperature was 43.7°C and 43.9°C for 2D and 3D analysis
respectively.
Figure 4.15 shows the predicted temperature history in the dam center at
different heights, this figure determines the elevation where the maximum
temperature occurs. For 2D and 3D analysis, 43.9 °C is the maximum
temperature that can occur in the dam during the construction; it is at 12 m
from the dam base as shown.
The temperature distribution shown in Figure.4.16 is for a specific
points located at a distance 12m from the dam base at different distance from
the dam upstream, once the RCC placed the temperature drop quickly to
24.1°C due to the convection on the layer surface then the temperature rise to
43.7°C for two dimensional analysis, the drop in 3D analysis was 24.1°C and
the maximum reached temperature was also 43.9°C.
50
Fig 4.13 Temperature Contour after 100 days using ANSYS
51
Fig 4.14 Temperature Contour at the End of Heat of Hydration, 410 days, using ANSYS
52
20222426283032343638404244464850
0 50 100 150 200 250 300 350 400 450
Time (Day)
Tem
pera
ture
(Deg
C)
At the dam base
12 m from the dam base
34 m from the dam base
45 m from the dam base
60 m from the dam base
20222426283032343638404244464850
0 50 100 150 200 250 300 350 400 450
Time (Day)
Tem
pera
ture
(Deg
C)
At the dam base12 m from the dam base22 m from the dam base34 m from the dam base45 m from the dam base60 m from the dam base
Fig 4.15 Predicted Temperature History in the Dam Center at Different Heights using ANSYS for 2D & 3D Analysis Respectively
53
20222426283032343638404244464850
0 50 100 150 200 250 300 350 400
Time (Day)
Tem
pera
ture
(Deg
C)
3 m from UpstreamCenter of dam4 m from Downstream
20222426283032343638404244464850
0 50 100 150 200 250 300 350 400 450
Time (Day)
Tem
pera
ture
(Deg
C)
3 m from UpstreamCenter of dam4 m from Downstream
Fig 4.16 Predicted Temperature History at Different Nodal Point at 12m from the Dam Base using ANSYS for 2D & 3D Analysis Respectively
54
4.6 Summary and Discussion
Table 4.1 summarizes the models analysis for both COSMOS and
ANSYS codes, also it summarizes the results that were obtained from theses
programs and then the crack analysis for theses results is also summarized.
Figure 4.17 and 4.18 show the predicted temperature history using two
and three dimensional analysis by ANSYS and COSMOS at a nodal point in
the dam center and at a point near the upstream face; both points are at 12 m
from the dam base.
Figure 4.19 shows the temperature distribution along the dam cross
section at an elevation of 22 m from the dam base using two and three
dimensional analysis by ANSYS and COSMOS at the end of heat of
hydration (410 Days). And Figure 4.20 shows the vertical temperature
distribution at the dam center at the end of heat of hydration using also two
and three-dimensional analysis. It is clearly seen that both two and three
dimension analysis gave nearly the same results, for both COSMOS and
ANSYS, so discussing one of these analysis will be enough.
From all these figures, it can be seen that the maximum temperature
obtained from ANSYS program are higher than that obtained from COSMOS
by nearly one degree.
Since the two meshes for ANSYS and COSMOS has the same number
of elements and nodes, and the same material properties applied on both of
them, it can be concluded that this difference in temperature may
55
occur due to only two factors, the first is the heat generation due to the heat
of hydration, and the other is the temperature drop due to the convection
effects.
The values of heat of hydration at each 10 days were used in the two
programs according to Figure 3.6, but 1 day increment was used, the heat of
hydration at this increment was interpolated by the programs, the
interpolation process that is done by COSMOS differs from the ANSYS
interpolation.
Once the RCC placed, the temperature dropped from 28°C to 23°C in
COSMOS analysis, while it dropped to 24°C in ANSYS as shown in Figure
4.17, this is one of the factors that affect the maximum temperature results.
This difference refers to the theories that each code is based on.
From the crack analysis presented in Table 4.1, it can be concluded that
ANSYS gives more conservative results; 42 contraction joints must be placed
according to ANSYS results while 40 contraction joints is enough according
to COSMOS results.
56
Table 4.1 Summary Results for COSMOS and ANSYS
COSMOS ASNYS DESCRIPTIONS
2D 3D 2D 3D
Output file size (GB) 0.24 1.6 0.14 0.72
Gen
eral
Run Time (hr) 1 4 0.5 3
No. of Elements 2266 11330 2266 11330
No. of Nodes 7074 14424 7074 14424
Element Type Plane 2D Solid Plane 77 Plane 70
Mod
el A
naly
sis
Time Simulation Time Curves Birth & Death
Peak Temperature 42.3 42.6 43.6 43.8
Elevation of Peak Temp (m) 12 12 12 12
Time of Peak Temp (days) 110 110 110 110 Res
ults
Temp. Drop due to Convection oC 23.2 23.1 24.2 24.1
∆T oC (Peak – Min. Ambient) 30.3 30.5 31.2 31.5
Induce strain (µmm) 142 143 148 149
No. of block 40 40 42 43
Cra
ck A
naly
sis
Length of block (m) 26 24 23 23
57
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0 50 100 150 200 250 300
Time (Day)
Tem
pera
ture
(Deg
C)
ANSYSCOSMOS
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
0 50 100 150 200 250 300 350
Time (Day)
Tem
pera
ture
(Deg
C)
ANSYS
COSMOS
Fig 4.17 Comparative Predicted Temperature History using ANSYS and COSMOS at the Dam Center and 12 m from the Dam Base using 3D Analysis
Fig 4.18 Comparative Predicted Temperature History using ANSYS and COSMOS at 3m from Upstream and 12 m from the Dam Base using 2D Analysis
58
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70 80
Distance (m)
Tem
pera
ture
(Deg
C)
ANSYS (2D)ANSYS (3D)COSMOS (2D)COSMOS (3D)
0
8
16
24
32
40
48
56
64
72
80
88
96
20 25 30 35 40 45 50
Temperature (Deg C)
Dis
tanc
e (m
) ANSYS (2D)ANSYS (3D)COSMOS (2D)COSMOS (3D)
Fig 4.19 Cross Section Temperature Distribution at 22 m from the Dam
Base using ANSYS and COSMOS
Fig 4.20 Vertical Temperature Distribution at the Dam Center using ANSYS and
COSMOS
59
CHAPTER FIVE
THERMAL AND STRESS ANALYSIS
5.1 Overview
Thermal analysis was carried out using both two and three-dimensional
Finite Element Method (FEM) in ANSYS program, the analysis done for
different RCC mix of different pozzolanic material (South Africa flyash,
Turkey flyash, Jordanian pozzolan, and rock flour) which have different heat
of hydration as discussed in the chapter three.
A parametric study to find the placement temperature that required
getting a 20 m spacing between contraction joints was also done by changing
the placement temperature (20, 24, 28, and 32 °C) and accordingly carrying
out the analysis.
One RCC mix using Jordanian pozzolan with 28°C placement
temperature were used to perform stress analysis using both two and three-
dimensional Finite Element Method (FEM). The analysis carried out using
ANSYS program only, some difficulties and insufficient time prevent us to
use COSMOS program for stress analysis.
60
5.2 Thermal Analysis for RCC Dam
5.2.1 Effect of Convection Coefficients
The forms are analytically removed (i.e., convection coefficients change
Values) one days after a lift is placed with lift placement proceeding at ten-
day intervals. This construction rate tends to be much faster than what
actually occurs on the job site. Nevertheless, the increased rate for form
removal will produce higher thermal gradients due to removal near the time
when peak temperatures are obtained producing a sudden cooling at the
surface. Also, placing lifts every ten days results in higher temperatures since
the new lift adds heat to the previous lift before a significant amount of
cooling can occur. The temperature of the convective medium, the air, is the
mean daily ambient temperature that is a function of time and represents the
project site conditions. A mean daily temperature is used because of the
difficulty in predicting changes in the temperature variations throughout the
day and to alleviate the need for an excessive number of time steps.
5.2.2 Effect of Heat of Hydration and placement Temperature
Heat of hydration of cementitious materials as well as placing
temperature is the principal parameters influencing the temperature rise in the
massive concrete structure.
5.2.3 Results and discussion of Thermal Analysis
Figure 5.1 shows the temperature contours at the end of heat of
hydration (410 days) for different placement temperatures (20, 24, 28°C) for
61
RCC mix containing South Africa flyash using two and three dimensional
analysis, it can be seen that the maximum temperature in the dam core
increases by increasing the placement temperature, for 2D analysis it is 41.16
°C when using 20°C placement temperature, increased then to 45.32 °C for
24°C placement temperature then increased to 47.5 for 28 °C placement
temperature, also for 3D analysis the peak temperature increased from 42.37
°C to 45.23 °C to 47.9 °C respectively, 21.3˚C which is equal to the average
ambient temperature is the minimum temperature reached in the dam, it is
located at the outer surface of the dam body where the ambient temperature
affects the dam.
Figures 5.2, 5.3, and 5.4 show also the temperature contours at the end
of heat of hydration for RCC mix of Turkey flyash, Jordanian Pozzolan, and
Rock Flour respectively. The peak temperatures in the dam core at the end of
heat of hydration for these different analyses are summarized in Table 5.1
62
Fig. 5.1 Temperature contour at the end of heat of hydration, 410 days for different placement temperature (20, 24, 28°C) for RCC mix of South Africa flyash
63
Fig. 5.2 Temperature contour at the end of heat of hydration, 410 days for different placement temperature (20, 24 and 28 °C) for RCC mix of Turkey flyash
64
Fig. 5.3 Temperature contour at the end of heat of hydration, 410 days for different placement temperature (20, 24, 28 and 32 °C) For RCC mix of Jordanian pozzolan
65
Fig. 5.4 Temperature contour at the end of heat of hydration, 410 days for different placement temperature (20, 24, 28 and 32 °C) For RCC mix of rock flour
66
Table 5.1, Peak temperature in the dam core at the end of heat of hydration
Figure.5.5 shows the comparison temperature history at 22m from the
base of the dam (in the middle of the eighth layer) at the dam center where
the maximum temperature occurred during the construction process for three
different placement temperatures (20, 24, 28°C) and also for RCC mixes
containing South Africa flyash using two-dimensional analysis. For example
when using 28˚C placement temperature, the placement of this layer started
in the day 70, the temperature increased from 28˚C to 43.3˚C in the first ten
days when the heat of hydration is the maximum, and then the temperature
decreased by 0.2˚C due to the effect of convection on the layer surface, the
temperature after that started a new increase but with a rate smaller than the
first one due to the decreasing of the heat of hydration rate with time, the
temperature reached its maximum (47.5˚C) after 100 days from the
placement (in the day 170, as shown), then it remained constant for a long
period of time because heat transfer from the core of dam to the surface is
very slow, and further more the heat conduction due to the construction of the
overlying layers of RCC prevents internal heat loss from the constructed lift
2D Analysis 3D Analysis Placement temp. oC 20 24 28 32 20 24 28 32 South Africa flyash 41.16 45.32 47.5 * 42.37 45.23 47.9 * Turkey flyash 39.66 42.84 46.02 * 41.02 43.67 46.35 * Jordanian pozzolan 38.49 41.67 45.8 48 39.79 42.45 45.12 47.78 Rock Flour 37.58 40.76 43.9 47.12 38.85 42.45 45.16 46.82
67
surface. The maximum temperature for 20˚C and 24˚C placement
temperature was 41.1˚C, 45.3˚C respectively.
Figures 5.6, 5.7, and 5.8 show also the comparison temperature history
at 22m from the dam base but for RCC mix of Turkey flyash, Jordanian
pozzolan, and Rock Flour respectively. The maximum temperatures occurred
during the construction process for these different analyses are shown in
Table 5.2.
Table 5.2, Maximum temperatures occurred during the construction process
Fig. 5.5 Predicted Temperature History in the Dam Center at 22 m from Base of Dam for
Different Placement Temperatures for RCC Mix of South Africa flyash
2D Analysis 3D Analysis Placement temp. oC 20 24 28 32 20 24 28 32 South Africa flyash 41.15 45.33 47.8 * 42.59 45.25 47.9 * Turkey flyash 39.67 43.12 46.3 * 40.58 43.7 46.4 * Jordanian Pozzolan 38.5 41.93 45.1 48.2 39.37 42.47 45.1 47.8 Rock Flour 37.59 41 45.2 47.3 38.4 41.5 45.2 46.84
15
20
25
30
35
40
45
50
0 100 200 300 400 500
Time (Day)
Tem
pera
ture
(Deg
C)
Placement Temp=20 deg C
Placement Temp=24 deg C
Placement Temp=28 deg C
Placement Temp=32 deg C
Starting Placement Time
68
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
0 100 200 300 400 500
Time (Day)
Tem
pera
ture
(Deg
C)
Placement Temp=20 deg C
Placement Temp=24 deg C
Placement Temp=28 deg C
Placement Temp=32 deg C
Starting Placement
Time
Fig. 5.6 Predicted Temperature History in the Dam Center at 22 m from Base of Dam for
Different Placement Temperatures for RCC Mix of Turkey flyash
Fig. 5.7 Predicted Temperature History in the Dam Center at 22 m from Base of Dam for
Different Placement Temperatures for RCC Mix of Jordanian pozzolan
15
20
25
30
35
40
45
50
0 100 200 300 400 500
Time (Day)
Tem
pera
ture
(Deg
C)
Placement Temp=20 deg C
Placement Temp=24 deg C
Placement Temp=28 deg C
Placement Temp=32 deg C
Starting Placement Time
69
Fig. 5.8 Predicted Temperature History in the Dam Center at 22 m from Base of Dam for Different Placement Temperatures for RCC Mix of rock flour
The temperature distribution shown in Figure.5.9 is for a specific points
located at a distance 12m from the dam base at two different distance from
the dam upstream for a placement temperature of 28oC, the analysis carried
for RCC mix of South Africa flyash using 2D and 3D analysis. The cleared
temperature drop down from 28 oC to 24 oC that is shown in the figure was
due to the convection on the layer surface, the drop as seen continued for one
day only, the temperature after that increased to 43 oC for the two nodal
points due to the heat generation, For the point near the upstream face (3m
from the upstream), once the temperature reached its maximum it started
decreasing because of the heat dissipation into the air, the temperature
15
20
25
30
35
40
45
50
0 100 200 300 400 500
Time (Day)
Tem
pera
ture
(Deg
C)
Placement Temp=20 deg C
Placement Temp=24 deg C
Placement Temp=28 deg C
Placement Temp=32 deg C
Starting Placement Time
70
decreased to 23.5oC after 420 days and this will continue to reach the ambient
temperature(21.3oC). While for the point in the dam center, the temperature
was continuing in its increasing (47.8oC) because it is far away from the
surface, so it gets more temperature from the nodal points above it that
starting their heat generation. It also can be seen that the temperature
distribution for 28 oC placement temperature was the same for two and three
dimensional analysis, which implementing that the 2D analysis could be
convenient for this type of problems.
Fig 5.9 Comparison 2D & 3D Analysis for Predicted Temperature History at Different Points at 12 m from Dam Base, Using 28°C Place_Temp for RCC Mix of South Africa
flyash
20
25
30
35
40
45
50
0 100 200 300 400 500
Time (Day)
Tem
pera
ture
(Deg
C)
3 m from Upstream (2D)Center of dam (2D)3 m from Upstream (3D)Center of dam (3D)
Starting Placement Time
71
Figures 5.10, 5.11, and 5.12 show also the temperature distribution for
the same specific points but for RCC mix of Turkey flyash, Jordanian
Pozzolan, and rock flour respectively. The maximum temperature as shown
for the RCC mix of South Africa flyash is the highest, then Turkey flyash,
Jordanian Pozzolan, and rock flour respectively.
Fig 5.10 Comparison 2D & 3D Analysis for Predicted Temperature History at Different Points at 12 m from Dam Base, Using 28°C Place_Temp for RCC Mix of Turkey flyash
20
25
30
35
40
45
50
0 100 200 300 400 500
Time (Day)
Tem
pera
ture
(Deg
C)
3 m from Upstream (2D)Center of dam (2D)3 m from Upstream (3D)Center of dam (3D)
Starting Placement Time
72
20
25
30
35
40
45
50
0 100 200 300 400 500
Time (Day)
Tem
pera
ture
(Deg
C)
3 m from Upstream (2D)Center of dam (2D)3 m from Upstream (3D)Center of dam (3D)
Starting Placement Time
Fig 5.11 Comparison 2D & 3D Analysis of Predicted Temperature History at Different Points at 12 m from Dam Base, Using 28°C Place_Temp for RCC Mix of Jordanian
pozzolan
Fig 5.12 Comparison 2D & 3D Analysis for Predicted Temperature History at Different Points at 12 m from Dam Base, Using 28°C Place_Temp for RCC Mix of Rock Flour
20
25
30
35
40
45
50
0 100 200 300 400 500
Time (Day)
Tem
pera
ture
(Deg
C)
3 m from Upstream (2D)Center of dam (2D)3 m from Upstream (3D)Center of dam (3D)
Starting Placement Time
73
Figure 5.13 shows the temperature distribution along the dam cross
section at an elevation of 22 m from the dam base for different placement
temperatures for RCC mix of South Africa flyash using two dimensional
analyses at the end of heat of hydration (410 Days). At the both sides of the
dam the temperature was 21.5 which is close to the ambient temperature,
while it increased as we come close to the dam center, it reached 41.4˚C,
45.3˚C, 47.5˚C for 20°C, 24°C, 28°C placement temperature respectively.
The effect of placement temperature is cleared perfectly in this figure.
Figures 5.14, 5.15, and 5.16 show also the temperature along the dam
cross section at an elevation of 22 m from the dam base but for RCC mix of
Turkey flyash, Jordanian Pozzolan, and rock flour respectively; Also the
maximum temperature for the RCC mix of South Africa fly ash was the
highest one.
74
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70 80
Distance (m)
Tem
pera
ture
(Deg
C)
Placement Temp=20 deg CPlacement Temp=24 deg CPlacement Temp=28 deg CPlacement Temp=32 deg C
Fig 5.13 Cross Section Temperature Distribution at 22 m from the Dam Base for Different Placement Temperatures for RCC Mix of South Africa flyash
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70 80
Distance (m)
Tem
pera
ture
(Deg
C)
Placement Temp=20 deg CPlacement Temp=24 deg CPlacement Temp=28 deg CPlacement Temp=32 deg C
Fig 5.14 Cross Section Temperature Distribution at 22 m from the Dam Base for Different Placement Temperatures for RCC Mix of Turkey flyash
75
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70 80
Distance (m)
Tem
pera
ture
(Deg
C)
Placement Temp=20 deg CPlacement Temp=24 deg CPlacement Temp=28 deg CPlacement Temp=32 deg C
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70 80
Distance (m)
Tem
pera
ture
(Deg
C)
Placement Temp=20 deg CPlacement Temp=24 deg CPlacement Temp=28 deg CPlacement Temp=32 deg C
Fig 5.15 Cross Section Temperature Distribution at 22 m from the Dam Base for Different
Placement Temperatures for RCC Mix of Jordanian pozzolan
Fig 5.16 Cross Section Temperature Distribution at 22 m from the Dam Base for Different
Placement Temperatures for RCC Mix of Rock Flour
76
0
10
20
30
40
50
60
70
80
90
100
20 25 30 35 40 45 50
Temperature (Deg C)
Dis
tanc
e (m
)
Placement Temp=20 deg CPlacement Temp=24 deg CPlacement Temp=28 deg CPlacement Temp=32 deg C
Figure 5.17 and 5.18 and 5.19 and 5.20 show the vertical temperature
distribution at the dam center for different placement Temperatures at the end
of heat of hydration for the four RCC mix respectively using two dimensional
analyses. The temperature gradient is high at region near the foundation. This
is due to the heat loses by conduction into the foundation. The maximum
temperature is about 41˚C for the first placement temperature at 20m from
the base.
Fig 5.17 Vertical Temperature Distribution at the Dam Center for Different Placement Temperatures for RCC Mix of South Africa flyash
77
0
10
20
30
40
50
60
70
80
90
100
20 25 30 35 40 45 50
Temperature (Deg C)
Dis
tanc
e (m
)
Placement Temp=20 deg CPlacement Temp=24 deg CPlacement Temp=28 deg CPlacement Temp=32 deg C
0
10
20
30
40
50
60
70
80
90
100
20 25 30 35 40 45 50
Temperature (Deg C)
Dis
tanc
e (m
)
Placement Temp=20 deg CPlacement Temp=24 deg CPlacement Temp=28 deg CPlacement Temp=32 deg C
Fig 5.18 Vertical Temperature Distribution at the Dam Center for Different Placement
Temperatures for RCC Mix of Turkey flyash
Fig 5.19 Vertical Temperature Distribution at the Dam Center for Different Placement
Temperatures for RCC Mix of Jordanian pozzolan
78
0
10
20
30
40
50
60
70
80
90
100
20 25 30 35 40 45 50
Temperature (Deg C)
Dis
tanc
e (m
)
Placement Temp=20 deg CPlacement Temp=24 deg CPlacement Temp=28 deg CPlacement Temp=32 deg C
Fig 5.20 Vertical Temperature Distribution at the Dam Center for Different Placement Temperatures for RCC Mix of Rock Flour
All the maximum temperatures that occurred in the dam during the
construction process using two and three-dimensional analysis are
summarized in Figure 5.21 for the different RCC mix using the four
placement temperature (20˚C, 24˚C, 28˚C, and 32˚C). It can be clearly seen
that South Africa flyash RCC mix has the highest temperature, and then the
mix of Turkey flyash, then Jordanian pozzolan mix, and rock flour RCC mix
has the lowest one. Also it can be seen that the three dimensional analysis
gives a values higher than two dimensional analyses for 20˚C, 24˚C, and
32˚C placement temperature, while for 28˚C placement temperature the
values are close to each other. The most important conclusion from this
figure is that for a maximum predicted temperature of 46˚C for example; the
79
36
37
38
39
40
41Pe
42
44
45
46
47
48
49
50
20 24 28 32
Placement Te perature oC
ak T
eat
ure
o C
43mpe
r
m
South Africa Flyash (2D)South Africa Flyash (3D)Turkey Flyash (2D)Turkey Flyash (3D)Jordanian Pozzolan (2D)Jordanian Pozzolan (3D)Rock Flour (2D)Rock Flour (3D)
placement temperature can be easily determined using this figure. It is
25.5˚C, 26.5˚C, 28˚C, 29.5˚C for the four RCC mix respectively.
Fig.5.21 Summary of the Maximum Temperatures in the Dam Body for Different RCC Mix and Different Placement Temperatures
5.3 Thermal Stresses in RCC Dam
5.3.1 Thermal Stress Due to Temperature Drop Near the Foundation
The case of RCC gravity dam is quite different from conventional
concrete gravity dam because there is no artificial cooling for joint grouting.
The dam is completed when the temperature in the interior of dam drops to
the final stable temperature. Thus, the temperature drop, the weight of
concrete must be superposed in the stress analysis for the study of
temperature control of RCC gravity dam.
80
5.3.2 Thermal Stresses Due to Temperature Deference between the
Surface and Interior of Dam.
The temperature in the interior of the dam rises after casting of concrete,
while the surface temperature is low because heat is dissipated in to the air.
As a result, there are tensile stresses in the surface of a concrete dam. There
is no artificial pipe cooling for joint grouting in RCC dams, so the internal
temperature drops very slowly, yet the surface temperature will be low in the
winter, thus, high tensile stresses will occur which may cause horizontal or
vertical cracks.
5.3.3 Thermal Stresses Due to Restraint of Foundation
Due to the conduction of heat from the dam body into the foundation,
the distribution of temperature drop in the concrete near the rock is not
uniform, thus the tensile stress is greater in a larger dam block.
5.3.4 Thermal Stresses Due to Vertical Temperature Difference
The vertical temperature difference is caused by the seasonal variation
of the placing temperature of the concrete and by stopping construction due
to flood or severe cold temperature in the winter. In RCC gravity dam, the
thermal stresses caused by vertical temperature difference may be large in
order to obtain the relation between the tensile stress due to vertical
temperature difference and the length of dam block. (Zhu B., et al. 1999).
81
5.3.5 Influence of Gallery in the Dam Body
In a solid gravity dam, the temperature difference inducing thermal
stresses is the difference between the highest temperature and the final stable
temperature. In a gravity dam with openings, such as gallery, the temperature
in the openings in winter is generally lower than the final stable temperature
for a solid gravity dam. So the thermal stresses around the openings may be
greater than those in a solid gravity dam. This is why cracks often appear
around the openings in a concrete dam. The influence of openings on thermal
stresses may be greater in a RCC gravity dam than in a conventional concrete
gravity dam with longitudinal joints because the length of dam block is
longer. (Zhu B., et al. 1999).
5.3.6 Results and Discussion of Structural Analysis
All the finite element results, which will be discussed, now were for the
RCC mix that contains Jordanian pozzolan using 28˚C as placement
temperature.
Figure 5.22 shows the stress envelope in the dam body in the direction
of river stream (x-direction) and in the dam axial direction (z-direction), and
also the major principal stress using two-dimensional structural analyses. For
the stress in x-direction, it can be seen that the tensile stress concentrated on
the gallery walls and also near the foundation surface, it was found from
figure 5.22 that the stress was about 0.94 MPa on the gallery walls and there
was some tensile stresses (0.5 MPa) developed near the foundation which
82
were caused by the external restraint by the foundation and the steeper
gradient of temperature. And also, it is about 0.6 MPa near the gallery for the
stress in z-direction, it can be seen also from the same figure for the axial
stress (z-direction) that the tensile stress mainly at the upstream and
downstream surface and at the surface of gallery. All theses results are
smaller than the allowable tensile strength to meet the demands against
cracking.
A plane strain model was adopted for two dimension structural analysis.
Plan strain is the condition for which the strains perpendicular to the plane of
the analysis are maintained at zero. Although, a plane strain analysis would
have given reasonable results, the actual effect of the finite dimension of
monolith was not observed. Accordingly, it is necessary to carry out the three
dimensional analysis. Figures 5.23 to 5.25 present three dimensional stress
contours at the end of heat of hydration. It can be noticed that the maximum
tensile stresses which were obtained from three-dimensional analysis were
high compared to that obtained from two-dimensional analysis, they were
0.88, 1.2, 1.2 MPa for σx, σ1, and σz respectively. For the stress in z-direction
it was found as shown in figure 5.25 that the tensile stresses concentrated also
at the upstream and downstream surface and at the surface of gallery, the
stresses reached a values more than the tensile strength of the RCC (1 MPa),
which may cause a cracks.
83
Fig 5.22 Different Stress Contour (σx, σz, N/m2) at the End of Heat of Hydration using 2D
Analysis.
84
Fig 5.23 3D Stress Contour (X-direction, N/m2) at the End of Heat of Hydration
Fig 5.24 3D Principal Stress Contour (σ1, N/m2) at the End of Heat of Hydration
85
Fig 5.25 3D Stress Contour (Z-direction, N/m2) at the End of Heat of Hydration
86
Stress history diagram of different stresses type (σ1 and σz) at 9m from
base of dam and at two different points, near the upstream face and near the
gallery are shown in Figures 5.26 and 5.27 respectively, using two dimension
analyses. It is obvious that the RCC near the gallery forcing a tensile stress
that is equal to 1.1 MPa and 0.9 MPa for (σ1 and σz) respectively. Which is
equal nearly to the tensile strength, the stress reached theses values after 150
days when the temperature decreased to its minimum. Also it can be seen that
the points at the upstream are in compression. While as shown in figure 5.28
and 5.29 for three dimension analysis that both points were in tension state
and have more stress compared with two dimension results.
Figure 5.30 shows a comparison in the axial stress (z-direction) between
two and three dimension structural analysis at 1.5m from base of dam at a
point near the upstream surface (2m from upstream). It can be seen from this
figure that the stresses which were obtained by three dimensional analysis
were higher than the stresses which were obtained by two dimensional
analysis, this is due to the assumption of a plain strain in two dimensional
analysis, which gives a zero value for strains perpendicular to the plane of the
analysis (εz=0.0). So using the two dimension structural model produces an
underestimate for axial stress developed in the dam body.
87
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
0.90
1.10
1.30
1.50
0 50 100 150 200 250 300 350
Time (Day)
Prin
cipa
l Stre
ss (
S1
) MPa
10 m from upstream face(Gallary Face)At Upstream
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
0 50 100 150 200 250 300 350
Time (Day)
Cro
ss v
alle
y St
ress
MPa
10 m from upstream face(Gallary Face)at Upstream
Fig 5.26 Principal Stresses History at Different Nodal Points at 9m from the Dam Base Using 2D Analysis
Fig 5.27 Cross Valley Stresses ( z-direction ) History at Different Nodal Points at 9m from
the Dam Base Using 2D Analysis
88
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0 100 200 300 400
Time (Day)
Prin
cipa
l Stre
ss (
S1
) MPa
10 m from upstream face(Gallary Face)At Upstream
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0 100 200 300 400 500
Time (Day)
Cro
ss v
alle
y St
ress
MPa
10 m from upstream face(Gallary Face)at Upstream
Fig 5.28 Principal Stresses History at Different Nodal Points at 6m from the Dam Base Using 3D Analysis
Fig 5.29 Cross Valley Stresses ( z-direction ) History at Different Nodal Points at 6m from the Dam Base Using 3D Analysis
89
-1.00
-0.90
-0.80
-0.70
-0.60
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0 50 100 150 200 250 300
Time (Day)
Cro
ss v
alle
y S
tress
(M
Pa)
3D Analysis
2D Analysis
Fig 5.30 Comparison Cross Valley Stresses ( z-direction ) History for 2D & 3D Analysis
at 1.5 m from base of dam and 2.5 m from upstream
Figure 5.31 shows the stress distribution (in z-direction) along the dam
cross section at an elevation of 9m from the base (top gallery surface) at
different period. It can be seen that the stresses inside the dam body are in
compression while the tensile stresses located at the outer surface and around
the gallery where the heat decreased rapidly and so the temperature gradient
increase. In the other hand, it can be seen that all the stresses along this
section tend to move to a compression state except the stresses on the gallery
surface, they were moved towered tension state, because the temperature
gradient in this location increasing with time. Figure 5.32 shows a
comparison principal stress across the same previous section using two and
three dimension analysis. It is clear that for the first 15m where the RCC
90
1.50
2.00
-1.00
-0.50
0.00
0.50
1.00
0 10 20 30 40 50 60 70 80 90 100
Distance (m)
Prin
cipa
l stre
ss (
S1
) MP
a
50 DayEnd of Heat of Hydration
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
0 10 20 30 40 50 60 70 80 90 100
Distance (m)
Prin
cipa
l stre
ss (
S1
)
2D Analysis3D Analysis
MP
a
exposed highly to the air; the stresses obtained from 2D was the highest,
while after that distance the principal stresses obtained from 3D analysis is
the highest.
Fig 5.31 Principal stresses across dam section at different time period (9 m from the dam
base) Using 2D Analysis
Fig 5.32 Comparison Principal stresses across dam section using 2D and 3D (9 m from the
dam base)
91
Figure 5.33 and 5.34 represent a comparison between the principal
stresses (σ1) and the cross valley stresses (σz) for a vertical section at the
center of the dam at different period of the dam construction using 2D and
3D analysis. It is cleared that most of the cross valley stresses is compression
stress which will not cause problems. After long time (410 days) the
temperature of RCC inside the dam body decreased which lead the tensile
stress to increase and the compression stress to decrease. The tensile stresses
at the top surface of the dam body are due to exposing the outer surface to the
ambient condition. Also, the zero stress temperature was developed near the
foundation at the end of construction of the dam, due to the difference in
stiffness between the foundation and the young RCC and the heat transfer
between the RCC face and the foundation. The maximum tensile stress is
reached 1.5 MPa at the end of construction and reduces to 0.6 MPa at the end
of heat of hydration due to the decreasing of temperature. The tensile stresses
obtained from 3D analysis are occupying more areas than that for 2D
analysis.
92
0
10
20
30
40
50
60
70
80
90
100
-2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00
Stress MPa
Elev
atio
n (m
)
S1 End of ConstructionS1 End of Heat of HydrationSZ at End of ConstructionSZ End of Heat of Hydration
0
10
20
30
40
50
60
70
80
90
100
-0.50 0.00 0.50 1.00 1.50 2.00
Stress MPa
Ele
vatio
n (m
)
S1 End of ConstructionS1 End of Heat of HydrationSZ at End of ConstructionSZ End of Heat of Hydration
Fig 5.33 Principal and Cross Valley Stresses Distribution at Vertical Section at the Dam Centre Using 2D Analysis
Fig 5.34 Principal and Cross Valley Stresses Distribution at Vertical Section at the Dam Centre Using 2D Analysis
93
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 50 100 150 200 250 300
Time (Day)
Cro
ss v
alle
y S
tress
(M
Pa)
15
20
25
30
35
40
45
Tem
pera
ture
(Deg
C)
StressTemperature
A comparison between temperature and cross valley stress distribution at
1.5m from the dam base and 2.5m from upstream surface is shown in Figures
5.35 and 5.36 for 2D and 3D analysis. It can be seen from these figures that
the stress (z-direction) adversely proportional with the temperature; stress
curve will rise up (decrease compression and increase tensile stresses) with
decreasing the temperature and vice versa. This behavior occurred because as
temperature of RCC increases due to heat generation, expansion in concrete
develops, but due to restraints on movement of RCC layers the expansion
leads to compression stresses in the concrete. And when temperature
decreases, this expansion will transform to contraction that leads to
decreasing the compression stresses and increasing tensile stresses.
Fig 5.35 Comparison between temperature and stresses in z-direction at 1.5 m from base
of dam and 2.5 m from upstream Using 2D Analysis
94
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0 50 100 150 200 250 300 350 400
Time (Day)
Cro
ss v
alle
y S
tress
(MP
a)
15
20
25
30
35
40
45
Tem
pera
ture
(Deg
C)
StressTemperature
Fig 5.36 Comparison between temperature and stresses in z-direction at 1.5 m from base of dam and 2.5 m from upstream using 3D Analysis
5.4 Cracking Analysis
5.4.1 Introduction
Thermal expansion of the outer face and temperature increase of the
interior concrete due to cement hydration are two mechanisms that cause the
cracks at the face of concrete dams as result of their combination. The surface
of the dam cools faster than the interior body. This causes a temperature
gradient between the cooled surface and the hot interior mass. Such a
difference will result in a thermal gradient that is likely to generate
undesirable thermal stresses which may cause cracks at the exterior surface.
This is not expected to be a structural problem unless the cracks extend
through to the drainage gallery, where the leakage of water may increase.
95
5.4.2 Transverse Contraction Joints.
Joints are required in most RCC dams. The potential for cracking may
be slightly lower in RCC because of the reduction in mixing water and
reduced temperature rise resulting from the rapid placement rate and lower
lift heights. In addition, the RCC characteristic of point-to-point aggregate
contact decreases the volume shrinkage. Thermal cracking may, however,
create a leakage path to the downstream face that is aesthetically undesirable.
Thermal studies should be performed to assess the need for contraction joints.
Contraction joints may also be required to control cracking if the site
configuration and foundation conditions may potentially restrain the dam. If
properly designed and installed, contraction joints will not interfere or
complicate the continuous placement operation of RCC.
5.4.3 Construction Joint Spacing Assessment
In order to assess the number of contraction joint, a crack analysis
should be performed in order to determine the predicted crack width and
consequently the number of required joints. Herein, a simplified method is
used to predict the crack with and number of contraction joints. The mass
gradient strain usually is determined by the following equation:
Induced strain= (Cth) (∆T) (KR) (Kf) 5.1
Where Cth= Coefficient of thermal expansion,
96
∆T= temperature difference, i.e., difference between the peak
temperature and the average annual ambient temperature.
KR= structure restraint factor, and
Kf= foundation restraint factor.
The coefficient KR is to be equal to 1.0 for conservative assumption and
maximum strain at the foundation base (Tatro and Schrader, 1992). The
coefficient Kf is determined form the following formula
ff
cgf
EAEAK
+=
1
1 =0.55
Where
Ag=gross area of concrete cross section at foundation plane
Af=area of foundation or zone restraining contraction of concrete,
Af= 2.5 Ag
Ef=modulus of elasticity of foundation or restraining element and it is taken
5.9 GPa
Ec= modulus of elasticity of mass concrete and it is taken 10 GPa.
The coefficient of thermal expansion (Cth) is strongly influenced by the
type of aggregate in the RCC mix, for Al Wehdah dam the aggregate is
basalt. A typical value for the coefficient of thermal expansion for the RCC
mass for Al Wehdah dam is taken as 8.6 E-6/ deg C. Table 5.3 summaries
the cracking analysis for Al Wehdah dam. As shown in this table, the number
97
of blocks depends on the placement temperature as well as the assumed width
of cracks that assumed to be 2mm. theses calculations made assuming that
the tensile capacity is 60 µmm, and the minimum ambient temperature (12.3
oC) was used to calculate the temperature differences.
Experience show that some superficial cracks with depth of 5~20cm
may appear on the upstream face of concrete dam during construction. Some
of these superficial cracks may develop suddenly into large cracks at some
time after completing of dam. The extending of superficial crack into large
crack may be illustrated by the mechanics of fracture (Zhu, et al. 1999).
98
Table 5.3 Crack Analysis in Al Wehda Dam for Different RCC Mix and Placement Temperatures.
South Africa Flyash 2D Analysis 3D Analysis
Placement temperature oC 20 24 28 20 24 28 Peak Temperature oC 41.15 45.33 47.8 42.59 45.25 47.9 ∆T oC 28.85 32.03 35.5 30.29 32.95 35.6 Induce strain (µmm) 136.46 151.50 167.92 143.27 155.85 168.39 Exceed strain (µmm) 76.46 91.50 107.92 83.27 95.85 108.39 Total Crack Width (mm) 37.08 45.38 52.34 40.39 46.49 52.57 No. of block 18 22 26 20 23 26 Length of block (m) 27 22 19 24 21 19
Turkey Flyash 2D Analysis 3D Analysis
Placement temperature oC 20 24 28 20 24 28 Peak Temperature oC 39.67 43.12 46.3 40.58 43.7 46.4 ∆T oC 27.37 30.82 34 28.28 31.4 35.1 Induce strain (µmm) 2 129.46 145.78 160.82 133.76 148.52 161.29 Exceed strain (µmm) 69.46 85.78 100.82 73.76 88.52 101.29 Total Crack Width (mm) 33.69 41.60 48.90 35.78 42.93 49.13 No. of block 16 20 24 17 21 24 Length of block (m) 30 24 20 29 23 20
Jordanian Pozzolan 2D Analysis 3D Analysis
Placement temperature oC 20 24 28 32 20 24 28 32 Peak Temperature oC 38.5 41.93 45.1 48.2 39.37 42.47 45.1 47.8 ∆T oC 26.2 29.63 32.8 35.9 27.07 30.17 32.8 35.5 Induce strain (µmm) 2 123.93 140.15 155.14 169.81 128.04 142.70 155.14 167.92Exceed strain (µmm) 63.93 80.15 95.14 109.81 68.04 82.70 95.14 107.92Total Crack Width (mm) 31.00 38.87 46.14 53.26 33.00 40.11 46.14 52.34 No. of block 15 19 23 26 16 20 23 26 Length of block (m) 32 26 21 19 30 24 21 19
Rock Flour 2D Analysis 3D Analysis
Placement temperature oC 20 24 28 32 20 24 28 32 Peak Temperature oC 37.59 41 45.2 47.3 38.4 41.5 45.2 46.84 ∆T oC 25.29 28.7 31.9 35 26.1 29.2 31.9 35.54 Induce strain (µmm) 2 119.62 135.75 150.89 165.55 123.45 138.12 150.89 163.37Exceed strain (µmm) 59.62 75.75 90.89 105.55 63.45 78.12 90.89 103.37Total Crack Width (mm) 28.92 36.74 45.08 51.19 30.77 37.89 45.08 50.14 No. of block 14 18 22 25 15 18 22 25 Length of block (m) 35 27 22 19 32 27 22 19
99
CHAPTER SIX
CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusions
The following conclusions may be drawn;
1. Thermal analysis is one of the most important analysis that should be
done for the RCC dam to provide the engineer with a means of predicting
excessive tensile stresses and strains, which could indicate possible cracking,
therefore, allowing the designer to take appropriate measures to limit or
control such potential cracks
2. The Al Wehdah RCC dam is to be constructed with a crest length of
485 m and 12 contraction joints at approximately 20 m spacing if Jordanian
Pozzolan is to be used to form the RCC mix.
3. Finite element models is becoming an increasingly powerful tool for
civil engineers to more accurately predict behavior of unprecedented
structures for which limited experience is available, such as RCC dams.
4. Using a commercially available finite element program such as
ANSYS and COSMOS and the available laboratory data, the incremental
100
construction process of mass-concrete structure can be modeled to produce
results that can be used in practical applications
5. The thermal results that obtained from ANSYS are more conservative
than the COSMOS results, the maximum temperature which were obtained
by ANSYS are higher than the temperature that were obtained by COSMOS
by one degree.
6. The thermal results for both 2D and 3D analysis are very close to each
other. So there is no need to do the 3D finite element analysis to estimate the
temperature distribution in the dam body.
7. The RCC mix which affects the heat of hydration, and the placement
temperature have the highest effect on the maximum temperature that will
develop in the dam body
8. The use of rock flour RCC mix allows us to use a higher placement
temperature than the use of Jordanian pozzolan or Turkey flyash or South
Africa flyash RCC mixes.
9. The temperature in the interior of a RCC gravity dam drops very
slowly, cracks may appear on the upstream and downstream face especially
in the winter, thus some measures must be taken to prevent these cracks. The
most effective measure is to insulate the concrete surface.
10. At the early age, RCC properties have significant effect on peak
stresses developed in RCC dam body.
101
11. In the contrary of thermal analysis, there are differences in stress
results between 2D and 3D structural analysis, the two dimensional structural
analysis overestimates the stresses.
6.2 Recommendations
The mathematical models should be closed to reality as possible as it
can be, for instant, The model should divides the RCC dam in to 320 layers,
each layer was 30 cm high and constructed within 1 day according to the
construction schedule instead of 32 layer in our model. The daily ambient
temperature should also be modeled instead of the average annual
temperature. Using the actual placement schedule and actual boundary
conditions in finite element analysis, certainly will lead to accurately
determine the actual maximum temperature anticipated in dam body. Also,
using the non-linear model for modulus of elasticity produces better estimate
for stresses develop in dam body.
Effort is recommended to improve the thermal analysis of RCC dam,
so that, the time and cost of the projects can be reduced.
102
References
American Concrete Institute (ACI). (1978). "Prediction of creep, shrinkage and temperature effects in concrete structure." ACI #209-78,2nd Draft, Detroit Andriolo, Francisco, (2002) "RCC- Materials Availability-Properties and Practices in Differnet Regions". Anonymous, (2002) “ANSYS User’s manual for revisions 5.4 and 7.0”. Swanson Analysis System Inc., Houston, PA, (1997, 2002). Ayotte E., Massicotte, B., Houde, J. and Gocevski V.(1997) “Modeling the Thermal Stresses at Early Ages in A Concrete Monolith,” ACI Material Journal, Vol. 94, No. 6, pp. 577-587. Crichton A.J., Benzenati, I., Qiu, T.J. and Williams, J.T. (1999) “Kinta RCC Dam- Are Over-Simplified Thermal-Structure Analysis Valid,” ANCOLD Conference on Dams, Australia, November. Forbes B. A. and Williams, J. T.(1998) “Thermal Stress Modeling, High Sand RCC Mixes and In-situ Modification of RCC Used for Construction of Candiangullong Dam NSW,” ANCOLD Bulletin, Sydney. Ishikawa M. (1991),“Thermal Stress Analysis of Concrete Dam,” Computers & Structures, Vol. 40, No. 2, pp. 347-352. Luna R. and Wu Y.(2000) "Simulation of Temperature and Stress Field During RCC Dam Construction," Journal of Construction Engineering and Management, September/October. Malkawi A.I.H., Mutasher S.A., and Qiu T.J.(2002) "Thermal-Structural Modeling and Temperature Control of RCC Gravity Dam,", Journal of Performance of Constructed Facilities, ASCE, Vol.17 , No.4, November. Malkawi A.I.H., Shaia H.A., and Mutasher S.A (2003)"A comparative study of mechanical properties of RCC trial mix using two different cementitious materials (fly ash and natural pozzolan)" Proceeding of the fourth international symposium on Roller Compacted Concrete (RCC) Dam, 17-19 November, Madrid, SPAIN.
103
Marulanda A.,Castro A., and Rubiano N. (2002) "RCC Quality Control for MIEI I Dam" Proceeding of International Conference on RCC Dam Construction in Middle East 7th-10th April 2002, Irbid, Jordan Nollet, M.J. (1994) " General Aspect of Design and Thermal Analysis of RCC Lac Robertson DAM". Schindler, A.K., (2003) “Effect of Temperature on the Hydration of Cementitious Materials,” ACI .Materials Journal, accepted for publication. Structural Research and Analysis Corporation (1997) “COSMOS/M CAD Interface User Guide version 2.0” December 1997 Truman K. Z., Petruska, D., Abdelkader F. and Barry F.(1991) “Nonlinear, Incremental Analysis of Mass-Concrete Lock Monolith,” Journal of Structural Engineering, Vol. 117, No. 6, June, pp. 1834-1851. U. S. Army Corps of Engineers "Engineering and Design GRAVITY DAM DESIGN," Engineering Manual (EM) 1110-2-2200, Washington, DC 20314-1000,1995 Zhu B., PingXu and Wang S.(1999) “Thermal Stresses and Temperature Control of RCC Gravity Dams,” CHINA * RCC'99. Zhu B., PingXu. ,(1999) “Thermal Stresses in Roller Compacted Concrete Gravity Dams,” Dam Engineering Vol VI Issue 3.
104
APPENDIX A
NUMERICAL EQUATIONS
105
106
107
108
108
109
110
111
لسدود الخرسانية المدحولة والاجهادات الحرارية في اإيجاد التوزيع الحراري للعناصر الحديّة مختلفين بإستخدام برنامجين
)دراسة مقارنة (
ايهاب سالم شطناوي: إعداد عبداالله ملكاوي. د.أ: إشراف
:ملخص
دة في الاردن ذو في هذه الرسالة تم انجاز التحليلين الانشائي و الحراري لسد الوح
ة )ANSYS + COSMOS (الخرسانة المدحولة ، باستخدام برنامجين للعناصر الحديّ
ى مجموعة من اثير الحراري عل م الت اد من اجل فه ة الابع ة و ثلاثي لكلتا الطريقتين ثنائي
ى تعناصر السد و مكوناته، و آذلك ل قييم تأثير تميه حرارة الخرسانة و ظروف صبها عل
.رارة و الاجهادات في جسم السدتوزيع الح
انة شاء صب الخرس ال ان ة و جدول اعم الخصائص الحرارية و الظروف المناخي
سابقة ال ال ا من الاعم م فرضها او حصل عليه ذه الدراسة ، ت ا في ه م .التي تم اعتباره ت
ة من عدة مضيفات اد (استخدام خلطات خرسانية مختلفة مكون ي، رم اد جنوب افريق رم
ى تصميم ) ولان اردني، و طحين صخور ترآي، بوز ه الحراري عل أثير التمي ، لدراسة ت
.فواصل الانكماش
ودج ل نم ن تحلي سوبة م رارة المح ائج الح أن نت ة ب رت الدراس (ANSYS)اظه
ك المحسوبة من نموذج ر حذرا من تل ى و اآث ، وان استخدام (COSMOS)آانت اعل
درجات حرارة طحين الصخور آمضيف لخلطات الخرسانة يسمح ل انة ب ا بصب الخرس ن
تم الحصول اعلى من استخدام رماد جنوب افريقيا او رماد ترآي اوالبوزولان الاردني ،
سد ي ال ادات ف رارة و الاجه ع الح ن توزي صيلية ع ات تف ى معلوم .عل
112