Embed Size (px)
Citation preview
1
THERMAL ANALYSIS OF CONCRETE DAMS DURING
CONSTRUCTION
Application to Alqueva’s Dam
Eloísa Castilho
Department of Civil Engineering, IST, Technical University of Lisbon
Abstract
With this work it is intended to analyse the thermal action on concrete dams, in particular during the construction
phase. Numerical simulation of dam’s thermal behaviour is very useful in taking decisions about the construction process,
because only by predicting the influence of each variable on the dam’s temperature it is possible to plan the construction in
order to control it. Among the factors that allow controlling the dam’s temperature it is possible to highlight: type of
formwork and time it remains in place, lift placement rate (lift height as well as time interval between the placement of lifts)
and, finally, concrete temperature control, either by using special cements, by prior cooling concrete’s constituent materials,
or by artificial cooling after pouring (post cooling). In order to achieve the goal of this work, the general laws of heat transfer
by radiation, convection and conduction are analysed. Climatic actions are evaluated as they affect thermal state of dams, at
the same time as concrete’s constituent materials and construction methods do. Regarding climatic factors, functions
describing air and water temperatures and also solar radiation are estimated. Climatic actions modelling, material properties
and the finite element model’s discretization are evaluated in exploration phase, by comparing model’s results with in situ
observed temperature. After validating these parameters, the construction phase is studied, which is the main purpose of this
work. Construction phase of the dam is simulated. For this purpose a program was developed, updating the model on every
construction date and evaluating existing elements as well as exposed and formwork faces at each stage. Hydration heat of
Alqueva’s Dam concrete is estimated, and then the construction phase calculation is performed. The methodology used in the
development of this work revealed to be suitable because, despite all the uncertainties characteristic of this type of problem,
variables are confirmed in exploration phase, allowing achieving results very close to the ones actually observed in
construction phase.
Key words: Thermal Analysis; Alqueva’s Dam; Climatic Actions; Solar Radiation; Hydration Heat; Construction Phase.
1. INTRODUCTION
A proper dam temperature forecast over time requires,
to begin with, the use of proper calculation models.
Numerical models, in particular based on the finite
elements method, make the temperature distribution
and consequent structural effects possible to predict
with sufficient accuracy, whenever the adopted
discretization has enough quality to analyse every
action the structure is subjected to. Therefore, it is
essential to adopt an appropriate refinement degree of
the mesh in order to obtain representative results for
all actions.
In addition, the finite element mesh should be
designed so that its elements enhance a correct
modelling of the constructive process (regarding the
layers volume and the contraction joints separation),
and also in order to provide representativeness in time,
simulating faithfully, through mesh increases, the
interval between consecutive lifts, as well as its
framework in the calendar of the year. These aspects
are fundamental to obtain consistent results with the
reality.
An accurate model of early ages concrete’s behaviour
is also of high relevance in the estimation of the dam’s
temperature field. Early age’s concrete is modelled as
a thermomechanical chemoreactive porous media. In
this way, the evolution of the hydration reaction is
formulated within the theoretical framework for
porous media and the thermodynamic problem to
solve is nonlinear in the variables temperature and
degree of hydration.
Additionally, generated temperatures by the heat of
hydration are changed by thermal action of the
environment. So, it is concluded that the climate
action modelling, characteristic of the dam’s location,
is also of extreme importance regarding the quality of
this analysis results. Hence, one of the focuses of this
study is the implementation of a solar radiation model.
2
2. GENERAL PRINCIPLES OF THE
THERMAL PHENOMENON
The temperature variations of a dam are related to the
thermal environmental actions (such as air and water
temperatures, as well as the effects of solar radiation)
and to internal heat generation of concrete during the
construction process.
2.1. Transmission of heat laws
Heat transfer occurs by conduction, convection and
radiation.
Conduction is a heat transfer mode that takes place in
stationary media as a result of a temperature gradient.
The law of heat conduction, also known as Fourier's
law, states that the time rate of heat transfer through a
material is proportional to the negative gradient in the
temperature and to the area, at right angles to that
gradient, through which the heat is flowing:
n
Tk
A
(1)
where Q is the heat amount crossing the area A , and
q represents the heat flow in the normal direction n
.
k is the materials’ thermal conductivity.
Heat transmission by convection is associated with
heat exchanges within a fluid, or between the fluid and
a surface in contact. It occurs as a result of the fluid
particles movement and is governed by Newton’s law,
expressing the proportionality between the amount of
heat exchanged by convection through a surface per
unit area and time, and the temperature difference
between the surface and the surrounding fluid
expressed by )( aw TT . A convection coefficient, ch ,
is settled, so that:
)( awc TThq (2)
Thermal radiation is a body’s radiant energy emission
process, whose quantity and quality depend on the
body’s temperature. It can be expressed by:
)( 21 TThq r (3)
where rh represents the radiation coefficient,
considered constant in the present work.
Heat exchanges by convection and thermal radiation
can be grouped in a single expression:
)( 21 TThq t (4)
where the parameter th is known as the total thermal
transmission coefficient.
2.2. Internal heat generation
Hydration of cement is a fairly complex set of
competing chemical reactions of different kinetics and
amplitudes [1]. It is a highly exothermic and thermally
activated reaction. Therefore, its simulation requires a
thermochemical model.
The free water present in the mixture reacts with the
unhydrated cement to form hydrates. The water
diffusion through the hydrates layers may be
considered as the dominant mechanism of the
hydration with respect to the kinetics [1].
According to Cervera [2], kinetics relationship can be
expressed in order to represent the normalized affinity,
A~
, as:
RT
EA
dt
d aexp)(~
(5)
where represents the hydration degree, aE is the
activation energy of the reaction, R the universal
constant of perfect gases (8,314 J/(mol K)) and T the
temperature.
2.3. Heat conduction equation
The general transient governing equation for heat
conduction, considering thermochemical coupling
(heat generation thermally activated) can be expressed
as follows:
t
Tc
dt
dmLG
z
Tk
zy
Tk
yx
Tk
xmzyx
(6)
where dtdmLm / corresponds to the thermochemical
coupling and represents the hydration reaction heat
generation. mL is the latent heat, and dtdm /
indicates the reaction speed.
Boundary conditions for the conduction heat equation
can be of two types:
Dirichlet conditions: TT in T (7)
3
Neumann conditions: Cn
Tkq
in q
(8)
Boundary condition for surfaces with fixed heat flux
and with heat changes by convection and radiation can
be expressed as:
0)(
azyx TThqn
z
Tkm
y
Tkl
x
Tk
in q
(9)
Time appears as a first-order term. Therefore, only
one initial value needs to be specified for the entire
body, that is:
oTT all over the domain at t = to (10)
3. THERMAL STATE QUANTIFICATION
The variables influencing the thermal behavior of
concrete dams are summarized in Table 1:
Table 1: Concrete dams thermal behavior influencing variables
CONSTRUCTION
METHOD
CHARACTERIZATION
Concrete colocation temperature
Contraction joints spacing
Formwork’s type and its placement
duration
Concreting rate
Temperature control measures
THERMAL
CHARACTERIZATION
OF CONCRETE
(Type of cement and its
dosage; Composition of concrete)
Thermal conductivity
Specific heat
Specific mass
Absorption coefficient
Emission coefficient
Hydration heat
GEOMETRICAL AND
LOCATION
CHARACTERIZATION
Latitude
Solar declination
Face azimuth
Thickness
Face slope
THERMAL
CHARACTERIZATION
OF THE
ENVIRONMENT
Air temperature
Water temperature
Convection coefficient (wind
velocity)
Solar radiation
Reflection coefficient of the
surroundings
3.1. Environment’s heat transfer characterization
In order to estimate the dam’s heat loss by its faces in
contact with the air, due to the effects of radiation and
convection, it is necessary to calculate the Newton's
formula coefficient for convection, and the heat loss
by radiation by the Boltzmann formula.
According to Mendes [3], in forced convection, the
respective coefficient can be expressed as:
VVhc (8,3 <50m/s) (11)
where V is the mean wind velocity.
Silveira [4], shown that, for the values of T
observed in reality, the radiation coefficient is nearly
constant, and has an average value of 5,23 W/(m2K).
3.2. Environment’s conditions simulation
In the usual analysis of dams, it is common to
represent the variation of air temperature over time as
the superposition of a medium temperature with two
harmonic functions, one with an annual period and
another with a daily period:
)'(2cos)'(
)'(365
2cos)'(
do
da
ao
aam
tttT
ttTTtT
(12)
where 't is the time, in days, since the beginning of
the year, mT is the average annual temperature, a
aT is
the annual’s wave semi-amplitude, )'(tT da is the daily
wave’s semi-amplitude, aot is the annual’s wave
phase, and dot is the daily wave’s phase.
Similarly, the reservoir’s water temperature presents
an evolution in time with seasonal nature, with the
particularity that the average temperature, )(yTm ,
semi-amplitude, )(yTa , and phase, )(0 yt , vary with
depth, y . In its modeling, it is simply assumed the
existence of an annual variation, disregarding the daily
variation. In this way, the reservoir’s water
temperature can be expressed as:
)('365
2cos)()()',( yttyTyTtyT oam
(13)
The knowledge of the average wind speed on a given
location is essential to determine the heat transfer
coefficient by forced convection and, consequently,
the total heat transmission coefficient between the
concrete’s surface and the air.
Information about the solar radiation, as well as
exposure conditions of the dam’s surfaces, are
fundamental to determine the temperature of these
surfaces, or, more specifically, their temperature
increase in relation to the air’s temperature. At the
4
ground level, short wavelength solar radiation (global
radiation), I , is given by the sum of three
components: direct or beam radiation, diffuse
radiation from the atmosphere and radiation reflected
by the ground.
3.3. Hydration heat quantification
Cervera et al. [2] normalized affinity’s expression is
used:
exp),(
~ 0
0k
AkTA (14)
In order to estimate Cervera et al. propose the
following expression, according to which, infinite
hydration degree is related with the cw/ (water-
cement) ratio:
cw
cw
/194,0
/031,1
(15)
Therefore, expression (5) results:
RT
En
k
A
n
k aexpexp0
0
(16)
3.4. Construction Methods
Dam’s construction methods influence the initial
conditions of the structure. It is possible, with special
construction processes, to control the temperature after
casting.
Related factors with the construction methods
affecting the temperature are: the spacing of the joints,
the type of formwork used and the time it remains in
place, concreting cadence (that is, the thickness of the
concrete layers and the time interval between placing)
and the temperature control of concrete (achieved
through the use of special cements, prior cooling of
material composition of the concrete, or by artificial
cooling).
When the surfaces have formwork, the total heat
transmission coefficient needs to be adapted.
According to ETL 1110-2-542 [5] it should be
modified as follows:
tformwork hk
bh
1
1'
(17)
4. SOLAR RADIATION LJGK1997 MODEL
IMPLEMENTATION
LJGK1997 model, presented in [6], is used in GIS
(Geographic Information System) implementations
[7], and it is an application of Liu and Jordan’s model
[8], which allows determining the different
components of the solar radiation (namely, the diffuse
one) on inclined plans. In addition, this model has
application anywhere in the world, allowing rough
estimates of the solar radiation amount, which may be
improved if there is locally measured radiation values
information.
From the calculation point of view, solar radiation is a
prescribed heat flux, depending not only on time but
also on the exposed surface orientation. This surface’s
orientation is defined by its normal vector.
4.1. Geometrical relationships
In the equatorial system, solar declination, δ, is
measured on the star’s hour circle from the equator to
the solar vector:
180))3(cos0201,0)3(sen1712,0
)2(cos3656,0)2(sen1149,0
)(cos758,0)(sen2567,233723,0(
(18)
with )346,79(25,365
2 N
[9], where N is the
day of the year considering a year with 365 days.
Hour angle, t, is measured on the equatorial plane
from the observer’s meridian to the projection of the
solar vector. In the local horizontal system, solar
zenith angle, Z, is the angle measured from the local
zenith to the sun, on the star’s hour circle:
tZ coscoscossensencos (19)
where is the latitude.
Solar altitude angle, s , is the complement of solar
zenith angle [6]. The azimuth, , is the angle defined
by the normal’s surface, counted from South, in the
clockwise movement’s direction. The surface’s
inclination angle, Y, is the angle between the
considered surface and the horizontal. The incidence
angle, , is the angle between the direct radiation
incident on a surface and the normal to that surface:
5
cossencoscossencos tCtBA (20)
with
sensen
cossensencoscos
coscossensencos
YC
YYB
YYA
(21)
4.2. Solar radiation calculation methods
Direct, diffuse and reflected components of radiation
respond differently to the incidence plan’s slope.
Therefore, a disaggregated estimate is needed.
In methods by integration, typically used in clear-sky
conditions, extra-terrestrial irradiance, 0H , and
optical mass of the air, m , are determined based on
Sun-Earth geometry [7]. The extra-terrestrial
irradiance on a surface normal to the solar vector,
nH0 , is given by:
0IHon (22)
Where is a correction factor, and 0I is the
empirical solar constant: 0I =1367 W/m2 (Allen et al.
1998).
In the LJGK1997 method is determined by
Hofierska & Suri expression [10]:
048869,0
25,365
2cos00344,01 N
(23)
(where N varies from 1 to 365 (366)).
4.3. LJGK1997 model
Solar beam radiation, incident on an inclined surface,
in clear sky conditions, icB , is given by:
BBnic FHB cos0 (24)
where BF is a variable which has the value 1 if the
solar disk is visible and 0 if it is hidden.
B represents the beam’s radiation atmospherical
attenuation. According to Kumar et al. [11] it is
estimated by:
)(56,0 )095,0()65.0( mmB ee (25)
where m is the optical air mass:
ssm sen614))sen614(1229( 5.02 (26)
Diffuse radiation is considered to be isotropic and
directly proportional to the visible fraction of the
celestial hemisphere from a given point. This
proportion is given by the sky-view factor, lskyF . .
Hence, in inclined surfaces, diffuse radiation in
clear-sky conditions is given by:
lskyDnskyi FHD .0,)cos( (27)
where, according to Liu & Jordan [8], atmospherical
attenuation to diffuse radiation, D , is estimated by:
BD 2939,02710,0 (28)
LJGK1997 model uses Gates expression to determine
the sky-view factor:
2
cos1
2cos2
,
YYF lsky
(29)
The hemisphere’s remaining fraction contributes with
reflected radiation by the ground. The reflected
radiation component is sometimes neglected, since it
has a low weight in total, except in conditions of high
albedo [7]. Therefore, in this work, this component is
not considered.
4.4. Adaptation to local real sky conditions
Solar radiation in clear sky conditions determined by
LJGK1997 model does not account for the elevation
of the location, nor for climate or environmental
conditions, among others. Therefore, it is not adjusted
to the real sky conditions, particulars to the effective
dam location.
In this work, the adaption to local real sky conditions
was achieved through the comparison of the
LGJK1997 model’s results with Silveira’s [4] solar
radiation values for global radiation on a horizontal
plane (obtained based on Évora registers made in the
50’s). The results are exposed on Fig. 1 and Fig. 2. In
these figures, LJGK1997 model’s clear-sky results (at
different days) are represented discrete and Silveira’s
real-sky values are continuous.
6
Fig. 1: LJGK1997 model and Silveira’s Global Radiation on a
horizontal plane
Fig. 2: LJGK1997 model’s Beam and Silveira’s Global Radiation
on a horizontal plane
Analysing this information one can observe that, for a
horizontal surface, the direct solar radiation portion
determined by LJGK1997 model adequately simulates
real sky conditions characteristic of the actual dam’s
location. Thus, in this work, this model was adapted to
Alqueva by not incorporating the diffuse component
of the solar radiation. It is important to mention that
this adjustment is clearly justified on horizontal plane.
However, bearing in mind that the different radiation
components respond differently to the dam’s slope,
these conclusions would have to be corroborated with
solar radiation on inclined plane data.
The LJGK1997 model estimated solar radiation flux,
adapted to real and local conditions (by the exclusive
use of the direct component, icB ), is considered in the
static boundary conditions expressed by eq. (2.40)
directly in the term q .
After the LJGK1997 model’s implementation, it is
possible to realize that, only with the introduction of
the dam’s latitude, it is conceivable, for any part of the
planet, to have a very reasonable estimation of the
solar radiation, which can be improved whenever local
registers of solar radiation are available. Therefore,
this model is considered to be a very useful tool in the
climate actions affecting dams’ modelling.
5. TEMPERATURE VARIATION
CALCULATION DURING ALQUEVA’S
DAM CONSTRUCTION
The aim of this work is related to the study of
Alqueva’s dam construction phase. However, given
the number of variables affecting the temperature of
dams under construction, it is necessary to start the
analysis with the study of the exploration phase, in
order to confirm the climate actions admitted
functions, as well as the materials assumed properties.
5.1. Alqueva’s dam characteristics
Alqueva’s dam is a double-curved arch dam. The
dome, with theoretical maximum height of 96,0m, and
development of 348,0m at the crest and 124,0m on the
valley floor, has a thickness of 33,5m at the base and
7,0m at the top. It consists of 24 blocks, generally with
14,5m, limited by vertical joints.
5.2. Materials’ thermal characteristics
In Table 2 thermal model’s properties are described.
Table 2: Thermal model’s properties.
0
200
400
600
800
1 000
1 200
0,0 0,2 0,4 0,6 0,8 1,0
I ch ;
Ih
(W
m-2
)
cos (Z)
0
200
400
600
800
1 000
1 200
0,0 0,2 0,4 0,6 0,8 1,0
Bch
; I h
(W
m-2
)
cos (Z)
Property Unit Value
FOUNDATION
Specific heat, c
Thermal conductivity, k
Specific mass,
Absorption coefficient, a
[J/(kg K)]
[W/(m K)]
[kg/m3]
[-]
879
4,6
2600
0
CONCRETE
Specific heat, c [J/(kg K)] 920
Thermal conductivity, k [W/(m K)] 2,62
Specific mass, [kg/m3] 2400
Absorption coefficient, a [-] 0,65
Total heat transmission coefficient, ht [W/(m2K)] 20,20
Formwork surfaces transm. coef., h’ [W/(m2K)] 2,02
Hydration degree at t , [-] 0,74
Activation energy, REa / [K] 4000
Normalized chemical affinity )(~A (see section 5.5):
0
k [1/s] 555,1360
k
A0
[-] 0,0015
[-] 5,4749
Latent heat, L [J/m3] 6,289.107
7
In the total heat transmission coefficient
determination, the convection coefficient is estimated
using expression (11), for a mean wind velocity in
Alqueva of 4,0m/s.
5.3. Environment thermal actions’ simulation
Following expression (12) it is possible to write the air
temperature’s function as:
)'(2cos)'()'()'( 1do
da tttTtTtT
(30)
where:
'
365
2sen'
365
2cos)'(1 tbtaTtT m
(31)
Taking into account the records of the daily maximum
and minimum temperature of the air, to Alqueva’s
dam location, the following results can be obtained:
mT =17,49ºC; a =-7,43ºC; b =-3,34ºC.
The annual’s variation of the daily wave’s amplitude
is represented by:
)'(
365
2cos)'()'(2 a
oaam
da tAAtAtT
(32)
where mA , aaA and
ao represent, respectively, the
annual average amplitude, the semi-amplitude of the
amplitude’s annual wave and the annual wave
amplitude’s phase. By doing:
'
365
2sen'
365
2cos)'( tbtaAtA m
(33)
it is obtained, to Alqueva’s dam location,
mA =10,48ºC; a =-3,99ºC; b =-0,82ºC.
In what the water temperature is concerned, in order to
achieve the greatest possible representation of the
hydrological regime, every thermometers belonging to
the upstream faces records were used. Zhu’s formulas
[12] were used to estimate the evolution of the (13)’s
expression parameters with the depth of the reservoir:
(34)
(35)
(36)
(37)
(38)
yefdy )( (39)
where s
mT is the average annual temperature in the
reservoir’s surface, s
aT is the reservoir surface
temperature’s wave semi-amplitude, b
mT is the average
annual temperature in the reservoir’s bottom, H is the
reservoir’s deep, arot is the air temperature’s wave
phase, )(y is the phase difference of the water
temperature relative to the air temperature and , , ,
d and f are constants.
Alqueva’s reservoir water parameters are described in
Table 3.
Table 3: Alqueva’s reservoir water parameters
Parameter Unit Value
smT [°C] 19,95
saT [°C] 7,55
bmT [°C] 11,49
[-] 0,0632
[-] 0,0434
[-] 0,0609
d [months] 3,313
f [months] 2,00
The radiation action implemented in this work is in
accordance with the LJGK1997 model previously
described. Solar radiation estimation requires the
knowledge of the dams’ latitude and orientation.
Alqueva’s dam has a 38º11 latitude and its axis has an
azimuth of 150º.
5.4. Thermal environment actions validation in
exploration phase
In exploration phase the initial temperature field is
estimated assuming an initial temperature, applying
boundary conditions, and performing the time
integration until stationary (cyclic) behavior is
achieved.
Boundary conditions used in exploration phase were:
upstream surfaces submersed (Fig. 3); bottom nodes
of the foundation with a prescribed temperature of
15ºC (Fig. 4); downstream and top faces of the dam
subjected to the solar radiation’s flux (Fig. 5); every
ys
mm ecTcyT )()(ys
aa eTyT )(
)()( ytyt ar
oo
)1/()( gTgTc s
m
b
m
Heg
8
exposed surfaces subjected to convection and
radiation heat exchanges (Fig. 6); lateral borders of the
model are considered to be adiabatic boundaries.
Fig. 3 – upstream submersed
surfaces Fig. 4 – bottom of foundation
Fig. 5 – solar radiation’s flux
exposed to surfaces
Fig. 6 – convection and radiation
heat exchanges exposed to surfaces
Several finite element model meshes were tested, with
increasing degree of refinement, in order to ensure the
model’s ability to represent the effect of the daily
wave air’s temperature. A model with 5 elements
differently spaced in thickness revealed to be suitable
(Fig. 7).
Fig. 7 – Exploration phase discretization.
In Fig. 8, the results of the exploration phase calculus
(using PAT_2 program [13]) are shown, for 3
particular nodes near the top of the dam, contrasted
with the instruments placed in the same sections
registers. Analyzing the results it is observed that, due
to the used scale, the effect of the air’s temperature
daily wave is reflected as an increase of the thickness
of the annual wave. It is evident this amplitude’s
decrease as the distance to the exposed face increases.
Fig. 8 – Exploration phase temperatures near the top of the dam
(z=141,0m), downstream, middle and upstream, respectively
5.5. Construction phase modelling
According to Ulm and Coussy’s model [1], early ages’
concrete is modeled as a thermomechanical
chemoreactive porous media.
The problem to solve is nonlinear in temperature and
hydration degree (the determination of the
temperature, as well as the hydration degree, depend
on the variables themselves). Furthermore, the
temperature field generated by the hydration heat is
changed by the thermal action coming from the
environment where the dam is located.
The cement used in the composition of Alqueva´s dam
concrete is type IV and class 32,5, according to ASTM
classification.
Analyzing [14] it is possible to understand that, for the
main composition of Alqueva’s dam concrete, the
average quantity of cement is 160,0kg/m3, and the
water-cement average relationship is 0,49.
Based on the results shown in [15], and considering
the composition of 160,0kg/m3 of cement, it is
possible to determine the values presented in Table 4:
0
10
20
30
40
50
0 50 100 150 200 250 300 350
T(ºC) valores calculadosvalores observadosT média ar
0
10
20
30
40
50
0 50 100 150 200 250 300 350
0
10
20
30
40
50
0 50 100 150 200 250 300 350days since the beginning of the year
Calculated values
Registered values
Average air’s temperature
9
Table 4: Alqueva’s concrete hydration heat.
Expression (15) allows calculating the final degree of
hydration with the average properties of Alqueva’s
concrete composition. Therefore:
74,049284,0194,0
49284,0031,1
(40)
Using the exponential curve suggested in [16] to
represent the accumulated generated heat, Q , it is
obtained to Alqueva’s dam concrete:
teQ
1.8,12
386,19
(41)
The constant Q represents the final amount of
liberated heat in ideal conditions. According to
Cervera [2]:
0TTC
Qad
(42)
where C is the specific heat of the material (920
J/(kgk)), 0T is the initial temperature of the adiabatic
experiment and ad
T is the final reached temperature.
The amount of released heat is given by:
QQ (43)
From the previous relationship it is obtained:
2,26
74,0
386,19
(44)
Cervera relates the hydration degree to the
temperature rise in the adiabatic experiment in the
form:
adad
ad
TT
T
(45)
where ad
T is the measured temperature of concrete
along the experiment.
Assuming an initial temperature of 20ºC, the
expression (42) ad
T =41,07ºC is obtained. It is then
possible to calculate the concrete’s temperature in the
experiment as well as its rate adT .
According to Cervera, the normalized affinity can be
expressed as:
ad
a
ad
ad
RT
E
TT
TA exp~
0
(46)
With this information it is conceivable, through the
analytical expression in Cervera’s model for this
function (expression (14)), to calibrate the properties
of the material which fully characterize the chemical
behavior of the concrete mixture. It is obtained:
0
k=555,14s
-1;
k
A0 =0,0015; =5,475
37J/mE29,6240010002,26 QL (47)
For the dam, in construction phase, a finite element
mesh developed in LNEC is used. This mesh has
layers of 2,0 to 3,0m height, and every block of the
dam is divided in 2 in development. The mesh has 4
elements equally spaced in thickness (Fig. 9).
According to section 5.4, the grid should be more
refined near the exposed faces. However, the current
mesh is already computationally demanding, so it was
chosen to maintain the mentioned grid. The results of
the exposed faces will have to be analyzed in the light
of this information. The difference in the obtained
temperature field of the exposed faces, using both
mentioned meshes, subjected to the exploration phase
actions, is presented in Fig. 10 .
The foundation is discretized in conformance with the
grid of the dam in a model with 18 857 elements and
90 434 nodes (Fig. 11).
A program was developed, in order to build the data
archive to be read by the program PATQ_2 [17]. The
designed program considers the evolution of the mesh
in every concreting or stripping phase, updating the
exposed faces (in blue in Fig. 12) as well as the faces
with formwork (in green), and its correspondent total
heat transmission coefficient. A typical output of this
program is the top figure of Fig. 12, which is
contrasted with a photo taken during the construction
of the dam. In red, assumed adiabatic faces are
represented.
t (days) Q (cal/g) Q (kJ/kg)
0 0,00 0,00
3 3,85 16,12
7 4,31 18,05
28 4,63 19,39
10
Fig. 9 – Construction phase discretization - detail.
Fig. 10 – Exploration phase temperatures near the top of the dam
(z=141,0m) - downstream.
Fig. 11 – Construction phase discretization – general view.
Fig. 12 – Construction process simulation.
In what the initial thermal field is concerned, for the
dam, it was considered that the concrete’s colocation
temperature is equal to the air’s temperature, except in
the cases where it doesn’t satisfy the 27.2 article of
[18]. Regarding the foundation, the initial temperature
field is calculated using PATQ_2 program and
considering the existence of only one phase, in which
every foundation belonging elements are placed,
during a calculus period of time long enough for the
thermal field to achieve the stationary behavior (10
years).
5.6. Results
In the interpretation of the following results it has to
be noticed that, in 2001, artificial cooling process was
carried on, and this action modelling wasn’t
considered in the present study. In Fig. 13 to Fig. 17,
registered temperature is represented in dots, as the
calculated temperature is represented in a continuous
line.
Typical results achieved near the base of the dam are
shown in Fig. 13 and Fig. 14. It is possible to observe
that, when the next layer is laid, there is a decrease in
temperature, due to the lower temperature of the
newly placed layer, followed by an increase due to the
heat generation originated in this second layer. The
same applies, but lighter, when the remaining layers
are placed. The studied instruments are within a layer
located near the base of the foundation (where the dam
is very thick). This location is revealed by the results,
as these nodes are indifferent to the annual’s air
temperature wave effect. In Fig. 13 it is appreciable
the difference in the assumption of the concrete’s
temperature (5ºC) effect. In Fig. 14 it is visible the
different adopted discretization in relation to the real
construction process effect. In this location, for the
layers placed in February ’99, the finite elements mesh
aggregates 3 concreting layers in a single element.
Therefore, the date when the layers are placed will
happen, in the model, later than in reality.
Consequently, they spend more time cooling than
what really has happened.
Characteristic results achieved in the middle height of
the dam, at half thickness, are shown in Fig. 15.
Regarding the studied instrument it should be noted
that the placement of the layer incorporating the quota
of the instrument occurred on 22-07-99 and the next
layer was placed, in reality, on 09-08-99. However,
according to the model’s discretization, it occurred
0
10
20
30
40
0 50 100 150 200 250 300 350
T(ºC)
days since the beginning of the year
valores calculados-malha fase definitiva
valores calculados-malha fase construtivaExploration phase mesh (Fig. 7) Construction phase mesh (Fig. 9)
11
only on 23-08-99. Therefore, the fact that the layer has
been exposed longer in the model than in reality, in
the summer, caused a higher temperature reached by
the nodes than the registered one.
Typical results achieved in the top of the dam, at half
thickness, are shown in Fig. 16 and Fig. 17. The
presented curves (both the calculated and the
registered one) reflect the position in height of the
studied nodes. In internal nodes near the dam’s crest
(where its thickness is smaller) the cooling is faster
than in lower sections, once exposed faced are closer
to the referred nodes, as well as since the heat is
dissipated more easily by the exposed surfaces than by
the foundation. Thus, the cooling curve has a slope
greater than lower level located sections do. It is also
evident that, for this dam’s thickness, temperature’s
seasonal variations are experimented by internal
nodes, while, at the bottom of the dam, internal nodes
are not affected by these oscillations. In early 2002,
when the curves corresponding to the observed
temperature decrease significantly relative to the
calculated temperature, it is understood that artificial
cooling has occurred in these quotas. This effect tends
to fade over time (as a result of the proximity to the
exposed faces), and the curves meet again, although
artificial cooling has not been modeled. In Fig. 16, the
initial difference is thought to be related to the
concrete’s colocation temperature, although there is no
available information to validate this assumption. In
what Fig. 17 is concerned, the quantity of cement is
identical in the model and in reality. It is inferred that
all other factors (concreting rate, placement
temperature, etc.) have been modeled similarly to
what happened in reality leading to an answer so
similar to what actually occurred.
Fig. 13 –Near the dam’s base results – G27.
Fig. 14 – Near the dam’s base results – G08.
Fig. 15 – Middle height dam’s results – T19.
Fig. 16 – Dam’s crest results – T49.
Fig. 17 – Dam’s crest results – T59.
5.7. Foundation influence
Regarding the effect of the foundation, it is known
that the modelation of the foundation, in relation to its
consideration as an adiabatic boundary, has effect in
the base nodes, since in the first case the heat flow can
be dissipated to the foundation. Thus, for a node in the
dam’s base, in a central section, calculated
temperatures in models with and without foundation
are represented, respectively, in blue and black in Fig.
18. Shown results support the mentioned above. It is
also found that this effect isn’t propagated in height:
by analyzing the mentioned models (with and without
considering the foundation), at the base instruments’
height (approximately distanced 20,0m from the base),
reported in Fig. 19, it is clear that there is no
difference between modeling the foundation or
considering it as simply adiabatic, since both curves
are coincident. It is concluded that, in these sections,
the heat is dissipated by the exposed surfaces and not
by the foundation.
Fig. 18 – Consideration of the foundation in the dam’s base nodes.
0
20
40
13-08-01 02-10-01 21-11-01 10-01-02 01-03-02 20-04-02
T(ºC)
0
20
40
06-01-99 25-07-99 10-02-00 28-08-00 16-03-01
T(ºC)
0
20
40
22-07-99 30-10-99 07-02-00 17-05-00 25-08-00 03-12-00 13-03-01 21-06-01
T(ºC)
0
20
40
06-11-01 25-05-02 11-12-02 29-06-03 15-01-04
T(ºC)
0
20
40
05-07-00 21-01-01 09-08-01 25-02-02 13-09-02 01-04-03 18-10-03
T(ºC)
0
20
40
16-07-98 01-02-99 20-08-99 07-03-00 23-09-00 11-04-01
T(ºC)
12
Fig. 19 – Consideration of the foundation near the dam’s base
nodes (approximately 20,0m - G05).
6. CONCLUSIONS
The thermal behavior study of dams is essential since
it allows reflecting on the progress of construction
processes, as well as on the different structural types
of concrete dams to adopt, in order to limit the
temperature and to moderate retraction effects
associated with the curing process and hardening of
concrete. Therefore, it is an important tool in the
assessment of the safety of the dams.
In order to plan efficiently the dam’s temperature
control measures, it is essential that this reflection is
based on reasonable estimations of the dam’s
temperature. After completing this study one came to
the understanding that it is possible, by using the
PATQ_2 [17] calculation program, to get very credible
estimates of the dam’s temperature during its
construction, as long as the most relevant factors are
well reproduced.
First of all, and starting with the obvious, it is
necessary to model the climatic action characteristic of
the dam’s location, as well as the materials properties.
Regarding the concrete, it is extremely important to
know its composition, as well as the type of cement
and its dosage, in order to represent the hydration
curve. It is also important to know the type of used
formwork and also the time it remains placed.
In what the finite elements mesh are concerned, it was
noticed that it is essential that its discretization is
adapted to the lift height, as well as to the spacing of
contraction joints, in order to provide the model the
flexibility to simulate the effective constructive
process. If the mesh is not adequately refined, and
combine multiple lifts in only one element, real
boundary conditions will not be well reproduced,
interfering with the hydration heat dissipation, with
repercussions on the elements temperature. Therefore,
it is essential that the finite element mesh has an
adapted discretization to the constructive phasing, not
only in the elements geometry, but also on its updating
over time (existing elements and exposure conditions,
for each phase of concreting or striking), allowing to
represent the real rhythm of casting.
Also regarding the model, it is necessary to refine the
mesh near the exposed faces, in order to be able to
precisely represent the daily wave air’s temperature.
The concrete’s placement temperature is also relevant
in the calculation of the concrete’s temperature rise.
The effect associated to this initial condition tends to
decrease over time, with intensity depending on the
layers exposure conditions. This observation confirms
the limited efficiency of the constituent concrete
materials’ pre-cooling as a technique of temperature
control.
It was found that the modeling of the foundation or its
consideration as an adiabatic boundary only affects the
dam’s base nodes temperature.
The combination of the correct simulation of all these
factors, as noted, allows obtaining very credible
estimates of concrete’s temperature variations during
construction. Thus, it is possible to rehearse, in the
design stage, different rates of concreting, joint
spacing, materials, or even the use of artificial
refrigeration cooling, in order to adopt, in a
knowledgeable manner, the most efficient and
economic construction process at the level of the
concrete’s temperature control.
7. BIBLIOGRAPHY
[1] F.-J. Ulm and O. Coussy, “Modeling of
thermochemomechanical couplings of concrete at
early ages,” Journal of Engineering Mechanics,
vol. 121(7), pp. 785-794, July 1995.
[2] M. Cervera, J. Oliver and T. Prato, “Thermo-
Chemo-Mechanical Model for Concrete. I:
Hydration and Aging,” Journal of Engineering
Mechanics, vol. 125(9), pp. 1018-1027,
September 1999.
[3] P. Mendes, "Acção Térmica Diferencial em
Pontes de Betão", Msc Thesis, IST, 1989.
[4] A. Silveira, "As variações de temperatura nas
barragens". Tese de Especialista LNEC. Memória
nº177, LNEC, 1961.
0
20
40
10-07-99 26-01-00 13-08-00 01-03-01
T(ºC)
13
[5] USACE - Engineering and Design - Thermal
studies of mass concrete structures, ETL 1110-2-
542, 1997.
[6] F. Néry and J. Matos, “Terrain Parameters in
solar radiation models,” in Proceedings of the
14th European Colloquium on Theoretical and
Quantitative Geography, Tomar, Portugal, 9 to
13 of September of 2005.
[7] F. Néry, "Análise de conjuntos de dados
geográficos de suporte à modelação ecológica da
distribuição de espécies", Phd Thesis, Instituto
Superior Técnico, 2009.
[8] B. Y. H. Liu and R. C. Jordan, The
interrelationship and characteristic distribution of
direct, diffuse and total solar radiation, 1960.
[9] J. G. Corripio, “Vectorial algebra algorithms for
calculating terrain parameters from DEMs and
solar radiation modelling in mountainous
terrain,” Int. J. Geographical Irformation
Science, vol. 17(1), pp. 1-23, 2003.
[10] J. Hofierka and M. Súri, “The solar radiation
model for Open source GIS: implementation and
applications,” in Proceedings of the Open source
GIS - GRASS users conference 2002, Trento,
Italy, 11-13 September 2002.
[11] L. Kumar, A. K. Skidmore and E. Knowles,
“Modelling topographic variation in solar
radiation in a GIS environment,” Int. J.
Geographical Information Science, vol. 11(5),
pp. 475-497, 1997.
[12] B. Zhu, “Prediction of Water temperature in deep
reservoirs,” Dam Engineering Vol VIII Issue I,
pp. 13-25, 1997.
[13] LNEC, “Análise Térmica de barragens de Betão -
Acções térmicas ambientais,” Report 185/2012-
DBB/NMMF, 2012.
[14] “Caracterização das propriedades reológicas do
betão da barragem de Alqueva,” LNEC - NO, (to
be published).
[15] LNEC, “Apreciação sobre o controlo da
qualidade do betão aplicado na barragem do
Alqueva - relatório final,” Report 106/2003 DM.
[16] L. G. d. Silva, “Caracterização das propriedades
termo-mecânicas do betão nas primeiras idades
para aplicação estrutural,” Msc Thesis, FEUP,
Porto, 2007.
[17] LNEC, “Análise Termoquímica de barragens de
betão - Reacção de hidratação,” LNEC Report (to
be published), 2012.
[18] “Regulamento de betões de ligantes hidráulicos,”
Decreto-Lei nº 445/89 de 30 de Dezembro.
Diário da república nº299/89 série I.
