Heat Loss Compensation for Semi-Adiabatic Calorimetric Tests

Heat Loss Compensation for Semi-Adiabati Calorimetri Tests Peter Fjellström M.S., Ph.D. Student Luleå University of Tehnology Dept. of Strutural Engineering SE - 9787 Luleå peter.fjellstrom@ltu.se Dr. Jan-Erik Jonasson Professor Luleå University of Tehnology Dept. of Strutural Engineering SE 9787 Luleå jan-erik.jonasson@ltu.se Dr. Mats Emborg Head of R&D, Betongindustri AB Professor, Head of Department Luleå University of Tehnology Dept. of Strutural Engineering SE 9787 Luleå mats.emborg@ltu.se Dr. Hans Hedlund Adj. Professor Skanska Sverige AB Tehnology Bridge and Civil Engineering SE 405 8 Göteborg hans.hedlund@skanska.se ABSTRACT Heat of hydration has long been of importane sine it affets the temperature levels within a onrete struture, and thus, potentially affets its durability. The only soure of energy is the reation between ement and water. This energy warms up the onrete sample and all the ambient materials. Therefore, in order to model these energies, the TSA (traditional semi-adiabat) setup is transformed into an assoiated sphere. By this, the temperature distribution and the energies within eah layer of the TSA an be alulated. The sum of all energies gives the total heat of hydration. A refined model using a orretion fator is introdued, whih aounts for energies lost to the TSA setup materials. Results show that the effet of this fator annot be disregarded, espeially not for TSAs with low ooling fators. Key words: onrete, heat of hydration, adiabati alorimetry, semiadiabati alorimetry, heat flow, orretion fator, ooling fator.

. INTRODUCTION. General The energy quantity of the exothermi reation between ement and water has long been of importane sine it affets the temperature levels within a onrete struture, whih an, based on risks of thermal raking, affet the durability. The temperature influenes the development of the pore struture in onrete [, ] and naturally its mehanial properties, e.g. strength [3]. For building engineering purposes heat of hydration has ommonly been determined by various versions of adiabati alorimeters, see Figure. Adiabati alorimetry True-adiabati Semi-adiabati A) Regulation of a small insulated ontainer, see [4, 5] B) Large insulated onrete blok, see [4, 6] Figure Shemati presentation of adiabati alorimetry. C) Heat flow is determined with a alibrated temperature transduer, see [4, 7, 8, 9] D) Heat flow is determined from a ooling fator or oeffiient of temperature loss, see [5, 6, 0, ] In both the true-adiabati and the semi-adiabati setups the onrete temperature is registered as a funtion of time. The differene is that in the true-adiabati setup no heat loss to the environment is supposed to be present. The semi-adiabati setup allows for energy losses, whih are aounted for in the evaluation proess. The true adiabati measurement is in theory preferred, sine it ould give a orret value of heat of hydration diret from the test results. However, in A) it is hard to regulate the temperature, whih an drift, and therefore the results are not always reliable []. In B) temperature measurement in the entre of a large onrete blok is estimated to have true adiabati temperature. However, in [6] they aount for heat flow as in C) for better auray. In the semi-adiabati methods, when heat flow is alulated from the temperature of the onrete sample, the following onditions have to be fulfilled The temperature in the onrete sample and the ambient are equal when starting the semi-adiabati measurement. The temperature is onstant during the test period. To ensure these onditions limits are usually speified, e.g. the temperature of the fresh onrete mix should be within ± C of the alorimeter temperature [5], and the ambient temperature where the alorimeter is plaed should be within the limit 0± C [5]. In [0] the laboratory, where the mixing of the onstituents of the onrete ours, the temperature should be within 0± C. The room, where the test is onduted, have the orresponding limit 0± C, and the referene temperature should not differ more than ±0,5 C throughout the test [0].

3 When heat flow is diretly measured with a alibrated temperature transduer, the points above are not that important. However, limits are still used, and in [7] the laboratory, where the test is onduted and where the mortar onstituents are stored, the room temperature should be within 0± C. In this paper, heat flow is alulated from the sample temperature, and, our limits are the same as in [7].. Existing models and limitations In order to determine the quantity of heat of hydration in a semi-adiabati test, heat losses must be determined. In [] a traditional semi-adiabati (TSA) setup is presented, and the ooling fator were formally expressed as hi Ai i a = V ρ () Based on measured values of a [] heat energy within the onrete sample, and heat losses based on heat flow, was expressed as t ρ qem = ( T ( t) T ) + a ( T ( t) T ) dt C () 0 where a [/s or /h] = ooling fator; h i [W/m C] = heat transfer oeffiient of the individual insulation material; A i [m ] = heat flow area of the individual insulation material; V [m 3 ] = volume of the onrete sample; [J/kg C] = heat apaity by weight of onrete; ρ [kg/m 3 ] = onrete density; q em [J/kg] = heat of hydration per kg of ement; C [kg/m 3 ] = ement ontent; T t [ C] = onrete temperature; and T [ C] = temperature. When heat of hydration is determined by Eq. the following onditions are usually stated. There should be small temperature gradients within the onrete sample. Then the average onrete temperature is easily measured and is representative when alulating energy stored in the onrete. A large temperature inrease in the onrete sample is favourable, sine the measured temperature hereby gives a reasonable piture of the energy involved. The onsequene of these onditions is that low values of the ooling fator or heat loss oeffiients are needed. Reommended values are less than 00 J/h C for the total heat loss oeffiient in [5, 0] and for the ooling fator less than 0,035 h - in [3]. In [] ooling fators between 0,00-0,05 h - are used, and lower values are reommended for reliable long term heat release measurements. However, when the amount of insulation is inreased, more energy will be stored within the materials of the alorimetri setup during the test, and this is not aounted for by the traditional method using Eq.. For the thermos vessels in [5, 0] this is taken into aount. However, these test setups are relatively ompliated and expensive ompared with TSAs. Therefore, this paper will fous on TSAs, and investigate the need of taking into aount the energy stored within its relatively few parts.

4. AIMS AND PURPOSES The TSA has the advantage that it an be built with inexpensive parts that are easily assembled. The temperature sensors are generally few, and the measurements an be performed quikly. The aims and purposes in this paper is to Demonstrate the existene and need of taking into aount the energy that is heating up the equipment using a TSA. Develop a reasonable simple model for evaluation of the heat of hydration in onrete, whih aounts for energy stored within the different parts of a TSA. Investigate how the different omponents of a TSA setup affet the amount of energy to be ompensated for. 3. REFINED HEAT OF HYDRATION EVALUATION METHOD 3. Test preparation and proedure First, onrete admixture proportions are determined in order to fulfil the speifi reipes requirements, i.e. slump, entrainment et. Dry reipe onstituents are mixed in the blender for minute before adding water, and the total mixing time is 5 minutes. The onrete sample, of volume 4L is plaed in a ylindrial metal buket. The heating devie, a Teflon arpet, is fixed around the buket with a steel girdle and steel lamps. The mass of the sample is reorded before and after the semi-adiabati test to ensure that no drying out has ourred. The onrete sample is put into the TSA about 5 minutes after mixing, and the temperature is reorded every 5 minute with sensors aording to the numbers in Figure. In the square setup only sensors Nos., and 4 exist. Temperature sensors Nos., and 3 are plaed in the onrete sample, and number 4 is loated in the ambient. In our laboratory, there exists two large (denoted A) and two small (denoted B) ylindrially shaped TSA, and three square (denoted C) TSAs. The ambient temperature in the laboratory varies very little and an be onsidered to be well within the range 0± C. Heat of hydration is measured until the onrete sample has approximately reahed the temperature of the ambient, whih usually takes about 7 days. Then, without removing the onrete sample from the TSA, the onrete sample is heated to a level of maximum measured hydration temperature + 5 C. An empirial value of the ooling fator an then be determined by analysing the spontaneously ooling behaviour.

5 Figure Sample, ylindrial and square TSA units are shown in order from left to right. All TSAs use ellular plasti as insulation material. In addition, the square setup has an outer layer of plywood. 3. Empirial determination of the ooling fator For a speifi TSA setup with a onstant volume of the onrete sample, the only variables should be the density and the thermal apaity of the onrete sample, see Eq.. However, other influening fators may exist, e.g. aging of the TSA or some deviations in the plaing of different omponents in the TSA setup. Therefore, to take possible variations into aount, it is preferred to measure the ooling fator on eah onrete sample before removing it from the test setup. A spontaneous ooling behaviour for a onrete sample is illustrated in Figure 3. Figure 3 Cooling behaviour for a mature onrete sample. The ommon definition of the ooling fator is dt a ( T ( t) T ) dt = (3)

6 Integrating this expression with the information given in Figure 3 results in Eq. 4, whih an be fitted against empirial data with regression analysis. Here, the so alled least square method is used. ( t t ) T t T ln T t T a = (4) where T ( t ) [ C] = temperature in the onrete sample at time t [s or h]; temperature in the onrete body at time t [s or h]. T t [ C] = 3.3 Evaluation and modelling of heat of hydration From the TSA measurement the evaluated heat of hydration produed per kg of ement an be determined by summation for eah time step of the energy stored within the onrete sample, within the TSA omponents, and the energy loss due to heat flow from the onrete sample to the surrounding, expressed by t ρ qem = η ( T ( t) T ) + a ( T ( t) T ) dt C (5) 0 where η [-] = orretion fator introdued in this paper aounting for heat energy used to warm up the TSAs omponents. It must be noted that the model in [5, 0] ould have been formulated in this way in order to fit both a thermos vessel and a TSA. Therefore, the model in this paper has been designed to suit any semi-adiabati setup. For normal weight onrete an approximate linear relationship exists between the water/ement ratio (w/c) of the onrete mixture and its thermal apaity [4]. However, it is quite umbersome to determine the orret thermal apaity from material point of view. We alulate energies from measured temperatures, and then, before appliation in alulations, translate these energies bak to temperatures. This is a mathematial reirulation, whih implies that information regarding onrete density and thermal apaity does not need to be known as time material properties. However, it is important to use the same values in the omplete hain of methodology [5, 6], and aeptable onstant values may be set to ρ = 350 000[J/m 3 C] (6) It has been shown that the heat of hydration is approximately proportional to the degree of hydration [7]. The formulation for the degree of hydration in [5] and [8] is modified and fitted against the empirial heat data expressed by

7 * t e qem = qu α = qu exp ln + t κ (7) * where α [-] = is the relative degree of hydration; t [s or h], κ [-] and q u [J/kg] are fitting parameters determined by the so alled least square method; t e [s or h] = equivalent time. The * notation relative means that α = reflets the ultimate heat of hydration, q u, at the individual final value for a tested onrete. It should be noted that the heat of hydration in Eq. 7 gives about the same results as the ommonly used Danish TPM (three point model) formulation in [9] for the deisive part of the heat of hydration desription. However, Eq. 7 is favourable for preditions outside the most deisive interval, speialty for more mature onrete [6], and, besides, Eq. 7 is zero when t = 0, whih is preferable in programming. e 4. DEVELOPED MODEL FOR THE CORRECTION FACTOR 4. General In order to get a reasonable estimation of the generated heat in onrete, hydration heat flow to the environment and heat energy stored in the involved materials must be determined. Thus, temperature measurement from initiation of the test until the system is in equilibrium in pratie with the ambient temperature is needed. The following observations are of importane for the presented model The exothermi reation between ement and water is the only soure of energy. The reation energy heats up the onrete body and the ambient materials. Heat flow in the surrounding insulation materials an be desribed by Fourier s Law of ondutive heat transfer. 4. Prerequisites for the model for the orretion fator The TSA unit an be transformed into an assoiated sphere, where the onrete volume is retained, and the measured ooling fator is refleted by the atual amount of insulation in the assoiated sphere. There is good thermal ontat between the materials involved. In reality, there is a small amount, less than 5L, of between the onrete sample and the ellular plasti for the TSAs in Figure. This volume is assumed to be quikly warmed up to the same temperature as the onrete. The thermal apaity by weight of is high and its density is low. Thus, its stored energy an be negleted in relation to the other involved materials, see Table. Calulations have shown that the energy stored in the affets the orretion fator by less than one thousandth for TSAs evaluated in this paper. Therefore, in the presented model using an assoiated sphere the first layer of insulation (ellular plasti) starts where the onrete ends.

8 Table Chosen values for the omponents involved in our TSA tests. Values within brakets are urrently not needed for the model in this paper. In literature, these values may vary. Conrete Steel Teflon Air Cellular plasti Plywood k [W/m C] (,-,7) 60 (0,5) (0,06) 0,036 0,8 [J/kg C] 000 450 000 (000) 500 700 ρ [kg/m 3 ] 350 7850 (50) (,) 5 800 The thermal ondutivity in the onrete is signifiantly higher than in the surrounding insulation materials, see Table. Thus, if enough insulation material is used, it is reasonable to assume that there are no, or negletable, temperature gradients within the onrete body. For our TSAs presented in Figure laboratory measurements show that the maximum temperature differene from the entre of the sample to its surfae is within the auray of the temperature sensors (±0,5 C). The temperature hanges in the onrete sample are relatively slow. Therefore a stationary heat flow is assumed for the assoiated sphere, whih signifiantly simplifies the temperature alulations in the insulation materials. To verify this laim, a ylindrial TSA that orresponds to the approximate average ooling fator observed during laboratory tests, a = 0,08 [/h] was simulated in D with ConTeSt Pro [0]. The resulting non-stationary temperature profiles were then ompared with stationary D alulations for a ylinder, see Figure 4. The stationary estimation is based on the average onrete temperature and follows the same proedure as the 3D stationary alulations presented in this paper for the assoiated sphere. 50 45 h stationary 36h stationary 40 40 9h 53h 35 35 7h 30 30 78h 5 5h 5 68h 0 0 0 0,05 0, 0,5 0, 0 0,05 0, 0,5 0, Distane [m] Distane [m] Figure 4 Stationary and non-stationary temperature profiles in D simulations. The onrete radius r =0,066m and the insulation thikness is 0,094m. The hosen onrete mix is based on the standard ement used in this paper, see ByggC in Setion 5.. Temperature [ C] ByggC w/c=0,55 temperature profiles inreasing to max temperature 8h non-stationary Temperature [ C] 50 45 ByggC w/c=0,55 temperature profiles dereaseing from max temperature 8h non-stationary A non-stationary behaviour an be observed for the hours that follow from start of the hydration proess, where the stationary alulation shows a higher temperature within the insulation. This type of deviation inreases for larger amount of insulation. The energy effet of this differene is illustrated by the orretion fator for non-stationary and stationary onditions in Figure 5. Here, the orretion fator is approximately equal after 0 hours. However, the onsequenes using a temporary wrong orretion fator

9 during this heat up period is negligible in pratie, as the total heat of hydration energy is very small in this period. η [-],040,030,00,00 Corretion fator non-stationary stationary,000 0 4 48 7 96 0 44 68 time [h] Figure 5 The quotient between the energy stored within the insulation and the energy in the onrete when estimating the stationary and non-stationary orretion fator. 4.3 Spherial heat transfer In order to fit the model of an assoiated sphere to our laboratory setups, the onrete sample with radius r is surrounded by two materials, thiknesses lm and l m, see Figure 6. heat flow area = the surfae area of a sphere at a speifi radius within the assoiated sphere: Figure 6 A ross setion of an assoiated sphere with a onrete sample surrounded by two layers of insulation materials. Ar[m ] = heat flow area at any radius ( r [m]). Based on the information in Figure 6 the heat flow an be desribed by ( r, t) dt Q ( rt) k r dr, = 4 π for r r r lm ( r, t) dt Q ( rt) k r dr + (8) m m, = m 4 π for r lm r r lm l m + + + (9)

0 3 4 π = + m + at m r r lm l m Q t h T t T r l l 4 π tot = tot at r r Q t h T t T r where i (, ) index i = or m; Q i ( rt, ) [W] = i (, ) thermal ondutivity in material i ; i (, ) material i ; Q ( t) = + + (0) = () Q rt [J] = energy in material i depending on time ( t [s or h]) and radius ( r [m]), and dq r t dt = heat flow in material i ; k i [W/m C] = T rt [ C] = temperature in material i ; l i [m] = thikness of [W] = heat flow from the outer surfae to ; h [W/m C] = heat transfer oeffiient from the outer surfae to ; T 3 [ C] = temperature at the outer surfae; T [ C] = temperature; Q tot ( t) [W] = heat flow from onrete to ; h tot [W/m C] = heat T t [ C] = temperature in the onrete body. transfer oeffiient from onrete to ; For a stationary heat flow Eqs. 8- desribe the same flow formulated by (, ) = (, ) = = = m tot hf Q r t Q r t Q t Q t Q t () where Q ( t) [W] = is the stationary heat flow at time t. hf All equations onerning heat flow and temperature distribution in the subsequent text in this hapter are based on stationary heat flow onditions. In order to determine the temperature T ( rt, ) at speifi point at time t within the material, the following integration needs to be performed Q t dr dt k π = hf 4 r r T ( r, t) (3) if the boundary onditions are known it beomes ( rt, ) r T Qhf t dr 4 π r = r T t k dt ( r, t) (4) whih gives ( t) Q hf = T t Tm rt km 4 π r r (, ) (5) The boundary temperature in the onrete sample, T the temperature material expressed by T rt, an be alulated for any point r r r lm t, an be measured at any time. Then, + at time t within the

Q hf t r r Tm ( rt, ) = T( t) km 4 π r r (6) At the end of material, where r r lm orresponding expression for material beomes = +, we let T ( rt, ) T( t) =, see Figure 6. Then, the (, ) T rt T t ( + ) 4 π Q t r r l hf m m = km r + lm r (7) At the end of material, where r r lm lm = + +, we let T ( rt, ) T( t) m 3 =, see Figure 6. Now, when the boundary onditions are known, T and T3 from Eqs. 6-7, by use of Eqs. 8- the temperature differene within eah material is expressed as T t T t Q t l hf = 4 π km r r + lm Q hf ( t) lm T t T3 t = 4 π k r + l r + l + l m m hf ( t) Q T ( t) T = h 4 π r + l + l 3 T t T = h m tot Q hf ( t) 4 π r (8) (9) (0) () Summation of the temperature differenes from the onrete sample to the gives ( ) ( 3) ( 3 ) T t T = T t T t + T t T t + T t T () Substituting Eqs. 8- into Eq. gives the total heat transfer oeffiient from the onrete sample to the expressed by h tot l l m = + + r km r ( r + lm ) km ( r + lm ) ( r + lm + lm) h ( r + lm + lm) (3) Thus, the individual temperatures within eah material, Eqs. 8-, an be determined by the heat flow expression in Eq..

4.4 Heat energy stored within the materials of the TSA In order to aount for the amount of energy heating up material of the TSA, the average ave temperature within the material, T, is expressed as r l + ave Tm = Tm ( r, t) 4 π r dr Vm r (4) where 4 π r + lm r 3 V [m 3 ] = 3 3 is the volume for material, whih gives T ( ) 3 3 htot T t T r r + lm r T ( t) 3 k 3 ave ( t) = 3 3 ( r + lm ) r htot ( T ( t) T ) r ( r + lm ) r + km (5) ave The orresponding expression for the average temperature in material, T m, is expressed by T ( t) 3 = ave m 3 3 ( r + lm + lm) ( r + lm ) h ( T ( t) T ) r ( r + l ) ( r + l + l ) ( r + l ) 3 3 tot m T ( t) + k m 3 h T t T r r l l r l km ( ) tot + + m + (6) Thus, the thermal energy in eah of the materials are expressed as Conrete ρ Q t = V T t T (7) Material 0 Qm 0 ( t) = ( ρ j j Vj ) ( T ( t) T ) ave Material ρ (8) j Q t = V T t T (9) ave Material ρ Q t = V T t T (30) m m m m m where 0 m = material 0 reflets the stored thermal energy for materials in diret ontat with the onrete sample, whih are onsidered to have the same temperature as the onrete sample; j = index for individual materials within material 0. In the TSA setup presented here, material 0

3 onsists of a steel buket ( j = ), a steel girdle ( j = ), steel lamps ( j = 3) and a heating arpet of Teflon ( j = 4 ). The heat of hydration energy stored within material 0, material and material are all proportional to the heat of hydration energy stored in the onrete sample. Therefore the energy orretion fator is expressed by η ( t) + + Q ( t) m0 m = + (3) Q t Q t Q t Eq. 3 formally desribes the orretion fator as a funtion of time. However, the energy in eah material is proportional to the energy stored in the onrete sample refleted by the term T t T. Therefore, the orretion fator is onstant and an be evaluated for any time t. ( ) In Figure 7 the total heat of hydration energy at any time t is the sum of the energy stored in the materials of the TSA, i.e. the sum of Eqs. 7-30, and the energy loss from the TSA due to the aumulated heat flow, see the seond part of Eq.. Based on a measured value of the ooling Q t, is expressed by fator, a in Eq. 4, the energy due to heat flow, t ρ ( ) hf hf 0 0 t Q t = Q t dt = V a T t T dt (3) hf Figure 7 The total energy is the sum of the energies stored in the onrete, the ambient materials and the energy loss to the surrounding, see Eqs. 7-30 and 3. Note that this figure only illustrates the energies involved without respet to real size relations. 4.5 Determination of stationary heat transfer oeffiient In order to alulate the assoiated stationary temperature distribution the total heat transfer oeffiient, h tot, has to be alulated. The stationary heat flow based on the rate of temperature hanges in the onrete sample is expressed by ( t) dt Q hf ( t) = V ρ dt (33)

4 Combining Eq. with Eqs. 3 and 33 gives 3 4 π r tot ρ ( ) 4 π ( ) h T t T r = a T t T (34) 3 whih results in h tot a r ρ = (35) 3 Eq. 35 expresses the parameter h tot for an assoiated sphere with the same ooling fator as the real TSA. 4.6 Steps to determine the orretion fator. Determine, or use Eq. 6, onrete density and heat apaity by weight. The volume of the onrete sample is known and is transformed into the assoiated onrete sphere with radius r. Heat apaity by weight for all materials in the TSA is also needed.. Determine, using data sheets or alibration, the thermal ondutivity of all material layers, k i, in the assoiated sphere. 3. The heat transfer oeffiient from outer surfae to should be estimated. For our laboratory onditions h is approximately set to 0 W/m C. 4. Evaluate a ooling fator from the laboratory tests and alulate the total heat transfer oeffiient, h tot using Eq. 35. 5. The total heat transfer oeffiient, h tot in Eq. 35, reflets the real ooling fator. By using Eq. 3 and an iteration tehnique l and l m an be determined. In ases with only one insulation material ( l > 0 and l m = 0 ) the use of Eq. 3 is straightforward. This is the ase here for two ylindrial TSAs, see Figure. 6. The square TSA used here, see Figure, has an outer layer of plywood. The assoiated sphere is onstruted with the ondition that the relation between the stored energy per temperature unit is maintained between the two materials, whih is expressed by δ, m ρ = ρ V V m m (36) whih gives V ρ V = δ ρ, m m m (37)

5 where V and V are the real volumes of material and material, respetively. The volume of material in the assoiated sphere is given by 4 3 3 Vm = π r + lm r 3 (38) and the volume of material in the assoiated sphere using Eq. 37 results in V m ρ V = δ ρ, m m m (39) and 4 π V = r + l + l r + l 3 3 3 m m (40) whih gives 3 3 Vm 3 m = + ( + ) l r l r l 4 π (4) 7. The onsequenes of Eqs. 36-4 are that l m and V m are expressed as funtions of l. So, h tot in Eq. 3 is solely a funtion of l, and the size of l is here determined by an iterative tehnique. l m is alulated using Eq. 4, and the size of the assoiated sphere is established. Now, the onstant orretion fator, Eq. 3, is determined for time t, see Figure 7. 5. EVALUATION OF THE EFFECT OF THE CORRECTION FACTOR 5. Tested onrete reipes Here the purpose is to show how the orretion fator affets the atual temperatures in a onrete struture. Two ommon Swedish ements are used, see Tables and 3. AnlC is a moderate heat ement, that generally is used for ivil engineering strutures. ByggC is a standard ement ausing higher onrete temperature than AnlC, and its appliation area is usually onerning housing. Table Oxides, linker minerals and speifi surfae of tested ements. ByggC is of type CEM II/A-LL 4,5 R ontaining about 3% LL, and AnlC is of type CEM I 4,5 N SR3 MH/LA produed by CEMENTA AB. Cement Oxides [%] Clinker minerals [%] Speifi surfae CaO SiO Al O 3 Fe O 3 SO 3 C 3 S C S C 3 A C 4 AF [m /kg] ByggC 6,4 8,7 3,9,8 3,5 54, 8,9 5, 7,8 460 AnlC 64,,4 3,7 4,5,4 48,0 8,0, 3,8 36

6 Table 3 Main onstituents of tested onretes. Reipe Cement Cement ontent [kg/m 3 ] w/c [-] ByggC 360 0,55 AnlC 340 0,55 5. Calulated values of the orretion fator The materials in diret onnetion with the onrete sample in the TSAs are weighted in order to determine their stored energy, see Table and 4. Table 4 Weighted omponents in diret onnetion with the onrete sample. The weight of the steel buket inludes the weight of a steel lid. Steel buket [kg] Steel lamps [kg] Steel girdle [kg] Teflon arpet [kg] TSA A and B 0,47 0,64 0,069 0,099 TSA C 0,465 0,408 The heat of hydration for the reipes in Table 3 was evaluated from measurements performed in TSA A and B. The ooling fators and other parameters needed for the iteration proess and their resulting orretion fators are presented in Table 5. Table 5 Parameters used in the iteration proess, and the resulting orretion fator. Reipe/ a [/h] k [W / m C] r [m] [m] h [W / m C] tot h [W / m C] 3 l m V [m ] η [-] TSA /A 0,037 0,507 0 0,036 0,0985 0,508 0,74,57 /B 0,037 0,704 0 0,036 0,0985 0,035 0,03,078 /A 0,059 0,555 0 0,036 0,0985 0,86 0,093,8 /B 0,034 0,6933 0 0,036 0,0985 0,06 0,03,079 In the assoiated sphere the radius depends on the thikness of the onrete sample and the insulation, see Figure 6. A small derease of the ooling fator gives a small inrease of insulation thikness in material ( l ). However, the volume is signifiantly greater sine it is a ubi funtion, see Eq. 38. Therefore, a small differene in ooling fator ( a ) for TSA A between reipe and in Table 5 results in a quite large differene in alulated volume ( V ). The differene in energy stored within these insulation volumes are refleted by the orretion fator in Table 5. 5.3 Evaluated heat of hydration Both the traditional method, Eq., and the refined method, Eq. 5, were used to evaluate heat of hydration ( q em ) for reipes and in Table 3. The parameters of Eq. 7 were fitted against the test results in Figure 8 from TSA A and B for eah reipe, see Table 6.

7 Heat of hydration [kj/kg] 350 300 50 00 50 00 50 0 Reipe, ByggC, w/c = 0,55 Traditional evaluation tested.tsa-a tested.tsa-b 0, 0 00 000 Equivalent time [h] Heat of hydration [kj/kg] Reipe, ByggC, w/c = 0,55 Refined evaluation 350 tested.tsa-a 300 tested.tsa-b 50 00 50 00 50 0 0, 0 00 000 Equivalent time [h] Heat of hydraton [kj/kg] 350 300 50 00 50 00 50 0 Reipe, AnlC, w/c = 0,55 Traditional evaluation tested.tsa-a tested.tsa-b 0, 0 00 000 Equivalent time [h] Figure 8 Evaluated heat of hydration using the traditional method, Eq., and the refined method, Eq. 5. Fitting parameters using Eq. 7 are presented in Table 6. TSA A has a onsiderable lower value of the ooling fator ompared to TSA B, see Table 5. This is aused by a higher amount of insulation material in TSA A. The energy stored in the insulation is refleted by the orretion fator, whih always is inreased with dereased ooling fator. The onsequene of not taking this energy into aount using a larger TSA will result in a lower heat of hydration ompared to a smaller TSA. This effet an be seen for the traditional evaluation in Figure 8 using the traditional evaluation, where TSA B is higher than TSA A. These results show that general reommendations onerning low ooling fators may result in too low heat of hydration using TSAs that are evaluated with the traditional method. By using the refined evaluation the heat of hydration urves beome approximately equal for the deisive part of the urves, see approximately equivalent time up to 00h in Figure 8. These results show that it is important to onsider energies stored within the TSA materials. Table 6 Model parameters for evaluated heat of hydration results, see Eq. 7. Heat of hydraton [kj/kg] Reipe/TSA Traditional evaluation (Eqs. and 6) Refined evaluation (Eqs. 5 and 6) q u [J/kg] q u t [h] κ [-] /A 96000 6,54,8 300000 5,9, 7 /B 309000 6,50,34 300000 6,3,96 /A 40000,83 0,58 345000,0 0,85 /B 358000,6 0,79 345000 0,39 0,87 350 300 50 00 50 00 50 0 Reipe, AnlC, w/c = 0,55 Refined evaluation tested.tsa-a tested.tsa-b 0, 0 00 000 Equivalent time [h]

8 5.4 Simulation of temperature development within walls In order to determine the effet of the orretion fator, the maximum temperature reahed within a onrete struture was determined using the parameters in Table 6. This simulation was performed with ConTeSt Pro in D [0], where five onrete walls of different thiknesses with a formwork of plywood were studied. The temperature was kept onstant at 0 C, and the heat transfer oeffiient from the outer surfae to ( h ) is set to 0 W/m C. The results are presented in Table 7 and 8 where TA and TB show the temperature differene between traditional and refined evaluation for TSA A and B, respetively; TABR shows the temperature differene between the refined evaluation using TSA A and B. Table 7 Maximum temperature reahed within a wall of different sizes, based on reipe. Wall Calulated temperatures, reipe, ByggC [ C] thikness /A /B /(A+B) [m] Traditional Refined T A Traditional Refined evaluation evaluation evaluation evaluation T B TABR 0, 36,6 40,7-4, 37,0 38,9 -,9,8 0, 4,9 47,4-4,5 43,6 45,7 -,,7 0,4 49,3 53,6-4,3 50,3 5, -,9,4 0,8 55,3 58,9-3,6 56,7 58, -,6 0,7,6 60,0 6,4 -,4 6,7 6,6-0,9-0, Table 8 Maximum temperature reahed within a wall of different sizes, based on reipe. Wall Calulated temperatures, reipe, AnlC [ C] thikness /A /B /(A+B) [m] Traditional Refined T A Traditional Refined evaluation evaluation evaluation evaluation T B TABR 0, 7,9 9, -, 8,9 9,7-0,8-0,6 0, 3,7 33, -,5 3,9 33,9 -,0-0,7 0,4 36,4 38,0 -,6 37,7 38,8 -, -0,8 0,8 4,8 43,4 -,5 43, 44, -,0-0,7,6 47,8 48,9 -, 48,7 49,4-0,8-0,5 The general behaviour for both ByggC and AnlC in Tables 7 and 8 are The maximum temperature level is higher for thiker walls for both traditional and refined evaluation. Traditional heat of hydration evaluation for TSA B gives a higher maximum temperature ompared with TSA A, sine less energy is lost to the smaller insulation material in TSA B. The temperature level is always higher for the refined evaluation ompared to the traditional evaluation, sine the energy in the surrounding materials are onsidered. ByggC is the standard ement with signifiantly higher heat of hydration during the deisive period and shows a higher maximum temperature ompared to AnlC. ByggC shows a larger temperature differene between TSA A and B ompared to AnlC, whih is a onsequene of that ByggC is the faster ement. The differenes in TABR are smallest for the refined evaluation and the largest wall. This indiates that the refined evaluation reflets the true material parameters, as the entre point of the thikest wall is most dependent on the heat of hydration.

9 The deviation of maximum temperatures between the traditional and the refined evaluation are of importane both for strength growth and rak risk alulations. For the larger TSA A and the faster ement ByggC the maximum differene in temperature is within 4,5 C, whih for the estimation of strength growth an be regarded on the safe side, i.e. too low strength values and too long hardening times are alulated, but this extra margin might not be wanted in pratie. For the alulation of rak risks, and espeially for risks of through raking at high restraint, 4,5 C underestimates the rak risk substantially. This is explained by the maximum addition of the design strain ratio [ = additional tensile strain/failure tensile strain] might be as big as 0,7 4,5/0 = 0,3 [, ]. Let us assume that the design strain ratio is alulated to be at most 0,7 (rather ommon requirement for ivil engineering strutures), the true strain ratio will be 0,7 + 0,3 =,0. A strain ratio > means obvious risk of raking. Even a small temperature differene of about C might result in an underestimation of the strain ratio with 0,4, whih also is a too large differene in the alulations (0,7+0,4=0,84). Even if the underestimation in alulated strain ratios does not result in raking, the margin in the safety fators are signifiantly redued. Therefore, these results show that it is important to onsider energies stored within the TSA materials. 5.5 Pre-alulated orretion fators for TSAs at Luleå University of Tehnology It has been shown that the orretion fator will hange due to the amount of insulation material in the TSA. For our ylindrial and square TSAs a normal span of ooling fators is between 0,03-0,034 /h and 0,040-0,045 /h, respetively. Therefore, an extended span with prealulated orretion fators for orresponding ooling fators will simplify future evaluations, see Figures 9 and 0. In addition, a reasonable interval for normal weight onretes and their effet on the orretion fator is shown. The thermal apaity by weight is kept onstant at 000 J/kg C sine it is umbersome to establish in hydrating onrete. Corretion fator [-] Cylindrial TSA - with ellular plasti insulation,400,350,300,50,00 density =,0E+06,50 density =,35E+06,00 density =,50E+06,050 0,0 0,04 0,06 0,08 0,030 0,03 0,034 0,036 0,038 0,040 0,04 Cooling fator [/h] Figure 9 Cooling and orretion fator onerning TSA A and B.

0 Corretion fator [-] Square TSA - with ellular plasti insulation and an outer layer of plywood,60,50,40,30,0 density =,0E+06,0 density =,35E+06,00 density =,50E+06,090,080 0,030 0,03 0,034 0,036 0,038 0,040 0,04 0,044 Cooling fator [/h] Figure 0 Cooling and orretion fator onerning TSA C. In Figure 9 and 0 it an be seen that the higher the density, the lower ooling and orretion fator. An inreased amount of insulation gives a lower ooling fator, but a higher orretion fator. Thus, it is again shown, that reommendations regarding low values of the ooling fator may result in too low hydration energy when evaluation is performed with the traditional method, Eq.. 0,046 0,048 0,050 0,05 6. SUMMARY AND CONCLUSIONS The energy quantity of the exothermi reation between ement and water has long been of importane sine it affets the temperature levels within a onrete struture. Several adiabati methods have been used to determine heat of hydration. The traditional semi-adiabat (TSA) has been popular to use for engineering purposes beause of its simple onstrution with heap parts. The traditional evaluation method was presented in 954 [] and is still used today. Improvements to this evaluation method are found in [5] and [0], where energy stored in the semi-adiabati setup is aounted for. However, the evaluation method in [5] and [0] only works for their speifi semi-adiabati setup using thermos vessels, and not for TSAs. Therefore, this paper presents a refined and general model that aounts for energies stored in the onrete sample and within all its surrounding materials, whih is refleted by a orretion fator formally inreasing the energy in the onrete sample. The onrete sample and the TSA are transformed into an assoiated sphere. The volume of the onrete sample is maintained in the assoiated sphere as the real volume in the TSA. The relative volume of the additional TSA materials within the assoiated sphere is determined by an iterative proess, with the ondition that the measured ooling fator is the same in the sphere. This paper presents a tehnique in whih the only iterated parameter is the thikness of the first layer of insulation. Heat of hydration energy is alulated as the sum of energies in the onrete sample and all the surrounding materials. The orretion fator reflets these additional energies in the surrounding materials. For our laboratory additional materials onsist of a steel buket, a

steel girdle, steel lamps, a heating arpet of Teflon and two layers of insulation. All these additional materials have a signifiant effet on the orretion fator. Two ommon Swedish ements are studied in this paper. ByggC is a standard ement and its appliation area is usually housing, and AnlC is a moderate heat ement generally used for ivil engineering strutures. The results from the heat of hydration evaluation using these onrete mixes show that TSA A has a onsiderable lower value of the ooling fator ompared to TSA B. This is aused by the higher amount of insulation material in TSA A, as TSAs with lower ooling fators always store more energy in the surrounding material for a speifi mix. Without ompensation for this additional energy in the evaluation proess, a lower ooling fator always results in a lower heat of hydration. Using the refined evaluation, i.e. inluding the energy ompensation, the heat of hydration urves beome approximately equal for TSA A and B. This shows that it is important to onsider energies stored within the TSA materials, and that general reommendations onerning low ooling fators may result in too low heat of hydration using TSAs that are evaluated with the traditional method. In order to investigate effets of the orretion fator for our two mixes, the evaluated parameters were applied in D strutural simulations. Five onrete walls of different thiknesses were used. The results show that temperatures are almost underestimated by 5 C for an ordinary ement, and C for a moderate heat ement. The onsequenes for alulated strength development are that the lower strength auses longer hardening time than needed, whih might be regarded as being on the safe side, but this extra margin might not be wanted in pratie. For rak risks, the alulated strain/stress ratios are underestimated with at most 0,3 (ordinary ement) and 0,4 (moderate heat ement). A rather ommon strain/stress ratio in design is 0,70, and based on that the true strain/stress ratio might be,0 and 0,84, respetively. For the true situation these underestimated temperatures may result in an obvious risk of raking or at least a signifiant redued safety fator. This onfirms that it is important to onsider energies stored within the TSA materials. ACKNOWLEDGEMENTS The authors of the paper aknowledge The Swedish Researh Counil Formas, Cementa AB and Betongindustri AB. The laboratory tests have been performed in ooperation with personnel from Complab at Luleå University of Tehnology, whih is hereby aknowledged. REFERENCES. Kjellsen, K.O., Detwiler, R.J., and Gjørv, O.E., Pore Struture of Plain Cement Pastes Hydrated at Different Temperatures, Cement and Conrete Researh, Vol. 0, No. 6, November 990, pp. 97-933.. Kjellsen, K.O., Detwiler, R.J., and Gjørv, O.E., Development of Mirostrutures in Plain Cement Pastes Hydrated at Different Temperatures, Cement and Conrete Researh, Vol., No., January 99, pp. 79-89. 3. Fjellström, P., Jonasson, J-E., Emborg, M., and Hedlund, H., Model for Conrete Strength Development Inluding Strength Redution at Elevated Temperatures, Nordi Conrete Researh, Vol. 45, No., June 0, pp. 5-44. 4. Conrete: Heat Development, Nordtest Method, NT BUILD 388, 99, 4 pp.

5. RILEM Tehnial Committee 9-TCE, Adiabati and Semi-Adiabati Calorimetry to Determine the temperature Inrease in Conrete due to Hydration Heat of Cement, RILEM Report 5, Prevention of Thermal Craking in Conrete at Early Ages, Edited by R. Springenshmid, E & FN Spon, London, 998, pp. 35-330. 6. Ng, P.L., Ng, I.Y.T., and Kwan, K.H., Heat Loss Compensation in Semi-Adiabati Curing Test of Conrete, ACI Materials Journal, Vol. 05, No., January-February 008, pp. 5-6. 7. Conrete: Heat Development, NordTest Method, NT BUILD 488, 997, 6 pp. 8. Poole, J.L., Riding, K.A., Folliard, K.J., Juenger, M.C.G., and Shindler, A.K., Hydration Study of Cementitious Materials using Semi-Adiabati Calorimetry, ACI Speial Publiation 4CD Conrete Heat Development: Monitoring, Predition & Management, Edited by K. Wang & A. Shindler, paper SP-4-5, Vol. 4, April 007, pp. 59-76. 9. Riding, K.A., Poole, J.L., Juenger, M.C.G., Shindler, A.K., and Folliard, K.J., Calorimetry Performed On-Site: Methods and Uses, ACI Speial Publiation 4CD Conrete Heat Development: Monitoring, Predition & Management, Edited by K. Wang & A. Shindler, paper SP-4-3, Vol. 4, April 007, pp. 5-38. 0. EN 96-9:00, Methods of Testing Cement Part 9: Heat of Hydration Semi- Adiabati Method, European Committee for Standardization (CEN), 00, Brussels.. Rastrup, E., Heat of Hydration in Conrete, Magazine of Conrete Researh, Vol. 6, No. 7, September 954, pp. 79-9.. Helland, S., Norwegian Standards on ativation energy and heat release, IPACS report no. BE96-3843/00:4-9, TU Luleå, Sweden, 00, 7 pp. 3. NS 3657:993, Conrete Testing Determination of Heat Release, Norwegian Standard, September 993. 4. Whiting, D., Litvin, A., and Goodwin, S.E., Speifi Heat of Seleted Conretes, Journal of the Amerian Conrete Institute, Vol. 75, No. 7, July 978, pp. 99-305. 5. Jonasson, J-E., Slipform Constrution Calulations for Assessing Protetion Against Early Freezing, Swedish Cement and Conrete Researh Institute Report, no. 4:84, 984, Stokholm, 70 pp. 6. Jonasson, J-E., Modelling of Temperature, Moisture and Stresses in Young Conrete, Dotoral thesis 994:53D, Luleå University of Tehnology, Luleå 994, 5 pp. 7. Danielsson, U., Condution Calorimeter Studies of the Heat of Hydration of a Portland Cement, Swedish Cement and Conrete Researh Institute Report, no. 38, 966, Stokholm, p. Cited from [9]. 8. Byfors, J., Plain Conrete at Early Ages, Swedish Cement and Conrete Researh Institute Report, no. 3:80, 980, Stokholm, 464 pp. 9. Freiesleben Hansen, P., and Erik, J.P., Curing of Conrete Strutures, Danish Conrete and Strutural Researh Institute, Report prepared for CEM General Task Group No. 0, Durability and Servie Life of Conrete strutures, Deember 984, pp. 45. 0. ConTeSt Pro, Användarhandbok ConTeSt Pro (Users manual Program for Temperature and Stress Calulations in Conrete), Developed by JEJMS Conrete AB in o-operation with Luleå University of Tehnology, Cementa AB and Peab Öst AB, Danderyd, Sweden: Cementa AB, pp. 07. (In Swedish).. Larson, M., Estimation of Crak Risk in Early Age Conrete: Simplified Methods for Pratial Use, Lientiate thesis 000:0, Luleå University of Tehnology, Luleå 000, pp. 56.. Jonasson, J-E., Wallin, K., Emborg, M., Gram, A., Saleh, I., Nilsson, M., Larson, M., and Hedlund, H., Temperature Craks in Conrete Strutures: Handbook with Diagrams for Crak Risk Estimation Inluding Measures for Typial Cases. Part D, Tehnial report 00:4, Luleå University of Tehnology, Luleå 00, pp. 07. (In Swedish)