Experimental study on temperature stress calculation and temperature control optimization of concrete based on early age parameters

HU Yintao，ZHOU Qiujing，YANG Ning，QIAO Yu，JIA Fan，Xin Jianda

(1.China Institute of Water Resources and Hydropower Research，Beijing 100038，China；2.China Three Gorges Construction Engineering Corporation，Beijing 101100，China)

Abstract：Temperature control curve is the key to achieving temperature control and crack prevention of high concrete dam during construction，and its rationality depends on the accurate measurement of temperature stress.With the simulation testing machine for the temperature stress，in the present study，we carried out the deformation process tests of concrete under three temperature curves：convex，straight and concave.Besides，we not only measured the early-age elastic modulus，creep parameters and stress process，but also proposed the preferred type.The results show that at early age，higher temperature always leads to greater elastic modulus and smaller creep.However，the traditional indoor experiments have underestimated the elastic modulus and creep development at early age，which makes the calculated value of temperature stress too small，thus increasing the cracking risk.In this study，the stress values of the three curves calculated based on the strain and early-age parameters are in good agreement with the temperature stress measured by the temperature stress testing machine，which verifies the method accuracy.When the temperature changes along the concave curve，the law of stress development is in consistent with that of strength.Under this condition，the stress fluctuation is small and the crack prevention safety of the concave type is higher，so the concave type is better.The test results provide a reliable basis and support for temperature control curve design and optimization of concrete dams.

Keywords：concrete dam；temperature control curve；early-age parameters；temperature stress testing machine；elastic modulus

1 Introduction

For such a long time，temperature control and crack prevention of concrete dams has long been a very important research direction in dam engineering[1]，involving concrete material properties[2-4]，structural design[5]，and temperature control measures[6].With the construction of high concrete dams in China，plenty of systematic and in-depth research work has been conducted and achieved fruitful results，effectively supporting the high-quality construction of projects.Meanwhile，a range of 300 m high arch dams such as Jinping level I[7]，Wudongde[8]and Baihetan[9]and 200 m high gravity dams such as Huangdeng[10]have been built.In the process of long-term practice，the core temperature control method by using cooling water under the condition of isolating the influence of external environment as much as possible has been gradually formed，and the stress and crack resistance safety control is realized by regulating temperature variation，which prevents the concrete from cracking.

Reasonable determination of temperature control curve is the key to accurately controlling the temperature and stress of concrete dam，while the verification of reasonable temperature control curve depends on accurate measurement of temperature stress.At present，the strain in monitoring the stress of dam concrete is mainly obtained by the strainometer，which is converted into stress combined with the monitoring results.However，concrete parameters such as elastic modulus and creep have a direct influence on the stress accuracy during this process.In current code，the parameters of elastic modulus are from the 28-day standard age concrete，especially the parameters in longer age after 7 d，and the early-age parameters within 7 d are lacked，which greatly affects the stress conversion accuracy.There have been numerous research results on this.For example，Liu[11]used ultrasonic nondestructive testing technology to test and measure the early-age elastic modulus，obtained an expression formula considering the age and strength grade of concrete，and put forward the influencing factors of early-age concrete elastic modulus.Jia[12]also tested and measured the early-age elastic modulus of C50 concrete，and found that the early elastic modulus changed obviously with the age.The elastic modulus of concrete at 3 d，5 d and 7 d is 85.6，89.6 and 94.5 of the elastic modulus at the age of 28 d. Xia[13]used a temperature stress testing machine to measure the early creep coefficient of two kinds of fly ash concrete，and found that the early tensile creep growth rate was large，which had obvious relaxation effect on tensile stress.Under normal conditions[14]，the 28-day creep accounts for 65 of the total creep in 180 d，and the 7-day creep in early age is the most severe.The above research showed that the accurate early-age parameters of concrete cannot be obtained easily because they vary dramatically in conventional tests，which makes the reliability of stress results difficult to guarantee.In dam engineering field especially，there are a few studies on early-age elastic modulus and creep parameters as well as the fruits used on stress calculation and analyses.To solve this，the anti-crack safety coefficient is usually amplified to mitigate the cracking risk.This is，to some extent，economically wasteful.

In recent years，the temperature stress testing machine and temperature stress synchronous simulation test system have been developed，and the real simulation for the influence of temperature history on concrete material parameters and temperature stress has been realized[15].Especially in the performance of early-age concrete，remarkable achievements have been achieved[16-18]，which provides good conditions for accurate analyses of early-age temperature stress.At the same time，traditional temperature control curves are appropriate for the artificial water cooling，but have the problems of large stress fluctuation and low anti-cracking safety at the end of secondary cooling.With the continuous development of intelligent water cooling and intelligent temperature control technology[19-20]，further optimization is urgently needed.

Focusing on the optimization of temperature control curves，the present study tested the stress and strain under three conditions by using temperature stress testing machine.Based on the monitored temperature and strain results，we not only studied the elastic modulus，creep parameter and stress change process at the early age，but also optimized the current dam temperature control curve，whichcan provide technical basis for the design of temperature control curves.

2 Experiment

2.1 Experimental equipmentFor precise control of the temperature changes of concrete specimens，we adopted TSTM developed by China Institute of Water Resources and Hydropower Research，and the schematic diagram is as shown in Fig.1. With the temperature control template and an artificial climate simulation box，the actual temperature，stress and strength changes of concrete in the whole process from pouring to hardening under a set temperature environment were simulated，and the deformation and stress-strain laws under different temperature drop conditions were obtained.The machine is mainly composed of a temperature control system，a load control system，and a displacement control system，wherein the temperature control accuracy is up to 0.1 ℃ and the displacement control accuracy is up to 1 μm.The temperature control template follows the principle that PID is adopted to control the flow and temperature of circulating water in input template.TSTM test was carried out with two same specimens simultaneously.One was taken as the main test specimen and used to impose constraints and lay out sensors；the other was completely unconstrained and had consistent temperature control conditions，which was used to measure the spontaneous volume deformation and temperature deformation generated during the test.

Fig.1 Temperature stress testing machine

2.2 Experiment contentZhao[21]studied the stress-strain change process in four temperature drop curves，and illustrated that the concave curve is a better condition from the aspect of numerical calculation. And the laboratorial experiment absent in his research will be verified by the test designed in the present study.The three set temperature control curves are shown in Fig.2，with the highest temperature of 28 ℃ and the lowest temperature of 23 ℃.They have the same temperature rise period and the rate is 1.4 ℃/h. The test duration of curve 1 is 7 days，that is，168 h，and the specimen broke at 114 h. Based on this，the test duration of curve 2 and curve 3 was set as 114 h. The three curves began to cool in about 22 to 23 hours.

Fig.2 Temperature drop curve[22]

Curve 1 is convex，the line type is parabolic，and the equation is：

T=-5.66·10-4·h2+0.023·h+28

Curve 2 is a straight line，and the equation is：

T=-0.054·h+29.08

Curve 3 is concave，the line type is also parabolic，and the equation is：

T=2.247·10-4·h2-0.083·h+29.6

2.3 Experimental measurementThe specimen has the length of 1000 mm and the section size of 150 mm×150 mm.the temperature and strain at the middle section were mainly measured.The arrangement of specimen temperature and strain monitoring instruments are shown in Fig.3. Besides，S01B，S02B and S03B denote FBG strain sensors，and T01 refers to the thermometer.The ambient temperature was monitored by the temperature testing instrument of the thermostat of the testing machine.The displacement of the movable end was monitored by LVDT displacement sensor.

Fig.3 Sample size and instrument layout(unit：mm)[22]

The measuring principle of creep and elastic modulus is as follows：

(1)Creep deformation

The creep coefficient or creep degree is commonly used to describe the creep of concrete at present.In the present study，the creep coefficient was defined as the ratio of creep deformation to elastic deformation of concrete from loading stress at timeτto timet，and is defined as follows：

The deformation of main specimen under 100 constraint was limited，and the total deformationεm(t) was 0：

εm(t)=εe(t)+εcr(t)+Gt(t)+εT(t)

(1)

WhereGt(t) is the autogenous volume deformation，εT(t) is the temperature deformation，εe(t) is the elastic deformation，εcr(t) is the creep deformation andtis the concrete age.The deformation of auxiliary machine without constraint is：

ε(t)=εT(t)+Gt(t)

(2)

Whereε(t) is the total creep.Creep deformation Eq.(3)can be obtained from Eq.(1)and Eq.(2)：

εcr(t)=ε(t)-εe(t)

(3)

(2)Elastic modulus

Whenever the shrinkage strain/expansive deformation of the restrained specimen reached the threshold value of 4 μm，the specimens were pressed or pulled back to its original length.According to the external load change value of the specimen in the process of deformation，the tangent modulus of the test concrete can be obtained：

(4)

Where Δσrefers to the external load change value andε0is the actual expansive(or shrinkage)value.

2.4 Experimental materialsIn the present study，the low heat cement concrete with strength grade C18030 and maximum particle size of 40 mm were used.The initial setting time of concrete was 17：10(hour：min)and the final setting time was 20：45(hour：min).The cement is Jiahua low-heat cement with a water-binder ratio of 0.5.

2.5 Experimental flowAt first，we prepared the concrete in the thermostatic chamber，and the prepared concrete were put into TSTM for standby to make sure that the temperature into the mold was basically consistent.

And then，we poured the mixed concrete into TSTM，whose thickness was about half of the specimen mold，and it was vibrated and compacted.Then，the strain sensor and temperature sensor were placed along the axial direction.Next the concrete was poured until the mold was full.After sufficient vibration，the whole cracking process simulation testing machine was closed.The actual pouring process was shown in Fig.4.

Fig.4 Sample pouring and instrument layout

Before data collection，we preset the allowable deformation threshold and the constraint degree as 4μm and 100 respectively，that is，after the specimen shrinks or expands to the threshold 4 μm each time，the loading device at the end immediately applies load to ensure the specimen to return to the initial position.

After that，the temperature process control curve was input，and the ambient temperature of the specimen was regulated by controlling the mold temperature.And then the temperature of the specimen was managed by heat conduction，which was basically consistent with the input temperature process curve.

When the experiment began，F(xiàn)BG strain sensor and thermometer collected data once every 15 s，and the data were collected throughout the whole test process to obtain strain and temperature data.

3 Results Analysis

3.1 Temperature analysisThe temperature of concrete specimen was influenced by hydration heat and ambient temperature，in which hydration heat made the specimen heat up evenly，while ambient temperature acted on the surface of the specimen and affected the internal temperature through heat conduction.There was a time difference in heat conduction，so a certain lag effect existed when the internal temperature changed and the ambient temperature reached the highest.Fig.5 compared the set temperature，the ambient temperature and the internal measured temperature，while Fig.6 compared the three measured temperature curves.Thus we know as follows.

Fig.5 Input set temperature，ambient temperature and internal temperature

Fig.6 Comparison of measured temperature curves[22]

(1)Under the same condition，the input set temperature，the ambient temperature，and the internal temperature were consistent.If conditions 1，2 and 3 were convex，straight and concave respectively，and the ambient temperature was controlled to be basically coincident with the set temperature，the temperature variation law with time was consistent with the expectation，which meets the requirements of test linear.

(2)The ambient temperature agreed with theset temperature in general，and the performance of the temperature control curve by TSTM was consistent with the expectation，but the measured internal temperature was obviously higher than the ambient temperature and the set temperature in the cooling stage，up to about 2 ℃.It could be predicted that there was obvious temperature difference between the inside and outside of the specimen.

(3)In general，the three groups of tests reached the highest temperature of 29.4 ℃，28.8 ℃ and 29.3 ℃ at the beginning of the test，and then began to cool down according to the set path，and were 23.7 ℃，23.5 ℃ and 23.3 ℃ at about 112 h(when the specimen 2 broke)，down by 5.7 ℃，5.3 ℃ and 6.0 ℃ respectively.Wherein，the temperature drop was the largest in condition 3.At 112 h，the temperature drop under condition 3 went on following the concave line.The specimen did not break at 172 h，even at 188h when the cooling rate continued to increase until the end of the test，as shown in Fig.5(c).

Fig.6 indicated that there were few differences in the actual temperature variation in straight and concave curves，and the analysis told that the elastic modulus and creep of them were almost the same.That is why convex and concave curves with great difference were selected in the following analysis of elastic modulus and creep in the early age，and the data of concave curves were used for the straight curve.

3.2 Analysis of the influence of different cooling curves on the strainThe comparison of the strain process at the same position with different cooling curves can be seen in Fig.7.The strain change law was basically the same，and the compressive strain increased at the movable end and fixed end in the temperature rise stage and decreased continuously in the temperature drop stage；the tensile strain in the middle of the specimen basically increased，decreased and increased again，which has good repeatability，so the results are reliable.

Fig.7 Strain process curve of the same part under different temperature curves

However，there were some differences in the values of strain variables at the same position due to differenttemperatures.At the temperature rising stage of the movable end and fixed end，the compressive strain basically increased linearly，and the maximum value at the movable end was about 67 to 72 με.The maximum compressive strain at the temperature rise stage of the fixed end was quite different，and the values of the compressive strain of the convex，linear and concave type were 103，55 and 84 με respectively.At the temperature drop stage，in terms of the convex curve，the compressive strain decreased significantly.As for the straight curve，the compressive strain reduction rate was basically constant.As for the concave curve，the compressive strain reduction rate was small.

The tensile strain in the middle of the specimen increased continuously before 15 h，but the magnitude was small，with the maximum value about 22 με.Since then，the specimen had a compression trend，and the overall tensile degree was slightly reduced，especially the concave and straight compression trends were more obvious.In the later period，the tensile strain continued to increase with the further decrease of temperature，in which the convex type first slowed down and then accelerated，the straight type basically increased linearly，and the concave type first sped up and then slowed down，with the smallest degree of tension.

In the middle part and the end part of the specimen，there are obvious differences in the strain process due to the different buried locations.Strainometer S02B in the middle section of the TSTM testing machinehas contact with the cooling template around，while the two ends only have cooling conditions at the top position.Therefore，the middle section was strongly affected by the temperature in the heating stage at the beginning，and there was a significant difference between the middle section and the end part.Due to the great expansion resulted from temperature rise，there was a tensile strain at the beginning.Since the constraint degree of the active end was smaller than that of the fixed end，the great difference between the two ends existed.

In general，all parts began to change from compression to tension after cooling.Under the same time and cooling gradient，the tensile strain growth under the convex curve was obviously higher than that of the other two curves.

3.3 Analysis of the influence of different cooling curves on early age

(1)Influence on elastic modulus

The elastic modulus of concrete at the corresponding ages under convex and concave curvesis shown in Fig.8.With the continuous hydration reaction of concrete，the development law of elastic modulus of concrete under different cooling curves was basically the same，and the hydration process of concrete at early age was relatively rapid and the elastic modulus increased quickly.

Fig.8 TSTM measured elastic modulus

We can know that the temperature performance had slight difference in the first 50 h of convex and concave curves，and the growth trend of elastic modulus was almost the same.As the temperature difference increased gradually，the elastic modulus of concave type was gradually lower than that of convex type，because higher temperature led to fuller hydration of concrete and faster hardening speed.

Fig.9 showed the comparison results between the growth curve of elastic modulus measured by TSTM in convex curve and the elastic modulus data in the laboratory.Both were increasing continuously in general，but there were obvious differences in numerical values.The measured elastic modulus was greater than that calculated in the conventional test at early age，indicating that the fitted value in conventional test underestimated the growth rate of elastic modulus in the early age.The maximum difference was about 6 GPa，which had a great influence on the accuracy of the calculated temperature stress.

Fig.9 Comparison of two types of elastic moduli in early age

(2)Influence on early age creep

The creep deformation of concrete is shown in Fig.10.At the heating stage，the creep foundation of concrete was consistent.When the temperature reached the highest point，the pressure creep continued to increase.After the concrete was cooled and compressed，there was some difference.Higher creep value existed in the concave curve at the same time，which had stronger relaxation effect on temperature stress.This is because the elastic modulus of concave curve concrete was lower than that of convex curve concrete，and the creep was larger.

Fig.10 Creep deformation of specimens under 100 constraint conditions in condition one and three

In this paper，not only the change process of early age creep with age was obtained by using TSTM，but also the typical creep prediction model CEB-FIP(MC90)[23]and the creep fitting data of 7 d，28 d，90 d，180 d and 360 d commonly used in engineering were calculated for comparison，as shown in Fig.11，and the results show that.

Fig.11 Comparison of creep coefficients one and three

The creep growth rate was rapid at the early stage，but slowed down with the increase of age.At the early age，the concrete with lower stiffness made the concrete have sufficient creep space，and the measured creep coefficient was more than 3.The reason may be that the creep deformation changed from the compressive deformation into the tensile creep.The predicted model of MC90 was in good agreement with the measured creep coefficient of TSTM.However，the calculation method based on long-term load-bearing regression underestimated the creep ability of early-age concrete，and the difference between it and the measured value reached 30 at 180 h.If this method was used to calculate the temperature stress of early-age concrete，the relaxation effect of creep on tensile strain would be underestimated，which will make the calculation result higher.To sum up，MC90 model can be used for preliminary prediction and calculation of early age creep coefficient.

3.4 Influence of cooling curve on temperature stressFor restrained specimens，the shrinkage deformation affected by external humidity of concrete can be ignored.The theoretical derivation of elastic strain separation of measuring points is as follows：

For the total strainεm(t)at any measuring point，the value in Eq.(1)cannot be 0：

εm(t)≠0

(5)

The calculation formula of creep coefficient is as follows：

(6)

Whereφ(t，τ) is the creep coefficient，tis the loading age，τis the load-bearing age Eq.(1)and Eq.(6)are combined：

(7)

This test is an axial tension-compression test，and the strain gauges were arranged along the axial direction of the specimen.Itcould be considered that the strain measured by the strain gauges was uniaxial strain，and the elastic strain was separated from the total strain by combining with the measured early-age creep coefficient.After that，the temperature stress increment can be obtained by using Eq.(3)：

With Eq.(4)，we can obtain：

Δσ(t)=Et(t)Δε

(8)

There are a total ofnuniaxial strain measurementsε1，ε2，…，εnof concrete at a certain moment from the start of measurement.The stress increment between two adjacent times is Δσ1，Δσ2，…，Δσnrespectively.

Δσ1=ε1E(τ1)

Δσ2=E(τ2)(ε2-ε1)

Δσ3=E(τ3)(ε3-ε2)

……

Δσn=E(τn)(εn-εn-1)

(9)

WhereE(τn) is the tangent modulus，and the measured stress at timenis

(10)

The temperature stress process curve of S02B sensor under each condition calculated by the above method is shown in Fig.12 and Fig.13，in which the measured elastic modulus was calculated under the condition 3.As a reference，the measured stress of TSTM was in good agreement with the measured stress under various conditions，which proves that the method of temperature stress-strain conversion using measured early age parameters in this paper was more accurate.

Fig.12 Temperature stress process curve

Fig.13 Development trend of temperature stress and tensile strength in early age

Twenty-four hours before the test，the temperature rising process was basically the same，and the growth process and maximum value of compressive stress were the same.After that，the specimen began to shrink and gradually turned into tensile state due to the influence of cooling，and the faster the cooling rate，the faster the tensile stress increased.The analysis showed that the temperature drop under three conditions was 5.7 ℃，5.3 ℃ and 6.0 ℃ respectively，with slight difference.The temperature stress of the convex curve was far higher than that of the other two curves，which was unfavorable for anti-cracking safety.The corresponding temperature stress of concave curve was relatively small，and the growth trend was the most consistent with the tensile strength growth of concrete tested in the laboratory，as shown in Fig.13，so its anti-cracking safety was the highest.In the test，the specimen in the convex and straight broke at 114 h and 112 h respectively，and that in the concave curve was not broken until 188 h.To a certain degree，the specimen in the concave curve had lower tension degree.In conclusion，the concave cooling curve was better.

3.5 Influence of early-age parameters on temperature stressIn the present study，there were differences between the parameters of this study and the conventional test parameter in the early age.Focusing on the temperature stress curves with the two parameters，a study was conducted and the influence of parameter difference on temperature stress was analyzed.

(1)Influence of elastic modulus on temperature stress

Fig.14 showed the calculated temperature stress using early-age elastic modulus and conventional elastic modulus respectively for each working condition.When the specimen was pulled to break，the difference of temperature tensile stress in the convex，straight and concave curves at about 110 h was 30，23 and 20.3，respectively.In the compression stage，the elastic modulus of conventional test had a great influence on the convex and straight curves，but had little influence on that of concave curve.Convex type had higher elastic modulus in early age due to later cooling time and higher temperature，and the error of elastic modulus in conventional test was also larger.Concave type had lower elastic modulus in early age，and the error was the smallest.However，the straight type and concave type had similar errors due to little difference in temperature history.The calculated small temperature stress will increase the risk of anti-cracking safety，which is unfavorable to temperature control.

Fig.14 The influence of elastic modulus values on temperature stress

(2)Influence of creep on temperature stress

Fig.15 showed the temperature stress calculation results of early-age TSTM creep and conventional test creep respectively for each working condition.It proves that the temperature stress calculation with conventional creep will underestimate the relaxation ability of early-age creep on stress，resulting in greater temperature stress，which is beneficial to temperature control to a certain extent.From the effect of creep and elastic modulus on stress，the effect of creep on temperature stress is less than that of elastic modulus.

Fig.15 Effect of creep on temperature stress

To sum up，the conventional test values of elastic modulus and creep will produce two opposite effects，in which the influence of creep on temperature stress is less than that of elastic modulus，and the calculated temperature stress is small，which increases the risk of cracking and is unfavorable to temperature control.

4 Conclusion

In the present study，the stress-strain process tests of early-age concrete under the conditions of convex，straight and concave temperature curves were carried out by combining TSTM，theelastic modulus and creep parameters were obtained.Besides，the temperature stress process was calculated and the basic temperature control curve was optimized，with the following conclusions obtained.

(1)The TSTM testing machine can make the temperature development of the specimen basically consistent with the input set temperature，whichsatisfies the linear requirement.However，affected by the heat conversion rate，there are obvious temperature differences between the inside and outside，with the maximum value of about 2 ℃，which may exert certain influence on the stress-strain.

(2)At the temperature drop stage，the specimen in the convex，straight and concave curves alltends to tension，and the increase amplitude of tensile strain in the convex curve is obviously higher than that of the other curves with the same time and temperature drop.

(3)The temperature drophas an influence on the elastic modulus and creep parameters.The higher temperature in the early age leads to larger elastic modulus and less creep value.Conventional test data have underestimated the elastic modulus in the early age.The maximum difference is about 6 GPa，which makes the calculated temperature stress smaller and increasesthe cracking risk of concrete.

(4)The calculated stress based on the measured strain valuesis in good agreement with the measured TSTM temperature stress，which shows that the stress-strain conversion method adopted in this paper is reliable.

(5)Under three cooling curves，the corresponding temperature stress of concave curve is relatively small，and the growth trend is the most consistent with the tensile strength growth of concrete，so it has higher anti-cracking safety and is a better temperature control curve.

Actually，the temperature drop of concrete lasted for tens of days.In the present study，only qualitative research was carried out within 7 d，and the subsequent research will be combined with the actual project construction.