Calibration of Material Models against TSTM Test for Crack Risk Assessment of Early-Age Concrete Containing Fly Ash

Making reliable cracking risk assessment involves experimental testing and advanced modeling of the timeand temperaturedependent behavior of the properties, the restraint conditions of the structure, and the external environmental conditions. Mineral additives such as silica fume (SF), blast furnace slag (BFS), and fly ash (FA) have been used extensively in production of high performance concrete in the last decades. *e mineral additives such as fly ash and blast furnace slag will reduce the hydration heat during the hardening phase, and the mineral additives also have significant influence on the development of mechanic and viscoelastic properties at early age. Within the NOR-CRACK project, extensive test programs were performed to investigate the material properties related to cracking risk of early-age concrete containing mineral additives. In current paper, the advanced modeling of the heat of hydration, volume changes (autogenous shrinkage and thermal dilation) during hardening, the development of mechanical properties (E-modulus, compressive strength, and tensile strength), and creep/relaxation properties are discussed. Tests were performed in “temperature stress testing machine” (TSTM) to measure the restraint stress, and welldocumented material models were verified by performing 1-D analysis of restraint stress development in the TSTM (Ji, 2008).


Introduction
Cracking of concrete structures may compromise not only structural integrity but also durability and long-term service life.High performance concretes, with low water/binder ratios, are experienced prone to early-age cracking.e main reason is that the high volume changes due to autogenous shrinkage (caused by chemical shrinkage and subsequent self-desiccation) and thermal dilation (caused by hydration heat) lead to significant stresses in conditions of high external restraint.
Early-age cracking has been the subject of extensive research.In recent years, more realistic insights have been gained through various research efforts in related fields, for example, on thermal cracking of early-age concrete by a RILEM technical committee (TC 195-DTD) [1].Furthermore, the growing number of applications of high performance concrete and the use of massive concrete structures generate a need for a comprehensive methodology to limit/prevent early-age cracking of concrete.e following material properties are main factors which influence the sensitivity of concrete to cracking at early age and which therefore are required for a full evaluation of cracking risk in hardening concrete structures: (i) e temperature sensitivity (activation energy) (ii) Heat of hydration (iii) Coefficient of thermal expansion (CTE) (iv) Autogenous shrinkage (AS) (v) Mechanical properties (E-modulus, compressive strength, and tensile strength) (vi) Creep/relaxation properties e influences of fly ash on abovementioned early-age concrete properties are investigated in the present study.
Today, there exist several commercially available computer programs capable of calculating the temperature and stress development in hardening concrete structure.Within the past IPACS project [2], a Round Robin calculation was performed, and ve di erent programs were used to simulate temperature and stress development in two examples of hardening concrete structure, and the results are shown in Figure 1 [3].All calculations were based on same set of laboratory test results describing speci c concrete properties.e deviation between the results obtained by di erent programs may be explained by di erences in material modeling, modeling of geometry, and restraint conditions.e deviations were considerable even in the case of stress simulation of hardening specimen in the "temperature stress testing machine" (TSTM) [4] with well-de ned temperature and restraining conditions; that is, the material modeling was the only reason for disagreement.e di erent material models were calibrated to the same experimental data, but in simulation of total behavior of a structure, they gave different results.e comparison gave rise to several questions.What kind of tests is most appropriate for characterization of di erent material properties?Although di erent material models are able to describe material properties separately, is the combination of the models able to describe the total behavior of hardening concrete structure or do the di erent material models match with each other?[3,5].
Within the NOR-CRACK project, extensive test programs were performed to investigate the material properties listed above [6][7][8][9].In the current paper, the material properties of early-age concrete with y ash and the advanced modeling of those material properties are presented.
e TSTM test results are used to verify the proposed material model and their applicability in the prediction of cracking risk of concrete during the hardening phase.

Concrete Composition.
e "SV 40" concrete is a typical high strength concrete used in bridges in Norway, and it has a water-binder ratio (w/b) of 0.42 with 5% silica fume (percentage of OPC weight).e "low-heat" concrete has w/b of 0.46 and contains 36% FA of binder weight (60% of OPC weight) in addition to 5% silica fume (percentage of OPC weight).
e composition of the two concretes is presented in Table 1 [10].
In the laboratory relevant concrete properties were measured, that is, heat of hydration; coe cient of thermal expansion; autogenous shrinkage; mechanical properties including the development of compressive strength, tensile strength, and modulus of elasticity; and creep properties [7,11].

Mechanical Properties.
e modi ed version of CEB-FIP MC 1990 is used to describe the development of the compressive strength, tensile strength, and modulus of elasticity, and t 0 is introduced in the equations to identify the start of signi cant mechanical properties development [12,13]: where t eq is the equivalent time, t 0 is the concrete age when the sti ness starts to increase from zero, s is a curve tting parameter which is determined from compressive strength development, while n t and n E are the curve tting parameters dedicated for the development of the tensile strength and the elastic Young's modulus, respectively.e parameters shown in Table 2 are later used in the numerical analysis of a full-scale eld test structure [14].e development of the compressive strength, tensile strength, and modulus of elasticity for SV 40 and low-heat concrete are shown in Figures 2 and 3.

2.3.
ermal Properties.e thermal properties are the thermal conductivity κ, the speci c heat capacity ϲ, and the heat of hydration.e hydration heat depends on the chemical composition of the cement-it increases with the C3S and C3A content-and on the neness of grinding.Mineral admixtures, such as silica fume (SF), blast furnace slag (BFS), and y ash (FA), have signi cant in uence on the heat of hydration.Increasing percentage of the BFS or FA content reduces the amount of heat of hydration signicantly.omas and Mukherjee [15] showed that when 50% of ordinary Portland cement (OPC) was replaced by slag, the heat of hydration decreased by 28% and the maximum temperature rise was reduced from 24 °C to 16 °C.e heat production is described by the approach based on the hydration degree (equivalent to maturity age) [16]: where Q ∞ , τ, and α are model parameters that can be determined from the adiabatic temperature curve derived from semiadiabatic measurements of the heat of hydration.e parameters of the activation energy were determined according to the Norwegian code (NS3656).e results from isothermal tests at three temperature levels, 5, 20, and 50 °C, were plotted against equivalent time.en, the activation energy was found by tting results at a level of 40% of maximum strength.2 Advances in Materials Science and Engineering e heat development of the low-heat concrete tested in the laboratory was rst used in the analysis, but the calculated maximum temperature was about 10 °C lower than the measured maximum temperature.It was later con rmed [18] that, for this particular eld experiment, the concrete manufacturer had put y ash into a silo previously used to store silica fume, but unfortunately, the silo was not completely cleaned, and probably some silica  e heat development applied in the thermal and structural analysis was about 35% higher than that of the lowheat concrete tested in the laboratory as shown in Table 3 [18].

Volume Change (Autogenous Shrinkage and ermal Dilation).
e free deformation was measured in the Dilation Rig with a stepwise realistic temperature history for both concretes in the NTNU laboratory [7].e maximum temperature for SV 40 and low-heat concrete was 56 and 45 °C, respectively, with an initial temperature of 20 °C, while the maximum temperature for low-heat concrete was 33 °C with the initial temperature of 11 °C.e autogenous shrinkage is then separated from the thermal dilation by assuming a constant value for the thermal dilation coe cient.
e autogenous shrinkage curves of the SV 40 and low-heat (60% FA) concrete are shown in Figure 5.  Advances in Materials Science and Engineering where

Calibration of the Material Models by the TSTM Test
e systems of the special designed temperature stress test machine (TSTM) as shown in Figure 7 are essentially a closed loop servosystem that can be operated either in load or deformation control mode.e TSTM is described in detail in [4,7,24].
e cross section of the specimen is 90 × 100 mm, and the total prismatic length is 1000 mm, and at the both ends, the dimensions are increased in crossheads forming the anchorage.e temperature control system of the TSTM is similar to that of the Dilation Rig. e specimen is sealed with an aluminium plastic foil impermeable to moisture, and drying shrinkage is thus avoided.In the current study, the TSTM is operated in the   Advances in Materials Science and Engineering deformation control mode, and tests were performed under full or partial restraint.e full (100%) restraint condition is provided by an electronic feedback system that moves the left anchoring head of the specimen to compensate for the any length change in the 700 mm midsection of the specimen.A load cell, connected to the right anchoring head, records the restraining force.A partial restraint situation is obtained simply by deactivating the feedback system, meaning that the restraint against deformation is provided by the sti steel frame of the rig and the anchorage of the specimen.Hence, the restraint degree may vary from test to test, but it is generally around 40%.When partial restraint is used, the deformation of the 700 mm section is recorded as well as the restraining force.e advantage with the partial restraint situation is that an early tensile failure of the specimen is avoided during variable temperature development [7].
e stress development measured in the TSTM is the net e ect of all the parameters acting to produce restraint stresses in hardening concrete (ise., thermal dilation, autogenous shrinkage, elastic modulus, and creep/relaxation properties).e TSTM results are used directly for cracking risk comparison of di erent types of concretes and/or to calibrate the material models by recalculating the restraint stress development in the TSTM.

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In the current study, the tests were performed parallel in the Dilation Rig and TSTM.ermal dilation and autogenous shrinkage occur simultaneously in the concrete specimens in TSTM and Dilation Rig. e amount of stress generated by thermal dilation and autogenous shrinkage in a given time interval depends on the degree of restraint in TSTM, the elastic modulus, and the creep/relaxation properties of the concrete.Figure 8 illustrates the interplay of these factors in the TSTM test, each of which changes with time.
e integral type of formulation is used in the 1D analysis of restraint stress development in the TSTM: Based on the principle of superposition, the time history is subdivided into time intervals: For continuously varying strain, the second-order algorithm [19], which is based on approximating the integral by the trapezoidal rule, is used to calculate the stress due to a strain increment (or decrement) Δε j occurring during the time Δt j , and a good accuracy can be achieved.e stress increment Δσ j is assumed applied in the middle of the jth interval (at time t j−1/2 ).e total loaded induced strain at the end of the jth interval is the sum of the strains due to stress increments Δσ j , applied during all the previous increments.
e constitutive behavior of young concrete in stress rig (TSTM) is de ned by the equation as proposed by the CEB-FIP [25]; the strain rate Δε j at time t j may be composed of thermal strain, autogenous strain, creep strain, elastic strain and transient thermal creep strain.

Δε t j
Δε th t j + Δε sh t j + Δε el t j + Δε cr t j + Δε ttc t j , with Δε el t j + Δε cr t j j i 1 Δε sh t j ε sh t j − ε sh t j−1 , where ε is the measured strain in TSTM, ε th is the thermal dilation, ε sh is the autogenous shrinkage, ε el is the elastic strain, ε cr is the creep strain, and ε ttc is the transient thermal creep strain.Free deformation measured in Dilation Rig under different temperatures is the sum of ε th and ε sh and is directly used in the stress calculation.Stress increment at time t j can be determined as e imposed temperature histories and measured stress developments in the TSTM for SV 40 and low-heat concrete are shown in Figures 9(a For the SV 40 concrete, the maximum temperature increase is about 36 °C from 20 °C to 56 °C, and the feedback system is deactivated at 76 hours, and the full restraint condition is then changed to the partial restraint condition to prevent break of the specimen during the test.For the low-heat concrete, the TSTM test was rst performed at the initial temperature of 20 °C, and the maximum temperature rise is 25 °C, and the full restraint condition is changed to the partial restraint condition at 120 hours.Another TSTM test was carried out at the initial temperature of 11 °C, which represented the approximate air temperature in the eld test, under full restraint condition, and the maximum temperature rise is about 22 °C.
e comparisons of calculated and measured stress development for SV 40 concrete are shown in Figure 12, and the development of the compressive stress in the rst 2 days is in good agreement with the test results, but the development of the tensile stress afterwards is lower than the test

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results.e E-modulus of SV 40 concrete at 28 day is relatively low, and it significantly reduces the calculated tensile stress development.e calculated and measured stress developments of the low-heat concrete with 20 °C initial temperature are shown in Figure 13(a), and the development of the compressive stress in the first 3 days is in good agreement with the test results, and the development of the tensile stress afterwards is slightly lower than the test results.
e stress development of the low-heat concrete with 11 °C initial temperature is shown in Figure 13(b), and the development in both compressive and tensile stress is slightly higher than the test results.In general, the material models used in the analysis give a rather good prediction of the stress development in the TSTM test.

Conclusion and Discussion
Crack risk assessment of early-age concrete should be based on specific (measured) concrete properties, and the following material properties are main factors which are required for a full evaluation of cracking risk in hardening concrete structures: (i) e temperature sensitivity (activation energy) e stress development measured in the TSTM is the net effect of all the parameters acting to produce stresses in hardening concrete (i.e., thermal dilation, autogenous shrinkage, E-modulus, and creep/relaxation properties).TSTM is a suitable tool to investigate the stress development in hardening concrete under realistic temperature conditions and to further optimize the concrete mix to reduce the cracking risk.e measured restraint stress at TSTM is used to verify the material models and its applicability for cracking assessment of early-age concrete.It is recommended to use this procedure to obtain reliable and robust material modeling and to ensure that the combination of the models is able to describe the total behavior of hardening concrete structure.

Figure 4 :
Figure 4: Heat evolutions of SV 40 and low-heat concrete.

Figure 6 :
Figure 6: Results of compressive creep tests and double power law.(a) SV 40 concrete.(b) low-heat concrete.

Figure 8 :Figure 9 :Figure 10 :
Figure 8: e main factors inducing restraint stress in the TSTM test.

Figure 11 :
Figure 11: Test results of TSTM and Dilation Rig for low-heat concrete with an initial temperature of 11 °C.(a) FA 60% at an initial temperature of 11 °C.(b) Deformation in Dilation Rig and TSTM.

Figure 12 :Figure 13 :
Figure 12: Stress development in the TSTM for SV 40 concrete.

(
ii) Heat of hydration (iii) Volume change: thermal dilation and autogenous shrinkage (iv) Mechanical properties: E-modulus, compressive strength, and tensile strength (v) Creep/relaxation properties It is necessary to perform experimental tests to establish the database for the material properties listed above.

Table 1 :
Concrete composition, all values in kg/m 3 .

Table 2 :
Mechanical properties of the SV 40 and low-heat concrete.
In general, two creep tests were performed for each of the loading ages.For the SV 40 concrete, the creep tests were carried out with loading time at 2 and 9 days, respectively, and is shown in Figure6(a); the model is in good agreement with the experimental results.For the low-heat concrete, the creep tests were carried out at 4 and 7 days, respectively, and it is seen from Figure6(b) that the estimated the creep strain is slightly lower than the test results.ecreepmodel parameters used in simulation are shown in Table4.
t is the concrete age, t ′ is the concrete age at loading, E(t e ′ )is the E-modulus at the loading age, and φ, d, and p are creep model parameters.

Table 3 :
ermal properties of SV 40 and low-heat concrete.