Thermal Cracking in High Volume of Fly Ash and GGBFS Concrete

The concrete mixes were produced with general purpose (GP) cement, fly ash and GGBFS. Table 1 summarises the chemical composition of the GP cement, fly ash and GGBFS by X-ray fluorescence (XRF) analysis according to (AS, 2564–1982, 1982). The coarse aggregate is basalt with a maximum nominal size of 10 mm, and local Sydney sand with a maximum nominal size of 2.36 mm is used as fine aggregate. The coefficient of thermal expansion (CTE) of basalt is determined as 6.8 × 10^–6 °C. The water absorption and specific gravities are 1.08% and 2.8 for coarse aggregate and 3.5% and 2.65 for fine aggregate, respectively. The particle size distribution (PSD) for coarse and fine aggregates is shown in Fig. 1.

Three concrete mixes were prepared to investigate the effect of fly ash and GGBFS on the concrete properties, including the time-dependent mechanical properties, autogenous shrinkage development, thermal stress and the risk of early age cracking potential. ‘N50’ was designated for the concrete mixes because the nominated compressive strength for all mixes was 50 MPa. Mixture ‘0’ was the reference concrete mixes without fly ash or GGBFS. Fly ash and GGBFS replace 30% and 60% of GP cement by weight because 30% fly ash and 60% are practical and widely used in Australian industry. Hence, ‘FA30’ and ‘G60’ were designated for fly ash and GGBFS concretes. Initially, the water-to-binder ratio of concrete mixes with fly ash and GGBFS was consistent with reference concrete. However, the compressive strength of fly ash and GGBFS concrete was significantly lower than that of the control mix. As such, the water-to-binder ratio of concrete with fly ash and GGBFS was reduced to achieve the targeted compressive strength. Moreover, a competitive market superplasticiser was utilised to improve the workability of the concrete mixes. The mix design proportions are presented in Table 2.

Since the temperature profile of mass concrete is difficult to obtain, the temperature profile was simulated using the software ConcreteWorks. ConcreteWorks has been developed to predict the temperature profile of mass concrete. ConcreteWorks provides the concrete temperature history of each concrete mixture based on the geometry of the element, mix design proportions, chemical composition of the cementitious materials, thermal coefficient of expansion of aggregates, and the environmental effects. In this study, the member type in ConcreteWorks was selected as mass concrete with rectangular columns. The dimension of width and depth were 1 m and 1.5 m, respectively. The minimum and maximum temperature was input as 22–23 °C according to the laboratory environmental conditions. The input number of days was 4 days (96 h). The input project location was selected as Port Arthur because the default location system in ConcreteWorks is US city and Port Arthur is a representative costal city, similar to Sydney. The type of fly ash was selected as Class F. Then the temperature profile can be obtained by ConcreteWorks. The simulated temperature profile was applied to the RCF, FSF and match-curing oven. In addition, the temperature profile was assumed at the centre point of the mass concrete element. It should be noted that ConcreteWorks considers the mixture designs assuming the statistically representative properties of Portland cement, fly ash and GGBFS, it cannot specifically consider the effect of fly ash and GGBFS used in this particular study. The effects of fly ash and GGBFS on heat generation and hydration may significantly vary depending on their chemical compositions of them. Fortunately, the results of temperature profile simulated by ConcreteWorks have been successfully used and validated in previous research (Byard et al., 2010; Sargam et al., 2019; Tankasala et al., 2017). As a result, this study assumed that the simulated profile was reasonably correct.

Mechanical properties of concrete, including the compressive strength, tensile strength and elastic modulus, were tested at the ages of 1, 3, 7, and 28 days based on the Australian Standard (AS1012.9–2014, 2014), (AS, 1012.10–2000, 2000) and (AS, 1012.17–1997, 1997), respectively. Note that the 1- and 3-day cylinders were cured in a match-curing oven, while the 7- and 28-day cylinders were moved to a standard curing condition (the temperature at 23 ± 2 °C and relative humidity of 95 ± 5%) after the RCF specimen had cracked (≈ 5 days). The dimension of the cylindrical specimen was 100 mm in diameter by 200 mm in height. The slump test evaluates the workability of concrete in accordance with (AS, 1012.3.1–2014, 2014). The air content of concrete was tested according to (AS, 1012.4.2–2014, 2014). The fresh density of concrete was obtained by weighing the concrete during pouring according to (AS, 1012.5–2014, 2014), which could eliminate the influence of hydration reaction.

Fig 2 presents the match-curing oven used to cure the concrete cylinders. To determine the development of mechanical properties of concrete placed in the RCF, tested cylinders are cured under the same temperature profile as the specimen in the RCF and FSF. As mentioned in the previous section, the match-curing oven was used to test the mechanical properties of concrete at the age of 1 and 3 days. The relative humidity in the match-curing oven was controlled at 95 ± 5% to avoid any moisture loss.

Due to the complex interaction of different factors such as thermal strain, elastic modulus, degree of restraint, and stress relaxation, traditional methods solely based on the measurement of concrete deformation (e.g. restrained ring test) cannot determine the thermal and other restraining stresses in young hardening concrete. The RCF test can give a measurement of thermal stress by inherently considering the influence of elastic modulus, autogenous shrinkage, tensile creep, etc. The RCF is made up of a concrete specimen held by two mild steel crossheads, which are fixed in place by two Invar sidebars, the dimension of the RCF cross-section is 150 × 150 mm, as shown in Fig. 3.

For the rigid sidebars to provide the proper restraint, the concrete specimen must be fixed at both ends. Therefore, the steel crossheads are constructed in such a way that they contain dovetails lined with teeth for gripping concrete. Crosshead braces are bolted to the top and bottom of each crosshead to prevent the slip of the concrete sample, and these restrain expansion as the concrete goes into tension. Since the midsection of the concrete sample in RCF test has a narrower width than the crosshead section. This concentrates the stress in the test area, so that cracks and most of the strain occur in midsection. The RCF is made with a thermally insulated formwork that enables measurements to begin immediately after fresh concrete has been placed and helps control the temperature of the sample.

To minimise the effect of temperature change on the length of the side bars, Invar steel is used to make the sidebars. Each bar was fitted with strain gauges capable of measuring the small axial strains produced by the combined effects of thermal and autogenous shrinkage in the concrete. In the central portion of the specimen, the stresses were uniaxial, and hence, a uniform stress distribution was assumed. The measured strains in the Invar sidebars could thus be used to compute the corresponding stress development in the restrained concrete specimen. The RCF test was set to follow the temperature profile simulated by ConcreteWorks within the first 96 h. If the specimen is not cracked during the test period, then it undergoes an artificially cooling process. In other words, the operator manually operates the computer to control the water circulator of the RCF, driving the RCF to cool down at a rate of 1 °C/hour to accelerate the development of tensile stress and induce thermal cracking. The temperature and stress of the specimen were continuously monitored until the specimen was cracked.

The FSF test was used to evaluate the free total deformation including thermal and autogenous shrinkage. As shown in Fig. 4, the FSF is the framework that is thermally controlled by copper tubing and a supporting Invar steel frame. Thus, the fresh concrete used in this study was allowed to be placed in FSF to cure at the same temperature profile as RCF. Two end steel plates measured the free total deformation with an Invar rod to a linear variable displacement transducer (LVDT). The dimension of the FSF was 150 × 150 × 600 mm. The FSF maintained the specimen under a sealed condition so that neither moisture loss during the test nor, thus, drying shrinkage occurred in the FSF test.

As mentioned in Sect. 2.6, the FSF allows for  measuring the total deformation including both autogenous shrinkage and thermal deformation (expansion and contraction). But these two deformations cannot be assessed separately using this test. Therefore, this section aims to assess the autogenous shrinkage using standard concrete prisms. The tests were carried out at the constant temperature of 23 °C. It should be noted that the autogenous shrinkage measured using concrete prisms at 23°C will not be identical to the autogenous shrinkage of mass concrete because of the difference in temperature, dimension and hydration degree. The increase in concrete autogenous shrinkage due to the increase in temperature was not accounted for in this study. As a result, the thermal deformation can be deduced from the difference between total deformation measured using the FSF and autogenous shrinkage measured using the standard concrete prisms. The autogenous shrinkage specimen is shown in Fig. 5. The size of the standard shrinkage prisms in Australia is 280 × 75 × 75 mm (AS1012.8.4–2015, 2015). After demoulding, all faces of autogenous shrinkage specimens were well-wrapped using a self-adhesive water-proof aluminium foil to avoid any moisture loss to the environment (Gibert et al., 2017). Measurements were carried out once a day for 5 days (120 h).

Fig 6 shows the temperature profile data obtained from ConcreteWorks. The peak temperature of the control mixture was higher than those of fly ash and GGBFS mixtures. The time for the maximum temperature was also delayed when the addition of fly ash and GGBFS. The peak temperature for the control mixture was 64.2 °C, and it occurred at 20 h after pouring concrete, which was higher and earlier than 51.4 °C, 26 h for FA30 concrete and 49.4 °C, 28 h for G60 concrete, respectively, which indicates that the fly ash and GGBFS could effectively reduce the heat of hydration and resultant thermal cracking in concrete structures.

Tables 3 and 4 show the mechanical properties of concrete, including the compressive strength, splitting tensile strength, elastic modulus and fresh properties such as slump, air content and fresh density for each concrete mix. It can be seen that the incorporation of fly ash and GGBFS decreased the compressive strength, tensile strength and elastic modulus compared to that of reference concrete, especially at an early age. This is attributed to the low activity of fly ash and GGBFS, which slows down the hydration process (Wang et al., 2015).

Fig 7 presents the stress development obtained from the RCF test and the free deformation development of reference and SCM concretes. It can be seen that all three mixtures exhibited swelling behaviour at a very early age. Previous studies also reported this phenomenon (Igarashi et al., 2000; Markandeya et al., 2018; Wei & Hansen, 2013). This could be attributed to thermal dilation due to the heat of hydration, absorption of bleeding water, water adsorption by filler, CH growth and primary ettringite formation (Bjøntegaard et al., 2004; Carette et al., 2018; Craeye et al., 2010). Reference concrete had the highest swelling deformation, which was also attributed to the higher temperature rise shown in Fig. 6 in addition to the possible reasons mentioned above. This also explained the highest compressive stress development for the reference concrete as determined by the RCF test (see Fig. 7a). In other words, under the restrained condition, the higher expansion of the reference mixture corresponded to a higher initial precompression. According to Wei and Hansen (Wei & Hansen, 2013), the strain for free shrinkage frame at the zero-stress temperature (\({\mathrm{T}}_{\mathrm{zs}}\)) (see Fig. 7a) is called zero-stress strain (\({\upvarepsilon }_{\mathrm{zs}}\)), and it is referred to as the starting point of contraction for comparison (see Fig. 7b). Note that the \({\upvarepsilon }_{\mathrm{zs}}\) is not necessarily zero because the compressive stress of young concrete is relaxed. Thus, by setting the value of \({\upvarepsilon }_{\mathrm{zs}}\) is numerically equal to zero, then the increase of free deformation after \({\upvarepsilon }_{\mathrm{zs}}\) is denoted as “absolute free total contraction” (see Fig. 7c). As such, the absolute free total contractions were compared for assessing the cracking risk.

Fig 7c shows the measured stress and absolute free total contraction of three concrete mixes. The absolute free total contraction of the control mixture was 295 με at 96 h, which was higher than that of N50-F30 and N50-G60 concretes with 160 and 241 με, respectively. After 96 h, the artificial cool process produced a high rate of contraction development. When the fly ash and GGBFS were incorporated into the concrete mixes, the significant reduction of the absolute free total deformation resulted in reduced tensile stress development This will be discussed in Sect. 3.5.

Fig 8 presents the mean value of the experimentally measured autogenous shrinkage for each concrete mixture. The measurement of autogenous shrinkage started 24 h after casting. The absolute value of autogenous shrinkage strain at 5 days (120 h) was 90 με, 56 με and 102 με, which decreased by 38% and increased by 13% for concrete mixes from 0% SCM to 30% fly ash and 60% GGBFS, respectively. Similar results can be found in (Gao et al., 2013; Lee et al., 2006). (Gao et al., 2013) demonstrated that the autogenous shrinkage for concrete mixes with 30% fly ash was approximately 30% lower than reference concrete at an early age. The results can be explained by fly ash as a filling powder material that does not take part in early hydration. Hence, the autogenous shrinkage is effectively decreased (Gao et al., 2013). (Lee et al., 2006) showed that the early age of autogenous shrinkage increased with GGBFS content. This is attributed to the incorporation of GGBFS leads to a finer pore structure, contributing to lower relative humidity, thus increasing the self-desiccation and autogenous shrinkage. The underlying logic of conducting the autogenous shrinkage test is that the absolute free deformation measured from FSF consists of thermal strain and autogenous shrinkage. After measuring autogenous shrinkage, the thermal strain can be simply deduced. Then the autogenous shrinkage-induced stress and thermal stress can be calculated separately. This will be discussed in Sect. 4.

The behaviour of concrete in the RCF can be described in five stages (Breitenbucher, 1990). The RCF test results of stress development for all concrete mixtures are presented in Fig. 9. The concrete specimen cracked at 62 h for the control mixture, and the cracking stress was 2.4 MPa. The cracking stress can be calculated using the product of the Invar strain and its elastic modulus. However, N50-FA30 did not fail in the first 96 h. It cracked after 8 h of artificial cooling, which indicated the decreased cracking potential of the mixture, while for the GGBFS mixture the cracking time was 92 h which was also significantly delayed compared to that of the reference mixture. In view of these results, the addition of SCMs lowered the early age cracking risk. This was attributed to the significant reduction in the free total deformation that will be discussed in Sect. 3.4 and Fig. 8 and the elastic modulus development (Table 3). Secondly, as shown in Fig. 6, the temperature rise decreased compared to that of the control mixture. Fly ash was more effective in reducing the cracking risk than GGBFS because the absolute free total contraction of GGBFS was higher than that of fly ash mixture as mentioned in Sect. 3.3. Although the tensile strength of SCMs concrete decreased, the combined effect of temperature rises and elastic modulus compensated for the negative impact of tensile strength, resulting in an overall enhancement in performance of resistance to cracking.

Table 5 summarises the time and temperature at a zero-stress state and the time and temperature at cracking. The incorporation of fly ash and GGBFS reduced the zero-stress temperature and the zero-stress time because of the lower peak temperature in the applied temperature profile. The addition of SCMs also decreased the cracking temperature and delays the time to cracking, and the lower cracking temperature indicated the better resistance to early age cracking of the mixes. This is attributed to the decreased rate of temperature development and elastic modulus development (Byard et al., 2010). Moreover, (Wei & Hansen, 2013) reported that the replacement of cement by GGBFS can effectively resist concrete cracking. (Markandeya et al., 2018) conducted the RCF tests using different types of GGBFS with the same percentage of replacement. They found that the temperature risk and cracking potential decreased compared to that of the control mixture regardless of the slag types. (Riding et al., 2008) reported that the introduction of fly ash in concrete delayed the tensile stress development, leading to a low-level tendency to crack. Therefore, the results that concrete cracking time is delayed with an increasing proportion of fly ash or GGBFS in this research are rational.

According to ACI 207.2 (ACI207.2R-07, 2007), the tensile stress due to restraint can be calculated using Eq. (1):where \({D}_{R}\) is the degree of restraint which can be computed based on the rigidity of restraining element and concrete, as shown in Eq. (2); \({\varepsilon }_{t}\) is the total contraction due to shrinkage and thermal deformation caused by heat dissipation; \({E}_{c}\) is the elastic modulus of concrete.where \({A}_{c}\) is the cross-sectional area of concrete which is equal to 22500 mm² in the RCF test; \({A}_{s}\) is the cross-section area of Invar side restraining bars in the RCF test, which is equal to 15710 mm²; \({E}_{I}\) is the elastic modulus of Invar side bar which is equal to 137 GPa.

As mentioned in the previous study of (Zhang et al., 2021, 2022), stress relaxation due to tensile creep is critical. Hence, in some existing codes, such as JCI guidelines (JCI, 2016), the effective elastic modulus method is utilised to take into account the creep effect (Maruyama & Lura, 2019). Although this approach captures the order of magnitude of stress relaxation that occurs in concrete, it might be a bit conservative because the creep increases more slowly under gradually increasing stress than under constant stress (Kovler, 1994). In this study, a reduced creep coefficient by implementing an ageing coefficient and age-adjusted effectively modulus method was adopted according to (Gilbert & Ranzi, 2011). Note that the ageing coefficient in age-adjusted effectively modulus method is less than 1.0 because a reduced creep coefficient can be used to calculate creep strain if stress is gradually applied. Also, the change of stress may be attributed to restraint to creep and shrinkage, or variations of temperature, or combinations of these. The expression of age-adjusted effective modulus is shown as follows:where \(\varphi (t,\tau )\) is the tensile creep coefficient which can be obtained from the tensile creep model in Sect. 4.3; \(\chi (t,\tau )\) is the ageing coefficient and the recommended value of the ageing coefficient is 0.80 for relaxation problems (Cheng et al., 2020; Gilbert & Ranzi, 2011).

Hence, the elastic modulus of concrete in Eqs. (1) and (2) should be changed to the age-adjusted effective modulus. The tensile stress and degree of restraint can be rewritten as shown in Eqs. (4) and (5):

It should be noted that the above analytical models have been validated in a previous study using 21 independent sets of experimental data (Zhang, et al., 2021). The calculated degree of restraint varied from 1.0 to 0.72, 1.0 to 0.76 and 1.0 to 0.78 for control, fly ash and GGBFS concrete mixes, respectively. Similar results were obtained by (Slatnick et al., 2011). They stated that the degree of restraint was equal to 1 when the concrete is fresh and decreased to approximately 0.73 for hardened concrete. The total contraction of concrete in Eq. (4) is considered as the sum of the autogenous shrinkage and thermal contraction due to heat dissipation, as shown in Eq. (6):where \({\varepsilon }_{au}\) is the autogenous shrinkage measured from concrete prism; \({\varepsilon }_{T}\) is the thermal contraction using the measured free deformation strain obtained from FSF minus the autogenous shrinkage or using the CTE multiples with temperature changes, as shown in Eq. (7):

By substituting Eqs. (5), (6) and (7) into Eq. (4), the total tensile stress of concrete can be expressed in terms of autogenous shrinkage induced stress and thermal stress, as shown in Eq. (8):where \({\sigma }_{au}\) and \({\sigma }_{T}\) are the autogenous shrinkage induced stress and thermal stress, respectively, as shown in Eq. (9a) and (9b):

The newly proposed analytical model from Eq. (9a) and Eq. (9b) can separate the autogenous shrinkage-induced stress and thermal stress. In this model, autogenous shrinkage of concrete can be simply measured on a prism test, elastic modulus can also be measured using a straightforward experimental test on concrete cylinders, and the temperature variation can be determined through the software ConcreteWorks. The other required parameters such as coefficient of thermal expansion and tensile creep coefficient will be explained in Sect. 4.2 and Sect. 4.3, respectively.

As mentioned above, the CTE of concrete is one of the most important parameters for evaluating thermally induced strain and stress. Concrete with a high CTE is generally leading to a higher risk of cracking. According to Eq. (7), CTE can be rewritten using the thermal strain divided by the temperature change, as shown in Eq. (10):

In Eq. (10), \({\varepsilon }_{T}\) can be determined using the absolute free deformation from FSF minus the measured autogenous shrinkage from the prism, \(\Delta T\) can be evaluated by calculating the temperature difference between two adjacent temperatures.

(Li et al., 2021) conducted a precise measurement of CTE of concrete at an early age using a newly built temperature stress testing machine (TSTM), stepped temperature profiles and temperature cycles ranging between 18 and 25 °C. They observed that the measured CTE showed a rising trend. The measured CTE increased from 7.2 to 12.3 × 10^–6 °C for concrete with a w/b of 0.42. However, in the current research, the CTE values are quite fluctuated over time within the range between 5.8 and 12.0 × 10^–6 °C, as shown in Fig. 10. This may be due to the difference between the TSTM test and the RCF test. Moreover, this study considered continuous temperature profiles based on the heat of hydration instead of stepped temperature profiles, which may affect the measured CTE values. As such, the CTE was calculated according to Eq. (10) and the average values were adopted, which were approximately equal to 8.5, 7.1 and 8.4 × 10^–6 °C for OPC, fly ash and GGBFS concrete, respectively. Similar results can be found in (Gao et al., 2011; Shui et al., 2010). (Shui et al., 2010) illustrated that replacing the cement with fly ash and GGBFS lowers the CTE of the hardened cement paste. The reduction in CTE of fly ash and GGBFS systems is mainly due to the change in the porosity and portlandite (CH) (Shui et al., 2010). (Gao et al., 2011) also showed that the CTE of fly ash concrete is lower than reference concrete. Thus, the results that CTE of concrete decreased with an increasing proportion of fly ash or GGBFS in this research seems to be reasonable.

It is critical to take into account the tensile creep of concrete into tensile stress development as it leads to stress relaxation. Most models such as (ACI209R, 2008) and (AS3600-, 2018, 2018) predominately apply compressive creep, and the drying and basic creep are not distinguished in these models. Instead, (FIB, 2010) is a commonly used code for predicting basic creep. It considers the effects of curing temperature and hydration degree on the creep coefficients by calculating the temperature-adjusted concrete age. However, according to (Dabarera et al., 2021), the basic tensile creep coefficient was underestimated by FIB, 2010 model. They also proposed a modified tensile creep model based on FIB, 2010 model and this model has been successfully validated by the results in (Atrushi, 2003; Ji et al., 2013). In this study, the experimental test conditions are similar to the test conditions conducted by (Dabarera et al., 2021). Therefore, the modified tensile creep model proposed by (Dabarera et al., 2021) is adopted for predicting the basic tensile creep coefficient \({\varphi }_{bc}\left(t,{t}_{0}\right)\) in this paper. The modified model is shown as follows (Dabarera et al., 2021):where \({\beta }_{bc}({f}_{cm})\) is the strength-dependent factor which is shown in Eq. (12a); \({\beta }_{bc}(t,{t}_{0})\) is the time-development function which is shown in Eq. (12b):where \({t}_{0,adj}\) is the modifying factor considering the effects of cement type and curing temperature to convert the age at loading \({t}_{0}\) to \({t}_{0,adj}\), which is equal to 8.03, 6.94 and 6.85 days for control, fly ash and GGBFS concrete, respectively, as shown in Eq. (12c):where α represents the coefficient ranging from − 1 to 1, depending on the type of cement, for example, − 1 for strength class 32.5 N, 0 for strength class 42.5 N and 1 for strength class 52.5 N, respectively (FIB, 2010). Moreover, (Dabarera et al., 2021) proved their model can work for different types of concrete (fly ash, silica fume concrete) without any adjustment. As a result, in this paper, the value of α is taken as 0 because the cement strength class of 42.5 is used. \({t}_{0,T}\) is the modified age at loading based on the curing history to take account into elevated or reduced temperatures on the maturity of concrete, as shown in Eq. (12d):where \({\Delta t}_{i}\) is the number of days where a temperature \(T\) occurs; \(T({\Delta t}_{i})\) is the temperature in °C during the period of \({\Delta t}_{i}\).

Fig 11 presents the predicted basic tensile creep coefficient of all the concrete mixes. The start of calculation is assumed to be the same as autogenous shrinkage measurement (at 24 h after demoulding) due to the modelling purpose. The results stopped at the cracking when experimentally observed, i.e. 62, 104 and 92 h for control, fly ash and GGBFS concrete, respectively. It can be seen that the prediction results for fly ash concrete and GGBFS concrete were similar because of the similar temperature profile, while the reference concrete exhibited slightly lower results compared to that of SCMs-based concrete. This is attributed to a greater temperature profile due to a higher early age hydration degree, resulting in increased stiffness properties, leading to a decrease in creep (Briffaut et al., 2012). It indicated that the modified model suggested by (Dabarera et al., 2021) captured the evolution of the temperature profile and the basic tensile creep coefficient of concrete. In addition, a slightly lower tensile creep coefficient of control concrete contributed to a less stress relaxation to compensate for the tensile stress development, explaining a reduced cracking time of control concrete compared to that of fly ash and GGBFS concrete.

Fig 12 shows the comparison of concrete tensile stress measured experimentally and tensile stress calculated analytically using Eq. (4). The experimental tensile stress can be computed using the measured Invar strain from strain gauges multiplied by the elastic modulus of Invar. The age-adjust effective modulus \({\overline{E} }_{e}\) can be calculated using the predicted values from the tensile creep coefficient model (see Fig. 11) and  the time-dependent elastic modulus of concrete (Table 3). As such, \({D}_{R}\) can be calculated using Eq. (5). The autogenous shrinkage-induced stress and thermally induced stress were calculated utilising Eqs. (9a) and (9b) are included for sensitivity analysis. It can be observed that the analytically calculated tensile stress as per Eq. (4) agrees well with experimentally measured tensile stress for all mixes, indicating the accurate prediction of the time-dependent tensile creep. The analytical maximum stress was also calculated using Eq. (1) to reveal the importance of tensile creep. The analytical maximum stress using Eq. (1) was greatly higher than experimental stress for all mixes, showing that the tensile creep can relax the concrete tensile stress and thus cannot be neglected. In addition, the thermal stress of reference concrete is much higher than that of fly ash and GGBFS concrete, leading to an accelerating cracking time.

The risk coefficient is commonly used to assess the risk of early age concrete cracking (Khan et al., 2019a, 2019b, 2020). It is defined as the ratio between the concrete tensile stress calculated using Eq. (4) and the tensile strength of concrete, both being time-dependent, as shown in Eq. (13):

When the risk coefficient equals 0, there is no tensile stress developed in concrete, and the cracking does not occur. When the risk coefficient increases as tensile stress is generated gradually, the cracking risk becomes higher. Fig 13 shows the calculated cracking risk coefficient for the tested specimens until cracking occurs. It can be observed that at the same time, the \(R(t)\) of N50-0 is the highest, followed by N50-G60, then N50-FA30. The calculated tensile stress of concrete at cracking is 72%, 70% and 65% of the splitting tensile strength for N50-0, N50-FA30 and N50-G60, respectively, which agrees with the results in (Altoubat & Lange, 2001; Khan et al., 2017). (Altoubat & Lange, 2001) reported that the cracking stress is taken to be 80% of direct tensile strength, and the direct tensile strength can be approximated as 80% of the splitting tensile strength for concrete at an age greater than 100 h. As such, the ratio of cracking stress to splitting tensile strength can be about 64%. (Khan et al., 2017) demonstrated that the cracking stress is equivalent to 65% of splitting tensile strength. Thus, these previous works supported the results of the calculated cracking risk coefficient of concrete in this research.