Influence of Rapid Heat Treatment on the Shrinkage and Strength of High-Performance Concrete

Resource-efficient precast concrete elements can be produced using high-performance concrete (HPC). A heat treatment accelerates hardening and thus enables early stripping. To minimise damages to the concrete structure, treatment time and temperature are regulated. This leads to temperature treatment times of more than 24 h, what seems too long for quick serial production (flow production) of HPC. To overcome this shortcoming and to accelerate production speed, the heat treatment is started here immediately after concreting. This in turn influences the shrinkage behaviour and the concrete strength. Therefore, shrinkage is investigated on prisms made from HPC with and without steel fibres, as well as on short beams with reinforcement ratios of 1.8% and 3.1%. Furthermore, the flexural and compressive strengths of the prisms are measured directly after heating and later on after 28 d. The specimens are heat-treated between 1 and 24 h at 80 °C and a relative humidity of 60%. Specimens without heating serve for reference. The results show that the shrinkage strain is pronouncedly reduced with increasing temperature duration and rebar ratio. Moreover, the compressive and flexural strength decrease with decreasing temperature duration, whereby the loss of strength can be compensated by adding steel fibres.


Introduction
Constructions with precast concrete elements like trusses, walls, tunnel lining segments [1], or beams (modules) made of high-performance concrete (HPC) [2,3] with a compressive strength between 55 and 100 MPa have been found to be advantageous compared to conventional cast-in place members. Elements are prefabricated independently of weather conditions and in a time-saving manner. Due to the high load-bearing capacity of HPC, filigree and slender elements arise. Their durability increases due to the dense pore structure of HPC [4]. The precast elements are assembled on-site via dry joints, bolted connections or socket joints, for example, so that construction times are shortened, and costs are reduced [5]. Since there are no tolerance compensating joints due to a direct force transmission, fast installation depends essentially on the shape stability of the concrete elements [6].
The main, load-independent deformations of concrete result from shrinkage, which is divided into drying, chemical, autogenous, and plastic shrinkage. Plastic shrinkage occurs in fresh concrete during hydration due to evaporation [7]. The capillary forces that arise during evaporation cause a volume change [8]. In drying shrinkage, the volume change is caused by the evaporation of the free pore water from the concrete matrix due to the low external ambient humidity [9].
In autogenous shrinkage, the volume change is caused by the loss of free water in the concrete matrix due to hydration [7]. The hydration products require a lower volume fraction (chemical shrinkage) [10]. The combination of chemical and autogenous shrinkage In this article, the shrinkage behaviour and strength development of rapidly heattreated HPC with and without steel fibres [36] and with reinforcing bars is experimentally investigated. Both the heating rate and pre-storage time are unlimited. The paper starts from the experimental campaign of small-scale samples in which heating time, fibre additions, and rebar amounts are varied. Shrinkage is isolated from thermal strains. Finally, strength values are provided and discussed relative to those of reference samples without heat treatment.

Materials and Methods
The investigations aim to empirically determine the shrinkage strain ε cs and the compressive and flexural strengths regarding the temperature duration T. The measurements are performed on prisms (L × W × H = 16 × 4 × 4 [cm]) without steel fibres and a steel fibre amount of V = 150 kg/m 3 (1.9 Vol.-%). For comparison, beams with a fibre amount of 150 kg/m 3 and reinforcement ratios of 1.8% and 3.1% are investigated, too. They serve to check the influence of rebars on the shrinkage strain. The reinforcement ratios reflect diameters of 6 mm and 8 mm, respectively. To ensure sufficient anchorage length, the length of the associated beams L has been increased to 40 cm. An HPC based on the binder Nanodur ® Compound 5941 [37] is used for all specimens. The mixture is listed inTable 1. Directly after concreting, the prisms and the beams are subjected to heat treatment at 80 • C and 60% relative humidity. Short temperature durations of T = [1,2,4,6] h, but also long durations of T = 24 h are investigated. Thereby, the temperature duration T includes the heating phase and the dwell time. Specimens without heat treatment (T = 0 h) serve for reference. After heat treatment, the test specimens-six per duration and type-are stripped and stored at 20 • C and 65% relative humidity for up to 90 days.
For each T, six beams and prisms are made independently of the rebar ratios r and steel fibre amount V. The series comprises 72 prisms and beams in total including the references. Table 2 lists all and provides the number of tested specimens in each case at the given concrete age after heating depending on the total number of samples. In parallel, 12 prisms with and without steel fibres for T = 2-24 h are made to determine the short-term mechanical properties. In total, this sums to 48 prisms without reinforcement, 120 with microfibres (incl. beams) and 72 beams with rebar and fibres.

Temperature Measurement
Due to heating, temperature strains occur that superimpose with the shrinkage strains. Therefore, the temperatures at the core and at the surface of selected prisms are measured. Figure 1 shows the test set-up for the temperature measurement. A heat sensor is embedded at the core of the prism for each temperature duration T and fibre amount V, to measure the core temperature ϑ m (section: A-A-A-A). After stripping, another sensor is glued on the face to measure the surface temperature ϑ w during cooling ( Figure 1, Detail: A).

Temperature Measurement
Due to heating, temperature strains occur that superimpose with the shrinkage strains. Therefore, the temperatures at the core and at the surface of selected prisms are measured. Figure 1 shows the test set-up for the temperature measurement. A heat sensor is embedded at the core of the prism for each temperature duration T and fibre amount V, to measure the core temperature ϑm (section: A-A-A-A). After stripping, another sensor is glued on the face to measure the surface temperature ϑw during cooling ( Figure 1, Detail: A).

Shrinkage Measurement
Shrinkage deformation is determined daily up to day 28 and then weekly up to day 90. A stress-measuring extensometer type "Pfender" (TESTING Bluhm & Feuerherdt GmbH, Berlin, Germany) with an accuracy of up to 1 μm is used. Figure 2 shows the experimental set-up of the measurement for the samples. For both, markers with an initial length of 100 mm were glued on the specimens directly after heat treatment. For the prisms, two measuring sections are provided on the upper la and lower side li (section: A-A-A-A). To measure shrinkage strains representative for the entire length of the beams, the central measuring sections lA,a and lA,i are supplemented by two more sections with the lengths lB,a and lB,i (cf. section: C-C-C-C). The alteration of length in the individual sections is evaluated according to [38]. The mean over all sections of a sample yields the length Rt at concrete age t. The first is the zero measurement R0 at time t0 * . The shrinkage strain εcs at time t is calculated to:

Shrinkage Measurement
Shrinkage deformation is determined daily up to day 28 and then weekly up to day 90. A stress-measuring extensometer type "Pfender" (TESTING Bluhm & Feuerherdt GmbH, Berlin, Germany) with an accuracy of up to 1 µm is used. Figure 2 shows the experimental set-up of the measurement for the samples. For both, markers with an initial length of 100 mm were glued on the specimens directly after heat treatment. For the prisms, two measuring sections are provided on the upper l a and lower side l i (section: A-A-A-A). To measure shrinkage strains representative for the entire length of the beams, the central measuring sections l A,a and l A,i are supplemented by two more sections with the lengths l B,a and l B,i (cf. section: C-C-C-C). The alteration of length in the individual sections is evaluated according to [38]. The mean over all sections of a sample yields the length R t at concrete age t. The first is the zero measurement R 0 at time t 0 * . The shrinkage strain ε cs at time t is calculated to:

Strength Measurement
Compressive and flexural strength is derived from prism tests. After 28 days, flexural fct,fl,28d [39] and compressive strength fcm,28d [40] are determined from three prisms for each T and V. For the short-term strength, an additional series of three prisms with and without fibres is used (cf. Table 2). The flexural fct,fl,0d and compressive strength fcm,0d are measured directly after heat treatment.

Results of the Temperature Measurement
The core temperature ϑm of the prisms during heat treatment is recorded and evaluated. Figure 3 shows a nonlinear increase and decrease of ϑm as well as a constant plateau during the dwell time. For comparison, the temperature curves of the prisms with (V = 150 kg/m³) and without (V = 0 kg/m³) fibres are shown for annealing times of T =1, 2, 4, 6, and 24 h along with the achieved maximum core temperatures ϑm,max and the shortest heat treatment times according to DAfStb guideline [25]. The prism without steel fibres and a treatment time of T = 1 h broke during the measurement. Thus, Figure 3 just shows the prisms with steel fibres for T = 1 h. The essential differences are the elimination of the prestorage times and the faster heating rate RA. The investigated heat treatment including the cooling phase is accelerated up to 86.8% (T = 1 h) and 67.2% (T = 6 h) in comparison.

Strength Measurement
Compressive and flexural strength is derived from prism tests. After 28 days, flexural f ct,fl,28d [39] and compressive strength f cm,28d [40] are determined from three prisms for each T and V. For the short-term strength, an additional series of three prisms with and without fibres is used (cf. Table 2). The flexural f ct,fl,0d and compressive strength f cm,0d are measured directly after heat treatment.

Results of the Temperature Measurement
The core temperature ϑ m of the prisms during heat treatment is recorded and evaluated. Figure 3 shows a nonlinear increase and decrease of ϑ m as well as a constant plateau during the dwell time. For comparison, the temperature curves of the prisms with (V = 150 kg/m 3 ) and without (V = 0 kg/m 3 ) fibres are shown for annealing times of T = 1, 2, 4, 6, and 24 h along with the achieved maximum core temperatures ϑ m,max and the shortest heat treatment times according to DAfStb guideline [25]. The prism without steel fibres and a treatment time of T = 1 h broke during the measurement. Thus, Figure 3 just shows the prisms with steel fibres for T = 1 h. The essential differences are the elimination of the pre-storage times and the faster heating rate R A . The investigated heat treatment including the cooling phase is accelerated up to 86.8% (T = 1 h) and 67.2% (T = 6 h) in comparison.
The average heating rate R A is calculated to Here, ϑ m,max represents the maximum core temperature, ϑ 0 the initial temperature of 20 to 23 • C and t A the time until the maximum core temperature is reached. Based on the measured core temperatures of the prisms without fibres, heating rates of R A = [45.9, 24.9, 15.9, 16.4 Figure 3. Core temperature ϑm of the prisms with and without fibres as well as the anneali according to [25].
The average heating rate RA is calculated to Here, ϑm,max represents the maximum core temperature, ϑ0 the initial tempe 20 to 23 °C and tA the time until the maximum core temperature is reached. Base measured core temperatures of the prisms without fibres, heating rates of RA = [4 15.9 It must be noted that for a temperature duration of T = 1 h (ϑm,max = 69.28 °C) h (ϑm,max = 72.92 °C) the intended temperature of 80 °C in the core was not rea rises linearly for all samples to approx. 70 °C and then nonlinearly to ϑm,max. T increase results from the free water in the concrete matrix that significantly influe moisture-dependent thermal properties such as thermal conductivity and heat [41]. The nonlinear increase results from hydration and binding of free water and the heat capacity up to 15% and the thermal conductivity in the course of hydr 10% [42]. The temperature profile of the prisms with and without fibres differs ma This is attributed to the low impact of steel fibres on the thermal properties of [43,44]. Hence, to limit the heating rates, temperature durations of T > 2 h are recom for the heat treatment presented here.

Shrinkage
The measured strains are superimposed contributions from shrinkage and ture due to heat treatment ( Figure 4). Plastic shrinkage (p. s.) starts when mixing the at time tmix and ends when hardened at t0. From t0 onwards, the volume reductio basic shrinkage or drying shrinkage εcs. Both are caused by chemical or physical p in the hardened pore structure of the concrete. The determination of t0, e.g., by t method [45], is not possible during heat treatment. The shrinkage strains after he . Core temperature ϑ m of the prisms with and without fibres as well as the annealing regime according to [25].
It must be noted that for a temperature duration of T = 1 h (ϑ m,max = 69.28 • C) and T = 2 h (ϑ m,max = 72.92 • C) the intended temperature of 80 • C in the core was not reached. ϑ m rises linearly for all samples to approx. 70 • C and then nonlinearly to ϑ m,max . The linear increase results from the free water in the concrete matrix that significantly influences the moisture-dependent thermal properties such as thermal conductivity and heat capacity [41]. The nonlinear increase results from hydration and binding of free water and reduces the heat capacity up to 15% and the thermal conductivity in the course of hydration by 10% [42]. The temperature profile of the prisms with and without fibres differs marginally. This is attributed to the low impact of steel fibres on the thermal properties of concrete [43,44]. Hence, to limit the heating rates, temperature durations of T > 2 h are recommended for the heat treatment presented here.

Shrinkage
The measured strains are superimposed contributions from shrinkage and temperature due to heat treatment ( Figure 4). Plastic shrinkage (p. s.) starts when mixing the concrete at time t mix and ends when hardened at t 0 . From t 0 onwards, the volume reduction causes basic shrinkage or drying shrinkage ε cs . Both are caused by chemical or physical processes in the hardened pore structure of the concrete. The determination of t 0 , e.g., by the Vikat method [45], is not possible during heat treatment. The shrinkage strains after heating ε cs * are determined from the time t 0 * when the measuring marks are attached. Thereby, the plastic shrinkage as well as shares of autogenous and drying shrinkage are not measurable (n. m.). Figures 5 and 6 illustrate the measured total strains ε tot over time. They are shown for both, prisms ( Figure 5) and beams (Figure 6), as a function of the treatment time T with respect to fibre amount V and for beams also with respect to the rebar ratio ρ. In general, ε tot increases strongly in the first days and seems to converge for both, prisms and beams, within 90 days. Additionally, the corresponding means and standard deviations are plotted as error-bars.  1,2,4,6,24] with and without fibres. σ unsystematically scatters. However, it tends to increase with T. Furthermore, σ is not constant over the time and increases abruptly for t * > 28 d (see Figure 5a,e,f).
In general, the unsystematic scatter can be explained by superposed measurement inaccuracies from material properties and slightly changing storage conditions [46].
The discontinuity at t * = 28 d in Figure 5 for the prisms arises from a jump in the number of samples. After 28 days, three out of six samples are used for the strength tests so that only three samples remain for the strain campaign (cf. Table 2 . Only the beams with ρ = 3.1% show a systematic influence on σ that increases with increasing annealing time. The standard deviation of the beams decreases with an increasing rebar ratio and it is lower compared to the prisms with fibres. As the portion of (almost) deterministic materials, namely the reinforcement, increases, the residual portion of scattering material properties of the concrete decreases and, consequently, also the overall standard deviation does.
Consideration of the initial temperature strain ε T .
To determine the residual shrinkage strain after heat treatment ε cs * , the temperature strain ε T according to Equation (3) is subtracted from the total strain ε tot .
The mean temperature of the samples ϑ is approximated using the Finite Element Method (FEM) [47]. The discretisation of the prisms in the program system ANSYS (2020 R2) [48] is done by eight nodes volume elements with trilinear shape functions. The reinforced bars are discretised according to [49].

Consideration of the initial temperature strain εT
To determine the residual shrinkage strain after heat treatment εcs * , the temperature strain εT according to Equation (3) is subtracted from the total strain εtot. cs * ( , ) = tot ( , ) − T ( tg , 0 * ) As boundary conditions, the temperature ϑ in the specimen at time t = 0 h is set constant to the initial temperature ϑ 0 , according to Equation (4).
The heat transfer to the environment is simplified as free convection according to Equation (5) with the specimen temperature ϑ at the edge of the component geometry.
The distance of the symmetry axis to the component edge corresponds to half the component width B. Figure 7 shows the numerical model for the thermal analysis of the beams. For this purpose, beam quarters exploiting the symmetry boundary conditions in the central axes with α → 0 W/(m 2 K) (insulated boundary) are used. The sections A-A-A-A and B-B-B-B represent the ambient temperature ϑ ∞ and the heat transfer coefficient α as boundary conditions for the beam surfaces. Furthermore, section B-B-B-B shows the reinforcement elements (EL 1 ) incorporated in the concrete, which are connected to the concrete elements (EL 2 ) via the coupling conditions according to Equations (6) and (7), so that ϑ and the heat flux . q λ at the element transition at time t are the same. An element transition exists when the distance in the plane h x -h y of the element position h to the axis origin corresponds to the radius of the rebar r B .
.  The numerical model [49] is validated by means of measured core ϑ m and surface temperatures ϑ w considered as Dirichlet boundary conditions. Figure 8 shows the strongly nonlinear temperature drops after stripping from initially 40 • C (a) and 70 • C (b) to room temperature (20 • C). Besides the empirical measurement, results of prisms with fibres (w/f.) and without fibres (w/o f.) are plotted along with the numerical results of the core ϑ n,m and surface temperature ϑ w,m exemplary for T equals 1 and 4 h. As mentioned, the prism without fibres for T = 1 h broke during stripping due to an insufficient early strength. Hence, no temperature data are available.  To account for the numerical deviations of the temperatures, the heat transfer coefficient α is adjusted so that the relative deviation of the numerical core temperature ϑn,m and To account for the numerical deviations of the temperatures, the heat transfer coefficient α is adjusted so that the relative deviation of the numerical core temperature ϑ n,m and ϑ m in the period t g is less than 1 • C. The period t g implies all start times t 0 * of the prisms with and without fibres as well as the beams depending on the rebar ratio r and is different for each temperature duration T. It defines the time required to glue the markers for deformation measurements and lasts up to 20 min. ε T is calculated with a coefficient of thermal expansion α C = 12 × 10 −6 m/K [37].
The heat capacity and thermal conductivity for the concrete elements EL 2 is set to c p,C = 1200 J/K and λ C = 3 W/(mK) according to [37], which correspond approximately to the thermal properties of already hardened concrete. The density of the prisms ρ C is measured and listed with the thermal properties in Figure 8. The thermal properties of the reinforcement elements (EL 1 ) are set to λ S = 50 W/(m K), ρ S = 7800 kg/m 3 und c p,S = 450 J/(kg K) for reinforced steel acc. to [47].
The relative deviations between numerical approximation of ϑ n,m and measured core temperatures The temperature deviations remain below 1 • C for all temperature durations T, except for T = 24 h (without fibres) where the temperature deviation yields 1.2 • C.
It must be noted that the numerical solutions of temperature durations T = 1 h deviate from the measured values at t < t g (c.f. Figure 8b). This is attributed to measurement errors caused by the small air pads between concrete surface and heat sensor (Figure 8b, detail). Already small differences in the height of the sensors lead to large temperature deviations, since the temperature of the resulting air layer is then measured instead of the surface temperature.
However, the more relevant behaviour after cooling is not affected. Compared to the time-dependent course of ε cs * according to Equation (3) for treatment times of 1 h (Figure 9a) and 6 h ( Figure 9b) the shrinkage curves show two physical discrepancies. On the one hand, the halved number of samples causes discontinuities at t * = 28 d. This is illustrated by the abrupt decrease or increase of ε cs * . On the other hand, a supposed swelling occurs for prisms without fibres at T = 1 h that is not physically justifiable. Furthermore, the influence of ε T , especially for the beams, leads to positive values of ε cs * at time t * = 0 d. The reason for this is that the numerical model overestimates the average temperature in the specimen. This holds especially true for the beams with a reinforcement ratio of 3.1% (Figure 9b).
The temperature deviations remain below 1 °C for all temperature durations T, except for T = 24 h (without fibres) where the temperature deviation yields 1.2 °C.
It must be noted that the numerical solutions of temperature durations T ≠ 1 h deviate from the measured values at t < tg (c.f. Figure 8b). This is attributed to measurement errors caused by the small air pads between concrete surface and heat sensor (Figure 8b, detail). Already small differences in the height of the sensors lead to large temperature deviations, since the temperature of the resulting air layer is then measured instead of the surface temperature.
However, the more relevant behaviour after cooling is not affected. Compared to the time-dependent course of εcs * according to Equation (3) for treatment times of 1 h ( Figure  9a) and 6 h ( Figure 9b) the shrinkage curves show two physical discrepancies. On the one hand, the halved number of samples causes discontinuities at t * = 28 d. This is illustrated by the abrupt decrease or increase of εcs * . On the other hand, a supposed swelling occurs for prisms without fibres at T = 1 h that is not physically justifiable. Furthermore, the influence of εT, especially for the beams, leads to positive values of εcs * at time t * = 0 d. The reason for this is that the numerical model overestimates the average temperature in the specimen. This holds especially true for the beams with a reinforcement ratio of 3.1% ( Figure  9b).  Shrinkage curve adjustments Physically unreasonable curves are adjusted in two aspects: First, the values are harmonised after 28 d; second, the origin is shifted.
To smoothen the discontinuities in the strain curves at t * = 28 d caused by the halved number of specimens, averaging is applied. The approach is schematically shown in Figure 10. In the upper part of Figure 10, the variables of the shrinkage strains of the first 28 days are plotted. For each individual prism n the shrinkage strains ε * t*,n are determined from an interval ∆t of approximately 1 d. This is done by the mean from m = 6 samples.
The lower part in Figure 10 shows the variables of the measured values after 28 days. Specimens n = 4-6 have been extracted for strength evaluations and thus only samples n = 1-3 remain. Moreover, the time interval ∆t of measurements is increased to 7 days. Missing shrinkage strains (n = 4-6) are interpolated, assuming constant strain increases ∆ε within each time increment i = ∆t. The calculative shrinkage strains ε * t*,n for n = 4-6 are estimated by adding average strains ∆ε m,i of the samples n = 1-3 to the last measured strains ε 28d,n * . For the time increments i+1, the sum of all ∆ε m,i is taken. Thus, the averaged total strain is calculated from three measured strains (n = 1-3) and three interpolated ones (n = 4-6).
are plotted. For each individual prism n the shrinkage strains ε * t*,n are determined from an interval Δt of approximately 1 d. This is done by the mean from m = 6 samples.
The lower part in Figure 10 shows the variables of the measured values after 28 days. Specimens n = 4-6 have been extracted for strength evaluations and thus only samples n = 1-3 remain. Moreover, the time interval Δt of measurements is increased to 7 days. Missing shrinkage strains (n = 4-6) are interpolated, assuming constant strain increases Δε within each time increment i = Δt. The calculative shrinkage strains ε * t*,n for n = 4-6 are estimated by adding average strains Δεm,i of the samples n = 1-3 to the last measured strains ε28d,n * . For the time increments i+1, the sum of all Δεm,i is taken. Thus, the averaged total strain is calculated from three measured strains (n = 1-3) and three interpolated ones (n = 4-6). Figure 10. Summary of the shrinkage measurement of εcs * and the adjustment for t * > 28 d.
The adjustment scheme is controlled using the total strains of the beams, since the shrinkage strains were measured up to 90 days for all 6 samples. Therefore, the strains εt*,4-6 * for t > 28 d are set to zero and then interpolated. Figure 11 represents the time course of the shrinkage strain of the beams with and without interpolation of the measured values The adjustment scheme is controlled using the total strains of the beams, since the shrinkage strains were measured up to 90 days for all 6 samples. Therefore, the strains ε t*,4-6 * for t > 28 d are set to zero and then interpolated. Figure 11  The results indicate that the shrinkage behaviour of the bars can be approximated even with a reduced number of specimens. The same applies to the prisms.
Thus, the fitted values represent the true shrinkage behaviour more likely than the discontinuous curves. A shift of the origin is applied to all shrinkage curves that do not start from zero strain at time t * = 0 d after calculated thermal shares are removed. This happens for beams with ρ = 3.1% and T = 4 and 6 h. Figure 12 shows the strain courses εcs * for the different fibre and rebar amounts over the next 90 days when the two adjustments are made (in red for T =1 (a) and in purple for T = 6 h (b)) relative to the originally determined values in grey. Discontinuities at t * = 28 d have disappeared and now all curves start from zero. Thus, these two adjustments are performed for all following analyses.  The results indicate that the shrinkage behaviour of the bars can be approximated even with a reduced number of specimens. The same applies to the prisms.
Thus, the fitted values represent the true shrinkage behaviour more likely than the discontinuous curves.
A shift of the origin is applied to all shrinkage curves that do not start from zero strain at time t * = 0 d after calculated thermal shares are removed. This happens for beams with ρ = 3.1% and T = 4 and 6 h. Figure 12 shows the strain courses ε cs * for the different fibre and rebar amounts over the next 90 days when the two adjustments are made (in red for T =1 (a) and in purple for T = 6 h (b)) relative to the originally determined values in grey. Discontinuities at t * = 28 d have disappeared and now all curves start from zero. Thus, these two adjustments are performed for all following analyses. n = 4-6. Shown are the interpolated (colours) and the measured shrinkage strains (grey, dashed) for T = [0, 1, 2] h (a) and T = [4,6,24] h (b). Both curves do almost coincide.
Thus, the fitted values represent the true shrinkage behaviour more likely than the discontinuous curves. Figure 11. Comparison of the interpolated (colours) and measured (grey, dashed) total strains of the beams for T = 0, 1, 2 h (a) and T = 4, 6, 24 h (b).
A shift of the origin is applied to all shrinkage curves that do not start from zero strain at time t * = 0 d after calculated thermal shares are removed. This happens for beams with ρ = 3.1% and T = 4 and 6 h. Figure 12 shows the strain courses εcs * for the different fibre and rebar amounts over the next 90 days when the two adjustments are made (in red for T =1 (a) and in purple for T = 6 h (b)) relative to the originally determined values in grey. Discontinuities at t * = 28 d have disappeared and now all curves start from zero. Thus, these two adjustments are performed for all following analyses.  Evaluation of shrinkage strains ε cs * Figure 13 shows the asymptotic courses of the shrinkage strains for prisms (top) and beams (bottom) with time. The single curves represent the average values of the residual strain ε cs * at concrete ages t * . They are plotted for prisms at T = [0, 1, 2] h (left) and T = [4,6,24] h (right) with and without steel fibres. The same is done for the beams (bottom) while the geometric rebar ratio is kept constant at 1.8%. For all specimensregardless of the treatment time, the fibre amount or the rebar ratio-shrinkage rises after heat treatment. However, it nearly converges after about 60 days. This is attributed to the latent-hydraulic blast furnace slag contained in the binder, giving rise to a slower hydration of the concrete [50]. ε cs * results to 0.383 mm/m after 90 days for the reference prisms. Fibre addition slightly lowers the strain to 0.364 mm/m due to stiffening through a higher Young's modulus of FRC [13]. ε cs * generally decreases from heating. Reductions amount to [5.7, 20.4, 45.9, 66.8]% for T = [2,4,6,24] h in case of no fibres due to accelerated hydration. Remember, that the strength tests in Section 3.3 revealed that hydration is almost completed after T = 24 h. This is also supported by a very low shrinkage rate of the prisms without fibres (top, right). Due to the high degree of hydration, the residual shrinkage strains most likely result from drying.

Flexural and Compressive Strength
Flexural and compressive strength tests are performed on the prisms using standard testing techniques (cf. Figure 14, right). The results are plotted in bar diagrams (cf. Figure  14, left) as functions of T and V and compared to reference samples with or without steel fibres. Short-term tests are performed directly after heating (brown and grey bars). Refer- Heat treatment also reduces shrinkage of specimens with fibres (prisms), but to a lower extent. Reductions amounts to [38.3, 36.7, 44.9]% for T = [4,6,24] h. A treatment time of T = 2 h has a negligible effect on the strains. It induces an increase of 5.3%. The prisms with treatment time equal to T = 1 h show higher shrinkage of 14.4% (without fibres) and 11.7% (with fibres) compared to the reference samples. These samples were still very moist after heating. Hence, it seems reasonable that the additional shrinkage results from drying. Comparing prisms with and without fibres and equal treatment times the shrinkage strains decrease by [7.7, 35.5]% for T = [1,4] h and increase by [5.9, 10.3, 36.7]% for T = [2,6,24] h showing an unsystematic combined impact of fibres and heat treatment.
On the one hand, steel fibres increase the stiffness and reduce the overall shrinkage strain. Moreover, they reduce the activation energy of the concrete [34], so that the cement hydrates quicker [51]. This lowers autogenous shrinkage, since larger portions of the strain are anticipated already during heat treatment.
On the other hand, steel fibres can enhance drying shrinkage as pores are connected and water permeability increases [17]. The increased porosity in the contact zone of cement matrix and steel fibres [16] can even enhance this effect.

Flexural and Compressive Strength
Flexural and compressive strength tests are performed on the prisms using standard testing techniques (cf. Figure 14, right). The results are plotted in bar diagrams (cf. Figure 14, left) as functions of T and V and compared to reference samples with or without steel fibres. Short-term tests are performed directly after heating (brown and grey bars). Reference tests are conducted after 28 days and the plotted initial heat treatment times (red and blue bars). Compressive strengths are presented by means f cm and scattering ranges in the top diagram, flexural strength values f ct,fl according to the same scheme but in the bottom diagram.
The reference specimen without heat treatment exhibits a mean compressive strength f cm,28d of 103.5 MPa. Additional steel fibres increase the strength by 22.1% to 126.3 MPa. The increase is mostly attributed to prevented lateral expansion by the fibres [53]. Generally, heat treatment reduces strength. f cm,28d decreases by [44.3, 19.3, 15.5, 14.9, 8.6]% for T = [1,2,4,6,24] h with no fibres. Obviously, the loss turns out less pronounced with increasing treatment time T. Especially, the steep rates R a > 20 K/h in the first two hours of heating induce internal stresses in the cement matrix that provoke structural damage. With increasing T, temperature gradients and thus the stresses reduce. This promotes also the formation of further hydration products that bridge microcracks [4].
Fibres help to reduce damage induced by heating. They bridge microcracks [31]. The samples also exhibit lower compressive strengths, but less distinct. The decrease yields [34.1, 8.0, 5.4, 5.4]% for T = [1,2,4,6] h. For T = 24 h the compressive strength is almost the same in the reference sample.
The standard deviation of the compressive strength lies between 5.0 and 7.8 MPa (no fibres)-so slightly above the expectation for laboratory concrete [54]-and decreases to 1.5 to 5.2 MPa, if fibres are added. The scatter generally seems independent of the heat treatment time T. As for the strength, fibres are proven to reduce scatter and homogenise the inner strength state by bridging cracks [31].

Conclusions
The influence of rapid heat treatment of 80 °C on the shrinkage behaviour and strength of HPC is investigated. The experimental investigations cover different treatment times between 0-24 h as well as the steel fibre amounts and rebar ratios. The main findings are as follows:    [16.4, 16.8, 9.7, 9.7]% to [9.1, 9.1, 9.9, 9.9] MPa for T = [1,2,4,6] h. On the contrary, 24 h heating gives rise to keep the strength almost constant (+2.7%).
Steel fibres significantly increase the flexural strength by activating the pull-out resistance [55]. This holds true for all heating regimes and time stages investigated. The specific HPC with particle sizes down to nano-scale provides the necessary adhesion to the smooth steel surfaces [37]. The reference sample achieves f ct,fl,28d = 16.0 MPa, what exceeds the value of the pure HPC by 46.9%.
Heat treatment just reduces the flexural strength on the short run for T = 1 h (10.7 MPa). In any other situation (T > 1 h), strength is enhanced up to 22.1% for T = 24 h.
The standard deviation of the flexural strength with fibres is [3.9, 1.2, 1.1, 1.7, 1.8, 2.1] MPa for T = [0, 1, 2, 4, 6, 24] h and lies above the strengths for prisms without fibres. This is mainly due to the scattered distribution and orientation of fibres [32,33,56] that is subjected to wall effects from the pouring process [57]. As the ratio of the cross-sectional width (40 mm) to the fibre length (13 mm) is small, fibres clearly orientate along the longitudinal prism axis and do not distribute isotropic.
In general, an addition of steel fibres is recommended for short-term heat treatments without consideration of prescribed heating rates and pre-storage times. That way a large share of the strength losses is compensated. Moreover, stripping of formwork might start early after T > 2 h; then sufficient short-term strength has already developed. The standard deviation of the flexural strength slightly increases by an addition of steel fibres.

Conclusions
The influence of rapid heat treatment of 80 • C on the shrinkage behaviour and strength of HPC is investigated. The experimental investigations cover different treatment times between 0-24 h as well as the steel fibre amounts and rebar ratios. The main findings are as follows: • With increasing treatment time T, the shrinkage strains decrease. For T = 24 h it is reduced to 66.8% (no fibres) or 44.9% (fibres) compared to the reference samples without heat treatment (0.383 mm/m without steel fibres and 0.364 mm/m with steel fibres for T = 0 h). • Short treatment times of T = 1 to 2 h have no beneficial or even slightly negative effects on shrinkage strains. Heat treatment durations greater than 2 h must be selected to improve the shrinkage behaviour. • For T = 4 and 6 h, the residual shrinkage strains can be reduced up to 0.176 mm/m for prisms and 0.09 mm/m for beams what corresponds to 45.9% and 33.8% compared to the reference samples without heat treatment. However, the investigations show high scatter for different treatment times and specimen types. • Rebar serves as a "shrinkage brake". Reinforcing bars reduce shrinkage proportional to its longitudinal stiffness.

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The compressive strength of the prisms decreases up to 44% for T = 1 h. To prevent losses of compressive strength due to structural damage, tempering of T ≥ 2 h is recommended. • An addition of steel fibres significantly increases the compressive strength as well as the flexural strength, as fibres prevent structural damage in the matrix induced by internal stresses.

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For practical application, the use of steel fibres and reinforcement is recommended to improve the shrinkage behaviour. • For practical applications it is recommended to use tempering at around 80 • C with durations greater than 2 h. Durations of 2 to about 6 h are most effective. Durations exceeding 24 h are not recommended, as the beneficial effect on shrinkage more and more decreases over time and then reaches a plateau. Micro steel fibres should be added to preserve the bearing abilities of the HPC that otherwise noticeably decreases by temperature induced constraints. Funding: The authors thank the German Research Foundation (DFG) for its financial support of the project with the grant number 423942391 within the framework of the priority program SPP 2187. Sincere thanks go to Thomas Deuse (Dyckerhoff GmbH) for providing the binder Nanodur ® Compound 5941.