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

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{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/m³ (1.9 Vol.-%). For comparison, beams with a fibre amount of 150 kg/m³ 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.

#### 2.1. Temperature Measurement

_{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).

#### 2.2. Shrinkage Measurement

_{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:

#### 2.3. Strength Measurement

_{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.

## 3. Results

#### 3.1. Results of the Temperature Measurement

_{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/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 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.

_{A}is calculated to

_{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, 16.3] K/h and R

_{A}= [47.1, 25.5, 15.6, 16.5, 16.6] K/h with fibres for T = [1, 2, 4, 6, 24] h are achieved.

_{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.

#### 3.2. Shrinkage

_{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.).

_{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. The measured values of all samples scatter significantly due to the different initial temperature strains. The average standard deviations σ of the prisms are σ = [0.046, 0.049, 0.045, 0.024, 0.073, 0.131] σ = [0.032, 0.059, 0.019, 0.069, 0.039, 0.077] mm/m and mm/m for T = [0, 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).

^{*}= 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).

_{T}.

_{cs}

^{*}, the temperature strain ε

_{T}according to Equation (3) is subtracted from the total strain ε

_{tot}.

_{0}, according to Equation (4).

_{∞}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 $\dot{{q}_{\mathsf{\lambda}}}$ 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}.

_{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.

_{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].

_{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/m³ und c

_{p,S}= 450 J/(kg K) for reinforced steel acc. to [47].

_{n,m}and measured core temperatures ϑ

_{m}are [-, 4.8, 0.9, 0.5, 0.7]% without fibres and [1.2, 1.6, 4.8, 0.1, 2.3]% with fibres for T = [1, 2, 4, 6, 24] h during time period t

_{g}. The relative deviations between the surface temperature ϑ

_{n,w}and ϑ

_{w}from numerical simulation are [-, 3.1, 1.6, 2.0, 5.5] without fibres and [0.5, 1.7, 4.5, 1.8, 1.5]% with fibres.

_{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.

_{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).

^{*}= 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 Δt of approximately 1 d. This is done by the mean from m = 6 samples.

^{*}

_{t*,n}for n = 4–6 are estimated by adding average strains Δε

_{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 Δε

_{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).

_{t*,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 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.

^{*}= 0 d after calculated thermal shares are removed. This happens for beams with ρ = 3.1% and T = 4 and 6 h.

_{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.

_{cs}

^{*}

_{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 specimens—regardless 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.

#### 3.3. Flexural and Compressive Strength

_{cm}and scattering ranges in the top diagram, flexural strength values f

_{ct,fl}according to the same scheme but in the bottom diagram.

_{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].

_{cm,0d}= [14.2, 53.7, 76.8, 90.3] MPa for T = [2, 4, 6, 24] h in case of pure HPC and [29.5, 87.5, 93.8, 116.0] MPa if fibres are added. One-day long heat treatment (24 h) almost completes hydration and hardening. Only 4.7 and 8.6%, respectively, of the long-term strength after 28 days is missing after 24 h.

_{ct,fl,28d}yields 10.9 MPa after 28 d. It holds true for pure HPC without heating. Heat treatment reduces this strength by [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%).

_{ct,fl,28d}= 16.0 MPa, what exceeds the value of the pure HPC by 46.9%.

## 4. Conclusions

- 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.
- 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.
- 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.

## Author Contributions

## Funding

^{®}Compound 5941.

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Core temperature ϑ

_{m}of the prisms with and without fibres as well as the annealing regime according to [25].

**Figure 5.**Total strain ε

_{tot}of the prisms as a function of fibre amount V for T = 0 h (

**a**), T = 1 h (

**b**), T = 2 h (

**c**), T = 4 h (

**d**), T = 6 h (

**e**) and T = 24 h (

**f**).

**Figure 6.**Total strain ε

_{tot}of the beams as a function of rebar ratio ρ for T = 0 h (

**a**), T = 1 h (

**b**), T = 2 h (

**c**), T = 4 h (

**d**), T = 6 h (

**e**) and T = 24 h (

**f**).

**Figure 8.**Comparison of measured core ${\vartheta}_{\mathrm{m}}$ and surface temperatures ${\vartheta}_{\mathrm{w}}$ along with the numerical expectations of core ${\vartheta}_{\mathrm{n},\mathrm{m}}$ and surface temperatures ${\vartheta}_{\mathrm{n},\mathrm{w}}$ of prisms for T = 1 h (

**a**) and T = 4 h (

**b**), respectively.

**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**).

**Figure 12.**Comparison of the adjusted and shifted (red, purple) as well as the measured shrinkage curves (grey) of prisms and beams for T = 1 h (

**a**) and T = 6 h (

**b**).

**Figure 13.**Results of the shrinkage strain ε

_{cs}

^{*}as a function of the fibre amount V [kg/m³] for the prisms for T = 0, 1, 2 (

**a**) and T = 4, 6, 24 (

**b**) or rebar ratio ρ [%] for the beams for T = 0, 1, 2 (

**c**) and T = 4, 6, 24 (

**d**).

**Figure 14.**Compressive- (

**a**) and flexural strengths (

**b**) of the prisms at t = 28 d (reference, red and blue columns) and directly after the heat treatment (brown and grey columns).

Component | Type | Mass [kg/m³] |
---|---|---|

River sand | 0/2 | 426.0 |

Crushed stone basalt | 1/3 | 882.0 |

Binder | Nanodur^{®} Compound 5941 | 1042.0 |

Water | - | 159.8 |

Superplasticizer | Master Glenium ACE 430 | 12.3 |

Shrinkage reducer | Eclipse Floor | 8.0 |

Hardening accelerator | Master X-Seed 100 | 12.3 |

Steel fibres | d/l = 0.19/13 [mm] | 0/150.0 |

**Table 2.**Summary of performed tests and ratio of the tested and the total number of samples, denoted by tested/total number of prisms/beams.

Experimental Set-Ups | Concrete Age t | Test Specimens | |||
---|---|---|---|---|---|

Prisms V = 0 kg/m³ | Prisms V = 150 kg/m³ | Beams ρ = 1.8% | Beams ρ = 3.1% | ||

Temperature measurement | ≤1 d | 6/36 | 6/36 | - | - |

Shrinkage | ≤28 d | 36/36 | 36/36 | 36/36 | 36/36 |

>28 d | 18/36 | 18/36 | 36/36 | 36/36 | |

Compressive strength | ≈0 h | 12/12 | 12/12 | - | - |

28 d | 18/36 | 18/36 | - | - | |

Flexural strength | ≈0 h | 12/12 | 12/12 | - | - |

28 d | 18/36 | 18/36 | - | - |

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## Share and Cite

**MDPI and ACS Style**

Stindt, J.; Forman, P.; Mark, P.
Influence of Rapid Heat Treatment on the Shrinkage and Strength of High-Performance Concrete. *Materials* **2021**, *14*, 4102.
https://doi.org/10.3390/ma14154102

**AMA Style**

Stindt J, Forman P, Mark P.
Influence of Rapid Heat Treatment on the Shrinkage and Strength of High-Performance Concrete. *Materials*. 2021; 14(15):4102.
https://doi.org/10.3390/ma14154102

**Chicago/Turabian Style**

Stindt, Jan, Patrick Forman, and Peter Mark.
2021. "Influence of Rapid Heat Treatment on the Shrinkage and Strength of High-Performance Concrete" *Materials* 14, no. 15: 4102.
https://doi.org/10.3390/ma14154102