**4. Heating Rate**

Although the gas temperature in a fire can rise extremely fast, as presented in Figure 3 [35], the temperature inside an element does not follow the same rate. The size of the concrete element, the high specific heat, and the thermal conductivity of around 1 W/mK result in very slow heat transfer throughout the element [2]. Additionally, the specific heat doubles at around 100 ◦C because the water changes state and the thermal conductivity decreases with rising temperature. Thus, only the external part of the cross-section is exposed to very high temperature, while internal parts record noticeably lower ones.

Although there are very different heating rates (3.5 and 10 ◦C/min) in [39], the test results obtained suggest a minimal influence of the heating rate. In [38], the influence of the heating rate was confirmed. However, no clear trend could be drawn in peak temperatures up to 600 ◦C. Beyond that level of peak temperature, no substantial influence was observed for different heating rates. The 2.5 ◦C/min rate applied in [24] results in a sharper decline in strength than with the 10 ◦C/min proposed in [23]. This leads to the conclusion that the damage caused by the high heating rate makes concrete less prone to further deterioration, while the low rate results in concrete that is susceptible to the effects of prolonged high temperature exposure. However, an immediate relationship has not been proven. Correlation factors between the heating rate and residual strength were calculated for the collected data, and the factors are presented in Table 5. Low positive values suggest a minimal influence in favor of the higher heating rate.

**Table 5.** Correlation factors between the heating rate and the relative residual strength for the peak temperature of 500 ◦C, presented by various authors.


#### **5. Cooling Regime**

After heating or a fire, an element subjected to high temperature cools down, and how it happens is called the cooling regime. There exist three basic types of the regime used in tests:


According to the available research (Table 6), the degradation of the mechanical properties depends on the type of cooling. Ambient temperature and water cooling were used in [40] but with cylindrical samples (diameter/height = 100/200 mm) heated to 330, 450, and 550 ◦C and removed from the furnace. Then, five types of cooling were performed: ambient temperature air cooling, water cooling by immersing samples in 15 ◦C water for 5, 10, 15, and 20 min and then air-cooled to room temperature. The next day, strength tests were performed. When air-cooled samples were compared with top-water-cooled samples, it appeared that peak temperature was not important for the decline rate of relative residual strength. Strength loss depends mainly on the duration of immersion in water (Figure 9).


**Table 6.** Summary of research on the cooling regime.

**Figure 9.** *frc*,*WC* (*t*) *frc*,*AC* as a function of the cooling time in water according to [40].

Similar tests are presented in [41–43], and the conclusions reached are the same. In [44], the impact of rapid water cooling on concrete made with the addition of slag was tested. Specimens were exposed to elevated temperatures of 400 and 800 ◦C and cooled in air or 20 ◦C water. For 400 ◦C, the strength loss of all water-cooled samples reaches an additional 20% compared to air cooling. It is interesting to note that for 800 ◦C samples made with OPC (ordinary Portland cement), the loss of an additional 14% points is observed when water-cooled samples made with a partial replacement of OPC by slag lose only 4–5% points. This phenomenon can be explained by the rehydration of CaO in Ca(OH)2 accompanied by the expansion and thus further deterioration of concrete.

In [45], cubic samples (100 mm) were tested by exposing them to elevated temperatures (from 50 to 700 ◦C) and then cooling in two ways: by leaving them to cool in the furnace and by immersing them in water. The conclusion was drawn that air cooling results in higher residual strength, especially in the 400–500 ◦C peak temperature range.

Cubic specimens (100 mm) specimens were tested 90 days after casting in [46]. Temperature exposure was carried out in an electric furnace with the heating rate set at 10 ◦C/min for the first 100 ◦C and 20 ◦C/min from 100 to 800 ◦C. After reachifng peak temperature, samples were divided. One part was taken out of the furnace and cooled at room temperature; the second part was left in the turned-off furnace (door closed). Then, the tests were performed in two groups: directly after and 30 days after cooling. The results provide interesting facts: high-temperature cooling causes an additional dehydration of hardened cement and further deterioration of the strength (Table 7). Air cooling stopped the dehydration process but caused more internal cracks due to the temperature gradient. When comparing results obtained directly after cooling, dehydration had a greater impact than internal cracks but is also more reversible. After 30 days of re-curing, cement rehydrates and concrete regains most of its initial strength, while internal cracks caused by temperature gradient are unable to close.

**Table 7.** Comparison of the relative residual strength for different cooling methods according to [46].


In [47], water and furnace (air) cooling is compared by heating the NSC and HSC samples to 800 ◦C at a rate of 5–7 ◦C/min and cooling them in either a turned-off furnace or in a water tank. The difference between the cooling methods was visible for the residual strength tested directly after cooling. The NSC strength was reduced to 0.32 for water and 0.45 for air cooling. The impact of the cooling regime on the residual strength of HSC was less pronounced, as the strength was reduced to 0.21 for water and 0.26 for air cooling.

A difference in the cooling regime for various peak temperatures is presented in [48]. Temperatures ranged from 200 to 800 ◦C. The residual strength resulting from slow air cooling was higher compared to water cooling for all temperature cases by 4–7% points. The difference was not substantial but noticeable. In [49], the influence of water cooling on the residual strength of concrete was tested. The samples were cooled in two ways: air-cooled in a furnace and water-cooled by sprinkling water for 30 min directly after temperature exposure. Compressive tests were performed one month after high-temperature exposure. The influence of the cooling regime was found for exposure temperature from 200 to 600 ◦C; water cooling resulted in lower residual strength by 5–7%. Only for 800 ◦C was there a difference of 1.5% (air cooling resulted in lower residual strength). The same cooling regime was used in [50]; later samples were tested after different re-curing times (0, 30, 60, and 90 days). The results proved that water cooling lowers the residual strength tested directly after cooling (especially after exposure to temperatures higher than 600 ◦C), but after re-curing for a longer period, the difference caused by the cooling method was minimal (Table 8).

**Table 8.** Difference between the relative residual strength for air and water cooling according to [49,50].


Three cooling methods were examined in [51]: that is, furnace air cooling, room temperature air cooling, and full immersion water cooling after exposure to 700 ◦C. Compressive tests were performed after the samples reached ambient temperatures. In contrast to the other experiments, samples cooled in water demonstrated the highest residual strength, whereas furnace and room temperature cooling showed very similar, but lower, results.

The cooling regime is an important factor in the evaluation of the residual strength of the concrete. According to [52], rapid cooling produces more internal damage due to the temperature gradient [53,54], but it stops dehydration processes. The slower cooling process results in longer exposure to high temperatures and longer dehydration. It is worth mentioning that water cooling results in lower weight loss [55].

The available data indicate that water cooling results in lower residual strength directly after cooling. Nevertheless, after post-fire re-curing, the difference between residual strengths for different cooling types becomes small and can be neglected.

#### **6. Post-Fire Re-Curing Effect on Residual Strength**

The recovery of the strength of concrete due to post-fire re-curing is important when assessing the residual strength of concrete, and it was proven in many articles (Table 9). This restoration can be attributed to the rehydration of cement that was dehydrated at high temperatures [56]. An essential factor in this phenomenon is moisture, which is similar to the initial curing of concrete. While full recovery is impossible (only the pore structure can return to pre-fire state), mechanical properties can return to surprisingly high levels. Some of the concrete phases form active products at elevated temperatures, such as limes

and calcium silicates; the effect of water and carbon dioxide on these can contribute to increased residual properties [57]. Post-fire re-curing methods can be classified into three basic categories: water post-fire re-curing, air–water post-fire re-curing, and air post-fire re-curing. [58].


**Table 9.** Summary of research on the post-fire re-curing.

The difference between them is defined by the supply of water, from full immersion for a whole amount of time to no water at all. In [59], concrete samples were exposed to various temperatures ranging from 200 to 800 ◦C and then re-cured in air. Compressive tests were performed after 1, 7, 30, and 90 days after cooling. The results presented for 200 and 400 ◦C show that there is a rapid decrease in residual strength for the first week and then a slow increase. At 90 days, re-cured residual strength is higher than the initial residual strength.

In [60], various concrete mixes were tested by heating samples to temperatures of 600 and 800 ◦C with a heating rate of 2.5 ◦C/min and a time maintained at the peak temperature of 1 h. After exposure, the specimens were tested at four different times: directly after cooling, 7, 28, and 56 days of re-curing. Moreover, two re-curing regimes were used; the first was water re-curing, where samples were cooled down to room temperature naturally and then placed in water, while the second consisted of cooling down to room temperature, soaking in water for 2 h, and air curing for the remaining time. Results show that post-fire re-curing can produce tremendous effect (Figure 10). Samples that were heated to 800 ◦C and water re-cured increased their compressive strength three times. The regaining of mechanical properties is rapid in the first 7 days when the average gain is 75% (compared to the test directly after cooling); later, growth is linear. At 28 days, the average increase is 100%, and at 56 days, it is 115%.

The re-curing method shows differences in the first 7 days, water re-curing rates at 100% of increase, while air curing rates at 50%, but later, the growth becomes linear and very similar for both methods. In [61], concrete samples were heated up to 300 or 600 ◦C (heating rate 1 ◦C/min) and then re-cured for 28, 56, or 112 days at three different re-curing regimes. First, samples were covered in plastic film (PF) to prevent any moisture from reaching the re-curing concrete. The second was standard air curing (AC), and the third was water re-curing (WC). Then, the results were compared with the strength before heating. It was found that residual strength growth is more pronounced at the beginning stage of re-curing, and it slows over time (Figure 11). The rate at which strength is regained varies, depending on the re-curing method, with the rule that more moisture gives better results. In [62], similar research was performed, and the statement that water re-curing gives better results than air re-curing was confirmed.

In [50], the residual compressive strength was tested as a function of re-curing time and the cooling regime, samples were re-cured after fire for 0, 30, 60, and 90 days depending on peak temperature with two different cooling regimes: air cooling and water cooling. The difference between air and water cooling is most visible for the test directly after cooling: the higher the temperature, the larger the initial difference. Then, with re-curing time increasing, the method of cooling is of small relevance (Figure 11).

Self-compacting concrete samples were examined in [63] by heating to 300, 450, and 600 ◦C and then tested after 0, 2, 7, and 28 days after cooling. The results prove the great potential of concrete to regain strength, in some instances even exceeding strength before high-temperature exposure (Figure 10). In [64], the recovery behavior of hybrid fiber HSC after fire exposure was tested. The samples were exposed to 200 and 400 ◦C. After exposure, strength tests were performed directly after, 90 days after, and 180 days after in two different re-curing conditions. Air re-curing resulted in a slight regain of compressive strength, while water re-curing essentially reinstated concrete to the initial strength. It is worth noticing that the regain occurred in the first 90 days; after that time, only a small increase was recorded.

**Figure 10.** Relative residual strength of concrete [60] and self-compacting concrete [64] as a function of re-curing time (t) for different re-curing methods (AC—air re-curing, WC—water re-curing) and different peak temperatures *θ* = 300, 450, 600, and 800 ◦C according to [60]—Poon and [63]—Mirmomeni.

**Figure 11.** Relative residual strength of concrete as a function of re-curing time (t) for different peak temperatures *θ* = 300, 450, 600, and 750 ◦C, and different re-curing methods (AC—air re-curing, WC—water re-curing, PF—re-curing in a plastic film) according to [61]—Souza and [50]—Li.

Initially, the insufficient concrete strength over time can become high enough to carry the necessary stresses. Correlation calculated for re-curing time and residual strength displays a positive relation (factors presented in Table 10). The values of the factors suggest that a monotonic relationship exists but does not have to be a linear one. This fact shows that post-fire re-curing is significant and must be taken into account. It is proven that the most rapid growth of mechanical properties takes place in the first 7 days; later, it slows down similar to the logarithmic function (Figure 12). Concrete recovery coincides with the rehydration of cement, and moisture is critical. Curing methods involving water provide better results while completely sealing the moisture flow results in a much slower regain of mechanical properties [65]. Although it should be noted that in concrete heated to less than 300 ◦C, ongoing deterioration of concrete can be observed due to sulfate-induced expansion [66]. This phenomenon can mitigate some residual strength gain and should be taken into account.

**Table 10.** Correlation factors between re-curing time and the relative residual strength for the peak temperature of 500 ◦C, presented by [61,63].

**Figure 12.** Range of the relative residual strength of concrete as a function of re-curing time. Collection of data from different heating rates, types of concrete, sample sizes, etc. presented by various authors.

#### **7. Concrete Composition**

The composition of the concrete mix determines its initial mechanical properties. The question about its influence on the residual strength was studied multiple times, as it is naturally supposed. Concrete is formed by mixing aggregates, cement, water, and additives. Furthermore, research on recycled materials was implemented, creating possibilities for future usage [67]. The influence of each component is analyzed and discussed in the following sections. As the amount of data on concrete composition is vast, a summary of the examined components in all papers analyzed in this paragraph can be found in the supplementary file attached to the paper.
