**1. Introduction**

Concrete provides the best fire resistance out of typically used construction materials. Compared to timber or steel, concrete has low thermal conductivity, high heat capacity, and its strength degrades slower with increasing temperature. As a result, it is a material that performs well not only as a separator between fire-affected spaces but also as a material for elements that need to perform under extreme thermal conditions. The vast majority of concrete structures can withstand fire conditions for the designed duration. This is due to the fact that concrete properties at high temperatures are well known and examined [1].

Standards provide safe approaches and mathematical models [2–4] that help design concrete structures for fire safety. Stress–strain curves for concrete exposed to high temperatures are also provided [5–7], and the behavior of concrete structures, elements, and sections are widely investigated, e.g., [8–10]. The research and design effort result in structures that handle fires so well that the question arises: Can this structure be used as it was before the fire?

Destructive and non-destructive assessment of strength is possible [11–14], but providing enough information for structural calculations is a crucial issue. The temperature field inside the concrete element depends on many uncertain parameters, and this results

**Citation:** Pasztetnik, M.; Wróblewski, R. A Literature Review of Concrete Ability to Sustain Strength after Fire Exposure Based on the Heat Accumulation Factor. *Materials* **2021**, *14*, 4719. https://doi.org/10.3390/ ma14164719

Academic Editor: Jeong-Gook Jang

Received: 21 July 2021 Accepted: 19 August 2021 Published: 21 August 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

in residual properties that are difficult to estimate. Therefore, to answer any question about residual properties, theoretical models would be helpful.

From both research and practical perspectives, the residual strength of concrete is a complex matter [15], because many factors must be considered, e.g., peak temperature, heating time, rate of increase in temperature, concrete composition, and others).

Since concrete is a composite material (composed of aggregate, cement, water, and additives), its final properties vary depending on the ratio and type of components used, but subjected to fire, other variables influence the properties. When a cement paste is exposed to high temperatures, the following physicochemical reactions are observed [16]:


These phenomena cause a degradation of the mechanical properties of the cement paste [17]. In addition, the thermal expansion of the aggregate leads to an increase in internal stresses and can result in microcracks of the concrete body. The deterioration of mechanical properties can be represented by the relative residual strength. Compressive and tensile strength degrade rapidly as they halve at 400 ◦C and 300 ◦C, respectively [18]. The decline is not only a function of the peak temperature but also of the heating time and rate. It was proven that a higher heating rate results in lower relative strength at the same peak temperature [19]. Heating time is also crucial, as maintaining a low temperature for a long time can cause more damage to the concrete than a higher peak temperature for a short time. What should be remembered is the fact that concrete becomes less brittle after exposure to a high temperature (intrinsic length increases) [20]. The size effect can influence the tensile strength. Although it has a marginal effect on compression [21], it makes the tensile test results sample size dependent. It was found that the strain rate does not influence compressive behavior [22].

After the concrete is cooled down to ambient temperature, it retains residual strength that is affected not only by the mentioned factors but also by the cooling regime, post-fire re-curing regime, and time. There exists a correlation between strength at high temperature and residual strength, but they cannot be treated in the same way.

This review paper summarizes up-to-date progress in experimental research on the residual strength of concrete after high-temperature exposure. The results of the tests on the most important factors that influence concrete residual strength are presented and discussed in the following sections of the article. Each section is dedicated to a separate factor. Although there are consistent results for obvious factors, such as peak temperature and heating time, the influence of less pronounced factors, such as the w/c ratio and cement type, still requires further research. Furthermore, current research lacks a general approach to the influences that will lead to a function or algorithm capable of assessing the residual strength of concrete.

#### **2. Peak Temperature**

According to [2], the strength of the concrete at high temperature is a function of only the temperature that the concrete reaches. With residual strength, more factors need to be considered, but peak temperature is crucial amongst them. Extensive research was done to connect the peak temperature and residual strength of the concrete (Table 1). Comparison between the results is very limited, as factors besides peak temperature are often disparate for different authors.


**Table 1.** Summary of research on the peak temperature.

In [23–25], cylindrical concrete samples were heated to temperatures ranging from 100 to 450 ◦C; then, after reaching steady state, they were cooled to room temperature inside the furnace, and the compressive strength was tested (Figure 1). In [26], research was performed for a very broad range of temperatures (200, 400, 600, 800, and 1000 ◦C). Concrete samples of size 40 mm × 40 mm × 160 mm at the age of 28 days were placed in the furnace and kept at the target temperature for 1.5 h; then, they were taken out and left to cool in an ambient environment. Compressive tests were performed on prism halves resulting from flexural tests.

**Figure 1.** Relative residual strength of concrete as a function of peak temperature for the different times maintained at peak temperature of 1, 3, 5, 6, and 9 h according to [23]—Toumi, [25]—Phan, and 0, 1, and 2 h according to [24]—Yang.

The HSC (high-strength concrete) samples [27] and the NSC (normal-strength concrete) samples [28] were heated in a furnace test (to temperatures: 200, 400, 600, 800, and 1000 ◦C). A low heating rate of 0.5 ◦C/min was applied, and the peak temperature was maintained for 3 h. Subsequently, the samples were cooled inside the furnace, taken out, and tested

(Figure 2). In [29], the samples were tested at 10 set temperature values (20, 100, ... , 900 ◦C). The temperature was increased according to the standard fire curve (Figure 3), and the peak temperature was maintained for 3 h. Then, the furnace door was opened, and the samples were cooled inside before compressive tests (Figure 2). In [30], HSC and NSC samples were heated to temperatures ranging from 400 to 1200 ◦C. After the specimens were allowed to cool naturally to room temperature, compressive tests were performed (Figure 2). In [31], the residual strength of NSC and HSC after exposure to elevated temperatures (from 200 to 600 ◦C) was compared.

**Figure 2.** Relative residual strength of different types of concrete (NSC and HSC) as a function of the peak temperature according to [26]—Netinger, [27]—Hager, [28]—Krzemien, [29]—Xiao, and [30]—Chan.

Moreover, the results demonstrate that the relative loss of strength is higher for HSC than for NSC. A similar conclusion was reached in [32,33]. Correlation factors were calculated for all the data collected, with respect to the heating time at peak temperature (Table 2). The Pearson and Spearman factors signify a strong negative linear relationship between relative residual strength and peak temperature. The Kendal coefficient supports this observation, as it indicates a monotonic relationship. The graphic representation of the collected results is presented in Figure 4. Residual strength behaves in a way similar to changes in concrete strength at high temperature according to, e.g., [2]. Varying the test conditions and concrete composition in the research considered in Figure 4 can make a substantial difference in residual strength for peak temperatures ranging from 300 to 750 ◦C. For peak temperatures lower than 300 ◦C, almost no loss is observed, and for peak temperatures higher than 750 ◦C, residual strength is almost equal to strength at high temperatures, meaning that concrete damaged to a very high degree exhibits a smaller ability to regain strength. Taking into account all this, the residual strength function for temperatures up to 300 ◦C and more than 750 ◦C can be derived based on the peak temperature only, but for the remaining range, a more accurate function would require considering other factors, which were mentioned further in this paper. In [34], a function was proposed to relate the residual strength with the maximum temperature, but it is considered as a rough approximation.

**Table 2.** Correlation factors between peak temperature and relative residual strength for two different heating times at peak temperature as presented by various authors.


**Figure 3.** Development of gas temperature in hydrocarbon, external, and standard fires according to [35].

**Figure 4.** Range of the relative residual strength of concrete as a function of peak temperature. Collection of data from different heating rates, types of concrete, sample sizes, etc. presented by various authors.

#### **3. Heating Time**

The heating time, that is, how long the peak temperature is kept, is crucial in assessing the residual strength of concrete, which is demonstrated in the research presented (Table 3). In [23], this relationship is presented based on concrete made of crushed limestone and CEM I 42.5 in two variants (Figure 5):


At 28 days, samples were heated at a rate of 10 ◦C/min to target temperatures 300, 500, and 700 ◦C and kept for 1, 3, 6, and 9 h. The samples were tested after 24 h of cooling at room temperature (Figure 5). In [36], concrete samples of compressive strength of 20, 30, and 35 MPa were investigated 28 days after casting; cubic (150 mm) samples were heated to 400 and 600 ◦C for a duration of 3, 6, or 9 h and tested after cooling to room temperature (Figure 6).


**Table 3.** Summary of the research for heating time.

**Figure 5.** Relative residual strength of NSC and HSC as a function of time maintained at the peak temperature of *θ* = 300, 500, and 700 ◦C according to [23].

**Figure 6.** Relative residual strength of the concrete class C20/25, C30/37, and C35/45 as a function of time maintained at the peak temperature of *θ* = 400 and 600 ◦C according to [36].

Cylindrical samples (100 mm in diameter and 200 mm high) were tested in [24] at the age of 90 days. Two water–cement (w/c) ratios were used: 0.58 and 0.68. The heating rate was set at 2.5 ◦C/min to achieve peak temperatures of 400, 500, 550, and 600 ◦C. Temperatures were maintained for 0, 1, and 2 h, and then strength tests were performed after 7 days of cooling (Figure 7).

**Figure 7.** Relative residual strength of concrete with different water to cement ratios (0.58 and 0.68) as a function of time maintained at peak temperature of *θ* = 400, 500, 550, and 600 ◦C according to [24].

Cylindrical specimens were also tested in [37] by exposing them to temperatures ranging from 200 to 600 ◦C. The heating rate was set at 5 ◦C/min, and the exposure time varied from 1 to 6 h. Compressive tests were performed directly after cooling down. Another test is reported in [38]. Cubic samples (100 mm) were heated to temperatures from 200 to 800 ◦C with various heating rates and exposure times. The tests were performed after 14 days of re-curing. It was found that the main strength loss occurs within the first two hours of high-temperature exposure, and later, the impact is minimal. Comparing all of the data, it is clear and confirmed that a longer heating time deteriorates the residual strength of concrete, where most of the loss occurs in the first two hours. The correlation between residual strength and time maintained at peak temperature was calculated for 500 ◦C (as it provides the broadest range of results), and the factors are presented in Table 4. A strong, negative, monotonic, and linear relationship is evident.

**Table 4.** Correlation factors between the time maintained at the peak temperature and the relative residual strength for a peak temperature of 500 ◦C, presented by various authors.


Data reported by different authors result in the strength dispersion presented in Figure 8. Peak temperature and other variables impact the residual strength, so the data range is very wide. The bottom line represents the loss of residual strength for higher temperature ranges (700 ◦C) and the top line represents the loss of residual strength for lower peak temperatures (300 ◦C). This suggests that it is impossible to develop a proper function based only on time maintained in peak temperature. However, the derivative of this function is constant in segments and does not depend on the peak temperature value. The first segment is from 0 to 2 h (rapid loss of strength) and from 2 h onward (minimal loss of strength). This derivative gives a chance to isolate the influence of heating time on residual strength in the form of a coefficient implemented on an already known strength value with longer (or shorter) heating time.

**Figure 8.** Range of the relative residual strength of the concrete as a function of time maintained at peak temperature. Collection of data from different heating rates, types of concrete, sample sizes, etc. presented by various authors.
