# Advanced Evaluation of the Freeze–Thaw Damage of Concrete Based on the Fracture Tests

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{3}is given in Table 1.

#### 2.1. Freeze–Thaw Test

#### 2.2. Test Method for Fundamental Longitudinal Frequency

_{rL}and dynamic Poisson’s ratio µ

_{r}of concretes during the F–T test. All specimens were measured before the start of the F–T test. The specimens subjected to the F–T action were measured at regular intervals (after each 25 F–T cycles) throughout the F–T test. The natural frequency of longitudinal and torsional vibrations was measured using a Handyscope HS4 oscilloscope equipped with an acoustic sensor. The readers are referred to [12] for more details about the principle of measurement. The absolute values of E

_{rL}and µ

_{r}were calculated in compliance with ASTM C215-19 [13] as follows:

_{rL}is the dynamic modulus of elasticity, L is the length of specimens, W and B are cross-section dimensions, m is the mass of specimens, and f

_{L}is the fundamental longitudinal frequency.

_{r}is the dimensionless dynamic Poisson’s ratio, and G

_{r}is the dynamic modulus of rigidity, calculated as

_{t}is the fundamental torsional frequency.

#### 2.3. Acoustic Emission Method

#### 2.4. Fracture Test

#### 2.5. Evaluation of the Fracture Tests

#### 2.5.1. Fracture Toughness

_{Ic}is calculated as follows [4]:

_{max}is the bending moment due to the maximum load F

_{max}and self-weight, B is the specimen width, W is the specimen depth, Y(α) is a function of geometry [4], and a is the initial notch depth.

#### 2.5.2. Effective Fracture Toughness

_{e}> a. The effective crack length a

_{e}is calculated from the secant stiffness of the concrete specimen corresponding to the maximum load F

_{max}and matching midspan deflection d

_{F}

_{max}. The value of a

_{e}for the prismatic specimen with a central edge notch tested in the three-point bending configuration was determined according to [4] from the following relationship:

_{e}= a

_{e}/W is relative notch depth, and Y(x) is the function of geometry shown in Equation (2), where α is replaced by α

_{e}. Since the effective crack length a

_{e}is expressed in Equation (4) as the argument of integral, the problem is solved using an iterative method.

_{Ice}value was calculated using a linear elastic fracture mechanics formula (Equation (1)), where α was replaced with α

_{e}in compliance with [4].

#### 2.5.3. Specific Fracture Energy

_{F}value, which was given by the area under the diagram. In this case, W

_{F}was calculated according to Stibor [20], where the area under the measured diagrams, the effect of the unmeasured part, and the self-weight of the specimen were considered. After that, the specific fracture energy G

_{F}value was determined according to the RILEM method [21].

_{F,1}considers the area under the F−d diagram up to the maximum load F

_{max}, and the second part G

_{F,2}considers the remaining area under the F−d diagram.

#### 2.5.4. The Double-K Fracture Model Parameters

_{Ic}

^{un}is defined as the critical stress intensity factor corresponding to the maximum load F

_{max}, and it represents the phase of unstable crack propagation. This parameter is of similar meaning to the effective fracture toughness used in the ECM by Karihaloo [4]. The equivalent elastic crack length a

_{c}was determined from the following equation [22]:

_{F}

_{max}is the CMOD corresponding to maximum load F

_{max}, and

_{c}= (a

_{c}+ H

_{0})/(W + H

_{0}); H

_{0}is the thickness of blades fixed on the bottom surface of the specimens between which the strain gauge was placed.

_{c}is known, K

_{Ic}

^{un}was determined according to Equation (1), where a

_{c}was substituted by a, and the geometry function in this case was expressed as follows [4]:

_{F}is a derivative parameter of this relationship, which represents the area under this curve (softening function). There are two methods to obtain the parameters of the softening function. The first is based on the experimental determination of G

_{F}from the uniaxial tensile strength test with deformation-controlled loading. The G

_{F}is then calculated as the area under the σ‒COD diagram. However, it is quite hard to perform such a test in a stable way for concrete specimens, i.e., to also record the post-peak branch of the diagram. The other method consists of an indirect method of determination of COD

_{c}. In this case, G

_{F}and f

_{t}, determined experimentally from the 3PBT and uniaxial tensile test, respectively, and a suitable shape of the softening function are the input parameters [23]. In the 2K model, the softening function has to be known to calculate the cohesive toughness at critical condition K

_{Ic}

^{c}, which can be interpreted as an increase in the resistance to crack propagation caused by the bridging of aggregate grains and other toughening mechanisms in the fracture process zone (FPZ) [22].

_{F}and f

_{t}obtained by inverse analysis [24] were used for the calculation of related fracture parameters. The cohesive stress σ(CTOD

_{c}) at the tip of an initial notch at the critical state could be then obtained from this softening function.

_{t}is the tensile strength, c

_{1}= 3 and c

_{2}= 6.93 and are the material constants, which were taken from (Hordijk, 1991), and CTOD

_{c}is the critical crack-tip opening displacement according to Jenq and Shah [25] [Jeng 1985].

_{c}is the critical crack opening displacement calculated according to

_{F}and tensile strength f

_{t}were obtained by an inverse analysis based on an artificial neural network using the FraMePID-3PB Software [24]. The principle consists of the identification of the material parameters, which gives identical F‒d diagram responses to those obtained during real-time specimen loading. It is presumed that such strength is very close to the uniaxial tensile strength.

_{Ic}

^{c}is determined as follows:

_{c}is used, and F(U, a

_{c}/W) is determined according to [26] [Xu 1999].

_{Ic}

^{ini}:

_{Ic}

^{ini}represents the phase of stable crack propagation.

_{ini}, which expresses the load at the outset of stable crack propagation from the initial notch, was determined according to

_{M}is the section modulus (calculated as S

_{M}= 1/6∙B∙W

^{2}), S is the span length, and Y(α) is the geometry function (Equation (8)), where α = a/W is used instead of a

_{c}/W.

## 3. Results and Discussion

_{max}) was also very similar. Similar results could also be observed in the values of selected fracture characteristics, such as crack strength, fracture toughness, unstable fracture toughness, and effective crack extension. The difference between these parameters for C1 and C2 was up to 5%. The highest difference is recorded in the value of fracture energy (G

_{F}), which was about 14% higher for concrete C2. The values of G

_{F,1}and G

_{F,2}suggest that this difference was especially caused by the different post-peak behavior of investigated concretes; G

_{F,2}was about 16% higher for C2, whereas G

_{F,1}was almost the same for both concretes. A similar difference was recorded in the values of splitting tensile strength, which was about 15% lower for C2 compared to C1, but the variability for C2 was more than twofold higher. Similarly, the values of F

_{ini}(critical force for the start of stable crack propagation), initial fracture toughness, and critical crack opening displacement (COD

_{c}) could not be simply compared because of the high differences in variability recorded for each concrete, which was about twofold higher (more than threefold for COD

_{c}) for C1 compared to C2.

_{n}is a relative value of a particular material characteristic determined for n F–T cycles (n = 0, 50, 100, and 200), P

_{n}is an average value of the set of specimens determined for a particular material characteristic after n F–T cycles, P

_{0}is an average value of the set of non-frost-attacked specimens determined for the particular material characteristic (for n = 0; RV

_{n}= 1).

_{n}is a relative value of the standard deviation of a particular material characteristic determined for n F–T cycles (n = 0, 50, 100, and 200), SSD

_{n}is a sample standard deviation of the set of specimens determined for a particular material characteristic after n F–T cycles, and CoV

_{n}is a coefficient of variation of the set specimens determined after n F–T cycles.

_{rL}was about 5% and was quite stabilized after reaching 25 F–T cycles for C1. No decrease in the compressive strength was observed for C1. In both cases, the results exhibited low variability. The situation differed for concrete C2; a gradual decrease in E

_{rL}and compressive strength up to about 20% was observed upon reaching 100 F–T cycles, after which the values of both parameters started to grow. The final decrease was about 15% and 4% for E

_{rL}and compressive strength, respectively. The long-term experience of the authors with the utilization of the resonance method as a nondestructive technique for monitoring of the F–T damage in concrete suggests that a decrease in E

_{rL}of about 15% indicates a decrease in the flexural or splitting tensile strength of at least about 25% [32,33]. This presumption is confirmed by the results presented in Figure 10a; the decrease in splitting tensile strength was about 40% for C2.

_{F}(see Figure 11) is one of the most commonly used parameters for the assessment of the degree of F–T deterioration. The total fracture energy was calculated herein based on the F−d diagrams (see Section 2.5.3, Equation (5)). The results showed an increase in G

_{F}of about 25% for C1 followed by a slight decrease after 50 F–T cycles. Nevertheless, the final value was about 12% higher than the value before the start of freezing. Similar findings were reported by Wardeh [36], who attributed this phenomenon to the presence of a microcrack network, which needs higher energy dissipation to complete fracture of the concrete. A slight increase of about 7% followed by a decrease with a final value of about 13% after 200 F–T cycles was observed for C2, which indicates an increase in brittleness with an increasing number of F–T cycles. Note that the value of G

_{F}is strongly influenced by the area of the fracture surface. Commonly, a projection of the fractured ligament area is used for calculation, which can substantially influence the absolute value of G

_{F}. The actual fractured area can be more precisely specified by scanning the relief of the fracture surface using laser scanning techniques, which is labor- and time-consuming [37,38].

_{F,1}represents the initial part of the energy consumed from the start of the fracture test up to the peak load, whereas G

_{F,2}represents the post-peak part of the fracture energy. The results show a substantial increase (of about 60%) in the value of G

_{F,1}for C1 after 50 F–T cycles, while almost the same value was recorded for C2 throughout the F–T test. According to the tensile behavior of concrete, as reported by Wardeh [36], the presence of a higher number of microcracks in C1 developed during the initial phase of loading could be confirmed, as also reflected in the post-peak behavior. However, the variability of the results was much higher for C1 than for C2 (see Figure 12a).

_{F,2}exhibited almost the same trend for both concretes with a different value of decrease at the end of the F–T test. The value of G

_{F,2}increased by about 20% and 10% for C1 and C2, respectively, after 50 F–T cycles and was almost the same as before the start of freezing for C1, while a decrease of about 14% was observed for C2 after 200 F–T cycles.

_{Ic}, determined according to the linear elastic fracture mechanics approach (Figure 13a) and effective fracture toughness K

_{Ice}, which includes the nonlinear behavior of concrete before reaching the peak load (Figure 13b). The trend of K

_{Ic}development was the same as observed for the crack strength throughout the F–T test (see Figure 10b). This complies with the linear fracture mechanics approach [4]. A different trend was observed for K

_{Ice}(see Figure 13b). The increase in this value was about 16% and even 25% after 50 and 200 F–T cycles, respectively, for concrete C1. On the other hand, a decrease of about 24% followed by a slow increase for concrete C2 was recorded after 50 F–T cycles. The final decrease in the value of K

_{Ice}was about 8% for C2. Moreover, the effective crack extension increased for C1 (of about 40%) and decreased for C2 (of about 20%) throughout the F–T test (see Figure 14a). This indicates increasing nonlinearity caused by a higher number of microcracks along the FPZ before failure in C1 due to the F–T exposure. According to the results, it can be stated that concrete C2 became more brittle due to exposure to F–T cycles compared to concrete C1.

_{Ic}

^{un}and cohesive fracture toughness K

_{Ic}

^{c}are two basic fracture parameters determined using the F−CMOD diagrams. The cohesive fracture toughness K

_{Ic}

^{c}, as a component of unstable fracture toughness K

_{Ic}

^{un}, reflects the cohesive mechanisms in the FPZ. Many micro-failure mechanisms such as matrix microcracking, debonding of the cement–matrix interface, crack deflection, grain bridging, and crack branching, which consume energy during the crack propagation, are responsible for the stress transfer [22]. If the component of cohesive fracture toughness K

_{Ic}

^{c}is subtracted from the unstable fracture toughness, the value of initiation fracture toughness K

_{Ic}

^{ini}is obtained. The critical values of the fracture toughness are obtained at the load level F

_{max}, upon reaching the equivalent elastic crack extension and critical crack-tip opening displacement (CTOD

_{c}).

_{c}of more than 60% for C1 after 200 F–T cycles. This indicates an increase in the fictitious crack width before the failure due to F–T exposure. An increase of about 34% followed by a steep decrease of about 50% was recorded for C2 after 50 F–T cycles. This indicates a gradual increase in brittleness of C2 with an increasing number of F–T cycles.

_{Ic}

^{c}), unstable (K

_{Ic}

^{un}), and initial fracture (K

_{Ic}

^{ini}) toughness after 50 F–T cycles, after which all toughness components were already stabilized during the remainder of the F–T test. In the case of concrete C2, the trend of development slightly differed for the three toughness components. No decrease in K

_{Ic}

^{c}was recorded after 50 F–T cycles, while a gradual and steep decrease was recorded for K

_{Ic}

^{un}and K

_{Ic}

^{ini}, respectively. A maximum decrease of about 11% and 17% followed by an increase in the value of cohesive and unstable fracture toughness, respectively, was observed after 100 F–T cycles. The final value of cohesive fracture toughness was about 8% higher compared to the value before the start of freezing.

_{Ic}

^{un}, K

_{Ic}

^{ini}, and K

_{Ic}

^{c}indicates higher deterioration of C2 accompanied by more brittle failure due to the F–T action compared to C1 concrete.

_{ini}/F

_{max}ratio for both concretes during the F–T test. The results show a gradual increase of up to 27% for C1 after 100 F–T cycles. The final value after 200 F–T cycles was about 16% higher than before the start of freezing. A gradual decrease of up to 15% was recorded for C2 after 200 F–T cycles. The increasing load ratio indicates an extension of the linear part of the diagram, which expresses the later onset of the stable crack propagation, i.e., the resistance to the crack onset increased during the F–T exposure for C1 concrete until reaching 100 F–T cycles.

_{ini}and F

_{max}. The changes in loading force at the selected load levels are displayed separately in Figure 18. The main changes in the values of F

_{ini}were recorded for both concretes after 50 F–T cycles. After that, the value of F

_{ini}was almost stabilized for both concretes. Concerning F

_{max}, a gradual decrease was observed for both concretes up to 100 F–T cycles, after which the value of F

_{max}increased for C1 and C2. The variability in the loading forces was reflected in the evaluation of the RMS values, which was determined for the region of the average value of F

_{ini}± standard deviation. The same procedure was applied for the load level F

_{max}and region 0–F

_{max}.

_{ini}(expected crack initiation) after 200 F–T cycles. Almost the same descending trend of RMS for C1 was recorded when evaluated for the load range of 0 up to the F

_{max}. The increasing deterioration of C2 was reflected in a steep decrease in RMS, the value of which was negligible compared to the non-frost-attacked specimens after 200 F–T cycles. Although the resonance test showed a resistance of C1 concrete to the F–T action, the AE measurement revealed a gradual degradation of internal structure, as reflected in a decrease in RMS value of about 40% after 200 F–T cycles. This proved the evolution of the microcrack network during the pre-peak loading phase, which was reflected in the increase of the fracture toughness, crack extension, and fracture energy.

## 4. Conclusions

_{300}, which were both higher for C1. It is important to emphasize that both concretes did not exhibit macro-defects throughout the F–T test duration, i.e., no surface scaling or macrocracks were observed.

- It can be supposed that C1 concrete exhibited better resistance to the F–T action compared to C2. All fracture parameters together indicated an enhancing resistance of C1 concrete to brittle fracture during the F–T test.
- It can be stated that the continuous AE measurement is beneficial for the assessment of the extent of concrete deterioration and suitably supplements the fracture test evaluation.
- The results showed that the F–T damage was more reflected in the fracture toughness parameters than in the fracture energy.
- The F–T damage of the investigated concretes was reflected in the value of fracture energy, which increased with an increase in the microcrack network and decreased for concrete with a more seriously damaged structure. To confirm the presence of microcracks, it seems to be beneficial to calculate the fracture energy G
_{F,1,}and G_{F,2}separately for pre- and post-peak load phases. The presence of microcracks led to an increase in the pre-peak fracture energy G_{F,1}(see Figure 12a). It can be stated that an increase in G_{F,1}for concrete C1 was caused especially by softening in the FPZ, as reflected by the increase in the value of effective and unstable fracture toughness (see Figure 13b or Figure 16b) and in the post-peak behavior. - It can be stated that the F–T damage was notably reflected in the characteristics of the fictitious crack represented herein by the effective crack extension and critical crack-tip opening displacement. Both parameters indicate the ductility/brittleness of the material. According to the results, it can be supposed that an increase in crack extension and opening indicates increasing nonlinear behavior before failure, implying an increase in ductility of C1 during F–T exposure. On the other hand, the C2 became more brittle with an increasing number of F–T cycles (see Figure 14a or Figure 15).
- The double-K model seems to be beneficial for the evaluation of F–T damage because it enables distinguishing the different phases of crack propagation. Additionally, it provides the possibility to calculate the cohesive component of the fracture toughness, which represents the action of cohesive forces along the fictitious crack and indicates the risk of brittle fracture.
- Comparing the results of fracture tests with the resonance method and splitting tensile strength test, it can be stated that all testing methods gave the same conclusion, i.e., C1 concrete is more F–T-resistant than C2. However, the fracture test evaluation provided more detailed information about the internal structure deterioration due to F–T exposure.
- The decrease in fracture parameters of C2 concrete corresponded well to the decrease in dynamic modulus of elasticity (see Figure 9a) recorded during the F–T test. Unfortunately, there are no criteria for related damage factors determined by the Czech standard. It can be supposed that the microcracks indicated by the fracture parameters for C1 were reflected by a slight decrease in its dynamic modulus (about 5%) determined by the resonance method. However, it is not possible to assess the ductility or brittleness using the resonance method.
- The main disadvantages of the fracture test performed in the context of F–T resistance are the time consumption (one test lasts at least 40 min), labor intensiveness, and the process of evaluation, which limit its wider utilization in standard practice.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Qin, X.-C.; Meng, S.-P.; Cao, D.-F.; Tu, Y.-M.; Sabourova, N.; Grip, N.; Ohlsson, U.; Blanksvärd, T.; Sas, G.; Elfgren, L. Evaluation of freeze-thaw damage on concrete material and prestressed concrete specimens. Constr. Build. Mater.
**2016**, 125, 892–904. [Google Scholar] [CrossRef] - Kuosa, H.; Ferreira, M.; Leivo, M. Freeze-Thaw Testing CSLA Projekct—Task 1: Literature Review; Research Report VTT-R-07364-12; VTT technical Research Centre of Finland: Espoo, Finland, 2013. [Google Scholar] [CrossRef]
- Ma, Z.; Zhao, T.; Yang, J. Fracture Behavior of Concrete Exposed to the Freeze-Thaw Environment. J. Mater. Civ. Eng.
**2017**, 29, 04017071. [Google Scholar] [CrossRef] - Karihaloo, B.L. Fracture Mechanics and Structural Concrete, 1st ed.; Longman Scientific & Technical: Harlow, Essex, UK, 1995; p. 330. [Google Scholar]
- Dong, Y.; Su, C.; Qiao, P.; Sun, L. Microstructural damage evolution and its effect on fracture behavior of concrete subjected to freeze-thaw cycles. Int. J. Damage Mech.
**2018**, 27, 1272–1288. [Google Scholar] [CrossRef] [Green Version] - Huang, M.; Duan, J.; Wang, J. Research on Basic Mechanical Properties and Fracture Damage of Coal Gangue Concrete Subjected to Freeze-Thaw Cycles. Adv. Mater. Sci. Eng.
**2021**, 2021, 6701628. [Google Scholar] [CrossRef] - Wardeh, G.; Ghorbel, E. Freezing-Thawing Cycles Effect on the Fracture Properties of Flowable Concrete. In Proceedings of the 8th International Conference on Fracture Mechanics of Concrete and Concrete Structures, FraMCoS-8, Toledo, Spain, 10–14 March 2013; International Center for Numerical Methods in Engineering (CIMNE): Barcelona, Spain, 2013; pp. 1818–1827. [Google Scholar]
- Zhang, Z.; Ansari, F. Fracture mechanics of air-entrained concrete subjected to compression. Eng. Fract. Mech.
**2006**, 73, 1913–1924. [Google Scholar] [CrossRef] - Jin, S.; Zhang, J.; Huang, B. Fractal analysis of effect of air void on freeze–thaw resistance of concrete. Constr. Build. Mater.
**2013**, 47, 126–130. [Google Scholar] [CrossRef] - Sika CZ. Available online: https://cze.sika.com/ (accessed on 19 October 2021).
- ČSN 73 1322 Determination of Frost Resistance of Concrete (in Czech); ÚNMZ: Prague, Czech Republic, 1968.
- Kocáb, D.; Halamová, R.; Bílek, V. Ratio between dynamic Young’s moduli of cementitious materials determined through different methods. In Proceedings of the SPECIAL CONCRETE AND COMPOSITES 2020: 17th International Conference, Bystřice nad Pernštejnem, Czech Republic, 14–15 October 2020; AIP Publishing: Melville, NY, USA, 2021; Volume 2322, p. 020011. [Google Scholar]
- ASTM C215-19: Standard Test Method for Fundamental Transverse, Longitudinal, and Torsional Resonant Frequencies of Concrete Specimens; ASTM International: West Conshohocken, PA, USA, 2019.
- Barsoum, F.F.; Suleman, J.; Korcak, A.; Hill, E.V.K. Acoustic Emission Monitoring and Fatigue Life Prediction in Axially Loaded Notched Steel Specimens. J. Acoust. Emiss.
**2009**, 27, 40–63. [Google Scholar] - Shateri, M.; Ghaib, M.; Svecova, D.; Thomson, D. On acoustic emission for damage detection and failure prediction in fiber reinforced polymer rods using pattern recognition analysis. Smart Mater. Struct.
**2017**, 26, 065023. [Google Scholar] [CrossRef] - Panasiuk, K.; Kyziol, L.; Dudzik, K.; Hajdukiewicz, G. Application of the Acoustic Emission Method and Kolmogorov-Sinai Metric Entropy in Determining the Yield Point in Aluminium Alloy. Materials
**2020**, 13, 1386. [Google Scholar] [CrossRef] [Green Version] - Niewiadomski, P.; Hoła, J. Failure process of compressed self-compacting concrete modified with nanoparticles assessed by acoustic emission method. Autom. Constr.
**2020**, 112, 103111. [Google Scholar] [CrossRef] - Frantík, P.; Mašek, J. GTDiPS Software. 2015. Available online: http://gtdips.kitnarf.cz/ (accessed on 1 October 2020).
- Šimonová, H.; Kucharczyková, B.; Bílek, V.; Malíková, L.; Miarka, P.; Lipowczan, M. Mechanical Fracture and Fatigue Characteristics of Fine-Grained Composite Based on Sodium Hydroxide-Activated Slag Cured under High Relative Humidity. Appl. Sci.
**2020**, 11, 259. [Google Scholar] [CrossRef] - Stibor, M. Fracture Parameters of Quasi-Brittle Materials and Their Determination. Ph.D. Thesis, Brno University of Technology, Brno, Czech Republic, 2004. (In Czech). [Google Scholar]
- RILEM TC—50 FMC (Recommendation): Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Mater. Struct.
**1985**, 18, 287–290. [CrossRef] - Kumar, S.; Barai, S.V. Concrete Fracture Models and Applications; Springer LLC: Berlin, Germany, 2011; p. 262. [Google Scholar]
- Hordijk, D.A. Local Approach to Fatigue of Concrete. Ph.D. Thesis, Technische Universiteit Delft, Delft, The Netherlands, 1991. [Google Scholar]
- Lehký, D.; Keršner, Z.; Novák, D. FraMePID-3PB software for material parameter identification using fracture tests and inverse analysis. Adv. Eng. Softw.
**2014**, 72, 147–154. [Google Scholar] [CrossRef] - Jenq, Y.S.; Shah, S.P. Two parameter fracture model for concrete. J. Eng. Mech.
**1985**, 111, 1227–1241. [Google Scholar] [CrossRef] - Xu, S.; Reinhardt, H.W. Determination of double-K criterion for crack propagation in quasibrittle fracture, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams. Int. J. Fract.
**1999**, 98, 151–177. [Google Scholar] [CrossRef] - Wawrzeńczyk, J.; Molendowska, A. Evaluation of Concrete Resistance to Freeze-thaw Based on Probabilistic Analysis of Damage. Procedia Eng.
**2017**, 193, 35–41. [Google Scholar] [CrossRef] - Kee, S.-H.; Kang, J.W.; Choi, B.-J.; Kwon, J.; Candelaria, M.D. Evaluation of Static and Dynamic Residual Mechanical Properties of Heat-Damaged Concrete for Nuclear Reactor Auxiliary Buildings in Korea Using Elastic Wave Velocity Measurements. Materials.
**2019**, 12, 2695. [Google Scholar] [CrossRef] [Green Version] - Stein, T.; Gafoor, A.; Dinkler, D. Modeling inelastic-anisotropic damage behavior of concrete considering lateral deformation. PAMM
**2021**, 20, e202000225. [Google Scholar] [CrossRef] - Poinard, C.; Malecot, Y.; Daudeville, L. Damage of concrete in a very high stress state: Experimental investigation. Mater. Struct.
**2010**, 43, 15–29. [Google Scholar] [CrossRef] - Prasad, M.; Xiaobing, S. Post-cracking Poisson Ratio of Concrete in Steel-Concrete-Steel Panels Subjected to Biaxial Tension Compression. IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 758, 012081. [Google Scholar] [CrossRef] - Kocáb, D.; Kucharczyková, B.; Daněk, P.; Vymazal, T.; Hanuš, P.; Halamová, R. Destructive and non-destructive assessment of the frost resistance of concrete with different aggregate. IOP Conf. Ser. Mater. Sci. Eng.
**2018**, 379, 012022. [Google Scholar] [CrossRef] - Kocáb, D.; Lišovský, M.; Žítt, P. Experimental determination of freeze-thaw resistance in self-compacting concretes. IOP Conf. Ser. Mater. Sci. Eng.
**2019**, 549, 012019. [Google Scholar] [CrossRef] - ČSN EN 12390-6: Testing Hardened Concrete—Part 6: Tensile Splitting Strength of Test Specimens; ÚNMZ: Prague, Czech Republic, 2010.
- ASTM E1823-20b: Standard Terminology Relating to Fatigue and Fracture Testing; ASTM International: West Conshohocken, PA, USA, 2020.
- Wardeh, G.; Ghorbel, E. Prediction of fracture parameters and strain-softening behavior of concrete: Effect of frost action. Mater. Struct.
**2013**, 48, 123–138. [Google Scholar] [CrossRef] - Sobek, J.; Frantík, P.; Trčka, T.; Lehký, D. Fractal Dimension Analysis of Three-Point Bending Concrete Test Specimens. MATEC Web Conf.
**2020**, 323, 01011. [Google Scholar] [CrossRef] - Rhee, I.; Lee, J.S.; Roh, Y.-S. Fracture Parameters of Cement Mortar with Different Structural Dimensions Under the Direct Tension Test. Materials
**2019**, 12, 1850. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ding, Y.; Bai, Y.-L.; Dai, J.-G.; Shi, C.-J. An Investigation of Softening Laws and Fracture Toughness of Slag-Based Geopolymer Concrete and Mortar. Materials
**2020**, 13, 5200. [Google Scholar] [CrossRef] - Topolář, L.; Kocáb, D.; Pazdera, L.; Vymazal, T. Analysis of Acoustic Emission Signals Recorded during Freeze-Thaw Cycling of Concrete. Materials
**2021**, 14, 1230. [Google Scholar] [CrossRef]

**Figure 1.**Arrangement of freeze–thaw test: (

**a**) automatic freeze–thaw cabinet KD 20; (

**b**) detail of specimens arrangement during F–T test; (

**c**) one F–T cycle.

**Figure 2.**Measurement of resonant frequencies (1—computer equipped with software for determination of resonant frequencies; 2—Handyscope HS4 oscilloscope; 3—acoustic sensor; 4—impact hammer).

**Figure 3.**(

**a**) Arrangement of fracture tests; (

**b**) details of the test specimens and sensors (1—inductive sensor in a frame; 2—rectifying screws in the middle of the span and above the support; 3—strain gauge between the blades; 4—applied load; 5—acoustic emission sensors).

**Figure 12.**(

**a**) Fracture energy G

_{F,1}(up to the peak load); (

**b**) fracture energy G

_{F,2}(post-peak part).

**Figure 15.**(

**a**) Equivalent elastic crack extension; (

**b**) critical crack-tip opening displacement (CTOD).

**Table 1.**Composition of C1 and C2 concrete in kg per 1 m

^{3}of fresh concrete and basic characteristics of fresh concretes.

Components/Characteristics | C1 | C2 |
---|---|---|

Cement CEM I 42.5 R | 390 | 390 |

Sand 0–4 mm (Tovačov, CZ) | 810 | 810 |

Gravel 4–8 mm (Luleč, CZ) | 160 | 160 |

Gravel 8–16 mm (Olbramovice, CZ) | 760 | 760 |

Admixture Sika ViscoCrete-4035 | 1.00 | 0.40 |

Air-entraining admixture LPS A 94 | 0.55 | 0.20 |

Admixture Sika ViscoFlow-25 | 1.60 | 0.64 |

Water | 178 | 198 |

w/c | 0.46 (0.43 *) | 0.51 (0.47 *) |

Density of fresh concrete (kg/m^{3}) | 2290 | 2340 |

Air content (%) | 4.3–5.0 | 2.1–2.5 |

Workability (flow-table test) (mm) | 420/430 | 410/420 |

Parameter | C1 | C2 |
---|---|---|

Total air-void content (%) | 4.26 (0.372) | 2.77 (0.127) |

Specific surface (mm^{−1}) | 24.4 (2.74) | 23.0 (1.56) |

Paste–air ratio | 7.22 (0.64) | 11.75 (0.54) |

Spacing factor (mm) | 0.23 (0.019) | 0.30 (0.026) |

A_{300} (%) | 1.31 (0.048) | 0.63 (0.014) |

**Table 3.**Mechanical, fracture, and AE characteristics of non-frost attacked concretes C1 and C2: average value (standard deviation).

Parameter | C1 | C2 |
---|---|---|

Dynamic modulus of elasticity (GPa) | 43.330 (0.976) | 42.980 (0.727) |

Compressive strength * (MPa) | 60.0 (0.1) | 57.0 (2.6) |

Splitting tensile strength * (MPa) | 5.41 (0.4) | 4.61 (0.85) |

Crack strength (MPa) | 5.02 (0.16) | 5.35 (0.40) |

Tensile strength, identification (MPa) | 3.20 (0.37) | 2.99 (0.21) |

Load level F_{ini} (kN) | 3.41 (0.59) | 3.95 (0.36) |

Maximum load F_{max} (kN) | 5.13 (0.13) | 5.31 (0.40) |

Effective fracture toughness (MPa.m^{1/2}) | 1.249 (0.105) | 1.371 (0.093) |

Fracture toughness (MPa.m^{1/2}) | 0.773 (0.022) | 0.823 (0.062) |

Fracture energy G_{F} (J/m^{2}) | 127.7 (12.33) | 146.0 (15.5) |

Fracture energy G_{F,1} (J/m^{2}) | 22.2 (3.00) | 23.4 (1.88) |

Fracture energy G_{F,2} (J/m^{2}) | 105.5 (9.71) | 122.7 (14.89) |

Initial fracture toughness (MPa.m^{1/2}) | 0.520 (0.09) | 0.619 (0.056) |

Unstable fracture toughness (MPa.m^{1/2}) | 1.225 (0.145) | 1.205 (0.128) |

Effective crack extension (mm) | 16.91 (2.6) | 17.83 (1.4) |

Equivalent crack extension (mm) | 15.56 (3.5) | 13.00 (3.9) |

Critical crack tip opening displacement (mm) | 0.0244 (0.003) | 0.0243 (0.007) |

RMS_{cumu}_F_{max} (mV) | 0.1663 (0.0405) | 0.124 (0.0182) |

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**MDPI and ACS Style**

Kucharczyková, B.; Šimonová, H.; Kocáb, D.; Topolář, L.
Advanced Evaluation of the Freeze–Thaw Damage of Concrete Based on the Fracture Tests. *Materials* **2021**, *14*, 6378.
https://doi.org/10.3390/ma14216378

**AMA Style**

Kucharczyková B, Šimonová H, Kocáb D, Topolář L.
Advanced Evaluation of the Freeze–Thaw Damage of Concrete Based on the Fracture Tests. *Materials*. 2021; 14(21):6378.
https://doi.org/10.3390/ma14216378

**Chicago/Turabian Style**

Kucharczyková, Barbara, Hana Šimonová, Dalibor Kocáb, and Libor Topolář.
2021. "Advanced Evaluation of the Freeze–Thaw Damage of Concrete Based on the Fracture Tests" *Materials* 14, no. 21: 6378.
https://doi.org/10.3390/ma14216378