# Fracture Toughness and Fracture Surface Morphology of Concretes Modified with Selected Additives of Pozzolanic Properties

## Abstract

**:**

_{Ic}

^{S}and elastic modulus E). Also, stereological and fractal tests were performed. The research program covered three separate experiment plans, adopting the water/binder ratio and the additive/binder mass ratio as the independent variables. The results of experiments and their analysis proved a statistically significant relationship between fracture morphology (fractal dimension D) and concrete composition and fracture toughness. A higher fractal dimension was found in concretes with a higher content of cement paste and a lower content of additive. No significant effect of the type of additive used in the above dependence was found. An original method enabling the determination of mechanical properties of concrete with no need for destructive testing has been developed.

## 1. Introduction

_{c}[3,4,5], the fracture toughness as expressed by the critical stress intensity factor K

_{c}or the fracture energy G

_{F}[4,6,7,8,9,10,11,12,13,14,15] and the elastic modulus E [4], on the other side.

## 2. Materials and Methods

^{3}, basalt grit to 16 mm with specific gravity of 3.06 kg/dm

^{3}and alternately: Silica fume (with 94% SiO

_{2}), activated fluidal ash (with 40 % SiO

_{2}, 30% Al

_{2}O

_{3}and 13% CaO content) or metakaolinite (with 53% SiO

_{2}and 42% Al

_{2}O

_{3}content). The silica fume SikaFume

^{®}HR used is characterized by specific gravity of 2.2 kg/dm

^{3}and a specific surface of 22 m

^{2}/g. The fluidal ash used was a mechanically activated fluidal ash. Compared with non-activated fluid ashes, activated fluidal ash accelerates the setting processes. This results from deagglomeration and structural defects on the surface of the ash particles. The specific gravity of activated fluidal ash is 2.53 kg/dm

^{3,}and the specific surface is 0.51 m

^{2}/g. Metakaolin is a pozzolanic material. It is obtained by the calcination of kaolinitic clay at a temperature ranging between 550 °C and 800 °C. The metakaolinite used in the test was obtained in the process of kaolin calcination at a temperature of around 800 °C, and its specific gravity was 2.54 kg/dm

^{3}. A diversity of grain sizes was observed, ranging from 0.1 µm to 100 µm, with the majority of sizes in the range from 1 µm to 10 µm (constituting around 60%). The share of grains below 1 µm was around 20% and the share of grains below 17 µm was 90%.

_{c}, critical stress intensity factor K

_{Ic}

^{S}, and elastic modulus E.

_{Ic}

^{S}and modulus E were calculated after [54]. During the fracture toughness tests, the dependence of the loading force on the crack mouth opening displacement (CMOD) was recorded. Examples of plots of the load vs. CMOD obtained for concrete with fluidal ash addition are shown in Figure 1.

_{Ic}

^{S}was calculated from the following relationship (Equation (1)):

_{max}- maximum load, W

_{0}- specimen weight, N and S, L, a

_{o}, d, b (according to Figure 2).

_{Ic}

^{S}were calculated on the basis of four results.

_{BC}, the box counting method was applied. The fractal analysis of concrete fracture surface profile lines was done with FRACTAL_Dimension2D (J. Konkol, FRACTAL_Dimension2D, a program, 2000). The fractal dimension was determined as the tangent of the slope in a double-logarithmic diagram of the relationship of the logarithm of the box number to the logarithm of the box dimension.

_{VP}was calculated. This surface, which is a measure of dispersion, was calculated as the total surface of pores by volume unit. The stereological analysis was also done for the stage of coarse aggregate, determining the relative area of coarse aggregate S

_{VK}.

## 3. Results

## 4. Discussion

_{Ic}

^{S}and w/b = 0.445, Table 4), the use of the F-test for analysis of test results obtained within concrete with a constant water/binder ratio indicated the difference between the mean values of compressive strength and critical stress intensity factor of these concretes.

_{Ic}

^{S}of the concretes modified with the selected additive (Table 4).

_{Ic}

^{S}was then accounted for by the variation of the compressive strength f

_{c}in 86.7% and the variation of other factors, including the random ones in 13.3%.

_{Ic}

^{S}. The points corresponding to the results for concretes modified with Flubet (FA), metakaolinite (MK) and silica fume (SF) have been marked.

_{c}, known from the literature, a statistical analysis was done for the model:

_{Ic}

^{S}and the water/binder ratio w/s affecting the class of concrete strength, and the fractal dimension D

_{BC}, which characterizes quantitatively the fracture surface during the cracking process. The analysis was done by means of a multiple regression method (Table 5), showing the significance of the effect of both values (w/b and D

_{BC}) on the change of factor K

_{Ic}

^{S}. An improvement of the correlation coefficient R = 0.931 for Equation (1) to 0.960 for Equation (6) was obtained:

_{Ic}

^{S}was thus accounted for by the variation of the water/binder ratio and the fractal dimension in 92.2%, and only 7.8% were other factors, including the random ones. At the same time, the values of the standardized coefficients of regression b* (Table 5) indicated the w/b variable contribution was higher by 3.5 than that of variable D

_{BC}in the prediction K

_{Ic}

^{S}. Figure 9 illustrates a plot of the values observed versus the predicted K

_{Ic}

^{S}, calculated on the basis of Equation (6).

_{Ic}

^{S}on the basis of Equation (6), it is necessary to know the fractal dimension, which is connected with the necessity of performing destructive testing and analyzing the fracture surface formed.

_{BC}, the technique of linear multiple regression was applied. Stereological parameters of the aggregate relative area S

_{VK}and the pore relative area S

_{VP}were adopted as the variables describing the phases of aggregate and pores (Table 3). Additionally, the additive to binder ratio AD/b, volume of cement paste V

_{Paste}and type of additive, as a qualitative variable, were adopted as variables.

_{VK}, pore relative area S

_{VP}and type of additive (p > 0.05, Table 6) were rejected. The model of multiple regression obtained the final form:

_{Paste}—content of cement paste in concrete mix.

_{Paste}contributed to the prediction of the fractal dimension twice as high as the additives (AD/b). The plot of the observed values D

_{BC}versus the predicted ones (Equation (7)) is shown in Figure 10.

_{VP}has also been shown. This insignificance also was confirmed in research on concretes modified with activated fluidal ash or metakaolinite [55]. The insignificance of the aggregate relative area S

_{VK}can be accounted for by small variation of this parameter, since the content of this aggregate was not a variable included in the experiment plan adopted. The proportion of the coarse aggregate was from 37 to 41% of the concrete volume.

_{BC}. An increased proportion of the cement paste in concrete, on the other hand, enlarges the fractal dimension D

_{BC}. This phenomenon can be explained by a higher roughness of the hardened cement paste on the fracture, compared with the roughness of the basalt grains. This is because a higher content of the paste results in a lower content of basalt aggregate.

_{Ic}

^{S}estimated was 4.0 %, the extreme values reached –12.1% and +10.4%. In 87% of the results, the K

_{Ic}

^{S}estimate error was in the range of –8% to +8%. The distribution of the K

_{Ic}

^{S}estimate error is shown in Figure 11. On the other hand, the mean difference between an individual K

_{Ic}

^{S}result and an average mean at the given point of the experiment plan was 4.9%, with the extreme values of +19.7% and –14.9% (Figure 12).

_{Ic}

^{S}, results, calculated on the basis of Equations (6) and (7), with the values of K

_{Ic}

^{S}obtained in testing is in Figure 13. The analysis of linear regression indicated that the observed values of K

_{Ic}

^{S}versus the predicted ones were distributed along a straight line, with a significant slope of 1.0. The result implied good compatibility of the predicted values with the observed ones. It also confirmed the reliability of the proposed solution.

## 5. Conclusions

_{c}, fracture toughness (determination of critical stress intensity factor K

_{Ic}

^{S}), and elastic modulus in bending E, it was sufficient to define the additive to binder mass ratio AD/b (the binder side additive is also included), water/binder ratio w/b (w/b = w/(c + AD)) and the content of concrete paste in concrete mix V

_{Paste}.

_{Ic}

^{S}to be determined, it was proved that the calculation error for K

_{Ic}

^{S}was smaller than the difference resulting from the scatter of the individual results of tests on K

_{Ic}

^{S}. Moreover, the linear relationship, which was statistically highly significant at the adopted significance level of 0.05, between the critical stress intensity factor K

_{Ic}

^{S}and compressive strength f

_{c}of modified concretes after 28 days of curing was shown. Equation (6) enabled the elasticity modulus in bending E to be determined.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**An example graph of crack mouth opening displacement (CMOD)–load relationship and schematic drawings of the specimen used in the fracture toughness examination according to Mode I (concrete with fluidal ash additive–series 5).

**Figure 2.**A mold for the manufacture of gypsum replicas (

**a**) and a gypsum replica strip (

**b**) scanned at definition resolution of 600 dpi together with the digitalization results (

**c**).

**Figure 3.**Test specimens surface with visible pores filled with zinc paste (

**a**), after treatment filling—white spots represent places identified as air pores sections (

**b**).

**Figure 4.**Method of identification of places of air pores occurrence (greyscale for pores from 170 to 255).

**Figure 5.**Compressive strength of concretes with no additives versus modified concretes (at w/b = 0.353; 0.445, and 0.537 additive content as for concrete series 5, 7 and 6 adopted in the experiment plan).

**Figure 6.**Critical stress intensity factor K

_{Ic}

^{S}of concretes with no additives versus modified concretes (at w/b = 0.353; 0.445, and 0.537 additive content as for concrete series 5, 7 and 6 adopted in the experiment plan).

**Figure 7.**Relation between the values of critical stress intensity factor K

_{Ic}

^{S}observed and that determined with Equation (4).

**Figure 8.**Exponential dependence between elastic modulus E and compressive strength f

_{c}of modified concretes.

**Figure 9.**Relation between critical stress intensity factor K

_{Ic}

^{S}observed and that determined with Equation (6).

**Figure 10.**Relation between fractal dimension D

_{BC}observed and that determined with Equation (7).

**Figure 11.**Histogram of K

_{Ic}

^{S}estimation error distribution determined after Equations (6) and (7) compared with K

_{Ic}

^{S}values determined in testing.

**Figure 12.**Histogram of distribution of differences between mean values of K

_{Ic}

^{S}, determined for each series of concretes, and values of K

_{Ic}

^{S}determined on the basis of individual results of tests.

**Figure 13.**K

_{Ic}

^{S}observed values versus predicted ones, determined on the basis of Equations (6) and (7).

Series no. | Variable | Concrete Mix Composition in kg After the Adopted Plan | ||||||
---|---|---|---|---|---|---|---|---|

w/b | FA/b or MK/b (SF/b)^{1} | Binder | Cement ^{1} | FA or MK (SF) ^{1} | Water | Sand | Basalt | |

1 | 0.380 | 0.04 (0.03) | 454 | 435.8 (440.4) | 18.2 (13.6) | 172.5 | 739.3 | 1212.5 |

2 | 0.380 | 0.13 (0.09) | 395.0 (413.1) | 59.0 (40.9) | 172.5 | |||

3 | 0.510 | 0.04 (0.03) | 435.8 (440.4) | 18.2 13.6) | 231.5 | |||

4 | 0.510 | 0.13 (0.09) | 395.0 (413.1) | 59.0 (40.9) | 231.5 | |||

5 | 0.353 | 0.085 (0.06) | 415.4 (426.8) | 38.6 (27.2) | 160.3 | |||

6 | 0.537 | 0.085 (0.06) | 415.4 (426.8) | 38.6 (27.2) | 243.8 | |||

7 | 0.445 | 0.02 (0.02) | 444.3 (446.0) | 9.7 (8.0) | 202.0 | |||

8 | 0.445 | 0.15 (0.10) | 386.5 (407.5) | 67.5 (46.5) | 202.0 | |||

9, 10 | 0.445 | 0.085 (0.06) | 415.4 (426.8) | 38.6 (27.2) | 202.0 |

^{1}The values in brackets refer to concrete mixes with silica fume (SF).

**Table 2.**Results of tests on compressive strength f

_{c}and critical stress intensity factor K

_{Ic}

^{S}after 28 days curing of concrete.

Series No. | Mechanical Properties of Modified Concrete | |||||
---|---|---|---|---|---|---|

Activated Fluidal Ash (FA) | Metakaolinite (MK) | Silica Fume (SF) | ||||

f_{c} ± Stand. ErrorMPa | K_{Ic}^{S} ± Stand. Error MN/m ^{3/2} | f_{c} ± Stand. ErrorMPa | K_{Ic}^{S} ± Stand. Error MN/m ^{3/2} | f_{c} ± Stand. ErrorMPa | K_{Ic}^{S} ± Stand. Error MN/m^{3/2} | |

1 | 58.3 ± 1.2 | 1.49 ± 0.03 | 53.7 ± 0.5 | 1.44 ± 0.04 | 54.8 ± 1.1 | 1.25 ± 0.04 |

2 | 61.0 ± 1.1 | 1.58 ± 0.03 | 61.0 ± 1.2 | 1.57 ± 0.02 | 65.3 ± 1.1 | 1.53 ± 0.05 |

3 | 40.0 ± 0.9 | 0.90 ± 0.05 | 40.8 ± 1.2 | 0.94 ± 0.03 | 39.2 ± 0.7 | 0.92 ± 0.02 |

4 | 40.9 ± 0.6 | 1.17 ± 0.03 | 41.3 ± 0.4 | 1.02 ± 0.06 | 40.2 ± 1.3 | 0.97 ± 0.03 |

5 | 63.8 ± 0.4 | 1.47 ± 0.05 | 63.7 ± 0.6 | 1.52 ± 0.03 | 66.1 ± 0.7 | 1.58 ± 0.01 |

6 | 41.5 ± 1.4 | 1.06 ± 0.05 | 37.2 ± 0.8 | 0.97 ± 0.01 | 38.6 ± 0.5 | 0.93 ± 0.03 |

7 | 45.2 ± 0.8 | 1.23 ± 0.04 | 46.7 ± 0.5 | 1.25 ± 0.05 | 46.7 ± 1.0 | 1.24 ± 0.06 |

8 | 47.3 ± 0.9 | 1.34 ± 0.10 | 51.5 ± 0.9 | 1.32 ± 0.02 | 54.8 ± 1.1 | 1.34 ± 0.04 |

9 | 45.5 ± 1.0 | 1.27 ± 0.04 | 47.8 ± 1.0 | 1.25 ± 0.06 | 48.8 ± 0.7 | 1.21 ± 0.03 |

10 | 45.9 ± 1.1 | 1.25 ± 0.12 | 48.0 ± 1.0 | 1.20 ± 0.04 | 49.2 ± 0.5 | 1.22 ± 0.01 |

Series No. | Fractal and Stereological Parameters of Modified Concrete | |||||
---|---|---|---|---|---|---|

Activated Fluidal Ash (FA) | Metakaolinite (MK) | Silica Fume (SF) | ||||

D_{BC} ± Stand. Error - | S_{VP} ± Stand. Errorcm ^{2}/cm^{3} | D_{BC} ± Stand. Error- | S_{VP} ± Stand. Errorcm ^{2}/cm^{3} | D_{BC} ± Stand. Error- | S_{VP} ± Stand. Errorcm ^{2}/cm^{3} | |

1 | 1.047 ± 0.001 | 2.69 ± 0.09 | 1.051 ± 0.001 | 2.36 ± 0.08 | 1.046 ± 0.001 | 2.75 ± 0.08 |

2 | 1.044 ± 0.001 | 2.38 ± 0.11 | 1.045 ± 0.001 | 2.32 ± 0.08 | 1.047 ± 0.001 | 2.56 ± 0.08 |

3 | 1.054 ± 0.001 | 2.35 ± 0.20 | 1.053 ± 0.001 | 1.68 ± 0.08 | 1.051 ± 0.001 | 2.73 ± 0.10 |

4 | 1.050 ± 0.001 | 2.49 ± 0.17 | 1.047 ± 0.001 | 1.97 ± 0.09 | 1.054 ± 0.001 | 2.64 ± 0.07 |

5 | 1.047 ± 0.001 | 2.62 ± 0.12 | 1.045 ± 0.001 | 2.17 ± 0.12 | 1.042 ± 0.001 | 2.49 ± 0.09 |

6 | 1.051 ± 0.001 | 2.09 ± 0.08 | 1.050 ± 0.001 | 1.91 ± 0.10 | 1.052 ± 0.001 | 1.65 ± 0.05 |

7 | 1.050 ± 0.001 | 2.27 ± 0.09 | 1.051 ± 0.001 | 2.48 ± 0.11 | 1.049 ± 0.001 | 2.46 ± 0.09 |

8 | 1.047 ± 0.001 | 2.75 ± 0.10 | 1.047 ± 0.001 | 1.80 ± 0.07 | 1.050 ± 0.001 | 2.46 ± 0.08 |

9 | 1.050 ± 0.001 | 2.59 ± 0.14 | 1.049 ± 0.001 | 2.13 ± 0.09 | 1.048 ± 0.001 | 2.42 ± 0.08 |

10 | 1.047 ± 0.002 | 2.16 ± 0.12 | 1.050 ± 0.001 | 1.95 ± 0.16 | 1.048 ± 0.001 | 2.46 ± 0.17 |

_{BC}calculated on the basis of the analysis of 16–22 profile lines, mean values of pore relative area S

_{VP}based on 12 images of 25 cm

^{2}each.

Concrete Type | Equality Test for Average Values | |||
---|---|---|---|---|

in the Case of Compressive Strength f_{c} | in the Case of the Critical Stress Intensity Factor K_{Ic}^{S} | |||

The Value of the F Test | Limit Level of Significance of the Test | The Value of the F Test | Limit Level of Significance of the Test | |

no additives | 205.6 | close to 0 | 152.5 | close to 0 |

with MK | 436.3 | close to 0 | 60.2 | close to 0 |

with FA | 176.7 | close to 0 | 21.9 | 0.0003 |

with SF | 388.6 | close to 0 | 66.7 | close to 0 |

Water/binder ratio w/b | The value of the F test | Limit level of significance of the test | The value of the F test | Limit level of significance of the test |

all concretes | ||||

0.353 | 27.1 | close to 0 | 5.21 | 0.0156 |

0.445 | 6.64 | 0.0018 | 0.56 | 0.6486 |

0.537 | 6.57 | 0.0019 | 5.35 | 0.0142 |

only concretes with additives | ||||

0.353 | 5.41 | 0.0127 | 2.51 | 0.1364 |

0.445 | 1.28 | 0.3023 | 0.07 | 0.9328 |

0.537 | 5.11 | 0.0175 | 3.63 | 0.0698 |

N = 30 | Summary Regression of the Dependent Variable K_{Ic}^{S}R = 0.960, R ^{2} = 0.922F (2.27) = 159.68, p < 0.00000, Std. Error Estimation: 0.0625 | |||||
---|---|---|---|---|---|---|

b^{*} | Stand. Error b^{*} | b | Stand. Error b | t(27) | p | |

Absolute term | 20.161 | 6.3245 | 3.188 | 0.0036 | ||

w/b | −0.7854 | 0.0802 | −2.869 | 0.2929 | −9.797 | 0.0000 |

D_{BC} | −0.2202 | 0.0802 | −16.813 | 6.1224 | −2.746 | 0.0106 |

N = 30 | Summary Regression of the Dependent Variable D_{BC}R = 0.811, R ^{2} = 0.657F (2.27) = 25.870, p < 0.00000, Std. Error Estimation: 0.0017 | |||||
---|---|---|---|---|---|---|

b^{*} | Stand. Error b^{*} | b | Stand. Error b | t(27) | p | |

Absolute term | 1.088 | 0.0063 | 159.25 | 0.0000 | ||

AD/b | −0.3567 | 0.1129 | −0.026 | 0.0082 | −3.161 | 0.0039 |

V_{Paste} | 0.7470 | 0.1129 | 0.123 | 0.0185 | 6.620 | 0.0000 |

© 2019 by the author. 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Konkol, J.
Fracture Toughness and Fracture Surface Morphology of Concretes Modified with Selected Additives of Pozzolanic Properties. *Buildings* **2019**, *9*, 174.
https://doi.org/10.3390/buildings9080174

**AMA Style**

Konkol J.
Fracture Toughness and Fracture Surface Morphology of Concretes Modified with Selected Additives of Pozzolanic Properties. *Buildings*. 2019; 9(8):174.
https://doi.org/10.3390/buildings9080174

**Chicago/Turabian Style**

Konkol, Janusz.
2019. "Fracture Toughness and Fracture Surface Morphology of Concretes Modified with Selected Additives of Pozzolanic Properties" *Buildings* 9, no. 8: 174.
https://doi.org/10.3390/buildings9080174