# Experimental Study on the Fracture Parameters of Concrete

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## Abstract

**:**

_{F}) on the critical stress intensity factor (K

_{IC}), fracture energy (G

_{F}), the deflection at failure(δ

_{0}), the critical crack mouth opening displacement (CMOD

_{C}) and the critical crack tip opening displacement (CTOD

_{C}) were studied. Through the analysis of test phenomena and test data such as the load-deflection (P-δ) curve, load-crack mouth opening displacement (P-CMOD) curve and load-crack tip opening displacement (P-CTOD) curve, the following conclusions are drawn: with the increase of the steel fiber volume fraction, some fracture parameters increase gradually and maintain a certain linear growth. The gain ratio of the fracture parameters increases significantly, and the gain effect is obvious. Through this law of growth, the experimental statistical formulas of fracture energy and the critical stress intensity factor are summarized.

## 1. Introduction

_{F}) [1]. F. Bencardino et al. [1] reported that adding fibers to concrete has a major influence on the fracture property and ductility of the FRC. According to Doo-Yeol Yoo et al. [2], a steel fiber content of more than 1.0% can significantly improve the flexural strength, flexural capacity and fracture energy of concrete, and these factors will also increase with the increase of the steel fiber content. M.T. Kazemi et al. [15] studied the fracture properties of SFHSC and found that the fracture properties of SFHSC increased with the increase of the steel fiber content. The above studies show that the content of steel fibers has a significant effect on the properties of concrete.

_{F}-G

_{F}), as well as the volume fraction of steel fibers and the critical stress intensity factor (V

_{F}-K

_{IC}) are established, where R

^{2}= 0.97 and 0.99, respectively. This study can further promote the understanding and application of steel fiber reinforced concrete.

## 2. Summary of Test

#### 2.1. Materials

#### 2.2. Mix Design

_{F}, the water dosage increased by 8 kg. In order to eliminate the influence of the strength variation of the matrix concrete on the test results, at the time of pouring SFRC, the ordinary concrete (OC) specimens with the same mix proportion as SFRC but without steel fiber were used as control specimens. The mix proportion of SFRC specimen and control group concrete is shown in Table 1.

#### 2.3. Specimen Preparation Procedure

_{0}/l, was 0.4. The design strength grade of SFRC was FC30.

#### 2.4. The Three-Point Bending Test

#### 2.5. Calculation Formula of the Fracture Parameters

_{IC})

_{IC}calculation formula in ASTM E399-1972 is often used. The calculation formula of K

_{IC}is as follows:

_{max}is the measured maximum load (N), S is the span of beam (mm), b is the width of the sample(mm), h is the height of the sample (mm) and a is the actual crack length (mm). The virtual crack length is used in this paper.

_{F}) [12,18]

_{0}is the area under the load-deflection curve (N·m), m is the total mass of specimens between supports (kg), g is the gravitational constant (N/kg), δ

_{0}is the deflection at failure (mm), h is the height of the sample (mm), a

_{0}is the depth of the notch (mm) and b is the width of the sample (mm).

## 3. Test Results and Analysis

#### 3.1. Fracture Toughness

_{F}on K

_{IC}is shown in Figure 3. It can be seen, when compared with the reference group concrete, that the addition of steel fiber significantly improves the fracture toughness of SFRC. And with the increase of V

_{F}, the K

_{IC}of SFRC specimens show a good increasing trend. For every 0.5% increase in the fiber fraction, the average increase in K

_{IC}is 33.7%. The K

_{IC}gain ratio of V

_{F}to SFRC can be seen in Table 2: with the addition of steel fiber, the K

_{IC}gain ratio of SFRC specimens is greater than 1, and with the increase of V

_{F}, the gain ratio shows a good increasing trend, the minimum gain ratio is 1.43, the maximum gain ratio is 3.45 and the average gain ratio is 2.275. Therefore, it can be considered that the addition of steel fiber improves the K

_{IC}of concrete.

^{2}= 0.9748. It can be seen that the increase of K

_{IC}is mainly affected by V

_{F}.

_{F}are compared, as shown in Figure 4 and Figure 5.

_{F}, the crack propagation path becomes more tortuous. Except for a small number of SFRC specimens with small content, some specimens were split in half, but most of the them were not completely split, which kept the integrity to a certain extent. On the other hand, the K

_{IC}of the ordinary concrete of the reference group and control group was small, and the bearing capacity of the specimens decreased rapidly after the test load reached the peak, which led to most of the specimens splitting into two parts. It can be judged that the addition of steel fiber greatly improves the fracture toughness of SFRC.

#### 3.2. Fracture Energy

_{F}on the G

_{F}of SFRC. It can be seen, compared with the reference group concrete, that the addition of steel fiber greatly improves the fracture energy of concrete matrix, and with the increase of V

_{F}, G

_{F}keeps an obvious linear increasing trend. For every 0.5 percentage point increase in V

_{F}, G

_{F}increases between 30.53% and 71.14%, with an average increase of 47.22%. It can be seen from Table 2 that, compared with the control group concrete, the G

_{F}gain ratio of SFRC specimens is between 5.88 and 20.52, and that the average gain ratio is 12.88. It can thus be seen that the addition of steel fiber greatly improves the energy absorption capacity of the concrete matrix.

_{IC}in this paper, the statistical analysis shows that:

^{2}= 0.9966. It can be seen that the increase of G

_{F}is mainly affected by V

_{F}.

_{F}conditions.

_{F}, the number of fibers across the cracks increases accordingly, and the ability to transfer stress is also relatively improved. The microcracks in the fracture process zone develop fully, and the absorbed external load energy increases accordingly, which is characterized by the increase of the peak load and ultimate deflection of the specimen. The test curve becomes fuller and the improvement of fracture performance is more sufficient.

#### 3.3. Crack Opening Displacement

_{C}and CTOD

_{C}of matrix concrete, and that with the increase of V

_{F}, CMOD

_{C}increases linearly, and the deflection corresponding to CMOD

_{C}also increases obviously.

## 4. Conclusions

- The addition of steel fiber to concrete can obviously improve the fracture toughness of concrete. With the increase of V
_{F}, the K_{IC}of SFRC specimens showed a good increasing trend. For every 0.5% increase in the fiber volume rate, the average increase of K_{IC}is 33.7%, and the average gain ratio is 2.275. - Adding steel fiber to concrete can obviously improve the fracture energy of concrete. With the increase of V
_{F}, the G_{F}and G_{F}gain ratio of SFRC specimens showed a good increasing trend. In the range of V_{F}, for every 0.5% increase of V_{F}, the average gain ratio of G_{F}is 47.22%, the average gain ratio is between 5.88 and 20.52, and the average gain ratio is 12.88. - With the addition of steel fiber, the peak loads, the deflection at failure and the critical crack opening displacement of concrete specimens increased.
- Two test statistical equations of V
_{F}-G_{F}and V_{F}-K_{IC}are established, where R^{2}= 0.97 and 0.99, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Mix No | Cement (kg/m^{3}) | Water (kg/m^{3}) | Sand (kg/m^{3}) | Stone (kg/m^{3}) | FDN-1 (kg/m^{3}) | Steel Fiber Content (kg/m^{3}) |
---|---|---|---|---|---|---|

MF00 | 341.7 | 164.0 | 661.1 | 1283.3 | 3.42 | 0.0 |

MF05 | 358.3 | 172.0 | 748.7 | 1171.0 | 3.58 | 39.3 |

MF05-0 | 358.3 | 172.0 | 748.7 | 1171.0 | 3.58 | 0.0 |

MF10 | 375.0 | 180.0 | 795.9 | 1099.1 | 3.75 | 78.6 |

MF10-0 | 375.0 | 180.0 | 795.9 | 1099.1 | 3.75 | 0.0 |

MF15 | 391.7 | 188.0 | 841.7 | 1028.7 | 3.92 | 117.9 |

MF15-0 | 391.7 | 188.0 | 841.7 | 1028.7 | 3.92 | 0.0 |

MF20 | 408.3 | 196.0 | 885.9 | 959.7 | 4.08 | 157.2 |

MF20-0 | 408.3 | 196.0 | 885.9 | 959.7 | 4.08 | 0.0 |

_{F}= 1.5% milling steel fiber reinforced concrete specimens. MF00 is the reference group of concrete specimens.

Mix No. | V_{F} (%) | P_{max} (kN) | K_{IC} MPa·m^{1/2} | K_{IC} Gain Ratio | G_{F} (N·m ^{−1}) | G_{F} Gain Ratio | CMOD_{C} (mm) | CTOD_{C} (mm) | δ_{0} (mm) |
---|---|---|---|---|---|---|---|---|---|

MF00 | 0.0 | 3.1802 | 1.7006 | - | 181.410 | - | 0.0618 | 0.0324 | 0.0893 |

MF05 | 0.5 | 3.3151 | 2.2146 | 1.43 | 1043.8433 | 5.88 | 0.0997 | 0.0566 | 0.1203 |

MF05-0 | 0.0 | 2.7759 | 1.5493 | - | 177.3862 | - | 0.0645 | 0.0397 | 0.1068 |

MF10 | 1.0 | 3.6335 | 2.9164 | 1.84 | 1786.4485 | 9.86 | 0.1739 | 0.0996 | 0.1894 |

MF10-0 | 0.0 | 2.8952 | 1.5884 | - | 181.1768 | - | 0.0656 | 0.0377 | 0.1076 |

MF15 | 1.5 | 4.6427 | 4.3073 | 2.38 | 2331.9664 | 15.27 | 0.2638 | 0.1446 | 0.3450 |

MF15-0 | 0.0 | 2.9000 | 1.8067 | - | 152.7245 | - | 0.0789 | 0.0330 | 0.0831 |

MF20 | 2.0 | 6.1080 | 5.3880 | 3.45 | 3264.4605 | 20.52 | 0.3060 | 0.1692 | 0.3941 |

MF20-0 | 0.0 | 2.7034 | 1.5616 | - | 159.0965 | - | 0.0629 | 0.0326 | 0.0807 |

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**MDPI and ACS Style**

Wang, Z.; Gou, J.; Gao, D. Experimental Study on the Fracture Parameters of Concrete. *Materials* **2021**, *14*, 129.
https://doi.org/10.3390/ma14010129

**AMA Style**

Wang Z, Gou J, Gao D. Experimental Study on the Fracture Parameters of Concrete. *Materials*. 2021; 14(1):129.
https://doi.org/10.3390/ma14010129

**Chicago/Turabian Style**

Wang, Zhanqiao, Jin Gou, and Danying Gao. 2021. "Experimental Study on the Fracture Parameters of Concrete" *Materials* 14, no. 1: 129.
https://doi.org/10.3390/ma14010129