# Research and Statistical Analysis on Impact Resistance of Steel Fiber Expanded Polystyrene Concrete and Expanded Polystyrene Concrete

^{1}

^{2}

^{*}

## Abstract

**:**

_{eps}), and steel fiber expanded polystyrene concrete (SFEPSC) specimens by adding 1% steel fiber (SF) based on the EPSC in this study. The relationship between compressive strength, the V

_{eps}and apparent density was revealed. The relationship between the first crack and the ultimate failure impact of SFEPSC specimens was obtained by a drop-weight test. The impact resistance of SFEPSC and EPSC and the variation law of V

_{eps}were studied by mathematical statistics. The log-normal and the two-parameter Weibull distributions were used to fit the probability distribution of impact resistance of the SFEPSC and EPSC specimens. Finally, both types of specimens’ destruction modes and mechanisms were analyzed. The mechanism of the EPS particles and the SFs dissipating impact load energy was analyzed from the energy point of view.

## 1. Introduction

_{eps}= 10%, 20%, 30%, 40% and 50%) were designed and marked as S0E10, S0E20, S0E30, S0E40, S0E50. Based on the EPSC, the SFEPSC specimens were prepared by adding 1% SF by volume, marked as S1E10, S1E20, S1E30, S1E40, and S1E50. A drop-weight test statistically analyzed the impact test results of SFEPSC and EPSC. The fatigue damage characteristics and energy dissipation mechanism of two types of concrete materials were also analyzed.

## 2. Experimental

#### 2.1. Materials and Mix Proportions

^{3}, and the diameter is 3–5 mm. Figure 1 shows the diameter gradation of the EPS particles used in the experiment. Corrugated steel fiber (SF) shown in Figure 2 was made of cold-rolled strip steel through a shearing and scoring process, which has high tensile strength, easy dispersion and good adhesion to concrete. The SF has a density of 7810 kg/m

^{3}, a length of 48 mm, and an aspect ratio (length of SF/diameter or width of SF) of 24. The tensile strength was 610 MPa.

^{3}and a medium sand fineness modulus of 2.73. The usage amount was 30% of the aggregate mass. The coarse aggregate (CA) was limestone, and its physical properties are shown in Table 2. Polycarboxylate superplasticizer (PS) was used, for which the water (W) reduction rate was 20–30%.

_{cu}) of the basis mix proportion marked S0E0 was 48.7 MPa (28-d). The specimen type number and mix proportion of SFEPSC and EPSC are shown in Table 3.

#### 2.2. The Influence of V_{eps} and Apparent Density on Compressive Strength

_{eps}and the apparent density of SFEPSC and EPSC. It can be seen in Figure 4 that: (1) the apparent density of two types of concrete decreases linearly with the increase in V

_{eps}, as shown in Figure 4a. The apparent density of SFEPSC decreases 4.9% faster than the apparent density of EPSC, and the compressive strength shows a quadratic curve decreasing trend with the increase in V

_{eps}shown in Figure 4b. (2) The compressive strength of both concrete specimens increases with the apparent density, as shown in Figure 4c. The compressive strength of SFEPSC increases at a slower rate than EPSC when the apparent density is less than 1250 kg/m

^{3}. When the apparent density is more than 1250 kg/m

^{3}, the compressive strength increase rate is opposite to that of less than 1250 kg/m

^{3}. (3) The compressive strength of SFEPSC at V

_{eps}equal to 10%, 20%, 30%, 40% and 50% are 49.1 MPa, 44.2 Mpa, 37.9 Mpa, 26.5 Mpa and 16.6 Mpa, as shown in Figure 4c. The apparent density is 95%, 84%, 75%, 65% and 55% of S0E0. The compressive strength of EPSC at V

_{eps}equal to 10%, 20%, 30%, 40% and 50% are 46.7 MPa, 41.3 MPa, 33.4 MPa, 19.8 MPa and 12.1 MPa. The apparent density is 90%, 80%, 71%, 61% and 51% of S0E0. The above results showed that the compressive strength of SFEPSC can be higher than S0E0 when the V

_{eps}is equal to 10%.

#### 2.3. Drop-Weight Test Device and Test Method

_{1}) of first-crack impact resistance in blows was recorded when the first visible crack appeared on the specimen. Impacts continued to occur until the specimen touched three baffles, and the number (N

_{2}) of the ultimate failure impact resistance in blows was recorded, along with the difference number (ΔN) of impacts between the first crack (N

_{1}) and the ultimate failure number (N

_{2}).

#### 2.4. Test Results and Statistical Analysis

_{1}, N

_{2}, and ΔN of SFEPSC and EPSC in the drop-weight test. About 70% of total EPSC specimens were completely destroyed at the first visible crack, and about 30% could bear the load before the first visible crack. The specimen impact resistance of V

_{eps}= 50% was about twice that of V

_{eps}= 10%.

_{1}, N

_{2}and ΔN were higher than EPSC. The SFEPSC specimen, in which the V

_{eps}was 20%, could still bear the highest load capacity after the first-crack impact, and the average impact resistance was up to 6.7 times greater than S0E20. The above showed that the overall impact resistance of SFEPSC is higher than EPSC.

_{2}= a × N

_{1}+ b

_{1}and N

_{2}, as shown in Figure 6 and Table 5. If we exclude the data (101/109) of S1E10 in Table 4, then the R

^{2}=0.8717 becomes R

^{2}= 0.9105. Therefore, the R

^{2}=0.8717 can still be used to describe the set of S1E10 specimens. Due to the small amount of EPSC specimen data, the linear relationship could not be well represented. If the data of the EPSC specimens was large enough, their functional relationship could be fully shown. For example, S0E30 and S0E50 both have linear functional relationships.

_{1}and N

_{2}shows volatility, which is less than 22.8%, as shown in Table 6. It can be seen that both N

_{1}and N

_{2}of SFEPSC are inversely proportional to the V

_{eps}when V

_{eps}< 30%. The SF and concrete together bear a large amount of load because of the small V

_{eps}, and the specimen showed larger SFC discrete features [29,30]. The fluctuation range of N

_{1}and N

_{2}of SFEPSC becomes smaller when V

_{eps}≥ 30%, and the overall fluctuation is stable at a constant value. The specimen shows a significant buffering effect at a big V

_{eps}.

_{eps}is less than 30%, the number of impacts of EPSC is inversely proportional to V

_{eps}. When V

_{eps}is more than 30%, the fluctuation range of the impact number of EPSC decreases, and the overall value tends to be a constant value. The EPSC has the highest impact resistance at V

_{eps}= 30%.

_{eps}, and the stability of impact resistance of SFEPSC is better than that of EPSC.

## 3. Probability Distribution Characteristics

#### 3.1. Log-Normal Distribution

_{(1)}≤ x

_{(2)}≤ … ≤ x

_{(n)}, where x

_{(i)}is called the i order statistic of specimen subset, which is a function of the specimen subset and also a random variable. Called the substandard i (i = 1, 2, …, n) of x

_{(i)}, the rank or order number of ${x}_{\left(i\right)}$. When the observations are equal, the average value of the substandard i is regarded as the rank of these observations. The first-order statistic x

_{(i)}of the specimen subset is the minimum value, and the end order statistic x

_{(i)}of the specimen subset is the maximum value. F

_{n}is written as:

_{n}(x) is the empirical distribution function. According to Bernoulli’s law of large numbers, F

_{n}(x) is almost close to F(x) when n is large enough. If (x, F

_{n}(x)) is drawn in the coordinate system, it should be close to a linear function. The linear relational expression is

#### 3.2. Weibull Distribution

_{1}and N

_{2}of SFEPSC can be described by the log-normal distribution and the Weibull distribution, as shown in Table 7 and Table 9. Since there were fewer EPSC specimens available for complete failure at the first visible crack (N

_{1}), only the distribution study of the N

_{1}of EPSC was carried out. The results show that the N

_{1}of EPSC can be described by two distributions (Figure 10 and Figure 12, Table 8 and Table 10).

#### 3.3. Curve of SFEPSC and EPSC Impact Resistance

_{1}and N

_{2}.

_{eps}− lgN

_{1}curve [31,35] of the impact resistance of SFEPSC and EPSC, as shown in Figure 13 and Figure 14, according to the data in Table 11. The numbers of the first crack of SFEPSC and EPSC and the V

_{eps}are shown in a conic relationship under different failure probabilities, and the concavity and convexity of the conic relationship are different. The curve normalized fitting is shown in formula (11), and the coefficients m, n and l are shown in Table 12.

## 4. Destruction Mode and Energy Consumption Mechanism

#### 4.1. Destruction Mode

_{eps}< 30%, as shown in Figure 17a. The pit on the specimen surface deepens when V

_{eps}≥ 30% and its failure surface becomes relatively rough, as shown in Figure 17b,c. The SFEPSC specimens are broken with deep pits, as shown in Figure 16. The fragments of the specimen are connected by SFs, and the failure surfaces are relatively rough, as shown in Figure 18. The pit on the surface of the specimen is relatively shallow when the V

_{eps}< 30%, and there are randomly distributed SF connections on the pit surface. The specimen surface was locally squeezed, large deformation occurred, and the SF bounced away. The specimen was dented and destroyed along the direction of force contact surface gradually transferred to the transmission direction, and the pit depth increased with increasing V

_{eps}.

_{eps}. The overall specimen stiffness was small, and the pit was deeper at a large V

_{eps}. The SF effectively connected EPSC fragments to improve their impact resistance, which was consistent with the role of SF in normal concrete.

#### 4.2. Energy Consumption Mechanism

_{eps}was larger, the local absorbed load was higher than the energy transferred from the pit to its surroundings. The larger the volume of EPS in the range of 10~50%, the better cushioning effect it had under impact. The impact force on the specimen bottom was small, and finally, the specimen’s partial damage led to overall damage.

## 5. Conclusions

_{eps}was between 10% and 50%, and the following conclusions could be drawn:

- The apparent density of the two types of concrete specimens had a linear relationship with V
_{eps}and compressive strength. The compressive strength had a quadratic relationship with V_{eps}. The apparent density and compressive strength of SFEPSC were higher than EPSC at the same volume of EPS; - By adding SF to EPSC, the impact resistance of SFEPSC was higher than EPSC. It had a highly linear relationship between the first visible crack, N
_{1}, and the ultimate failure, N_{2}, and S1E20 had the best impact resistance; - The log-normal distribution and the two-parameter Weibull distribution could better describe the impact resistance of the first visible crack and the ultimate failure of SFEPSC and the EPSC at the first visible crack;
- Under different failure probabilities, the impact resistance of SFEPSC had a concave quadratic relationship with V
_{eps}, while EPSC had a convex quadratic relationship. The impact resistance of both types could be tested and predicted by the P − V_{eps}− lgN curve; - The failure modes of the two types of concrete specimens were different. By adding SF, the pits of EPSC specimens became deepened before splitting. The pit depth of both specimens increased with the increase in V
_{eps}, and the fractures were relatively rough; - The energy consumption mechanism of both types of concrete specimens was different. EPSC dissipated shock loads by the EPS particles. By adding SF to EPSC, especially after the first cracking of the specimen, the SF energy absorption and friction energy dissipation characteristics were more obvious.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**The relationship between compressive strength, the V

_{eps}and apparent density of SFEPSC and EPSC: (

**a**) relationship between apparent density and V

_{eps}; (

**b**) relationship between compressive strength and V

_{eps}; (

**c**) relationship between compressive strength and apparent density.

**Figure 6.**Scatter diagram of impact data with fitted regression line for SFEPSC and EPSC: (

**a**) S1E20; (

**b**) S0E30.

**Figure 15.**Destruction mode of EPSC specimens: (

**a**) S0E10; (

**b**) S0E20; (

**c**) S0E30; (

**d**) S0E40; (

**e**) S0E50.

**Figure 16.**Destruction mode of SFEPSC specimens: (

**a**) S1E10; (

**b**) S1E20; (

**c**) S1E30; (

**d**) S1E40; (

**e**) S1E50.

**Figure 18.**S1E20 failure mode: (

**a**) A-1 and A-2 of the major specimen are the SF and SF hole, respectively; (

**b**) the A-1 and A-2 of crushed specimen block are the SF hole and SF, respectively.

Oxide | SiO_{2} | Al_{2}O_{3} | Fe_{2}O_{3} | CaO | MgO | Na_{2}O | K_{2}O | SO_{3} | NaO | Loss |
---|---|---|---|---|---|---|---|---|---|---|

PC (%) | 21.60 | 4.13 | 4.72 | 64.44 | 2.06 | 0.11 | 0.56 | 0.74 | - | 1.64 |

Ms (%) | 94.43 | 0.93 | 0.97 | 0.28 | 0.77 | - | - | - | 1.39 | 1.23 |

Particle Size/mm | Apparent Density | Bulk Density | Mud Content | Crush Index/% |
---|---|---|---|---|

<10 | 2490 | 1370 | 0.57 | 7.9 |

Type | W/B | W (kg) | Binders (kg) | FA (kg) | CA (kg) | PS (kg) | SF (%) | EPS (kg) | Slump (mm) | ρ_{d}(kg/m ^{3}) | |
---|---|---|---|---|---|---|---|---|---|---|---|

PC | Ms | ||||||||||

S0E0 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | - | - | 115 | 1568 |

S1E10 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | 78.5 | 2.8 | 71 | 1495 |

S1E20 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | 78.5 | 3.1 | 84 | 1320 |

S1E30 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | 78.5 | 10.7 | 98 | 1174 |

S1E40 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | 78.5 | 16.7 | 117 | 1016 |

S1E50 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | 78.5 | 25 | 124 | 857 |

S0E10 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | - | 2.8 | 110 | 1413 |

S0E20 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | - | 3.1 | 116 | 1257 |

S0E30 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | - | 10.7 | 123 | 1115 |

S0E40 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | - | 16.7 | 129 | 958 |

S0E50 | 0.44 | 238.2 | 487.2 | 54.1 | 230 | 536 | 2.8 | - | 25 | 135 | 805 |

Number | N_{1}/N_{2} | ΔN | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

S1E10 | S1E20 | S1E30 | S1E40 | S1E50 | S1E10 | S1E20 | S1E30 | S1E40 | S1E50 | |

1 | 36/52 | 24/42 | 57/66 | 62/69 | 61/75 | 16 | 18 | 9 | 7 | 14 |

2 | 20/22 | 38/57 | 21/28 | 75/83 | 34/43 | 2 | 19 | 7 | 8 | 9 |

3 | 49/78 | 13/28 | 39/48 | 10/19 | 33/41 | 29 | 15 | 9 | 9 | 8 |

4 | 28/59 | 21/52 | 60/68 | 54/59 | 80/91 | 31 | 31 | 8 | 5 | 11 |

5 | 101/109 | 59/73 | 23/34 | 41/48 | 37/42 | 8 | 14 | 11 | 7 | 5 |

6 | 34/40 | 97/104 | 41/50 | 89/98 | 51/60 | 6 | 7 | 9 | 9 | 9 |

7 | 69/79 | 57/83 | 33/45 | 66/69 | 62/73 | 10 | 26 | 12 | 3 | 11 |

8 | 60/84 | 44/61 | 25/33 | 50/61 | 47/55 | 24 | 17 | 8 | 11 | 8 |

9 | 39/54 | 47/59 | 69/77 | 58/64 | 31/43 | 15 | 12 | 8 | 6 | 12 |

10 | 69/84 | 63/79 | 27/33 | 43/55 | 36/44 | 15 | 16 | 6 | 12 | 8 |

11 | 82/97 | 57/66 | 87/96 | 17/24 | 34/42 | 15 | 9 | 20 | 7 | 8 |

12 | 57/69 | 51/59 | 32/41 | 43/52 | 34/41 | 12 | 8 | 9 | 9 | 7 |

Number | S0E10 | S0E20 | S0E30 | S0E40 | S0E50 | S0E10 | S0E20 | S0E30 | S0E40 | S0E50 |

1 | 21/22 | 16/17 | 3 | 3 | 9/12 | 1 | 1 | 0 | 0 | 3 |

2 | 2 | 3 | 6 | 5 | 12/15 | 0 | 0 | 0 | 0 | 3 |

3 | 3 | 4 | 6 | 5 | 7 | 0 | 0 | 0 | 0 | 0 |

4 | 2 | 6 | 7/8 | 6 | 7 | 0 | 0 | 1 | 0 | 0 |

5 | 4 | 7/8 | 7 | 15/17 | 9 | 0 | 1 | 0 | 2 | 0 |

6 | 6 | 7/8 | 17/18 | 7 | 13/15 | 0 | 1 | 1 | 0 | 2 |

7 | 6 | 7/9 | 9 | 8 | 11/12 | 0 | 2 | 0 | 0 | 1 |

8 | 11/12 | 10/11 | 11/12 | 8 | 8/9 | 1 | 1 | 1 | 0 | 1 |

9 | 3 | 9 | 13/15 | 10/12 | 8 | 0 | 0 | 2 | 2 | 0 |

10 | 4 | 6/7 | 7 | 7 | 7 | 0 | 1 | 0 | 0 | 0 |

11 | 2 | 4 | 2 | 5 | 4 | 0 | 0 | 0 | 0 | 0 |

12 | 5 | 6 | 24/25 | 9/10 | 6 | 0 | 0 | 1 | 1 | 0 |

_{1}.

Specimen Type | Rank | a | b | R^{2} |
---|---|---|---|---|

S1E10 | 12 | 0.9619 | 17.297 | 0.8717 |

S1E20 | 12 | 0.8368 | 23.767 | 0.9056 |

S1E30 | 12 | 0.9993 | 8.7812 | 0.9941 |

S1E40 | 12 | 0.9796 | 8.7839 | 0.9876 |

S1E50 | 12 | 1.085 | 5.3405 | 0.9854 |

S0E10 | 2 | / | / | / |

S0E20 | 6 | 0.5589 | 4.3181 | 0.4356 * |

S0E30 | 5 | 0.9916 | 1.3206 | 0.9952 |

S0E40 | 3 | / | / | / |

S0E50 | 5 | 1.1163 | 0.7674 | 0.8505 |

^{2}= coefficient of determination. * Low precision, not included in analysis.

Statistical Parameters | N_{1}/N_{2} | ΔN | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

S1E10 | S1E20 | S1E30 | S1E40 | S1E5`0 | S1E10 | S1E20 | S1E30 | S1E40 | S1E50 | |

Rank | 12/12 | 12/12 | 12/12 | 12/12 | 12/12 | 12 | 12 | 12 | 12 | 12 |

$\overline{x}$ | 54/69 | 48/64 | 43/53 | 51/58 | 45/54 | 15 | 16 | 10 | 7 | 9 |

σ | 24/25 | 22/20 | 21/21 | 22/22 | 16/17 | 9 | 7 | 4 | 3 | 2 |

COV% | 44/36 | 45/31 | 49/39 | 43/38 | 35/31 | 60 | 44 | 40 | 43 | 22 |

S0E10 | S0E20 | S0E30 | S0E40 | S0E50 | S0E10 | S0E20 | S0E30 | S0E40 | S0E50 | |

Rank | 12/2 | 12/6 | 12/5 | 12/3 | 12/5 | 2 | 6 | 5 | 3 | 5 |

$\overline{x}$ | 6/17 | 8/10 | 9/20 | 7/13 | 8/13 | 3 | 3 | 2 | 4 | 3 |

σ | 5/7 | 4/4 | 6/6 | 3/4 | 3/3 | 0.4 ^{┌} | 0.7 ^{┌} | 0.7 ^{┌} | 0.8 ^{┌} | 1.2 ^{┌} |

COV% | 83/41 | 50/40 | 66/30 | 43/31 | 38/23 | 13 | 23 | 35 | 20 | 40 |

^{┌}Qualitative analysis by score.

Blows | Specimen Type | Rank | α_{1} | β_{1} | R^{2} |
---|---|---|---|---|---|

N_{1} | S1E10 | 12 | 1.7699 | 6.8763 | 0.981 |

S1E20 | 12 | 1.4526 | 5.4318 | 0.9044 | |

S1E30 | 12 | 1.8015 | 6.5863 | 0.9672 | |

S1E40 | 12 | 1.2228 | 4.6319 | 0.8114 | |

S1E50 | 12 | 2.536 | 9.5326 | 0.8723 | |

N_{2} | S1E10 | 12 | 1.8087 | 7.5191 | 0.8802 |

S1E20 | 12 | 2.4043 | 9.8664 | 0.9202 | |

S1E30 | 12 | 2.1558 | 8.3488 | 0.9657 | |

S1E40 | 12 | 1.6411 | 6.5333 | 0.8409 | |

S1E50 | 12 | 2.711 | 10.715 | 0.8253 | |

ΔN | S1E10 | 12 | 1.0574 | 2.6636 | 0.8838 |

S1E20 | 12 | 1.8639 | 4.9994 | 0.9736 | |

S1E30 | 12 | 2.5355 | 5.6296 | 0.8299 | |

S1E40 | 12 | 2.1484 | 4.2773 | 0.8922 | |

S1E50 | 12 | 2.9983 | 6.5431 | 0.9297 |

Blows | Specimen Type | Rank | α_{1} | β_{1} | R^{2} |
---|---|---|---|---|---|

N_{1} | S0E10 | 12 | 1.1292 | 1.6642 | 0.9114 |

S0E20 | 12 | 1.631 | 3.1423 | 0.9615 | |

S0E30 | 12 | 1.2035 | 2.4456 | 0.9503 | |

S0E40 | 12 | 2.0013 | 3.832 | 0.9480 | |

S0E50 | 12 | 2.5494 | 5.3148 | 0.9392 | |

N_{2} | S0E10 | 2 | / | / | / |

S0E20 | 6 | 1.3246 | 3.6669 | 0.7554 * | |

S0E30 | 5 | 1.0304 | 3.5533 | 0.9871 | |

S0E40 | 3 | / | / | / | |

S0E50 | 5 | 2.0239 | 5.8892 | 0.9199 | |

ΔN | S0E10 | 2 | / | / | / |

S0E20 | 6 | 1.2931 | 0.5297 | 0.5594 * | |

S0E30 | 5 | 1.1369 | 0.638 | 0.6292 * | |

S0E40 | 3 | / | / | / | |

S0E50 | 5 | 0.734 | 0.3714 | 0.8348 * |

Blows | Specimen Type | Rank | α_{2} | β_{2} | R^{2} |
---|---|---|---|---|---|

N_{1} | S1E10 | 12 | 2.1463 | 8.8421 | 0.9895 |

S1E20 | 12 | 1.8045 | 7.2513 | 0.9538 | |

S1E30 | 12 | 2.1105 | 8.2194 | 0.9071 | |

S1E40 | 12 | 1.5533 | 6.3873 | 0.8947 | |

S1E50 | 12 | 2.8833 | 11.341 | 0.7705 | |

N_{2} | S1E10 | 12 | 2.2727 | 9.9512 | 0.9497 |

S1E20 | 12 | 2.9517 | 12.638 | 0.9512 | |

S1E30 | 12 | 2.5281 | 10.294 | 0.9075 | |

S1E40 | 12 | 2.0628 | 8.7153 | 0.9078 | |

S1E50 | 12 | 3.0452 | 12.54 | 0.7116 | |

ΔN | S1E10 | 12 | 1.3215 | 3.8322 | 0.9432 |

S1E20 | 12 | 2.2399 | 6.5114 | 0.9609 | |

S1E30 | 12 | 2.9144 | 6.9744 | 0.7493 | |

S1E40 | 12 | 2.677 | 5.8332 | 0.9467 | |

S1E50 | 12 | 3.6184 | 8.3999 | 0.9254 |

Blows | Specimen Type | Rank | α_{2} | β_{2} | R^{2} |
---|---|---|---|---|---|

N_{1} | S0E10 | 12 | 1.297 | 2.4149 | 0.8217 |

S0E20 | 12 | 1.9356 | 4.2325 | 0.9254 | |

S0E30 | 12 | 1.4566 | 3.4633 | 0.9513 | |

S0E40 | 12 | 2.4008 | 5.1005 | 0.9323 | |

S0E50 | 12 | 3.1015 | 6.9694 | 0.9499 | |

N_{2} | S0E10 | 2 | / | / | / |

S0E20 | 6 | 1.9619 | 5.7343 | 0.6989 * | |

S0E30 | 5 | 1.6363 | 5.8544 | 0.9769 | |

S0E40 | 3 | / | / | / | |

S0E50 | 5 | 3.2481 | 9.6494 | 0.9298 | |

ΔN | S0E10 | 2 | / | / | / |

S0E20 | 6 | 2.1052 | 1.066 | 0.6252 * | |

S0E30 | 5 | 1.8973 | 1.2126 | 0.6851 * | |

S0E40 | 3 | / | / | / | |

S0E50 | 5 | 1.1474 | 0.8118 | 0.8007 * |

Blows | Failure Probability | Log-Normal Distribution | Weibull Distribution | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

S1E10 | S1E20 | S1E30 | S1E40 | S1E50 | S1E10 | S1E20 | S1E30 | S1E40 | S1E50 | ||

N_{1} | 0.05 | 19 | 14 | 16 | 12 | 22 | 9 | 5 | 7 | 4 | 13 |

0.10 | 24 | 17 | 19 | 15 | 26 | 14 | 9 | 11 | 7 | 18 | |

0.15 | 27 | 20 | 22 | 19 | 29 | 17 | 12 | 14 | 10 | 21 | |

0.20 | 30 | 24 | 24 | 22 | 31 | 21 | 15 | 17 | 13 | 24 | |

0.25 | 33 | 26 | 27 | 25 | 33 | 24 | 18 | 19 | 16 | 26 | |

0.30 | 36 | 29 | 29 | 29 | 35 | 27 | 21 | 22 | 19 | 29 | |

N_{2} | 0.05 | 26 | 31 | 22 | 20 | 28 | 12 | 17 | 12 | 9 | 17 |

0.10 | 31 | 36 | 27 | 25 | 32 | 18 | 24 | 17 | 14 | 23 | |

0.15 | 36 | 39 | 30 | 28 | 36 | 23 | 28 | 21 | 18 | 27 | |

0.20 | 40 | 43 | 33 | 32 | 38 | 28 | 32 | 24 | 21 | 30 | |

0.25 | 44 | 46 | 35 | 36 | 41 | 32 | 36 | 27 | 25 | 33 | |

0.30 | 48 | 49 | 38 | 39 | 43 | 36 | 39 | 30 | 29 | 36 | |

S0E10 | S0E20 | S0E30 | S0E40 | S0E50 | S0E10 | S0E20 | S0E30 | S0E40 | S0E50 | ||

N_{1} | 0.05 | 1.8 | 3.8 | 3.5 | 4.2 | 5.6 | 0.7 | 1.9 | 1.4 | 2.4 | 3.6 |

0.10 | 2.4 | 4.6 | 4.5 | 4.9 | 6.3 | 1.1 | 2.8 | 2.3 | 3.3 | 4.6 | |

0.15 | 2.9 | 5.2 | 5.3 | 5.4 | 6.8 | 1.6 | 3.5 | 3.1 | 3.9 | 5.3 | |

0.20 | 3.4 | 5.8 | 6.0 | 5.9 | 7.2 | 2.0 | 4.1 | 3.8 | 4.5 | 5.8 | |

0.25 | 3.8 | 6.3 | 6.8 | 6.3 | 7.6 | 2.5 | 4.7 | 4.6 | 5.0 | 6.3 | |

0.30 | 4.3 | 6.8 | 7.5 | 6.7 | 8 | 2.9 | 5.2 | 5.3 | 5.4 | 6.8 |

Concrete Type | P | Log-Normal Distribution | Weibull Distribution | |||||||
---|---|---|---|---|---|---|---|---|---|---|

m | n | l | R^{2} | m | n | l | R^{2} | |||

SFEPSC | 0.05 | 4.9524 | 2.9085 | 1.5316 | 0.7469 | 7.8211 | 4.5077 | 1.3480 | 0.6315 | |

0.10 | 4.1660 | 2.4702 | 1.5819 | 0.8143 | 6.2630 | 3.6392 | 1.4477 | 0.6781 | ||

0.15 | 3.6355 | 2.1744 | 1.6158 | 0.8785 | 5.3249 | 3.1162 | 1.5077 | 0.7231 | ||

0.20 | 3.2138 | 1.9393 | 1.6428 | 0.8943 | 4.6387 | 2.7337 | 1.5516 | 0.7706 | ||

0.25 | 2.8520 | 1.7377 | 1.6659 | 0.9259 | 4.0889 | 2.4271 | 1.5868 | 0.8226 | ||

0.30 | 2.5272 | 1.5566 | 1.6867 | 0.9789 | 3.6236 | 2.1678 | 1.6116 | 0.9001 | ||

EPSC | 0.05 | −2.0230 | −2.2338 | 0.1027 | 0.8428 | −1.5322 | −2.5134 | −0.3475 | 0.8159 | |

0.10 | −2.1575 | −2.1571 | 0.2261 | 0.8940 | −1.7988 | −2.3615 | −0.1030 | 0.8801 | ||

0.15 | −2.2482 | −2.1054 | 0.3093 | 0.9179 | −1.9592 | −2.2701 | 0.0442 | 0.9194 | ||

0.20 | −2.3204 | −2.0643 | 0.3755 | 0.9436 | −2.0766 | −2.2032 | 0.1519 | 0.9453 | ||

0.25 | −2.3822 | −2.0290 | 0.4323 | 0.9348 | −2.1707 | −2.1496 | 0.2382 | 0.9482 | ||

0.30 | −2.4378 | −1.9974 | 0.4833 | 0.9208 | −2.2503 | −2.1042 | 0.3112 | 0.9479 |

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## Share and Cite

**MDPI and ACS Style**

Huo, W.; Zhang, S.
Research and Statistical Analysis on Impact Resistance of Steel Fiber Expanded Polystyrene Concrete and Expanded Polystyrene Concrete. *Materials* **2022**, *15*, 4216.
https://doi.org/10.3390/ma15124216

**AMA Style**

Huo W, Zhang S.
Research and Statistical Analysis on Impact Resistance of Steel Fiber Expanded Polystyrene Concrete and Expanded Polystyrene Concrete. *Materials*. 2022; 15(12):4216.
https://doi.org/10.3390/ma15124216

**Chicago/Turabian Style**

Huo, Wenlong, and Sherong Zhang.
2022. "Research and Statistical Analysis on Impact Resistance of Steel Fiber Expanded Polystyrene Concrete and Expanded Polystyrene Concrete" *Materials* 15, no. 12: 4216.
https://doi.org/10.3390/ma15124216