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In recent years, the development and application of high performance fiber reinforced concrete or cementitious composites are increasing due to their high ductility and energy absorption characteristics . However, it is difficult to obtain the required properties of the FRCC by simply adding fiber to the concrete matrix. Many researchers are paying attention to fiber reinforced polymers (FRP) for the reinforcement of construction structures because of their significant advantages over high strain rates . However, the actual FRP products are skill-dependent, and the quality may not be uniform. Therefore, in this study, two-way punching tests were carried out to evaluate the performances of FRP strengthened and steel and polyvinyl alcohol (PVA) fiber reinforced concrete specimens for impact and static loads. The FRP reinforced normal concrete (NC), steel fiber reinforced concrete (SFRC), and PVA FRCC specimens showed twice the amount of enhanced dissipated energy (total energy) under impact loadings than the non-retrofitted specimens. In the low-velocity impact test of the two-way NC specimens strengthened by FRPs, the total dissipated energy increased by 4 to 5 times greater than the plain NC series. For the two-way specimens, the total energy increased by 217% between the non-retrofitted SFRC and NC specimens . The total dissipated energy of the CFRP retrofitted SFRC was twice greater than that of the plain SFRC series. The PVA FRCC specimens showed 4 times greater dissipated energy than for the energy of the plain NC specimens. For the penetration of two-way specimens with fibers, the Hughes formula considering the tensile strength of concrete was a better predictor than other empirical formulae.

The addition of fiber reinforcement is one of the most effective methods for enhancing the performance of concrete [

Many researchers are paying attention to fiber reinforced polymers (FRP) for the reinforcement of construction structures because of their significant advantages over high strain rates [

to evaluate the performances of FRP strengthened and steel and synthetic fiber reinforced concrete specimens for impact and static loads.

The test variables in this study are summarized in

Variable | Details | Notation |
---|---|---|

Concrete | Normal concrete (NC) | N |

Steel fiber reinforced concrete (SFRC) | S | |

Hybrid PVA fiber reinforced cementitious composite (FRCC) | P | |

FRP strengthening | Not retrofitted | |

GFRP | G | |

CFRP | C | |

Angle of fabrics | ±45° | ±45 |

0/90° | 0/90 |

W/C (%) | S/a (%) | Unit weight (kg/m^{3}) | S.P.^{a}^{)} | v_{f}^{b}^{)} | |||
---|---|---|---|---|---|---|---|

Water | Cement | Fine aggregate | Coarse aggregate | ||||

50 | 50.4 | 204 | 408 | 876 | 863 | 1.0% | 0.75% |

^{a)}high range water reducing admixture to cement ratio. ^{b)}volume fraction of steel fiber on SFRC.

W/C (%) | Unit weight (kg/m^{3}) | S.P. | M.C.^{a}^{)} | v_{f} ^{b)} | ||
---|---|---|---|---|---|---|

Water | Cement | Silica sand | ||||

50 | 375 | 750 | 954 | 2.0% | 0.05% | 2.0 |

^{a)}hydroxypropyl methylcelluose to cement ratio. ^{b)}total volume fraction of PVA fibers.

Fiber | Length l_{f }(mm) | Diameter d_{f}_{ }(mm) | Tensile strength σ_{f}_{ }(MPa) | Density (g/cm^{3}) | |
---|---|---|---|---|---|

Steel fiber | 30 | 500 | 1196 | 7.9 | |

PVA fiber | REC15 | 12 | 40 | 1600 | 1.3 |

RF4000 | 30 | 660 | 900 | 1.3 |

Volume fraction of fiber, v_{f} (%) | f_{cu}_{ } (MPa) | f_{1,crack} (MPa) | f_{ult} (MPa) | f_{sp} (MPa) | T_{JSCE} (kN・mm) | F_{JSCE} (MPa) | |
---|---|---|---|---|---|---|---|

REC15 | RF4000 | ||||||

2.0 1.9 1.8 1.7 1.6 1.5 1.4 | 0 0.1 0.2 0.3 0.4 0.5 0.6 | 60.99 53.63 56.34 66.93 71.26 67.24 69.12 | 6.76 6.61 6.03 6.81 6.16 6.64 6.03 | 10.23 10.34 10.3 10.65 13.07 8.63 10.04 | 7.39 6.63 7.3 6.19 7.61 7.14 7.33 | 42.83 47.84 47.47 49.85 63.11 33.84 35.28 | 6.42 7.18 7.11 7.48 9.47 5.08 5.29 |

f_{cu} = compressive strength; f_{1,crack} = flexural strength at first crack; f_{r} = flexural strength; f_{sp} = splitting tensile strength; T_{JSCE} = toughness of JSCE method; F_{JSCE} = equivalent flexural strength of JSCE method.

Note that, in the mixture of Kim et al. [

For the measurement of flexural tensile strength, 100 × 100 × 400 mm prismatic specimens were fabricated and square specimens of 50 × 350 × 350 mm were prepared for punching test. The cast specimens were stored in water at 20˚C ± 3˚C for two weeks. Fourteen days after casting, the FRPs were adhered and then cured for 14 more days at 50% ± 5% relative humidity and at a temperature of 20˚C ± 3˚C. The unidirectional E-glass and high strength carbon fiber sheets were attached with epoxy resin along the shapes of punching test specimens, with a crossing at right angles of ±45 and 0/90 degrees. Glass fiber reinforced polymer (GFRP) was only used with the normal concrete, while the carbon fiber reinforced polymer (CFRP) was used with the three matrices. The mechanical properties of fiber sheets and resins are summarized in

The restraint conditions of punching tests are illustrated in

The low-velocity impact tests were carried out with a drop weight test machine that has a maximum capacity of about 800 Joules, as shown in

Sheet | Tensile strength (MPa) | Elastic modulus (GPa) | Ultimate strain (%) | Thickness (mm) | |
---|---|---|---|---|---|

E-glass sheet | 2300 | 76 | 3.0 | 0.35 | |

High strength carbon | 4900 | 230 | 2.1 | 0.111 | |

Resin | Tensile strength (MPa) | Tensile modulus (GPa) | Ultimate strain (%) | Density (g/cm^{3}) | |

Epoxy | 90 | 3 | 8.0 | 1.2 |

Tests for mechanical properties of concrete such as compressive and flexural tensile strength were carried out according to ASTM C39 and C1609. The material properties of each matrix are summarized in

The test results of two-way static punching tests are summarized in

In the case of the PVA FRCC, both the non-retrofitted specimens and reinforced specimens with CFRP after maximum loads showed strain softening. However, the peak loads of the CFRP retrofitted PVA FRCC series is not greater than that of the plain PVA FRCC specimens. The FRP retrofitted NC specimens

Materials | Compressive strength (MPa) | Flexural strength (MPa) |
---|---|---|

NC | 53.20 | 4.79 |

SFRC | 50.40 | 6.80 |

PVA FRCC | 54.23 | 10.32 |

Specimen | Maximum load (kN) | Deflection at max load (mm) | Dissipated energy (J) |
---|---|---|---|

N-N N-G-±45 N-G-0/90 N-C-±45 NC-C-0/90 | 14.90 43.05 45.18 39.48 44.66 | 0.29 1.14 1.33 1.11 1.36 | 35.77 45.10 49.78 45.16 46.11 |

S-N S-C-±45 | 22.24 63.13 | 5.74 1.25 | 90.58 106.29 |

P-N P-C-±0/90 | 45.39 54.21 | 1.61 0.89 | 161.48 460.82 |

and plain SFRC specimens showed complex failure patterns of splitting and punching. In addition, in the failure cases of the splitting of concrete matrices, the deboning of FRPs were more serious. However, all the PVA FRCC series had typical punching failure as shown in

In the PVA FRCC series, the P-N specimens showed 4 times larger dissipated energy than for the energy of the N-N specimens. However, the CFRP retrofitted PVA FRCC specimens had similar capacities to the CFRP retrofitted SFRC elements. Also, identically to the SFRC’s cases, retrofitted specimens showed a plateau at the first blow and nonlinearity of time-deflection curve, and almost failed by one blow (

Specimen | Maximum load (kN) | Deflection at max load (mm) | Dissipated energy (J) |
---|---|---|---|

N-N N-G-0/90 N-C-±45 N-C-0/90 | 53.23 71.19 70.30 70.13 | 2.54 4.55 3.61 4.53 | 128.08 522.52 534.07 653.28 |

SC-N S-C-±45 1st blow 2nd blow | 63.48 73.40 16.03 | 2.09 3.16 9.23 | 405.85 767.33 106.99 |

P-N P-C-0/90 1st blow 2nd blow | 55.99 73.51 22.22 | N.A. 5.43 3.87 | 543.7 736.78 154.03 |

Kennedy (1976) [

In this study, the penetration depths were assessed, and various empirical formulas of penetration depth due to missile impact are shown in appendix.

The modified Petry, ACE, modified NDRC, and BRL formulae are from the tests for a lightweight and high-velocity rigid missile, whereas the Kar, Hughes, Haldar-Hamieh, and Adeli-Amin formulae are based on experiments for heavy and low-velocity impact. Formulae for perforation and scabbing [

Formula | Penetration depth (mm) | ||
---|---|---|---|

NC | SFRC | PVA FRCC | |

Experiment | 36.49 | 29.55 | 27.76 |

Modified Petry | 35.88 | 52.14 | 52.52 |

BRL | 77.92 | 102.67 | 99.45 |

ACE | 50.43 | 59.59 | 58.53 |

Modified NDRC | 55.93 | 58.53 | 58.27 |

Ammann & Whitney | 93.59 | 134.64 | 130.64 |

Whiffen | 186.55 | 221.26 | 235.40 |

Kar | 55.93 | 58.53 | 58.27 |

UKAEA | 55.93 | 58.53 | 58.27 |

Haldar & Hamieh | 12.30 | 19.70 | 18.34 |

Adeli & Amin | 12.18 | 17.30 | 16.37 |

Hughes | 29.07 | 29.30 | 25.51 |

Healey & Weissman | 56.80 | 59.78 | 59.49 |

IRS | 0.77 | 0.79 | 0.76 |

CRIEPI | 1.00 | 1.81 | 1.34 |

formulae. The given conditions are: the weight and tup are steel (hence, E = 2.00 × 10^{9} Pa), the mass of the projectile is 33.62 kg, the diameter of the projectile is 25 mm, and the aggregate diameter is 20 mm. The compressive and tensile strength used are the values of

As can be seen in _{0} = 4.9 and 5.9 m/s, also lozenge shaped dots means the average perforation depth of each matrix.

Punching tests were performed in order to observe the behaviors of fiber reinforced polymer (FRP) strengthened and fiber reinforced concrete specimens for quasi-static and low-velocity impact loads by using the universal testing machine (UTM) and drop weight testing machine. The following is an outline of concluding remarks for the material tests:

1) Two-way square specimens were fabricated with normal concrete (NC), steel fiber reinforced concrete (SFRC), and hybrid PVA fiber reinforced cementitious composite (PVA FRCC). For the hybrid PVA FRCC, two different types of fiber were used, and the FRPs were attached along the shapes of the specimens at ±45 and 0/90 degrees.

2) The maximum load of FRP reinforced NC specimens increased by 2.65 to 3.03 times greater than the plain NC series under quasi-static loadings, and the deflections of center at the maximum loads increased by 3.8 to 4.7 times. The ultimate loads of the SFRC-N series increased by 38% more than the N-N series, and for the PVA FRCC, the carbon fiber reinforced polymer (CFRP) strengthening improves 62% of the peak load. The loads of SFRC-N specimens gradually increased, but the specimens reinforced with CFRP showed strain softening after the maximum loads. Both the non-retrofitted specimens and reinforced PVA FRCC specimens with CFRP after maximum loads exhibited strain softening.

3) The FRP reinforced NC, SFRC, and PVA FRCC specimens showed twice the amount of enhanced dissipated energy (total energy) under impact loadings than the non-retrofitted specimens. In the low-velocity impact test of the two-way NC specimens strengthened by FRPs, the ultimate impact loads increased by 1.33 times, and the total dissipated energy increased by 4 to 5 times greater than the plain NC series. For the two-way specimens, the total energy increased by 217% between the non-retrofitted SFRC and NC specimens. The total dissipated energy of the CFRP retrofitted SFRC was twice greater than that of the plain SFRC series. In the PVA FRCC series, the P-N specimens showed 4 times greater dissipated energy than for the energy of the N-N specimens. However, the CFRP retrofitted PVA FRCC specimens had similar capacities to the CFRP retrofitted SFRC elements.

4) For the penetration of two-way specimens with steel fiber, the Hughes formula considering the tensile strength of concrete was a better predictor than other empirical formulae. However, for plain concrete, specimens need to be of larger size to avoid splitting failure. In addition, penetration depth due to missile impact may be much different due to the tensile strength of fiber reinforced concrete, so it should be improved through various experiments.

Min, K.-H. (2018) Punching and Local Damages of Fiber and FRP Reinforced Concrete under Low-Velocity Impact Load. Open Journal of Civil Engineering, 8, 64-81. https://doi.org/10.4236/ojce.2018.81006

Modified Petry formula [

x = k M d 3 log 10 ( 1 + V 0 2 19 , 974 ) (1)

where, k = 6.36 × 10^{−4} for massive plain concrete;

= 3.39 × 10^{−4} for normal reinforced concrete; and

= 2.26 × 10^{−4} for specially reinforced concrete in modification Petry I.

Ballistic Research Laboratory (BRL) formula [

x d = 1.33 × 10 − 3 f ′ c ( M d 3 ) d 0.2 V 0 1.33 (2)

Army corps of engineers (ACE) formula [

x d = 3.5 × 10 − 4 f ′ c ( M d 3 ) d 0.215 V 0 1.5 + 0.5 (3)

Modified NDRC formula [

x / d = 2 G 0.5 for G ≥ 1 (4a)

x / d = G + 1 for G < 1 (4b)

G = 3.8 × 10 − 5 N * M d f ′ c ( V 0 d ) 1.8 (4c)

Ammann and Whitney formula [

x d = 6 × 10 − 4 f ′ c N * ( M d 3 ) d 0.2 V 0 1.8 (5)

Whiffen formula [

x d = ( 2.61 f ′ c ) ( M d 3 ) ( d a ) 0.1 ( V 533.4 ) n (6)

where, n = 97.51 / ( f ′ c ) 0.25 , and about ±15% prediction accuracy, the corresponding ranges of application are 5.52 < f ′ c < 68.95 MPa, 0.136 < M < 9979.2 kg, 12.7 < d < 965.2 mm, and 0 < V_{0} < 11.27.8 m/s.

Kar formula [

x / d = 2 G 0.5 for G ≥ 1 (7a)

x / d = G + 1 for G < 1 (7b)

G = 3.8 × 10 − 5 ( E E s ) 1.25 N * M d f ′ c ( V 0 d ) 1.8 (7c)

where, E, E_{s} = elastic moduli of the projectile and steel, respectively. If the projectile is steel, formula is identical to the modified NDRC formula.

UKAEA formula [

x / d = 0.275 − [ 0.0756 − G ] 0.5 for G ≤ 0 .0726 (8a)

x / d = [ 4 G − 0.242 ] 0.5 for0 .0726< G ≤ 1 .065 (8b)

x / d = G + 0.9395 for G > 1 .065 (8b)

G = 3.8 × 10 − 5 N * M d f ′ c ( V 0 d ) 1.8 (8c)

Within 25 < V 0 < 300 m/s, 22 < f ′ c < 44 MPa, and 500 < M/d^{3} < 200,000 kg/m^{3}, the prediction accuracy is ±20% for x/d > 0.75, and +100% to −50% for x/d < 0.75.

Haldar-Hamieh formula [

x / d = − 0.0308 + 0.2251 I a for 0. 3 ≤ I a ≤ 4 .0 (9a)

x / d = 0.6740 + 0.0567 I a for 4.0 < I a ≤ 21 .0 (9b)

x / d = 1.1875 + 0.0299 I a for21 .0 < I a ≤ 455 (9b)

I a = M N * V 0 2 d 3 f ′ c ; suggestedimpactfactor (9c)

Adeli-Amin formula [

x / d = 0.0416 + 0.1698 I a − 0.0045 I a 2 for 0. 3 ≤ I a ≤ 4 .0 (10a)

x / d = 0.0123 + 0.196 I a − 0.008 I a 2 + 0.0001 I a 3 for4 .0 < I a ≤ 21 .0 (10b)

Hughes formula [

x d = 0.19 N h I h S (11a)

I h = M V 0 2 d 3 f t (11b)

S = 1.0 + 12.3 ln ( 1.0 + 0.03 I h ) (11c)

Healey and Weissman formula [

x / d = 2 G 0.5 for G ≥ 1 ; (12a)

x / d = G + 1 for G < 1 (12b)

G = 4.36 × 10 − 5 ( E E s ) N * M d f ′ c ( V 0 d ) 1.8 (12c)

IRS formula [

For penetration

x = 3703.376 ( f ′ c ) − 0.5 + 1673 ( f ′ c ) − 0.18 exp [ − 0.104 ( f ′ c ) 0.18 ] (13a)

For total protection of the penetration, perforation, and scabbing, the minimum wall thickness is

S V O L L = 3913.119 ( f ′ c ) − 0.5 + 132.409 ( f ′ c ) − 0.18 exp [ − 0.104 ( f ′ c ) 0.18 ] (13b)

CRIEPI formula [

x d = 0.0265 N * M d 0.2 V 0 2 ( 114 − 6.83 × 10 − 4 f c 2 / 3 ) f c 2 / 3 × [ ( d + 1.25 H r ) H r ( d + 1.25 H 0 ) H 0 ] (14)

a = aggregate diameter (m)

d = diameter of the projectile (m)

f ′ c = unconfined compressive strength of concrete (Pa)

f t = tensile strength of concrete (Pa)

H 0 = thickness of the concrete target

H r = 0.2 m

M = mass of the projectile (kg)

N h = projectile nose shape coefficient (1.0, 0.12, 1.26, and 1.39 for flat, blunt, spherical and very sharp noses, respectively)

N * = nose shape factor (0.72, 0.84, 1.0, and 1.14 for flat, hemispherical, blunt, and very sharp noses, respectively)

V 0 = projectile impacting velocity (m/s), and

x = penetration depth (m).