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Size Effect of Synthetic Fibre Reinforced Concrete – Investigation using a Semi-Discrete Analytical Beam Model

Mária Erdélyiné Tóth

Mária Erdélyiné Tóth

Budapest University of Technology and EconomicsBudapest, Hungary
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Tóth, Mária Erdélyiné
 y 
Anikó Pluzsik

Anikó Pluzsik

Budapest University of Technology and EconomicsBudapest, Hungary
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Pluzsik, Anikó
  
20 oct 2023
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Publicado en línea: 20 oct 2023
Páginas: 117 - 129
Recibido: 12 may 2022
Aceptado: 17 abr 2023
DOI: https://doi.org/10.2478/acee-2023-0039
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© 2023 Mária Erdélyiné Tóth et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Size effect on the strength of concrete (adapted from Bazant and Planas [1])
Size effect on the strength of concrete (adapted from Bazant and Planas [1])

Figure 2.

Specimen dimensions and experimental layout
Specimen dimensions and experimental layout

Figure 3.

Measurement of the crack opening
Measurement of the crack opening

Figure 4.

Comparison of manual and machine CMOD measurement in the case of FRC_M_03
Comparison of manual and machine CMOD measurement in the case of FRC_M_03

Figure 5.

Cracked cross-sections divided into five zones
Cracked cross-sections divided into five zones

Figure 6.

Appearance of pulled-out and broken fibres
Appearance of pulled-out and broken fibres

Figure 7.

Experimental F-CMOD results of PC (left) and FRC (right) beams
Experimental F-CMOD results of PC (left) and FRC (right) beams

Figure 8.

Experimental and theoretical τ-s and F-u curves of the pulled-out fibres (Reprinted from Tóth and Pluzsik [19])
Experimental and theoretical τ-s and F-u curves of the pulled-out fibres (Reprinted from Tóth and Pluzsik [19])

Figure 9.

Softening curve of plain concrete (Reprinted from Tóth and Pluzsik [23])
Softening curve of plain concrete (Reprinted from Tóth and Pluzsik [23])

Figure 10.

Stress distribution and distances along the cross-section (Reprinted from Tóth and Pluzsik [19])
Stress distribution and distances along the cross-section (Reprinted from Tóth and Pluzsik [19])

Figure 11.

Size effect of Bazant compared to experimental results of PC
Size effect of Bazant compared to experimental results of PC

Figure 12.

Experimental and theoretical F-CMOD curves of PC_M (q = 15 N/mm3)
Experimental and theoretical F-CMOD curves of PC_M (q = 15 N/mm3)

Figure 13.

Size effect of Bazant compared to experimental results of FRC
Size effect of Bazant compared to experimental results of FRC

Figure 14.

Experimental and theoretical F-CMOD curves of FRC_S_04 (left: q = 15 N/mm3, τmax = 3.4 N/mm2) and FRC_M_05 (right: q = 15 N/mm3, τmax = 4 N/mm2)
Experimental and theoretical F-CMOD curves of FRC_S_04 (left: q = 15 N/mm3, τmax = 3.4 N/mm2) and FRC_M_05 (right: q = 15 N/mm3, τmax = 4 N/mm2)

Figure 15.

Residual nominal strength (σRN) depending on the beam depth (D)
Residual nominal strength (σRN) depending on the beam depth (D)

Proportions of concrete matrix

Component Dosage [kg/m3]
Cement 350
Water 192
Aggregate 0/4 631
Aggregate 4/8 685
Aggregate 8/16 487
Superplasticizer 2

Nominal stresses and τmax values of FRC specimens

Specimen ID Nominal stress (σN) [N/mm2] Average of σN2 [N/mm2] τmax [N/mm2] Average of τmax [N/mm2] Deviation of τmax [%] Pulled-out fibres [pcs] Broken fibres [pcs] Rate of pulled-out fibres [%]
FRC_S_01 3.29 3.47 3.4 3.16 8% 47 7 87%
FRC_S_02 3.47 2.4 −24% 51 10 84%
FRC_S_03 3.34 3.0 −5% 52 10 84%
FRC_S_04 4.25 3.4 8% 30 22 58%
FRC_S_05 3 3.6 14% 39 13 75%
FRC_M_01 3.43 3.10 3.6 3.64 −1% 82 26 76%
FRC_M_02 2.67 3.6 −1% 87 26 77%
FRC_M_03 2.94 3.4 −7% 70 35 67%
FRC_M_04 3.18 3.6 −1% 83 42 66%
FRC_M_05 3.3 4.0 10% 108 32 77%
FRC_L_01 2.58 2.71 2.6 3.52 −26% 179 15 92%
FRC_L_02 2.83 3.6 −2% 179 20 90%
FRC_L_03 2.88 4.4 25% 119 35 77%
FRC_L_04 2.47 3.8 8% 160 36 82%
FRC_L_05 2.79 3.2 −9% 159 24 87%

Comparison of the performed experiment and the recommendation of RILEM [20]

Proportions RILEM recommendation Performed experiment
l/D ratio >2.5 3.33
a0/D ratio 0.15<a0/D<0.5 0.083
notch width <0.5da (8 mm) 0.125 da (2 mm)
b >3da (48 mm) 9.4 da (150 mm)
Dmin <5da (80 mm) 4.7da (75 mm)
Dmax >10da (160 mm) 18.75da (300 mm)
Dmax/Dmin ≥4 4

Dimensions of the test specimens

Specimen ID Beam depth (D) [mm] Span (l) [mm] Notch depth (a0) [mm]
FRC_S 75 250 6.25
FRC_M 150 500 12.5
FRC_L 300 1000 25

Nominal stresses and q values of PC specimens

Specimen ID Beam depth (D) [mm] Nominal stress (σN) [N/mm2] Average of σN [N/mm2] Deviation of σN [%] Slope of the softening curve (q) [N/mm3]
PC_S_06 75 2.73 2.9 −5.9 15
PC_S_07 75 3.07 5.9
PC_M_06 150 2.84 2.81 1.2 15
PC_M_07 150 2.77 −1.2
PC_L_06 300 2.50 2.48 1 15
PC_L_07 300 2.45 −1
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