Evaluation of the maximum load value and cracking load in fiber-reinforced concrete

Lima, Iva Emanuelly Pereira; Barboza, Aline Silva Ramos

doi:10.1590/S1983-41952025000200012

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 18 (2) • 2025 • https://doi.org/10.1590/S1983-41952025000200012 linkcopy

Evaluation of the maximum load value and cracking load in fiber-reinforced concrete

Avaliação do valor de carga máxima e carga de fissuração em um concreto reforçado com fibras

Authorship SCIMAGO INSTITUTIONS RANKINGS

In fiber-reinforced fluid concrete (FRFC), it is possible to use the casting flow of the concrete to guide the fibers in the places and directions of greater stresses, which is a relevant aspect when you want to use the fiber-reinforced concrete (FRC) for structural purposes. However, the normative instructions referring to the sizing aspects of the FRC still do not verify the validity of this preferential orientation of the fibers since they consider that the maximum load corresponds to the cracking load when using dispersed fibers in the matrix, and they base their studies on this hypothesis. In view of this and knowing the significant change that the preferential orientation of the fibers can provide to the FRC, it is necessary to carry out a study regarding the relationship between this orientation and the resistance load of the concrete. From this, a study is presented associated with the relationship between the maximum load and the cracking load of a sample of concrete reinforced with steel fibers (SFRC) and another of concrete reinforced with polymeric fibers (PFRC), both with the preferential orientation of the fibers that will be used later for structural applications. According to the study, it was observed that when the element exhibits hardening behavior and the fiber has a high modulus of elasticity, there is no statistically significant difference between the loads. However, when the element exhibits softening behavior and the fiber has a low modulus of elasticity, there is a statistically significant difference between the loads. Thus, it can be concluded that, when using the preferential orientation of the fibers in the composite, the maximum load may not correspond to the cracking load, making it necessary later to determine the design load and, consequently, the possible variations in the dimensioning aspects.

Keywords:
fiber-reinforced concrete; preferential orientation of the fibers; maximum load; cracking load

Ratio	Value
Water/cement ( $w / c$ )	0.50
Superplasticizer/cement ( $s p / c$ )	0.50
RBMG/cement ( $r / c$ )	0.50
Initial water/total water (iw/tw)	0.76
Volume of fine aggregate (%)	47.5
Volume of coarse aggregate (%)	52.5
Volume of paste (%)	38.0

Materials	Mass (kg)
Cement	377.90
RBMG	188.95
Fine aggregate	774.53
Coarse aggregate	813.75
Initial water	151.16
Complementary water	37.75
Absorption water	11.17
Superplasticizer	6.30
For the SFRC
Steel fibers	25.98 ( $V_{f} =$ 0.4%)
For the PFRC
Polymeric fibers	3.78 ( $V_{f} =$ 1.0%)

Sample	$P_{m a x}$ (kN)	$P_{c r a c k}$ (kN)	Behavior
V1	19.65	19.63	Hardening
V2	19.50	17.33	Hardening
V3	25.73	20.50	Hardening
V4	25.73	20.33	Hardening
V5	25.42	24.33	Hardening
V6	17.17	16.83	Hardening
V7	16.17	14.67	Hardening
V8	17.58	16.67	Hardening
Average	20.87	18.79
Standard deviation	4.10	3.03
Variance	16.84	9.16
Coefficient of variation (%)	19.67	16.11

Sample	$P_{m a x}$ (kN)	$P_{c r a c k}$ (kN)	Variation (%)
V1	19.65	19.63	+0.10
V2	19.50	17.33	+12.52
V3	25.73	20.50	+25.51
V4	25.73	20.33	+26.56
V5	25.42	24.33	+4.48
V6	17.17	16.83	+2.02
V7	16.17	14.67	+10.22
V8	17.58	16.67	+5.46

Method	Variable analyzed	$α$	p-value	Condition	Conclusion
Jarque-Bera	$P_{m a x}$	0.05	0.45	If p-value $> α$ There is no evidence to reject $H_{0}$ Data follow a normal distribution	They follow a normal distribution
Jarque-Bera	$P_{c r a c k}$	0.05	0.76	If p-value $> α$ There is no evidence to reject $H_{0}$ Data follow a normal distribution	They follow a normal distribution

Method	$α$	p-value	Condition	Conclusion
Bartlett	0.05	0.44	If p-value $> α$ → There is no evidence to reject $H_{0}$ → The variances are equivalent	The variances are equivalent
Hartley	0.05	0.22	If p-value $> α$ → There is no evidence to reject $H_{0}$ → The variances are equivalent	The variances are equivalent

Method	$α$	p-value	Condition	Conclusion
T test	0.025	0.267	If p-value $> α$ → There is no evidence to reject $H_{0}$ → Differences are not statistically significant	The loads are statistically equivalent

Sample	$P_{m a x}$ (kN)	$P_{c r a c k}$ (kN)	Behavior
V1	16.92	6.33	Softening
V2	14.42	5.33	Softening
V3	14.92	4.42	Softening
V4	14.42	4.17	Softening
V5	15.17	4.17	Softening
V6	14.67	5.17	Softening
V7	14.33	5.33	Softening
V8	15.17	4.83	Softening
Average	15.00	4.97
Standard deviation	0.84	0.73
Variance	0.71	0.54
Coefficient of variation (%)	5.62	14.76

Sample	$P_{m a x}$ (kN)	$P_{c r a c k}$ (kN)	Variation (%)
V1	16.92	6.33	+167.30
V2	14.42	5.33	+170.54
V3	14.92	4.42	+237.56
V4	14.42	4.17	+245.80
V5	15.17	4.17	+263.79
V6	14.67	5.17	+183.75
V7	14.33	5.33	+168.86
V8	15.17	4.83	+214.08

Method	Variable analyzed	$α$	p-value	Condition	Conclusion
Jarque-Bera	$P_{m a x}$	0.050	0.002	If p-value $> α$ → There is no evidence to reject $H_{0}$ → Data follow a normal distribution	Do not follow a normal distribution
Jarque-Bera	$P_{c r a c k}$	0.050	0.710	If p-value $> α$ → There is no evidence to reject $H_{0}$ → Data follow a normal distribution	They follow a normal distribution

Method	$α$	p-value	Condition	Conclusion
Levene	0.05	0.97	If p-value $> α$ → There is no evidence to reject $H_{0}$ → The variances are equivalent	The variances are equivalent

Method	$α$	p-value	Condition	Conclusion
Mann-Whitney	0.050	0.0002	If p-value $> α$ → There is no evidence to reject $H_{0}$ → Differences are not statistically significant	The loads are not statistically equivalent.

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Steel fibers
Design
Classification	Fiber with anchoring at the extremities
Form	Type AI
Length (mm)	60
Equivalent diameter (mm)	0.75
Form factor	80
Longitudinal modulus of elasticity (GPa)	210
Traction strength (MPa)	1100
Polymeric fibers
Design
Classification	Synthetic macrofiber
Length (mm)	40
Equivalent diameter (mm)	0.44
Form factor	90
Longitudinal modulus of elasticity (GPa)	9.50
Traction strength (MPa)	600 – 650