Flexural behaviour and evaluation of ultra-high-performance fibre reinforced concrete beams cured at room temperature

Heat treatment is often required for ultra-high-performance concrete (UHPC) to achieve high strength. To broad its use in construction, the effect of different curing conditions on the properties of UHPC has been developed for many years. The experimental investigation of large scale ultra-high-performance fibre reinforced concrete (UHPFRC) beams is limited. In the present study, UHPFRC specimens and concrete cured at 20 °C were prepared to investigate the properties and flexural behaviour. The standard cubic compressive strength of UHPFRC specimens cannot be achieved at curing temperature of 20 °C. The bearing capacity under flexure was enhanced with the increase of reinforcement ratio. The failure modes of beams changed from ductile to brittle as the reinforcement ratio increased from 1.26 to 9.50%. The flexural behaviour of UHPFRC beams cured at room temperature was in accordance with the UHPFRC beams cured at high temperature in previous studies. In addition, the calculation model of CECS38-2004 underestimated the bending moment capacity of the under-reinforced UHPFRC beams (with reinforcement ratio from 0 to 7.85%) and overestimated the bending moment capacity of the UHPFRC beams with high reinforcement ration of 9.50%.

Materials and mixture proportion. An ultra-high-performance fibre-reinforced cementitious composite was prepared in this study. The range of mixture ratios to acquire excellent UHPFRC were examined and summarized by many research studies. In order to manufacture UHPFRC specimens with high quality, the mixture proportions were chosen from the tests database 5 . Preferably, the water-cement ratio maintained at 0.16 www.nature.com/scientificreports/ to 0.20. The silica fume and silica flour of 10% to 30% of the cement mass were required to fill the voids between cement particles. The proportions of aggregate and superplasticizer were 110% and 2% of the cement mass, respectively. Moreover, the steel fibres content was recommended as a volume fraction of 2% to 3% based on the workability and mechanical performance of UHPFRC. The mixture proportions used in this study are summarized in Table 2. The cement used in this study was Ordinary Portland cement 42.5R. Silica sand with diameter of 360 to 600 μm and 600 to 840 μm was used as aggregates. Silica fume including 94% SiO 2 with a diameter of 0.1 μm and silica flour with a diameter of 50 μm were added as fillers. The Dramix steel fibres were added at 2% by volume of the entire mix. As shown in Fig. 1, the steel fibres had 13 mm length and 0.2 mm diameter with a yield strength of 2850 MPa as reported by the manufacturer.
UHPFRC mix design. The mixing procedure consisted of mixing the cement, silica fume, silica flour and sand in dry state for 2 min. Then, the water mixed with superplasticizer was added into the dry mixture and mixed for 6 min. When the mixture became visibly flowable, the steel fibres were added and mixed for further 5 min.

Specimens and test methods. Compressive, tensile and flexural strength tests. A series compression
and tension tests were conducted to characterize the material properties. To identify the compressive strength, specimens with dimensions of 100 × 100 × 100 mm 3 and 100 × 100 × 300 mm 3 were casted and tested. Dog-bone shaped specimens with a rectangular cross section of 50 mm × 100 mm and length of 368 mm were fabricated and tested for axial tensile strength as shown in Fig. 2. Specimens with dimension of 100 × 100 × 400 mm 3 were tested for flexural tensile strength. All test specimens were reinforced with steel fibres but without rebars. These specimens were covered with plastic sheets immediately after casting and demoulded after 24 h. To identify the effect of curing temperature on the properties of UHPFRC, specimens with dimension of 100 × 100 × 100 mm 3 were cured at three conditions including room temperature of 20 °C ± 0.5 °C and steam curing at 60 °C ± 0.5 °C and 90 °C ± 0.5 °C for 48 h after demoulded. Specimens were then cured in a fog room at room temperature for 28 days and then tested. Specimens with dimensions of 100 × 100 × 300 mm 3 and 100 × 100 × 400 mm 3 were cured in a fog room at room temperature for 28 days after demoulded and then tested. The compressive strength, tensile strength and flexural strength for each group were determined with three specimens.
Large scale beam specimens. Six groups of beams with different reinforcement ratios were fabricated and tested in this study as shown in Fig. 3. Each group consisted of three specimens. Control beams without any reinforcement were labelled as NR. For reinforced beams, rebars at the top were kept same i.e., single layer of two bars with 8 mm diameter. The beams were designated according to the arrangement of bottom reinforcement rebars. Beams with one rebar layer at the bottom with two 12 mm rebars were labelled as R12-1. R18-1 had one rebar layer at the bottom with two bars of 18 mm diameter. R18-2 had two layers of reinforcement at the bottom with two rebars of 18 mm in each layer while R20-2 had two reinforcement layers at the bottom containing two rebars of 20 mm per layer. R22-2 had two layers of rebars with two bars of 22 mm in each layer. All beams had the similar dimensions with an effective span length of 1600 mm and cross-section of 100 mm × 200 mm. To prevent www.nature.com/scientificreports/ any premature shear failure of the beam, shear reinforcement was provided. The shear reinforcement consisted of stirrups of 8 mm diameter spaced at 100 mm centre to centre throughout the beam. The beams were fabricated one at a time because of the concrete mixer of 1000 L capacity and the larger quantity of mixtures required. The beams were fabricated by placing the concrete using back and forth placement method along the span of the beam. The specimens were covered with wet hessian and plastic sheets immediately after concrete casting and cured at room temperature for the first 24 h, prior to demolding. After demolding, the specimens were cured in a fog room at room temperature of 20 °C ± 0.5 °C for 28 days.
Test setup. Compressive, tensile and flexural strength tests setup. The compressive strength and flexural strength of the steel fibre-reinforced concrete were determined based on GB50081-2019. Specimens with dimension of 100 × 100 × 100 mm 3 and 100 × 100 × 300 mm 3 were used to determine the compressive strength by uniaxial compressive load applied at rate of 0.8 to 1.0 MPa/s. For the specimens with dimension of 100 × 100 × 300 mm 3 , the electrical strain gauges of 80.1 mm length were attached at the mid height to record the axial and lateral strains as show in Fig. 4a. Additionally, a dial gauge was used to measure the platen-to-platen displacement to measure the strains of the whole specimen to determine the elastic modulus.
To determine the tensile strength, as shown in Fig. 4b, the dog-bone shaped specimens with a rectangular cross section of 50 mm × 100 mm and length of 368 mm were loaded at rate of 0.05 mm/min according to 41 . The strain of specimens was measured by digital image correlation (DIC). DIC is a reliable non-destructive method based on speckle tracking and is used to analyse the full displacement field on the surface of specimens by digital images [42][43][44] .
To determine the flexural strength, specimens with a dimension of 100 × 100 × 400 mm 3 were loaded at rate of 0.08 to 0.1 MPa/s according to GB50081-2019. Three electrical strain gauges with a length of 80.1 mm were glued on the side surface of the specimen at midspan at different heights to measure the strain as shown in Fig. 4c.   Figure 5 shows the loading configuration details of concrete beams. The beam was set up on a steel frame with a capacity of 1000 kN. A single hydraulically actuated jack was used to supply the monotonically increasing load. Load was supplied through displacement control method at the rate of 10 mm/min. As shown in Fig. 5, LVDTs and electrical resistance strain gauges were used to measure the deflections and strains of the beams. Five gauges with a length of 80.1 mm were glued on the side surface of the beam at midspan at different heights and two gauges were located on the bottom surface of the beam at midspan. In addition, electrical strain gauges with length of 1 mm were glued to the steel rebar at midspan before the casting of the beam to measure the strains of steel.

Results and discussion
Properties of the UHPFRC specimens.   where F is the applied load at failure, l is the length of span measured bearing to bearing, b is the width of crosssection and h is the depth of cross-section.
The axial tensile strength acquired from the dog-bone shaped specimen was 8.38 MPa.
Test results for beams. Crack pattern and failure mode. For all the beams, the load increased linearly until the formation of first crack. The presence of the first cracks was audibly indicated followed by the first visible micro-cracks at the bottom surface of the beams between the loading points. The number of micro-cracks increased with the increase of the load, and new cracks propagated toward the upper face. One or two cracks in the middle portion of the beam became significantly visible whereas other cracks did not show any visible increase in width. In addition, the compression zone of concrete moved toward to the top as the cracks developing. As the test progressing, a noticeable increase in the number of cracks occurred and the steel fibres began to pull out. Given that steel fibres carried the tensile load and resisted the opening of the crack, the width of the cracks increased more rapidly with slight increase in load after the steel fibres began to pull out. The tensile load on the other nearby fibres increased, leading to pulling out of even more steel fibres. As shown in Fig. 6, the increase of reinforcement ratio increased the number of cracks and reduced the width of cracks. Three to five visible cracks were observed for NR group beams between the loading points. The cracks of NR group beams propagated to the depth of 0.5 h (height of the beam) at failure. All R group beams exhibited vertical cracks. In addition to vertical cracks, the number of diagonal cracks in the region between the loading point and the support increased with the increase of reinforcement ratio. One or two major cracks were formed during failure and then developed rapidly in length and width. Moreover, the depth of the crack increased with the increase of reinforcement ratio from 1.26 to 7.85%. At the end of the tests, the depths of crack for R12-1, R18-1, and R18-2 were about 0.60 h, 0.70 h, and 0.75 h, respectively. The depths of the crack for R20-2 and R22-2 were about 0.85 h and 0.7 h, respectively.
Concrete is known as a brittle material and shows immediate loss of load carrying capacity without reinforcement at failure 45 . Brittle failure was observed in NR beams as the ordinary concrete. The failure modes of R group beams were different from those of NR group beams, depending on the longitudinal reinforcement ratio. In terms of reinforcement ratio, the beams can be divided in to three groups: under-reinforced beams, balanced-reinforced beams and over-reinforced beams. Failure of under-reinforced beams was gradual and was accompanied by fairly large deflection. The ultimate load capacity of the beams increased with an increase in tensile reinforcement ratio but the deflection ductility decreased, leading to brittle failure 34 . Thus, failure of over-reinforced beams was more abrupt. The balanced-reinforced beams behaved in an intermediate manner between those of under-reinforced and over-reinforced beams. Moreover, ductile failure was always observed in under-reinforced beams while brittle failure was observed in over-reinforced beams. The balanced-reinforced beams appeared to fail in a fairly brittle manner 35 . Ductile failure occurred in under-reinforced beams because the steel yields and the concrete crushes simultaneously, causing considerable deformation 34 . With an increase of reinforcement ratio, the loading capacity of beams increases and the load distribution on each steel decreases. The concrete was crushed without prior yielding of the steel (less deformation), leading to a rapid propagation of cracks and sudden failure of concrete beams 35 . Ductile failure was observed for the beams R12-1, R18-1 and R18-2 with large deflection. As shown in Fig. 6b, c, d, the compression zone of the concrete crushing is small at failure. Thus, the reinforcement yielded before the beams reach the ultimate limit state in flexure. The yielding of reinforcement produced a ductile failure for these beams because the tensile reinforcement ratios of these beams were under-reinforced 27 . As shown in Fig. 6e, f, brittle failure was observed for the beams R20-2 and R22-2, accompanying with large concrete crushing of compression zone. The brittle failure indicated that the beams R20-2 and R22-2 could be balanced-reinforced or over-reinforced beams.
(1)  Table 4. It is clear to see that the flexural capacity of UHPFRC beams increased as reinforcement ratio increased. This trend is similar to other investigation 27,29,32,46 . The deflection was measured at the mid span of the beam. Figure 7 shows the load-deflection relationship of the tested beams. Three distinct regions of the load-deflection relation can be observed in the NR group beams, including the linear zone before first cracking, yield stage, and rupture stage. The yield stage began when first cracking occurred and ended before reaching the maximum load. The rupture stage corresponded to that of strength losing. It can be seen that initial response of NR group beams was similar up to the peak load and then ruptured. The exact occurrence of the first crack was difficult to observe visually due to the multiple-cracking property of the UHPFRC. Thus, the crack load in this paper was defined as the load at the end of the initial linear www.nature.com/scientificreports/ stage in the load-deflection curve. The average peak load for the NR group beams was 40 kN and the average deflection measured for this load was 2.32 mm. After the peak was achieved, the specimens underwent into a softening stage, which showed a brittle failure pattern. The beams R12-1, R18-1 and R18-2 showed similar trend in load-deflection behaviour. The deflection increased linearly and was proportional to the load until reaching the peak value of the load. After the peak value was achieved, the deflection increased while the load kept constant, showing a ductile failure pattern.
The load-deflection behaviour of the beams R20-2 and R22-2 was similar. The deflection increased linearly to the load until reaching its peak value. Then the load decreased progressively with the increase of the deflection.
Load-strain relationship. The load-strain curves of the beams were shown in Fig. 8. The strain was measured by the strain gauges attached to the concrete and rebar surfaces. Negative strains represented compressive strains while positive strains represented tensile strains. As shown in Fig. 8a, the load-strain curves of the concrete at the bottom face elevated. The load-strain relationships were similar for all reinforcement ratios. The strain was linear at first followed by a nonlinear region. The nonlinear region started at the initiation of cracking. There is no abrupt change of strain at nonlinear region. The reason is that the steel fibres in the cement matrix resisted the tensile force after the initiation of cracking 32 . Unfortunately, most of the strain gauges attached to the bottom face of concrete came off due to the developing cracks. Thus, only load-strain relationship at strain from 0 to 700 με were shown in Fig. 8a. Figure 8b shows that the strain of tensile rebars of all beams increased linearly at the beginning. Greater tensile strains were generated after the yielding of rebar occurred. It can be seen that the yielding point of tensile reinforcement increased as the reinforcement ratio increased. For the beams R12-1, R18-1 and R18-2, the tensile reinforcement yielded before the concrete crushed, indicating that the reinforcement ratio of these beams were under-reinforced. For the beams R20-2 and R22-2, as shown in Figs. 7 and 8, the load at the yield of tensile reinforcements closed to the load at the concrete crushed, indicating that the reinforcement ratios for R20-2 and R22-2 approached to balance-reinforced. The load-strain behaviour of tensile reinforcements is consistent to the failure modes of the concrete beams.
Ductility. The ductility of concrete beams can be quantified using the ductility index, which is expressed by the deflection ductility index, curvature ductility index or rotational ductility index 32 . Deflection of ductility index was adopted in this study as expressed in Eq. (2). where µ is the ductility index of the member, Δ u is the mid-span deflection at the ultimate load, and Δ y is the mid-span deflection at the yielding load. The ductility index for all the beams are shown in Table 5. www.nature.com/scientificreports/ It is well known that the natural brittleness of plain concrete disqualified it to be applied separately to the structure due to the requirement of ductility for safety. The addition of steel fibre increased the ductility of the NR beam to 2.55. The improvement of ductility by fibres has been discussed in previous studies [47][48][49] . The fibre reinforcement in a concrete mix can make complementary and additive contributions to tensile behaviour of the beam 49 . This is because the fibres induced the delay of macrocracks formation 48 . For the beams with rebar, the ductility decreased as the reinforcement ratio increased. The effect of the reinforcement ratio on the ductility of the beams is similar to previous studies 35,50,51 . This is because the tensile rebar yield before the concrete in the compression zone is crushed for low reinforcement ratio. As the reinforcement ratio increasing, the concrete will be crushed without prior yielding of tensile rebar, causing a brittle failure manner. Thus, the ductility of the beams decreased with the increase of reinforcement ratio 35 . However, the ductility indexes of beams R20-2 and R22-2 were less than that without rebar, indicating that the addition of steel fibre can improve the ductility of beams without reinforcement but weaken the ductility of beams with high reinforcement ratio. The reduced ductility index of beams with rebar by adding steel fibres was also reported in previous studies 52,53 . The reduction was caused by the smaller deflection capacity resulted from the crack bridging capability of fibres, leading to the decreases in differences between deflections at steel rebar yield and peak load 54 .

Estimation of bending moment capacity
In China, the bending moment capacity of UHPFRC members is predicted by the calculation model in CECS38-2004. As shown in Fig. 9, the results of the compressive stress and tensile stress of concrete give: R12-1 compressive rebar R18-1 compressive rebar R18-2 compressive rebar R20-2 compressive rebar R22-2 compressive rebar R12-1 tensile rebar R18-1 tensile rebar R18-2 tensile rebar R20-2 tensile rebar R22-2 tensile rebar The ultimate moment can be evaluated as Table 5. Value of load-deflection behaviour (ρ represents reinforcement ratio, p y represents the yielding load, p u represents the ultimate load, and Ave represents the mean value, Stdev represents the standard deviation).  Detailed properties of the beams are given in Table 6.
To calculate the ultimate moment of the concrete beams, the parameters α 2 , β and x c are needed to be determined. The equivalent of stress distribution at failure is from the assumption of stress distribution of cross-section at failure based on the constitutive relationship of UHPFRC at DBJ43T325-2017 as shown in Fig. 10.
The compressive stress and tensile stress resultant from the assumption of stress distribution at failure can be determined as follows.
The moment of the compressive stress resultant about the neutral axis is where σ c is the compressive stress of concrete and σ t the tensile stress of the concrete.
The parameters α 1 α 2 , β and x c can be determined by combing equations of (3), (4), (5), (6), (8), (9), and (10) as follows.   Table 7. The details of calculating process are provided in "Appendix A". Table 8 gives the experimental and predicted bending moment capacity. It can be seen that the experimental bending moment capacity of the UHPFRC beams with reinforcement ratio from 0 to 7.85% were underestimated while that with reinforcement ratio of 9.50% were overestimated. The reason why the bending moment capacity was overestimated is that the stress distribution of concrete was based on ductile failure of concrete beams. The concrete crushed and the steel yielded simultaneously. However, as discussed in previous sections, the concrete was crushed without prior yielding of the steel for concrete beam of R22-2, leading to smaller stress distribution of concrete when the concrete beam was failure. Thus, this calculation model is not suitable for the beams with high reinforcement ratio. The stress distribution at DBJ43T325-2017 should be modified to a lower value. A possible stress distribution of concrete is shown in Fig. 11.

Conclusion
The properties of UHPFRC specimens with different dimensions curing at different temperature and the flexural behaviour of UHPFRC beams with reinforcement ratio from 0 to 9.5% curing at room temperature were investigated in the present study. Moreover, test results were used to compare with the theoretical results based on the numerical models from the Chinese standards. The following conclusions can be made.
The materials and mix proportions can be used to manufacture UHPFRC specimens with compressive strength over 150 MPa at curing temperature of 90 °C. The compressive strength of cubic UHPFRC specimens significantly decreased with the decrease of curing temperature from 90 to 20 °C. The cubic compressive strength of specimen with dimension of 100 × 100 × 100 mm 3 cured at 20 °C and the prismatic compressive strength of specimen with dimension of 100 × 100 × 300 mm 3 cured at 20 °C were 102.90 MPa and 79.08 MPa, respectively. The tensile strength and flexural strength of UHPFRC specimens cured at 20 °C were 8.38 MPa and 17.7 MPa, respectively.
The bearing capacity of UHPFRC beams cured at 20 °C under flexure was enhanced as the increase of reinforcement ratio. The failure modes of UHPFRC beams changed from ductile to brittle as the reinforcement ratio increased from 1.26 to 9.5%. Moreover, the ductility of UHPFRC beams decreased with the increase of reinforcement ratio. The effect of reinforcement ratio on the flexural behaviour of UHPFRC beams cured at room temperature exhibited similar effect on those cured at high temperature. However, the standard strength level of UHPFRC specimens cannot be achieved at curing temperature of 20 °C. Although there is some reduction in strength, the UHPFRC beams cured at room temperature showed good performance and the flexural behaviour of these beams were in accordance with the UHPFRC beams cured at high temperature.