Analysis of the mechanical and fracture behavior of heated ultra-high-performance fiber-reinforced concrete by X-ray computed tomography

Analysis of the mechanical and fracture behavior of heated ultra-high-performance fiber-reinforced concrete by X-ray computed tomography Jos´ e D. R´ ıosa, H´ ector Cifuentesa,∗, Carlos Leivab, Stanislav Seitlc aSchool of Engineering, Department of Continuum Mechanics and Structural Analysis. University of Seville, Camino de los Descubrimientos, s/n, 41092, Seville, Spain bSchool of Engineering, Department of Chemical and Environmental Engineering. University of Seville, Camino de los Descubrimientos, s/n, 41092, Seville, Spain cAcademy of Sciences of the Czech Republic, Institute of Physics of Materials, ˚ Aœi ˚ A¨ Ykova 22, 616 62 Brno, Czech Republic Abstract This work analyzes the effects of temperature (300 oC) on mechanical and fracture behavior of an ultra-high-performance steel-fiber-reinforced concrete. The deterioration of the pore structure due to thermal damage of the fiber-reinforced concrete and its un-reinforced matrix was analyzed by X-ray computed tomography. Complementary, a thermogravimetric analysis was performed to relate the observed phase changes, due to dehydration and decomposition, with the deterioration of pore structure. Additionally, an analysis of their mechanical and fracture properties was also done at room temperature and 300 oC. Finally, it was established a connection between the damage within the concrete matrix and its corresponding mechanical behavior. From results, it has been ascertained that the propagation of thermal damage within the matrix affects in different ways depending on the pore-size. The presence of fibers modifies the pore structure and consequently the evolution of the thermal damage in the ultra-high- performance concrete, inferring into its mechanical and fracture behavior. Keywords: ultra-high performance concrete, X-ray computed tomography, steel fibers, high temperature, thermal effects, fracture ∗Corresponding author Email address: [email protected] (H´ ector Cifuentes) Preprint submitted to Cement and Concrete Research September 7, 2018 1. Introduction Ultra-high-performance fiber-reinforced concrete (UHPFRC) is characterized by a water-to-binder ratio usually below 0.2 and by being made from constituents with very fine particle size to fill the matrix tiny holes and enhance the hydration process [1, 2]. This leads to a high matrix packing density that provides exceptional durability and5 high brittleness[3, 4]. The reinforcement of this type of concrete, commonly with steel fibers in quantities of more than 2% by volume, infers a significant improvement on its mechanical properties, especially on the tensile and flexural strength, as well as an excellent energy absorption capacity and ductility[5, 6]. Nevertheless, several studies reveal that the addition of fibers can alter the distribution of the pore structure [7, 8], as10 well as increase the porosity in the matrix [9, 10]. Furthermore, the pore morphology is an important factor on thermal conductivity of concrete [11, 12] and as a consequence, on generation of the thermal gradients in the concrete matrix at temperature exposure. The internal stresses generated by the thermal gradients combined with the pore pressure from the water evaporation can reach the tensile strength of concrete and produce15 explosive spalling [11, 13, 14, 15]. The spalling effects produce more severe deterioration in the UHPFRC than those of normal concrete (NC) or high-strength concrete (HSC) due to its lower porosity which does not allow that the evaporated water can flow outside through the pore connection of the matrix [15, 16, 17]. Although there are numerous research paper focused20 on the mechanical behavior [18, 19, 20, 21, 22] and fracture properties of UHPFRC [23, 24, 25, 26, 27], there are no many studies that relate the mechanical or fracture properties of UHPFRC with the matrix pore structure [20, 28]. On the other hand, most of research related with the influence of temperature on the behavior of UHPFRC have been focused on fire resistance [29, 30, 31] due to this25 type of concrete is widely applied in civil structures. As UHPFRC contains a high amount of cement, the shrinkage cracking is similarly of research interest into this type of concrete [6, 32, 33, 34]. Several studies have been focused on curing or recuring processes since the temperature exposure during the curing stage or its useful life modify the strength evolution [11, 19, 35]. However, in some applications the30 2 UHPFRC must be capable of bearing thermal and mechanical loads simultaneously for long periods of time, like in structures for molten salt or water vapor storage tanks in solar power plants, as well as in energy storage systems by solid medium, in which, the concrete material directly stores the thermal energy. In this regard, to know the evolution of the mechanical and fracture behavior of UHPFRC at moderate temperature35 exposure for long periods of time is worthy of study. This kind of study, relating the mechanical and fracture properties with the porosity evolution inside the UHPFRC at room and moderately elevated temperature, are really scarce the literature. This work is focused on the influence of temperature exposure for significant periods on the pore structure deterioration and the consequences on the mechanical and40 fracture properties of an UHPFRC. To this, a comprehensive experimental campaign to determine the mechanical and fracture properties of a UHPFRC and its corresponding non-reinforced matrix at room temperature and 300 oC was performed. The influence of porous morphology on the mechanical and fracture behavior at each temperature was measured through X-ray computed tomography (CT) scan. A post-processing of45 the X-ray CT images allowed for us to obtain a three-dimensional reconstruction of samples in order to identify the pore distribution in the concrete matrix and to obtain the main porosity parameters for a wide range of pore sizes. These were determined for fiber-reinforced concrete (UHPFRC) and its corresponding matrix without any reinforcement (UHPC) at room temperature and for exactly the same samples heated to50 300oC. Additionally, a thermogravimetric analyses of the concrete matrix (UHPC) was conducted from room temperature to 400 oC in order to determine the phase changes due to dehydration or decomposition at each temperature [16, 36] and an X-ray crystallography analysis to determine the mineral composition of UHPC. Finally, it was established a connection among the results from thermoanalytic techniques, X-ray CT55 scan and the mechanical and fracture properties at room temperature and 300 oC. In this way, the mechanisms by which the changes in microstructure of the matrix, originated by the presence of fibers and the increase of the temperature, determine the mechanical and fracture properties of concrete has been thoroughly analyzed. This paper is structured in the following manner: A description of experimental60 procedure and thermal analyses techniques are presented in Section 2, the results of the 3 tests are exposed and discussed in Section 3 and finally the conclusions are found in Section 4. 2. Experimental procedure In this section, a summary of the materials, TG analyses, X-ray CT scan and exper-65 imental tests performed are shown. 2.1. Materials and mix design In this work, two different ultra-high-performance concrete mixes were manufactured. The former was a non fiber-reinforced concrete (UHPC) used as control mix and the latter was a fiber-reinforced concrete (UHPFRC). The concrete matrix was exactly70 the same for both mixes and following the proportions shown in Table 1. The mix design was done in accordance with the recommendations postulated by Deeb et al. [37]. Three constituents comprise the binder materials: the type I cement of 52.5 R/SR, the silica fume S-92-D from SIKA company and the ground granulated blast-furnace slag (ggbs) provided by Arcelor company. Two quartz sands were added as aggregate: the75 former with a maximum size of 315 µm and the latter with 800 µm. The superplasticizer, used as reducer of water, was a third generation polycarboxylic ether-based type (Master-Glenium ACE 325) with a specific gravity of 1.05 provided by BASF Company. 4 Table 1: Nomenclature and mix proportions Constituent UHPC (kg/m3) UHPFRC (kg/m3) cement 544 544 silica fume 214 214 ggbs 312 312 water 188 188 fine sand (<315 µm) 470 470 coarse sand (<800 µm) 470 470 superplasticizer (BASF ACE 325) 42 42 steel fiber OL 13/0.2 - 98 steel fiber C80/30BP - 98 w/c ratio 0.34 0.34 w/binder ratio 0.17 0.17 In the UHPFRC, the reinforcement was exclusively using micro and macro steel80 fibers. The shortest smooth micro-fibers were the OL 13/0.2 model manufactured by the Bekaert company and with 13 mm in length, 0.20 mm in diameter and straight ends. The macrofibers were the C80/30BP model by the same company, measuring 30 mm in length, 0.38 mm in diameter and fitted with hooked ends. The UHPFRC mix has a fiber content of 2.5% by volume fraction which means 196 kg/m3in a 50%85 ratio of each type of fiber. The nomenclature of concrete and fiber proportions can be also seen in Table 1. The mineral composition of UHPC after 28 days obtained by X-ray diffraction technique is shown in Figure 1. The main mineral compounds at room temperature were fundamentally quartz, C3S:Ca3SiO5and Ca2FeAlO5. The pozzolanic reaction between the large amount of active SiO2(siica fume) in the high-90 strength admixture and Ca(OH)2generated during the cement hydration, has formed a lot of C-S-H gel and reducing Ca(OH)2and CaCO3content, as it can be seen in Figure 1 [16]. 5 Figure 1: Mineral composition of UHPC 2.2. Thermoanalytic tests Simultaneous thermogravimetric analyses (TA), differential thermal analyses (DTA)95 and differential scanning calorimetric (DSC) measurements were performed at the Functional Characterization Service (University of Seville, Spain) on a TA (model Q600-SDT) instrument, using alumina as reference material. The specimens were placed into crucibles in a chamber within ambient air during the entire heating period. The temperature was increased at a constant rate of 10 oC/min from room temperature100 to 400 oC. 2.3. Mechanical and fracture tests Cubic specimens with 100 mm in length, cylindrical with 100 mm in diameter and 200 mm in height and 440 ×100 ×100 mm3prismatic specimens were casted for measuring standardized mechanical and fracture properties at room temperature and105 300 oC. 2.3.1. Testing at room temperature The compressive strength was measured on four cubic specimens in accordance with the EN 12390-3 standard [38]. The tests were performed in a servo-hydraulic testing machine equipped with a load capacity of 3000 kN. The Young’s modulus was110 experimentally determined by four cylindrical specimens for every mixture according 6 to the EN 12390-13 standard [39]. This test was performed by gradually loading, with the same servo-hydraulic machine used for compression, until a third of its failure load and measuring the relative strain by two linear variable differential transformer (LVDT) sensors, 25 mm in length, one in front of the other, surrounding the cylinder.115 Four notched prismatic specimens were subjected to three-point bending tests for the determination of the fracture energy in accordance with the RILEM work-of-fracture method [40] and with the corrections proposed by Guinea et al. [41, 42, 43]. An inverse analyses based on the non-linear hinge model [44, 45, 46, 47] in order to obtain the values of the bilinear tension softening diagram (Figure 2) was also performed.120 The bilinear softening diagram allows for the numerical simulation of concrete in real applications [48]. Every specimen was sawn with a notch to depth ratio of one sixth. The specimens were set up with a LVDT, 30 mm in length, mounted on a rigid frame to avoid torsional effects, for both UHPC and UHPFRC to measure the mid-span deflection and a clip gage to measure the crack mouth opening displacement (CMOD).125 The utilization of the high range LVDT transducer allows the recording of the complete load-displacement curve even for the fiber-reinforced mix.              Figure 2: Bilinear tension softening diagram 2.3.2. Testing at 300 oC The kind of tests and the number of specimens tested were the same as at room temperature. Nevertheless, some modifications had to be carried out owing to the tem-130 perature. The main drawback of high temperature tests is the impossibility of set the 7 sensors on specimens. The three-point bending tests were done during entire testing within a furnace at 300 oC. In this way, the tests were performed on hot specimens with the fracture energy reaching lower values than in case of residual cooled specimens [49]. All specimens were heating for at least 24 hours before testing to ensure an ho-135 mogeneous temperature in the material. The testing equipment of the aforementioned servo-hydraulic machine was specifically designed to be settled in a furnace. Thus, the actuator and supporting framework can be entered inside the chamber. Notwithstanding the foregoing, only load and actuator position data can be reported due to the transducers cannot bear such high temperatures.140 For the estimation of the load-deflection curves from three point bending tests at 300 oC, this procedure was followed: •It is assumed that the difference between the mid-span deflection and the actuator displacement is due to the machine appliance strain during the loading process. •From the room temperature tests, it is established a mid-span to deflection-145 actuator displacement ratio, Ω, for each load applied. Ω = Xdef i Xpos i ,(1) where Xpos iand Xdef iare the actuator displacement and the mid-span deflection at RT respectively. •At 300 oC tests, it is estimated the mid-span deflection data from the Ωratio for each load recorded as follows:150 X0def i300 = ΩXpos i300 (2) where the Xpos i300 and X0def i300 are the actuator position and the estimated mid-span deflection at 300 oC respectively. For the estimation of the stress-strain curves on the Young’s modulus tests the same procedure was followed but using LVDT data where the mid-span deflection. 8 2.4. X-ray computed tomography and image analyses155 The micro X-ray computed tomography technique was used to measure the porosity by air entrapped during manufacturing and thermal damage generated as result of the temperature exposure within the concrete matrix when the specimens reach 300 oC. The X-ray inspection equipment, model Y.Cougar SMT of the YXLON company, from the X-ray Characterization Service of the University of Seville, Spain was used. It160 consists of a multi-focus tube and wolframio target which allows the inspection in the range between 25-160 kV and 0.01-1 mA intensity. The equipment let generate 2D and 3D images with a maximum geometric magnification of 2000×. The post-processing of reconstruction and treatment of images were carried out using the VGStudio MAX 2.2.3 software of the X-ray Service of the University of Seville. The X-ray CT samples165 analyzed were sawn from the prismatic specimens similar to those of the three-point bending tests (440 ×100 ×100 mm3) to avoid boundary effects in fiber distribution and their dimensions were approximately 100 ×25 ×25 mm3. A schematic overview of the dimensions and the zone from where every sample was extracted is shown in Figure 3.a. Eight samples, four of each mix (UHPC and UHPFRC) were analyzed,170 each sample was extracted from a different prismatic specimen. The same four samples were scanned at RT and after being subjected at 300 oC. 100 100 440 (a) pores fibers (b) Figure 3: (a) Extraction of the sawn core from prismatic specimens (b) pores and fibers in grey-scale image 9 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 1 2 3 4 5 6 Porosity (%) Eq. diameter (mm) UHPC_RT UHPC_300 UHPFRC_300 UHPFRC_RT (a) Cumulative pore volume (%) UHPC_RT UHPC_300 UHPFRC_RT UHPFRC_300 100 90 80 70 60 50 40 30 20 10 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Eq. diameter (mm) (b) Figure 8: Equivalent diameter distribution: (a) porosity and (b) cumulative pore volume The heating of the material to 300 oC increases its porosity (Figure 8.a), from 3.9%235 to 5.0% for UHPC and from 1.9% to 2.6% for UHPFRC (Table 2), which implies a thermal damage generated within the material. The heating of UHPC samples causes high internal pressure as a result of two processes: the evaporation of free water, between 20 and 250 oC [54], and dehydration of C-S-H gel [53, 54], between 250 and 400 oC, as additionally was confirmed for these mixes from the thermogravimetric analyses (Fig-240 ure 7), as described in the previous subsection. These effects in conjunction with the lower porosity of the matrix in UHPC with respect to ordinary concrete [1, 56], leads to high internal stresses that infer into the propagation of thermal damage. If the damage is significantly high, might lead to an explosive spalling [11, 13, 14, 15]. Figure 8.b reveals that the UHPC shows an almost identical pore-size distribution curve at RT and245 300 oC. However, the UHPFRC shows a wider difference on the pore-size distribution by thermal effect that infer no homogenization with regard to damage propagation. 3.2.1. Diagrams of equivalent diameter Using the geometrical data of each pore, the diagrams of equivalent diameter at RT and 300 oC have been performed for each mixture, UHPC in Figure 9 and UHPFRC in250 Figure 10, from the division of the entire range of values into intervals. These diagrams (Figure 9 or Figure 10) represent pore density, which is defined as the number of pores per cubic millimeter. 16 In Figure 9, it is observed that the maximum concentration of pores is in the interval range 0.15-0.20 mm of the equivalent diameter and more than 50% of pore den-255 sity is between 0.10-0.25 mm. That implies a high packing density of matrix in a UHPC as was expected [57]. The amount of pores with an equivalent diameter higher than 0.6 mm is almost nonexistent. When the UHPC is heated at 300 oC, the generated thermal damage in the matrix of concrete clearly increased pore density in every pore-diameter interval. It is worth noting that as the damage affected more severely260 to the lowest equivalent diameter and the interval range most influenced was the 0.15- 0.20 mm range which is the interval of the highest pore density at RT. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Pore density (mm-3) UHPC_RT UHPC_300 0.10-0.15 0.15-0.20 0.20-0.25 0.25-0.30 0.30-0.35 0.35-0.40 0.40-0.45 0.45-0.50 0.50-0.55 0.55-0.60 Eq. diameter (mm) Figure 9: Equivalent diameter distribution of UHPC at RT and 300 oC represented by pore density Regarding the UHPFRC equivalent diameter results (Figure 10), it is shown a decrease of porosity at RT, always below the UHPC values (Figure 9), so that the addition of steel fibers decrease the porosity of matrix, as demonstrated in Table 2 and265 Figure 8. The interval range of equivalent diameter with higher pore density is between 17 0.15-0.30 mm and the higher value 0.04 pores/mm3. The pore density diagram is remarkably flat which infers a significant low porosity and a uniform distribution of pore size in comparison with UHPC (Figure 9). When the UHPFRC concrete is heated to 300 oC (Figure 10), it is observed as the thermal damage modifies the pore distribution270 in the concrete matrix due to an increase of pore density specially in the interval range 0.10-0.25 mm, as shown in Figure 10. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Pore density (mm-3) UHPFRC_RT UHPFRC_300 0.10-0.15 0.15-0.20 0.20-0.25 0.25-0.30 0.30-0.35 0.35-0.40 0.40-0.45 0.45-0.50 0.50-0.55 0.55-0.60 Eq. diameter (mm) Figure 10: Equivalent diameter distribution of UHPFRC at RT and 300 oC The maximum interval range of pore density is 0.15-0.20 mm, as occurred in UHPC at any temperature although the pore density value is lower than those cases (0.16 pores/mm3).275 3.2.2. Diagrams of pore volume Diagrams of pore volume for each mixture, UHPC in Figure 11 and UHPFRC in Figure 12, are represented from the division of the entire range of values into intervals. 18 The x-axis represents the range of pore volume (in mm3) and the y-axis displays pore density.280 Regarding the UHPC, the Figure 11 shows that the most significant concentration of pores is contained in the 0.001-0.002 mm3interval range with pore density value of 0.14 pores/mm3. There is a higher pore concentration (more than 50%) in the range below 0.009 mm3that confirms the low porosity of matrix expected for this type of concrete. When the temperature in the UHPC reaches 300 oC, the thermal damage in285 the matrix is derived into a higher pore density in the interval range of pore volume below 0.017 mm3. It is interesting remark as the biggest pores are not influences by the thermal damage. The maximum pore density occurs in the same maximum interval range (0.001-0.002 mm3), yet the value rises into 0.18 pores/mm3. Pore volume (mm3) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Pore density (mm-3) UHPC_RT UHPC_300 0.000-0.001 0.002-0.003 0.004-0.005 0.006-0.007 0.008-0.009 0.010-0.011 0.012-0.013 0.014-0.015 0.016-0.017 0.018-0.019 Figure 11: Pore volume distribution of UHPC at RT and 300 oC: (a) pore density and (b) percentage of pores In the UHPFRC at RT (Figure 12), it is observed a significant decrease of pore290 density in all interval range leading to a greatly low porosity due to the addition of 19 steel fibers. The maximum pore density is between 0.001-0.002 mm3with a value of 0.018 pores/mm3. The effects of thermal damage at 300 oC in the pore density diagram (Figure 12) showed a sizeable increment in the pore volume range below 0.005 mm3 (50% of pore volume) but not a significant influence for higher pore volume. The295 maximum pore density is generated in the interval range 0.001-0.002 mm3. This is in accordance with that results observed for equivalent diameter diagrams. Pore volume (mm3) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Pore density (mm-3) UHPFRC_RT UHPFRC_300 0.000-0.001 0.002-0.003 0.004-0.005 0.006-0.007 0.008-0.009 0.010-0.011 0.012-0.013 0.014-0.015 0.016-0.017 0.018-0.019 Figure 12: Pore volume distribution of UHPFRC at RT and 300 oC: (a) pore density and (b) percentage of pores Table 3 summaries pore density (in pores/cm3) and outlines the pore volume intervals higher than 0.1 mm3, in which the amount of pores are less numerous and as a consequence they were not included in Figure 11 and Figure 12. Regarding the ther-300 mal effect in the UHPC in comparison to the UHPFRC, it is shown as the porosity with pore volume higher than 0.5 mm3is not affected, as it is inferred of the invariability of pore density for any type of mixture (UHPC and UHPFRC) and temperature (RT and 20 300 oC). Nevertheless, pore density lower than 0.5 mm3rises due to the thermal damage. In that interval, there is a slight increase of pores in the range 0.5-0.1 mm3which305 is still more significant in the range below 0.1 mm3as was observed in the diagrams. In the UHPFRC clearly the number of pores is centralized in the smallest interval (below 0.1 mm3), with a 162% of increment, because of the bridging effect of the fibers that avoid the free crack propagation [58, 59] in comparison with the UHPC with a 64% of increment in the same interval.310 Table 3: Pore density results organized by pore volume ranges at RT and 300 oC Pore density (pores/cm3) >1mm31−0.5mm30.5−0.1mm3<0.1mm3 UHPC RT 3±1 6 ±2 67 ±13 1020 ±254 UHPC 300 oC3±1 6 ±3 90 ±7 1680 ±625 UHPFRC RT 3±1 4 ±1 26 ±7 245 ±115 UHPFRC 300 oC3±0 4 ±0 31 ±3 644 ±40 From the sphericity results for each pore, the average value is shown in Table 2 for each mixture and temperature. As observed, the thermal effect has not significant influence on the sphericity of both mixes (UHPC or UHPFRC) because only the smallest pore-size, whose Vpore/Apore ratio is higher, are deteriorated by thermal damage. Thus, the sphericity does not suffer significant variations in their values, as can be seen315 in Table 2. Regarding the UHPC in comparison with UHPFRC, it is observed as the fiber addition infers a slight reduction on the sphericity due to air bubbles generated in the casting of fresh concrete that are positioned around steel fiber and it produces the pore structure deformation [9, 10], as can be observed in Figure 13. 21 Figure 13: Pores around fibers with sphericity lower than 0.4 At 300 oC, it is concluded that small pores are the most numerous in concrete, both320 in equivalent diameter and in volume in any type of concrete, UHPC or UHPFRC. The internal pressure produced by the temperature exposure affects more strongly to the smallest pores but the damage propagation in the concrete matrix by heating depends on the mix, UHPC or UHPFRC. In the UHPC, the absent of steel fibers, which act like barriers avoiding the damage propagation, generates higher total porosity and a325 more uniformly pore-size distribution in the concrete matrix. In the UHPFRC, the total porosity is reduced by the presence of an elevated amount of fibers, yet the pore-size is slightly higher due to the air bubbles concentration around fibers, as can be seen in dav eq and dmax eq at RT (Table 2). Furthermore, the thermal damage propagation leads to a clear concentration of porosity in the smallest pore-size range due to the bridge effect330 of fibers that prevent damage propagation. This is in accordance with dav eq in Table 2 whereby this is practically constant for UHPC and lower for UHPFRC at 300 oC. 3.3. Mechanical and fracture properties In this section, the mechanical and fracture properties of UHPC and UHPFRC are shown. All results correspond to the average of four specimens tested for each mixture335 and temperature with indication of the standard deviation. 22 3.3.1. Mechanical properties From the mechanical property tests, the compressive strength, fc, and Young’s modulus, Ec, of each mix and temperature are shown in Table 4. Comparing the UHPC and the UHPFRC at RT, the compressive strength in the UHPFRC is higher due to the340 presence of fibers reducing the total porosity of the material, as shown in the porosity values in Table 2 and the bridge effect of fibers which difficult the crack propagation. The Young’s modulus slightly increased, showing that the fiber reinforcement does not provide remarkable enhancement, as obtained by other authors [60]. Regarding the UHPC and UHPFRC at 300 oC, both materials led to a lower compressive strength and345 Young’s modulus due to the higher porosity generated by thermal damage within the concrete matrix. The main difference was that the decreasing in UHPFRC was significantly higher than UHPC, in 15% and 8% respectively because the pore density change is higher in UHPFRC, as shown in Figure 12. Table 4: Mechanical properties of UHPC and UHPFRC at room temperature and 300 oC room temperature 300 oC UHPC UHPFRC UHPC UHPFRC fc(MPa) 124.6±7.7% 147.4±6.4% 114.1±19.0% 125.5±13.9% Ec(GPa)∗47.7±3.2% 49.2±2.9% 28.2±5.4% 30.4±4.2% ∗Measured on cooled specimens (residual property) 3.3.2. Fracture properties350 The fracture properties of UHPC and UHPFRC at RT and 300 oC are shown in Table 5. The tensile strength, ft, was determined from the bilinear softening diagram parameters in the UHPFRC and from the splitting test in the UHPC because is not possible to obtain a softening behavior at 300 oC. To identify the parameters of the bilinear tension softening diagrams of the mixes an inverse procedure was used based355 on the non-linear hinge concept [44, 45, 46]. The size-independent fracture energy was determined according to the work-of-fracture method of RILEM with the corrections proposed by Guinea et al. [41, 42, 43]. The fracture energy and the characteristic 23 length are defined as follows: GF=WF.M +WF.NM Alig ,(6) lch =GFEc f2 t ,(7) where WF.M is the measured work-of-fracture (area under the measured load-360 displacement curve), WF.NM is the non-measured work-of-fracture and Alig is the ligament area. Regarding the room temperature tests, as the tensile strength results, ft, of UHPC were determined by splitting tensile tests and of UHPFRC by bilinear inverse analyses. This leads to cannot compare the results of UHPC with UHPFRC although it is pos-365 sible to do a qualitative comparison. In both mixes, it is showed a significant increase of tensile strength due to the fiber-reinforcement, as expected. The steel fibers have a bridge effect on the crack front that avoid any eventual micro-cracking. The fracture energy, GF, and characteristic length, lch, are extremely higher in UHPFRC than UHPC due to the presence of fibers. In the UHPC and UHPFRC at 300 oC, the tensile370 strength greatly decreased due to the same reasons that the thermal damage affected the compressive strength. The fracture energy was reduced to 40% on UHPFRC. For UHPC it could not be determined because the CMOD and LVDT transducers does not support that temperature. The characteristic length was strongly increased up to 64% due to having greater porosity in the matrix.375 24 Table 5: Fracture properties of UHPC and UHPFRC at room temperature and 300 oC room temperature 300 oC UHPC UHPFRC UHPC UHPFRC ft(MPa) 5.9±16.3% 16.3±25.0% 3.7∗±7.4% 9.4±19.6% GF(N/m) 63.36 ±5.3% 54973 ±8.1% −26919 ±18.6% lch (mm) −3315 ±8.1% −9339 ±18.6% ∗This property was determined by splitting tensile tests on cooled cylindrical specimens. 3.3.3. Bilinear softening diagrams Figure 14 shows the result of the non-linear hinge model method over the loaddeflection curves. The experimental load-deflection curve (continuous line) is the average of four tests. The hinge model method was applied on the mean load-deflection curves of UHPFRC at RT (Figure 14.a) and 300 oC (Figure 14.b). 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