Numerical model for tracing the response of Ultra-High performance concrete beams exposed to fire

This paper presents a numerical procedure for evaluating the thermo-mechanical response of Ultra-High Performance Concrete (UHPC) beams exposed to fire. The numerical model is based on a macroscopic finite element formulation and utilizes sectional moment-curvature relations to trace the response of UHPC beams from the linear elastic stage to collapse under combined effects of fire and structural loading. Fire-induced spalling, temperature-dependent properties of concrete and steel reinforcement, and realistic failure criteria are incorporated into the analysis. Specifically, an advanced analysis approach for evaluating spalling is incorporated in the model by considering the stresses arising from the combined effects of thermal gradients, structural loading, and pore pressure generated in the concrete section. Com-parisons of the predictions from the model with data from fire resistance experiments show a good correlation, indicating the proposed model can reliably pre-dict the thermo-mechanical response, including the extent of spalling in UHPC beams subjected to fire exposure. The applicability of the model for undertaking advanced analysis is shown by conducting a case study to illustrate the influence of load level and fire scenario on the fire response of the UHPC beams.


| INTRODUCTION
Ultra-High Performance Concrete (UHPC) is an advanced cementitious material exhibiting excellent strength, toughness, ductility, and durability characteristics. 1 These improved mechanical properties of UHPC are attributed to its very low water to binder ratio, presence of a high amount of fine admixtures, superplasticizer, and steel fibers. 2,3 Owing to its exceptional mechanical properties, structural members made of UHPC have higher load carrying capacity, which in turn results in reduced sectional dimensions (smaller dead load) and this lowers the overall construction costs. 4,5 The structural and economic advantages, offered by UHPC, have led to its increasing use in construction applications such as bridges, and to a limited extent in highrise buildings. 6 When used in buildings, structural members are required to satisfy fire resistance requirements as specified in building codes. 7 Fire resistance of concrete members is largely evaluated through tabulated listings and simplified fire design equations specified in fire design codes, such as ACI 216.1-14 8 and Eurocode 2. 9 These fire resistance calculation methods in design codes were formulated based on data from fire tests, primarily on conventional normal strength concrete (NSC) members under standard fire exposure. 8,10 It is well documented that structural members made of NSC exhibit good performance under fire situations due to low thermal conductivity, high specific heat capacity, and slow degradation of strength and stiffness properties of concrete. 11 Therefore, NSC members can attain required fire ratings prescribed in design codes without any additional fireproofing requirement. On the contrary, recent studies have shown that High Strength Concrete (HSC) and Ultra-High Performance Concrete (UHPC) members do not exhibit the same level of fire performance as that of NSC members. [12][13][14] This is mainly due to the rapid deterioration of mechanical properties of HSC and UHPC with temperature, as well as their high susceptibility to fire-induced spalling.
Spalling in a concrete member leads to a reduction in cross-section, in turn resulting in higher sectional temperatures, which might lead to early structural failure and lower fire resistance. In the last three decades, there have been numerous studies to improve the fire performance of HSC members. [15][16][17] However, since UHPC is relatively a new construction material, there are no guidelines in codes and standards for the fire resistance design of structural members made of UHPC. Moreover, there are no well-established guidelines or methods in current design standards or codes for incorporating the occurrence and effect of spalling in evaluating fire resistance of UHPC structures. Therefore, the fire resistance calculation procedures laid out in the current design codes may not be directly applicable for UHPC members without modifications. To develop guidelines for the fireresistant design of UHPC members, there is a need to investigate the performance of UHPC under fire conditions. 10 Previous research on the high-temperature behavior of UHPC has been dominantly focused on material-level testing to evaluate the temperature-induced strength loss and microstructural changes. [18][19][20][21][22] Until now, only a handful of experimental studies have been undertaken to investigate the fire performance of UHPC structural members. 12,14,23,24 A review of reported fire experiments has shown that UHPC is more vulnerable to spalling under fire conditions than conventional concretes (NSC, HSC), due to its dense microstructure and low permeability. 25,26 Large-scale fire tests on structural members are time-consuming, labor-intensive, complex, and expensive. An alternative to full-scale fire tests is the application of numerical models for evaluating the fire resistance of reinforced concrete (RC) structures.
Although some fire tests are required for model validation, accurate numerical models can significantly reduce the time and cost of evaluating the fire behavior of structures. Once validated, numerical models can be utilized to conduct parametric studies to quantify the effects of different critical parameters on the fire performance of structural members.
Previously reported numerical studies on simulating the fire behavior of RC structures have mostly focused on NSC and HSC members, with limited consideration to fire-induced spalling, without fully accounting for the combined effects of thermal, hydral, and mechanical processes in a heated and loaded concrete member. At present, there is a lack of validated numerical models for tracing the fire response of UHPC members. 26 The few numerical studies which have been undertaken on evaluating the fire response of UHPC members have neglected fire-induced spalling, which can be an influencing factor due to the high susceptibility of UHPC to spall. [27][28][29] Only in a recent study by Ren et al., 30 spalling in UHPC beams was evaluated by spatial stress superposition. However, the distributions of different components of stresses were not specifically considered in this study and although the level of spalling is inconsistent along the length of the member, spalling was analyzed only at the mid-section of the beam. It should be noted that the mid-section may not be the critical section from a spalling point of view. To overcome these current limitations, a numerical model for predicting the fire performance of UHPC beams is developed, with special consideration to fire-induced spalling and other critical factors that are specific to UHPC.

| General methodology
For the fire resistance analysis, the beam is divided into a number of segments along its length and the mid-section of each segment is assumed to represent the overall behavior of that segment as shown in Figure 1. For each segment, the mid-section is further discretized into a two-dimensional mesh of bilinear iso-parametric four noded rectangular elements. The fire exposure time is incremented in small time steps and the response of the UHPC beam is evaluated at each time step, till the failure of the beam or end of fire exposure.
At each time step, thermal analysis is carried out to evaluate the elemental temperature distribution within the cross-section of each beam segment. Following thermal analysis, spalling is evaluated through a sub-model that utilizes hydro-thermo-mechanical stresses.
The elements in which the spalling criteria are met are removed and the updated concrete cross-sections at each segment are considered in the following time steps. Thereafter, strength analysis is carried out wherein, time-dependent sectional moment-curvature (M-κ) relations are generated for each segment along the length of the beam at various time steps. Next, structural analysis is undertaken, wherein the load-carrying capacity of the beam at any particular time step is evaluated by taking the maximum moment from the time (or temperature) dependent M-κ curve. The deflection of the beam at each time step is calculated through the moment-area method. The strength and stiffness of the beam decrease with fire exposure time, resulting in decreasing moment capacity and increasing deflection, and failure is said to occur when one of the applicable failure limit states is exceeded. A flowchart depicting the numerical procedure for fire resistance calculations is illustrated in Figure 2 and the procedure is described in the following sections. The flowchart for the spalling submodel and its integration with the main program is illustrated elsewhere. 33

| Fire temperatures
The beam is assumed to be exposed to fire from the bottom surface and two sides, with unexposed conditions on the upper surface for replicating an overlying slab as in practice. The fire temperatures for any standard fire exposure such as ASTM E119 34 or ISO 834, 35 or design fire scenario 24 can be specified through time-temperature relations. For instance, the time-temperature relation for ASTM E119 standard fire is calculated by the following equation: where t h = time(h); T 0 = initial temperature ( C); and T f = fire temperature ( C). For design fires, the parametric fires specified in Eurocode 1 36 are built into the model. In addition, to incorporate hydrocarbon fire scenarios, the time-temperature relationship specified in ASTM E1529 37 is utilized.

| Thermal analysis
The temperatures within the beam cross-section of each segment are computed using the finite element method using the fire temperatures computed above. Conduction is the primary heat transfer process within the solid cross-section, whereas convection and radiation are the mechanisms for heat transmission from the surrounding environment to the surfaces of the beam (either exposed or unexposed to fire). The governing equation for transient heat conduction is: where k = thermal conductivity; ρ = density; c = specific heat; r = Laplacian differential operator; T = temperature; t = time; and Q = internal heat source. The governing equation for the convective and radiative heat transfer analysis at the beam surfaces can be expressed as: where n y and n z = components of the vector outward normal to the surface in the plane of the cross-section; h rad = radiative heat transfer coefficient; h con = convective heat transfer coefficient; T E = temperature of the environment surrounding the boundary depending on exposure conditions (fire or room temperature). The radiation heat transfer coefficient is given by: F I G U R E 1 Typical layout of beam and beam discretization into segments and elements where σ = Stefan-Boltzman constant 5.67x10 À8 W/(m 2 C 4 ); and ε = emissivity factor. In the current study, an emissivity (ε) value of 0.4 and convective heat transfer coefficient (h con ) of 25 W/(m 2 C) for fire-exposed surface and 9 W/(m 2 C) for unexposed surface were used. The emissivity value was determined by undertaking a sensitivity analysis codal recommendations 36 and commonly used emissivity values by numerical studies in the literature, which were in the range of 0.4 to 0.8. [38][39][40][41] The convective heat transfer coefficients were taken from the unanimous recommendations in published literature [42][43][44] and design codes. 36 Galerkin finite element formulation is applied to solve the heat transfer partial differential equation. In this F I G U R E 2 Flow chart illustrating steps in the fire resistance analysis of UHPC beam formulation, the material property matrices (stiffness matrix K e , mass matrix M e ) and the equivalent nodal heat flux (F e ) are generated for each element. These matrices are given by the following equations: where N = vector of the shape functions; Q = heat source; s = distance along the boundary; α = heat transfer coefficient depending on the boundary condition Г; A = area of the element; and T E = fire or ambient temperature depending on boundary condition Г.
Once the element matrices are computed, they are assembled into a global system of differential equations and is expressed as: The temperature at the center of the rebar is taken as the temperature of the steel reinforcement for the subsequent analyses.

| Spalling analysis
After evaluation of cross-sectional temperatures through thermal analysis, the extent of spalling is calculated at the mid-section of each segment along the length of the beam. In the previous version of the spalling model by Dwaikat and Kodur, 31 a hydro-thermal-based model was applied to evaluate spalling and this approach accounts for stresses due to pore pressure, but not for stresses due to thermal gradients and structural loading. Recently, Kodur and Banerji 33 developed an improved spalling model that accounts for the effect of stresses owing to structural load and temperature gradients together with stresses due to pore pressure.
In this updated spalling analysis, the stress due to temperature gradients or thermal stress (σ th ) in the concrete elements is evaluated by calculating the elemental free thermal expansion using the elemental temperatures and temperature-dependent thermal expansion coefficient of concrete. The computed free thermal expansion is then utilized to calculate the thermal stress generated due to the geometrical constraint to the free thermal expansion of heated concrete elements. The mechanical stress (σ me ) generated in each concrete element from the applied loading on the beam, is computed by using the high-temperature stress-strain relations of concrete corresponding to the mechanical strain determined from the strength analysis and is explained in the following sub-section. The stress due to pore pressure (σ p ) is evaluated by calculating the elemental pore pressure (P v ) through a finite element-based mass transfer analysis, accounting for the vaporization and movement of moisture in heated concrete.
The updated model accounts for the influence of increasing temperature, pore pressure, and structural loading on the variation of permeability over the beam cross-section and along the beam length for evaluating pore pressure. Detailed steps for the calculation of hydrothermo-mechanical stresses and permeability variation of concrete at high temperature for assessing spalling with equations are provided in the published research by Kodur and Banerji. 33 For calculating pore pressure in the model, the liquid water inside concrete is determined by utilizing the well-established isotherms developed by Bazant. 31,45 The authors would like to point out that in a recent numerical study on spalling in UHPC beams by Ren et al., 30 empirically formulated isotherms by Davie et al. 46 were used which are a function of high-temperature transport properties of concrete, such as porosity and permeability. For reliably calculating pore pressure using such relations, it is critical to accurately measure the high-temperature transport properties of concrete. However, no standardized instrumentation or procedures for evaluating concrete transport properties at high temperatures exist at this time. 47 Moreover, a comparison of the calculated pore pressure plots using Bazant's and Davie's isotherms by Ren et al. 30 shows a maximum difference of 0.3 MPa, which is not significant. Thus, it is fitting to use the widely accepted Bazant's isotherms for pore pressure calculations.
Following the calculation of the stresses due to temperature gradients (σ th ), structural loading (σ me ), and pore pressure (σ p ), spalling is assessed using a two-step procedure that considers fracture of concrete, as shown in Figure 3. For evaluating spalling, the elements located in the first layer of a discretized concrete section directly exposed to fire are termed as boundary elements, whereas the elements located in layers beneath the first fire-exposed layer, that is, in second, third, fourth layer, and so on are termed as interior elements as shown in Figure 1. At each time step, the boundary conditions are updated and the elements are accordingly flagged as either a boundary or an interior element based on its updated boundary conditions.
Heat transfer in boundary elements is through convection and radiation, whereas heat transfer in interior elements is through conduction.
In the first step of the spalling assessment, the onset of fracture in mode I ( Figure 4) is assessed by comparing whether the tensile stress exerted by pore pressure (σ p ) is exceeding the thermally degraded tensile strength of concrete (f' tT ) in each concrete element. However, pore pressure is usually higher in the interior concrete elements at a distance from the heated boundaries since water vapor escapes from the boundary elements located next to the fire-exposed surface, due to exposure to high temperatures. As per the second step, the cracks developed in the initial step widen and propagate through the tensile transverse stresses induced by thermal and mechanical loading, along with stresses due to pore pressure, resulting in fracture of the damaged concrete elements in mode II ( Figure 4). In this second step, spalling is evaluated by comparing the summation of tensile stress due to pore pressure (σ p ), the transverse tensile thermal (σ th ), and mechanical (σ me ) stresses against the temperature-dependent tensile strength of concrete (f' tT ) in the concrete elements located ahead of the interior elements identified in the first step. When spalling is assessed to occur in an element, that element is deleted from the cross-section, and the boundary conditions are updated for consequent analysis.
Unlike previous studies by other researchers, spalling levels are calculated based on hydro-thermo-mechanical stress distributions at midsections in all the segments along the length of the beam, instead of assuming the same level of spalling throughout the beam length as that in the section at mid-span. This aspect is critical for evaluating realistic fire response since the mid-section of a beam may not represent critical section from spalling consideration as spalling is a stochastic phenomenon.

| Structural analysis
The strength calculations are performed using the same mesh from the previous analysis steps, and the temperature of each concrete element is computed through the average of its nodal temperatures.
where ε t = total strain, ε 0 = strain at the geometrical centroid of beam cross-section, κ = curvature, and y = distance from the geometrical centroid of beam cross-section to the center of the element. Following the calculation of total strain in each concrete and steel element of concrete and steel, the mechanical strain in each of these elements is computed using: where, ε mech = mechanical strain; ε th = thermal strain; ε cr = creep strain; and ε tr = transient strain (only for concrete). The superscripts

| Failure limit states
To determine failure, each beam segment is checked against predefined strength and deflection limit states at each time increment. 34 Based on the strength limit state, failure is considered if the moment capacity in any beam segment is lower than the moment due to the applied load. According to the deflection limit state, failure is deemed to occur when in any beam segment, the deflection is greater than L 2 /400d or the rate of deflection is greater than L 2 /9000d (mm/min) where, L is the span length of the beam (mm) and, d is the effective depth of the beam (mm). wherein, the strength at each elevated temperature is normalized using the peak strength at ambient temperature. The tensile stressstrain model captures linear elastic range upto initial cracking, followed by strain hardening facilitated by fiber bridging till peak stress, which is further followed by softening branch due to crack opening.

| High-temperature material properties
where f 0 C and f 0 T are the compressive and tensile strength respectively of UHPC (with non-zero steel fiber content) and SF is the steel fiber content by % of volume. Previous studies have reported that with an increase in polypropylene (PP) fiber dosage, the risk of fire-induced spalling reduces but the compressive strength of concrete further reduces due to lower density and formation of weaker zones in the specimen. 17,57,58 For reliable fire resistance evaluation of members made with UHPC mix incorporating polypropylene fibers, information on the corresponding compressive strength is required. Rasul et al. 52 proposed the following relation for the effect of polypropylene fiber content on the compressive and tensile strength of UHPC based on results from their experimental study: where f 0 C-PP is the compressive strength of UHPC with polypropylene fibers, f 0 C is the compressive strength of UHPC without polypropylene fibers (with only steel fibers), f 0 T-PP is the tensile strength of UHPC with polypropylene fibers (and steel fibers), f' T is the tensile strength of UHPC without polypropylene fibers, and PPF is the polypropylene fiber content by % of volume. The above strength relations were derived for typical UHPC mixes with steel fibers and are not applicable for unconventional UHPC mixes, without steel fibers, as UHPC mixes without steel fibers exhibit lower strength and ductility properties than UHPC mixes with steel fibers.
Along with data on tensile strength, information on the permeability of concrete is critical for predicting fire-induced spalling in concrete. The initial gas permeability of undamaged concrete at room temperature is taken as 2.3 Â 10 À18 m 2 for UHPC based on experimental studies in the available literature. 21 Upon addition of polypropylene (PP) fibers, the permeability of concrete increases at temperatures above 160 C, that is, after melting of polypropylene fibers. The increase in permeability after melting of PP fibers is related to the increase in fiber connectivity, depending on the dosage (or volume fraction) and the aspect ratio (length/diameter) of PP fiber. 59,60 Fiber connectivity results from the arrangement and percolation of fiber clusters which generate randomly according to their gradation. [61][62][63][64][65][66] Based on polypropylene fiber percolation model developed by Tran et al., 67 concrete is treated as a composite of fibers and concrete matrix arranged in series or parallel with the fluid flow, and its permeability can be equated as: where k m = initial permeability of UHPC (matrix) without any PP fiber, and k f = permeability of fiber tunnels can be expressed by the directional Poiseuille transport of fluids 70 along fiber tunnels as: not exceed 600 C, steel rebars exhibit a reversible behavior. 71 When the temperature in the steel rebar exceeds 600 C, the residual yield strength for reinforcing steel is calculated using the temperatureinduced degradation trends reported by Neves et al.. 72 For concrete, a 10% loss in compressive and tensile strength is considered during cool down to room temperature, according to Eurocode 4 provisions. 73 A partial recovery in the thermal strain of concrete is assumed based on test data reported in the literature, 74 whereas transient creep strains of concrete are irreversible and do not recover during cooling down. 71 Specific heat and thermal conductivity of concrete are taken as irreversible as these thermal properties mainly depend on moisture of concrete and water are not re-condensed in concrete during the cooling phase. 75 The residual properties of concrete are adopted from studies on conventional concrete types as currently, there is a lack of residual test data and residual property relations for UHPC subjected to the cooling phase.

| MODEL VALIDATION
The validity of the above-developed numerical model is established by comparing the predicted response parameters against data measured in tests conducted on five UHPC beams, designated as U-B1, U-B2, U-B3, U-B10, and U-B11 tested by Banerji et al. 24 This study was selected for model validation as it provides comprehensive information on the fire behavior of UHPC beams tested under realistic loading and fire conditions.

| Details of UHPC beams used for validation
Details of the UHPC beams selected for validation of the numerical model are shown in Table 1. Although the model was validated for five UHPC beams, the discussion and plots for comparison of predicted parameters with measured data are presented for three UHPC beams (U-B1, U-B3, and U-B10) due to space constraints and comprehensive information can be found elsewhere. 13,26 Beams U-B1 and U-B3 were made of UHPC with steel fibers, while beam U-B10 was made using UHPC with both steel and polypropylene (PP) fibers.
Beam U-B3 was tested at room temperature to benchmark at ambient conditions and subjected to monotonic flexural loading until failure, while beams U-B1 and U-B10 were tested under fire conditions and were subjected to load ratios of 40% and 45% respectively, of their ultimate capacity at room temperature. All the UHPC beams had a rectangular cross-section with a depth of 270 mm, a width of 180 mm, and a total length of 4000 mm, with three steel reinforcing bars having a diameter of 13 mm as the longitudinal tensile reinforcement as illustrated in Figure 8. The beams were tested under simply supported end conditions and were subjected to two-point flexural loading, wherein each point load was located at 1.4 m from the end support as shown in Figure 8. In the fire tests, the middle 2.4 m portion of the beam was exposed to "design fire" (DF) to simulate a typical office fire as shown in Figure 9.

| Validation at ambient conditions
To establish validation of the developed model at room temperature, the predicted load-deflection response at the mid-span of UHPC beam U-B3 is compared to the measured response in Figure 10A.
Beam U-B3 exhibited a linear elastic load-deflection response until initial cracking occurred in concrete at an applied loading of 26 kN.
In the post-cracking stage, deflection increased at a higher rate due to a reduction in stiffness of the beam resulting from an increased number of cracks and their progression. As a result of higher cracking in concrete, stresses in steel reinforcement bars increased at a faster rate and the rebars yielded at an applied loading of 81 kN. After the yielding of the steel rebar, beam U-B3 endured strain hardening with an increase of load-carrying capacity till reaching the peak load. From Figure 10A, it can be observed that the predicted and measured loaddeflection response are in good agreement. The peak load is predicted by the model as 100 kN, which is very close to the measured peak load of 97 kN. The attainment of peak load is followed by a rapid rise in deflection owing to the softening of concrete till the failure of the beam. Compared with the measured response, the predicted loaddeflection response of beam U-B3 is slightly stiffer after rebar yielding, which can be attributed to variations involved in the adaptation of mechanical properties of steel rebars in the numerical model.
Further, the predicted load-strain response of beam U-B3 is compared in Figure 10B    Thus, the developed numerical model is capable of predicting the response of UHPC beams at ambient conditions.

| Validation under fire conditions
The developed numerical model is validated for high-temperature exposure by comparing model predictions against measured data from fire tests on UHPC beams.  Figure 11. The predicted and measured temperatures at locations closer to the fire-exposed sides are higher than the interior concrete layers farther from the exposed surface. This can be attributed to low thermal conductivity and high specific heat of concrete that delays heat penetration to the inner concrete layers. 25 Slightly higher temperatures are predicted by the model at certain locations making temperature predictions slightly conservative, such as, at quarter depth and mid-depth from the bottom exposed surface in the analyzed beams. These variations between predicted and measured temperatures can be attributed to the minor variation in the actual extent of spalling during the fire test and the predicted spalling in the analysis.
It can be seen from the results in Figure 11, that the temperature rise in the beam with polypropylene (PP) fibers, U-B10, occurs at a slower rate than the beam without PP fibers, U-B1. Polypropylene fibers in beam U-B10 helped to mitigate spalling and minimized loss of cross-section during fire exposure, thereby slowing down temperature rise in the interior of the section. In addition, the rapid rise in sectional temperatures in beam U-B1 after the first 10 min of fire is due to the occurrence and progression of spalling, which led to the loss of cross-section and in turn exposed interior layers to increasing heating.
Further, some undulations in the form of peaks can be seen in the measured sectional temperature trends of the UHPC beam without PP fibers, U-B1, at quarter depth and mid-depth from the bottom exposed surface, potentially due to sudden temperature rise resulting from loss of cross-section due to localized spalling taking place in U-B1 at the sides of the beam. The numerical model was not able to capture these abrupt temperature undulations, however, the temperature predictions for beam U-B1 were in range with the reported data.
F I G U R E 1 1 Comparison of predicted and measured temperatures as a function of time in the analyzed UHPC beams F I G U R E 1 2 Measured and predicted extent of spalling as a function of time in the analyzed UHPC beams These temperature protuberances were not present in the measured temperature trends of the other UHPC beam with PP fibers, U-B10 due to lower levels of spalling as compared to beam U-B1. Overall, predicted and measured temperature trends match reasonably well and temperatures are close to each other for the analyzed UHPC beams and thus, the model is deemed to be capable of capturing the thermal response of UHPC beams.

| Spalling response
The spalling predictions from the model are validated by comparing the progression of spalling (time at which spalling started and stopped) and its extent, with the measured values from the fire tests. The spalling progression was recorded through auditory and visual observations from the windows of the furnace during the fire test. In addition, the extent of spalling was measured through the volumetric loss of concrete in the UHPC beams after the fire tests. 24 The predicted and measured extent of spalling at the end of fire tests are tabulated in Table 1 and are plotted in Figure 12  The test data in Figure 12 shows that for the UHPC beam with-  Table 1 is fitting and the model predictions for spalling, thermal, and structural response, and fire resistance, are within the range of the actual data for the analyzed beams. It should be noted that lower spalling is predicted in UHPC beam with PP fibers than UHPC beam without PP fibers due to the release of pore pressure and increase in permeability through melting of PP fibers.
To further investigate the spalling response of the analyzed UHPC beams, mid-span pore pressure values as computed by the numerical model, at 40 mm inwards from the fire-exposed right side and 40 mm depth from the unexposed top surface are plotted in Figure 13. The analysis results show that a peak pore pressure of be mentioned that pore pressure could not be measured in the fire tests owing to limitations in measuring methods and sensors that can reliably measure pore pressure at high temperatures. 47 In comparison to pore pressure values in UHPC, typical pore pressure ranges from 1 to 3 MPa in fire-exposed Normal Strength Concrete (NSC) due to the ease of release of vapor owing to its high permeability. The higher pore pressure in UHPC is due to their low permeability and dense microstructure, and this directly contributes to a higher extent of spalling in UHPC beams.

| Structural response
As part of the structural response validation, the mid-span deflections predicted by the model for the analyzed UHPC beams U-B1 and U-B10 are compared with the measured deflections in Figure 14

| Fire resistance
Fire resistance of the UHPC beams was evaluated by applying strength and deflection criteria, in which the lower of the two failure times, is taken as the governing fire resistance. The predicted failure times are compared with those from fire tests in Table 1 where T c = temperature ( C) of fire curve in cooling phase; T f,max = peak fire temperature ( C) attained during heating phase; t = time in hours; and DHP = the duration of the heating phase in hours. The thermal response of the analyzed UHPC beams is illustrated by plotting the temperatures at the corner rebar in Figure 15.
It can be seen from Figure 15 that the rate of increase in sectional temperatures of all the UHPC beams depends on the temperature rise in time-temperature curves of respective fire exposure scenarios. The beams subjected to ASTM E1529 (hydrocarbon fire) and Fire 3 have the fastest temperature progression, followed by ASTM E119 and Fire 2, and lastly followed by Fire 1. The temperature rise in the beam subjected to ASTM E119 was similar to the beam exposed to Fire 2, as well as the beam subjected to ASTM E1529 was similar to the beam exposed to Fire 3. This is because the time-temperature curves during the heating phase of Fire 2 and Fire 3 are the same as the ASTM E119 and ASTM E1529 standard fire exposures, respectively.
Fire 2 has a shorter duration of heating phase than Fire 1 and has a lower fire severity than Fire 3. The heat propagation within the beam subjected to Fire 2 stops when the decay phase starts, and gradually, the rise in sectional temperatures ceases and starts to decrease. The rebar temperatures in the beam subjected to Fire 2 remain below the critical temperature limit of 593 C. 34 However, the rebar temperatures in the beams exposed to the standard fire exposures (ASTM E119 and ASTM E1529) and the other design fires, Fire 1 and Fire 3 reach critical temperature limit of 593 C, resulting in faster degradation of stiffness and early failure of the beam prior to entering the cooling phase. In addition, Figure 15 shows that despite being subjected to the fire exposure of lowest severity that is, Fire 1, the corner rebar in this UHPC beam attained the critical temperature limit of 593 C. This can be attributed to the longer duration of 90 min in heating phase of Fire 1 followed by a slower cooling rate as compared to the other design fire exposure scenarios which although had higher fire severity, but comprised of shorter heating phase, followed by a faster cooling rate. Therefore, along with the fire severity, duration of the heating phase and subsequent cooling rate are critical for inferring sectional temperatures in UHPC beams.
The extent of spalling in the analyzed UHPC beams is shown in Figure 16 as a function of fire exposure time. The amount of spalling is the lowest (5.35%) for the beam under Fire 1, due to the lower fire intensity and a lower rate of heating in Fire 1, which in turn resulted in lower thermal gradients and slower drying of concrete inducing lower hydro-thermal stresses in the beam. ASTM E1529 and Fire 3 encompass high heating rates, resulting in the generation of high pore pressure and thermal stresses, leading to higher spalling (6.17%) in the UHPC beams, as compared to the beam subjected to Fire 1. However, the fast heating in ASTM E1529 and Fire 3 leads to excessive microcracking in concrete and releases pore pressure, slightly lowering the extent of spalling in the exposed beams than contributed to the attainment of the highest fire resistance among the beams that failed. Therefore, these results infer that the fire scenario has a significant influence on the fire response of the UHPC beams, wherein the rate of increase in deflection is dependent on the severity and the rate of rise in fire temperatures.

| Effect of load level
To study the influence of load level on fire response, UHPC beams were analyzed under varying load ratios of 30%, 40%, 50%, 60%, and 70%, and exposed to ASTM E119 standard fire. The load ratio is the proportion of the bending moment because of applied loading under fire conditions to the flexural capacity of the beam at room temperature. Results from the analysis show that the sectional temperatures are higher in UHPC beams subjected to a load ratio of below 50%. This is mainly due to the higher extent of spalling in the beams under lower load ratio, due to lower load-induced cracking, resulting in lower permeability and in turn restricting the release of pore pressure. The extent of spalling in UHPC beams with varying load ratios is plotted in Figure 18, and it can be observed that the extent of spalling significantly increases when UHPC beams are subjected to load ratios lower than 50%. It is worth noting that studies in the literature have demonstrated that in NSC and HSC beams, varying load ratios do not influence the thermal response of RC beams. 76,77 However, the applied loading level influences the rate of temperature rise in fire-exposed UHPC beams.
Additionally, the level of loading can significantly impact the structural behavior of fire-exposed UHPC beams. As shown in Figure 19, the deflection and rate of deflection increase with increasing load ratio. This is because a higher load level produces higher internal stresses, which in turn causes early deterioration in the strength and stiffness properties of concrete and steel. This degradation in properties of constituent materials causes lower stiffness in the beam and results in increasing deflections and lower fire resistance with increasing load ratio. Therefore, it can be deduced from the current set of analyses that the effect of load ratio on fire resistance of UHPC beams is complex and counteracting in nature.
On one hand, the extent of spalling and sectional temperatures tend to be lower with increasing load ratio (>40%), whereas, on the other hand, increasing load ratio causes a faster rise in deflections. Further, a higher load ratio also generates load-induced mechanical stresses which can accelerate spalling.

| CONCLUSIONS
Based on the results presented in this paper, the following conclusions can be drawn: • The proposed macroscopic finite element-based numerical model is capable of predicting the thermal, spalling, and structural response of UHPC beams from initial loading to collapse stage under combined effects of fire exposure and structural loading.
• The model accounts for varying spalling patterns along the beam length, temperature-dependent concrete permeability variations, different strain components, high-temperature material properties of UHPC and steel reinforcement, and realistic failure criteria. Specifically, spalling sub-model takes into consideration stresses due to pore pressure in addition to often neglected stresses from structural loading and thermal gradients based on the newly proposed theory for spalling.
• The addition of polypropylene fibers to UHPC lowers the extent of fire-induced spalling in UHPC beams, by decreasing the built-up pore pressure through increased permeability in concrete caused by the melting of polypropylene fibers.