Concrete has superior fire resistance among structural materials, but its behavior under high temperature conditions is quite different from that under general conditions. The temperature of a very thick RC structure generally does not increase globally due to its low thermal conductivity, therefore it is considered as a fire resistant structure. However, the surface of concrete exposed to a high temperature fire can be torn off by explosive spalling. Studies have been done on the prevention of concrete spalling and temperature increase of the steel embedded in the concrete [1,2,3,4, and 5]. Kim et al  applied a fiber cocktail, which consists of PP and steel fiber, to concrete and evaluated the thermal characteristics of the fiber cocktail embedded concrete including compressive strength, elastic modulus and specific heat.
The stress-strain curve of a concrete structure is greatly affected by thermal loading. To evaluate the resistance of a structure right after thermal damage, a material model with proper thermal parameters must be chosen. Lie  proposed a stress-strain relation that considered the temperature effect based on the model by Ritter  and Hognestad . Schneider suggested another stress-strain curve that considered the temperature parameter, which referred to EUROCODE 2 . Shi et al  made a model whose loading curve was different from the unloading curve under thermal load. Nan et al  proposed a model, whose behavior was consistent up to 300℃ and the strength decreased with increasing maximum strain for temperatures over 300℃ EUROCODE 2  specified a model, which was divided by an initial curved line of hardening, followed by a straight line of softening. The stress-strain curve of a steel member is strongly affected by thermal load, but it recovers its original shape after the member cools down .
In this study, one ordinary specimen and one fire resistant specimen with 0.1% PP fiber (Fig. 1) were assumed to be simply supported and tested according to ISO 834 (Fig. 2), and the temperature was measured at several depths of the concrete slab. After the thermal loading test, the resistance of the cooled down structure was evaluated. Related to this study, the performance of an undamaged
concrete slab was evaluated by C.-H. Chung et al . The stress-strain relations of existing studies were reviewed and calibrated using the recorded temperature at each depth. These stress-strain relations were selected for nonlinear finite element analysis. The effect of thermal loading was best described by a specific material model and this finding is one of the main purposes of this study.
Lie  suggested stress-strain relations (1)-(3) considering the temperature effect based on the stress-strain curve proposed by Ritter  and Hognestad . This model is well presented in Fig. 3, in which the result of Schneider and Haksever  is included and the creep at high temperature is considered.
fc : strength of concrete at T℃(MPa)
fc´ : strength of cylinder concrete at T℃(MPa
f´co : strength of cylinder concrete at room temperature (MPa)
εc : strain of concrete at temperature 20℃
εmax : strain of concrete at the maximum stress
Schneider  suggested a temperature dependent stress-strain curve, as given by eq. (4), where the maximum strain
εc1, T : strain value corresponding to compressive strength fc, T at temperature T℃.
fc, T : compressive strength of concrete at temperature T℃(MPa)
εcu, T : ultimate strain at temperature T℃
n : 3
fc : compressive strength of concrete at T=20℃ (MPa)
The compressive strength of concrete
？？o : strain corresponding to fc at room temperature
Compressive Strength Ratio, fc, t/fc, εc1, T and εcu, T 
εσo : strain corresponding to fcT at temperature T℃
A temperature increase leads to both the decrease of
f : stress of concrete (MPa)
Fig. 6 presents another model by Nan et al , where the compressive strength of concrete decreases and the corresponding maximum strain increases above a temperature of 300℃. The stress-strain relation is described in eq. (10), and the compressive strength and maximum strain of concrete are determined by eq. (13) ~ eq. (15).
fc : compressive strength of concrete at room temperature
fcT : compressive strength of concrete at T℃ (MPa)
εcT : strain corresponding to fcT
εc : strain corresponding to fcT
εp : the maximum strain at room temperature (=0.0025)
The stress-strain curve of EUROCODE 2  is presented in eq. (16) and Fig. 7, which is characterized by a parabolic increase and a linear decrease curve. The curve is described by eq. (16a) for strains less than or equal to
fc, T : compressive strength of concrete at T℃(MPa) (table 1)
εc1, T : strain corresponding to fc, T (table 1)
εcu, T : the maximum strain (table 1)
Many researchers have proposed temperature dependent stress-strain relations of a steel member as shown in Fig. 8, where the yield stress decreases rapidly according to the temperature increases. However, steel recovers its original yield strength when it cools to room temperature in a few studies .
As described previously, steel rebar loses a significant part of its elastic modulus and yield strength during thermal loading but recovers almost all of them when it cools down to the ambient temperature. In this study, an embedded steel rebar recovered after a thermal loading experiment is used to measure the yield stress and tensile strength of the cooled rebar. For a parametric study, eight specimens including one that does not undergo thermal loading, another one without PP fiber (thermal loading) content, and a third one with 0.1% PP fiber (thermal loading) content were prepared for experiments. Measured yield stresses and tensile strengths of rebar are summarized in table 2, where almost all of the steel rebars, regardless of the thermal loading and PP fiber content, recovered to their original yield stresses and tensile strengths after cooling down. Therefore, it is concluded that the strength of a steel rebar drops significantly during thermal loading due to fire, but it recovers to its original strength after cooling down to room temperature.
An RC slab specimen used in the fire loading and structural testing is shown in Fig. 9. This specimen describes the wall part of an underground box structure for a power supply. The thickness and rebar arrangement of the test specimen follow the actual specification of the box structure. The temperature sensors (K-type thermocouple) are located 20mm, 50mm (main rebar), 100mm, and 150mm (compressive rebar) from the fire exposed surface of the slab. Taking into consideration the construction errors of
Yield Stress and Tensile Strength of Steel Rebar before Thermal Loading and after Cooling Down to Room Temperature.
the specimen and the data collection errors of the fire test, the thermocouples were installed at two different places as shown in Fig. 9 (b). The specifications of the test specimen are listed in table 3. To prevent explosive spalling due to temperature increase, the percent of PP fiber in the test specimen was set to 0.10 vol.%.
The characteristics of the PP fiber in the test specimen are listed in table 4, and the mix proportions of concrete with 35MPa design strength are shown in table 5. A cylindrical standard specimen has an average of 30MPa 28- day strength due to air curing
The ISO 834 curve (, ), specified mainly for building structures, is widely applied in standard fireresistance tests as a temperature condition. The ISO 834 fire curve is determined by eq. (17).
t : fire exposure time (min)
T(t) : temperature at time t (℃)
Ta : ambient temperature (20℃)
The fire-resistance test is the thermal loading of an ISO 834 fire curve on one surface of a specimen for 180 minutes. The shape of furnace and the specimen after the test are shown in Figs. 10(a) and 10(b).
The surface condition of the thermally loaded concrete is shown in Fig. 11. The general specimen without PP fiber exhibited damage due to a small explosion, whereas the specimen with 0.1vol.%. PP fiber showed no sign of popping expansion damage. The thickness at which the slab separated due to the spalling varied from point to point.
The time history of temperature measured inside the
Types of Test Specimen
Properties of PP Fibers
Mix Proportions of Concrete with 35MPa Design Strength (kg/m3)
test specimens is presented in Fig. 12. In the case of the general specimen without PP fiber content in Fig. 12(a), the temperature at a depth of 20mm was very similar to that of the thermal loading temperature because some of the concrete separated during the thermal loading due to explosive spalling. As depth increased, the temperature dropped and converged at depths over 150mm. In the case of the specimen with PP fiber contents shown in Fig. 12(b), the temperature dropped significantly even at a depth of 20mm because the concrete had no separation due to a spalling.
Fig. 13 presents measured temperatures according to the position from the surface of the concrete at specific times during the thermal loading. Temperature decreases up to a depth of 150mm and converges afterwards. The specimen with PP fiber contents showed temperature variations up to a depth of 100mm but converged afterwards.
KS (Korea Standard) F 2257-7 specifies that the average temperature of rebar in columns and beams should be 538℃ and that it should be less than 649℃ under the ISO 834 fire test. After 120 minutes of fire attack, a rebar close to the surface of the specimen without PP fiber contents violated this specification, whereas the temperature of the rebar in the specimen with PP fiber contents remained below the KS F 2257-7 specification (Table 6).
Temperature of Steel Rebar (℃)
The specimens used in the ISO 834 fire test were cooled down to room temperature and the structural loading test followed. To yield bending failure, the edges of the RC slab were simply supported and the remaining strength of the structure was evaluated after the fire damage. A 1000kN actuator was used to produce and measure the deflection at the center. The test setup is shown in Fig. 14.
The load-deflection curve from the structural load test is shown in Fig. 15. The maximum resistant load of the specimen without PP fiber content was 253.8kN, which was about 80% of that of the specimen with PP fiber content (316.9kN). Furthermore, although both specimens showed similar ductile behavior, the stiffness and maximum strength of the specimen without PP fiber content were significantly lower than those of the specimen with PP fiber content. This difference is due to the explosive separation of concrete following the increase in temperature.
The stress-strain relation of the concrete specimen used in the fire test was determined from the curve of the measured temperature versus depth of the cross section, and nonlinear structural analyses were performed using this relationship. The mechanical characteristics of concrete cannot recover from damage due to temperature increase. It is generally assumed that the stress-strain relation of concrete after cooling down is similar to that of the heated (damaged) concrete. The material characteristics of a steel
rebar are affected by the temperature increase significantly, but a rebar recovers its original strength after the cooling process . In this analysis, an elastic-perfect plastic model at room temperature (20℃) is chosen among the temperature dependent steel models suggested by Lie . A general purpose finite element program ‘Abaqus’ with ‘Concrete’ model was utilized for analysis .
Temperature dependent stress-strain curves of concrete from the references are all different from one another and they are compared and investigated. The maximum temperatures measured versus the cross section concrete depth during a fire test is summarized in table 7.
In the case of specimens without PP fiber content, the formula of Schneider  showed decreasing material performance up to 150mm depth, whereas the formula from EUROCODE 2  showed the convergence of material performance around 100mm depth. The Lie  formula showed weakening material up to 100mm depth, whereas the Shi et al  and Nan et al  formulae showed convergence of the material strength at around 50mm depth. In the case of specimens with PP fiber content, overall performance near the surface of thermal loading was enhanced. Figures (Fig. 16-Fig. 20) present various material models.
Maximum Temperature Versus Depth of the Concrete Cross Section
Temperature dependent stress-strain relations for each depth are presented in Fig. 21 and Fig. 22 according to the above mentioned formulae. Fig. 21 shows the case of concrete with 0% PP fiber content: the strength is very
small up to 50mm depth and the strains at the maximum calculated stresses show large differences. Fig. 22 presents the case of concrete with 0.1vol.% PP fiber content: a good portion of the strength is maintained within the 50mm depth area. The strength of the concrete does not vary much for each formula, whereas the magnitude of strain varies at 100mm depth.
Using the stress-strain relations presented in the previous section, the resistances of the cross section after fire damage were evaluated by nonlinear finite element analysis. In the stress-strain relations of concrete, the maximum temperature during the fire test was applied according to Fig. 23. The strength reduction of the steel was not considered, and an elastic-perfect plasticity model  was applied to all analyses.
The maximum resistances of all cases are listed in Table 8. The results in Fig. 24 present the case of the specimen without PP fiber content. The Lie model  yielded curves which matched well with the test results. The result using EUROCODE2  showed some differences of the stiffness near the initial stage. The difference of the maximum resistance was about 5.8%. The Schneider  model and Nan et al.  models matched the test results well, whereas the Shi et al  model estimated the resistance of the cross section to be about 19% lower than that of the actual test.
The results in Fig. 25 present the case of the specimen with 0.1% PP fiber content. The Lie  model and Nan et al  model closely estimated the test results at about 101~103%, whereas the EUROCODE 2  model and Schneider  model underestimated the results at about 91~95%. Table 11 shows that the measured resistance load
Maximum Resistance (Test and Analysis Result)
of the 0.1vol.% PP specimen during the test increased by about 24% from that of the 0 vol.% case. In the analysis, the resistance load of each model increased by 107~155% compared to the non-PP fiber case, and the Lie model most closely matched the actual resistance load level.
In this study, the temperatures of an RC slab at each depth are measured during a fire experiment (thermal loading test) based on the ISO 834 fire curve. The remaining strength of the structure after the thermal loading is evaluated at room temperature. Applications of the temperature curve obtained from the thermal test to the stress-strain curves from many previous studies are investigated. Nonlinear finite element analyses using the stress-strain-temperature relation are performed and the following conclusions are made:
1. An explosive spalling was witnessed during the fire experiment for the specimen without PP fiber, but not for the specimen with PP fiber. The thickness at which the slab separated due to the spalling varied from point to point.
2. In the case of the specimen without PP fiber, the temperature at a depth of 20mm was very close to that of the thermal loading itself because the concrete surface was separated due to spalling, whereas in the case of the specimen with PP fiber, temperature decreased significantly at a depth of 20mm because the concrete surface had no damage. Regardless of the type of specimen, temperature decreased up to a depth of 150mm and showed no significant change afterwards.
3. Measured temperatures during the fire experiment were applied to the models of Schneider, EUROCODE 2, Lie, Shi et al, and Nan et al, where the stressstrain relationship for each depth was set accordingly. The strengths of the specimen without PP fiber predicted by the various models were very low up to a depth of 50mm and they were similar at a depth of 100mm, whereas the corresponding strains were quite different depending on the model used. The strengths of the specimen with PP fiber were maintained relatively well within a depth of 50mm and they were similar at 100mm depth. The overall performance of the specimen with PP fiber was enhanced near the surface of thermal loading.
4. The ultimate strengths of real specimens were compared with analytic results obtained from the various concrete stress-strain-temperature models. For the specimen without PP fiber, Lie’s model gave results that were the closest to the test results. The stiffness predicted by the EUROCODE 2 model was different from the test result and it underestimated the strength by about 5.8%. The Schneider model and Nan et al model predicted the test results well, whereas the Shi et al model underestimated the strength at about 81%. For the specimen with PP fiber, the EUROCODE 2 model and Schneider model underestimated the strength at about 91% and 95%, respectively, whereas the other models gave relatively accurate estimations at about 101-103%.
5. The test result showed that the addition of 0.1vol.% PP fiber enhanced the strength of the specimen up to 124%. The analyses using several material models estimated 107% to 155% strength enhancement, whereas the Lie model estimated the actual strength enhancement the closest at 125%.