Study on the Prediction of Residual Life of Concrete Rectangular Beams after Fire

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Introduction
According to statistics, there are about 150,000 building fres in China and 3.6 million worldwide annually [1]. Fires often lead to severe structural damage or even collapse, destroying the space where people live, taking away people's lives, and creating panic and anxiety in society. Nowadays, reinforced concrete structures are widely used in engineering felds, so the fre resistance of reinforced concrete structures has attracted signifcant attention. However, there is a consensus that the fre resistance of concrete structures is superior, so researchers have focused on the fre performance of steel structures and should have paid more attention to the study of the critical issues of fre resistance of concrete structures [2]. However, even if the concrete is a thermally inert material, the design is very likely to be deformed or even destroyed and collapse under the high-temperature environment, and along with the development and popularization of new materials and new types of structures to improve the load-bearing capacity, it forces us to research the structural fre problem, especially the remaining service life of the system after the fre [3].
Domestic and international research on the remaining service life and other properties of concrete has been going on for many years, and fruitful research results have been achieved. Bentz [4] used the Monte Carlo method to calculate the service life and summarized the service life prediction model of the one-dimensional difusion of chloride ions by derivation. Shim [5] established a model of remaining service life, and the two-dimensional distribution of chloride ions was considered. Angst [6] investigated the remaining service life of concrete after the fre, especially after the fre, and studied the corrosion of reinforced concrete materials by chloride ions and the efect on the remaining life of the structure. By comparing the computational results of fnite element numerical simulation with the existing test results, he found that even the more rigorous model still has a poor prediction of erosion time and remaining life, and pointing out that the main bottleneck lies in the lack of determination of the onset of erosion, ignoring the efect of size efect on localized corrosion, and using the test results are not very representative. Yang and Zhang [7] established a model for reinforced concrete beams after steel plates were attached and supported, considering the two-dimensional difusion of chloride ions. Yang and Zhang [7] modeled a reinforced concrete beam after reinforcement, divided the force of the member into the original part and the newly added feature, adjusted the degree of unloading as well as the area of the pasted steel plate to allocate and regulate the force of the two parts, to make the two reliabilities compatible, and calculated the life prediction of the reinforced and adjusted member. Yao [8] modeled and analyzed the residual loadcarrying capacity and performance degradation of steelconcrete composite beams considering the conditions of chloride erosion and service loading and then based on the JC method of programming to derive the reliability and residual life of the members. Zhou et al. [9] used the degree of decay up to 10% as a criterion to judge the failure of the structure, established a model of the remaining life based on the degree of pollution and the relationship between the speed and time, based on this model, considered the possible impact of cost, maintenance, and reinforcement factors on the remaining life, and further researched and analyzed the economic remaining life prediction model of reinforced concrete structures.
At present, there are also scholars on the remaining life of concrete structural members to carry out research and calculation, but most of them are on the structure in the service environment, loading, and seismic conditions of the study; the results of the research are challenging to be summarized into a total and do not make a certain amount of research on the structural members of the situation after the fre. Terefore, this study will focus on the remaining life's concrete members after the fre to carry out the research.

Material Intrinsic Coefcients
2.1.1. Termal Conductivity of Concrete. Te thermal conductivity coefcient is the amount of heat that passes through the unit isothermal area of the material under the gradient of unit temperature per unit time, and its crew is W/ (m·k). Tis study adopts the Tongji University Lu Zhou guide [10] through the generalization of the experimental data that put forward the calculation formula of the thermal conductivity coefcient: (1)

Coefcient of Termal Expansion of Concrete.
Te coefcient of thermal expansion α c is conceptualized as the amount of change per unit length, i.e., the strain value, when the temperature of an object is increased by 1°C. Terefore, it can be learned that the coefcient of thermal expansion does not directly afect the temperature transfer process. Still, it will directly afect the stress-strain of the overall structure. Terefore, the coefcient of thermal expansion is also a parameter that we should not ignore in the fre test. Lie and Celikkol [11] in his study stipulated that the change in the type of aggregate while performing the calculations does not afect the coefcient of thermal expansion of the structural members and gives the formula for calculating the coefcient of thermal expansion of concrete: where α c is the coefcient of thermal expansion of concrete and T is the ambient temperature to which the concrete is subjected.

Specifc Heat Capacity of Concrete.
Specifc heat capacity is a frequently referenced index in thermodynamics. It is a parameter used to analyze the temperature feld, which refers to the amount of heat absorbed per unit mass of material for every 1°C rise, and its unit is J/(kg·K). Research by many scholars has shown that specifc heat capacity is not a fxed material parameter but changes slowly depending on the temperature.
Terefore, the Eurocode [12] has used a segmental formula for diferent temperatures to express the specifc heat capacity of concrete at high temperatures: where C c is the specifc heat capacity of concrete.

Density of Concrete.
Density usually refers to the mass of the material itself per unit volume; the unit is kg/m 3 ; many scholars and researchers, through a large number of tests, found that the density of concrete by the ambient temperature change is minimal compared to other thermal parameters by the temperature efect, almost negligible, and to simplify the calculation, this study will be the density of concrete as an invariant constant, that is, take the value of ρ c � 2400 kg/m 3 .

Stress-Strain Relationship of Concrete Beams under High Temperature
(1) Stress-Strain Relationship of Concrete. Te research shows that the increase of ambient temperature in fre will cause the stress-strain curve of concrete to gradually fatten, and the peak value of the curve will shift downward and right, which may be caused by the deterioration of concrete materials caused by high temperature, resulting in a series of changes such as the reduction of compressive strength, the increase of strain peak value, and the reduction of elastic modulus. Lie and Denham [13] concluded that the calculation formula of the constitutive equation of concrete under high temperature is as follows: where ε is the strain that occurs in the concrete under normal temperature conditions, ε 0 (T) � 0.0025 + ( T + 0.04T 2 ) × 10 − , σ is the stress of the concrete, f c is the compressive strength of the concrete, and T is the environmental temperature of the concrete.
(2) Stress-Strain Relationship of Steel Bars. Te stress-strain relationship of steel bars under high temperatures can be divided into two types: broken line type and smooth type. Te polygonal curve looks simpler, is easier to read, and also facilitates computational convergence. Smooth curves are more complex but closer to the actual stress-strain relationship of steel bars. In general, the calculation of the stress-strain relationship under high-temperature action will use a broken line type. According to experiments conducted by Guo and Shi [14], the stress-strain formulas for steel bars are divided into the elastic yield stage and postyield strengthening stage: Te relative coordinates obtained during the reinforcement phase are as follows: where ε is the strain that occurs in concrete under normal temperature conditions; ε T y is the strain that occurs in steel bars under high-temperature T; ε T u is the ultimate strain that steel bars reach under high-temperature T conditions; ε T y is the ultimate strain reached by the steel bar under hightemperature T conditions; and E 5 (T) is the initial value of the elastic modulus achieved by the steel bar under hightemperature T conditions.

Model Parameters.
In order to take into account the possible infuence on the fre resistance of concrete beams, six sets of concrete beam models will be established, and the details are shown in Table 1. Te concrete beam L1 will be used as the basic model in this study to analyze the model under diferent working conditions. Among them, the length of the longitudinal reinforcement is 5000 mm, and the size of the stirrup is 365 mm × 515 mm. Te specifc dimensions of the components are shown in Figure 1.

Basic Assumptions
(1) Te heat energy released inside the member concrete structure is not considered, and q d � 0 is taken. (2) Concrete is a homogeneous and uniform material, (3) Te efect of the coefcient of thermal expansion of concrete is not taken into account, the density is taken as a constant, and the transfer of heat due to factors such as evaporation of water is not taken into account. (4) Concrete under the action of high temperature will occur cracking, bursting, and even peeling phenomena, and the occurrence of these phenomena is difcult to predict, so do not consider the impact of these damages on the temperature feld analysis. (5) Bond performance: According to existing research at home and abroad, the bond-slip constitutive curve between steel bars and concrete is afected by high temperatures. As the high-temperature time increases, the bond performance decreases more signifcantly. Moreover, under the combination of vertical and horizontal repeated loads, the bond performance of steel bars and concrete will accumulate damage and cannot be restored, resulting in a rapid decline in bond performance. Under the action of high temperatures, some scholars have provided a calculation formula for the change in bond strength. Although the constitutive model is still in the theoretical stage, the temperature is defned by "tensile hardening" to be closer to the true bond-slip constitutive situation, and no treatment is performed under other conditions to more accurately simulate the true change pattern of the bondslip constitutive model.

Modeling Points.
In this section, the fnite soft component ABAQUS will model the concrete beam. Te main points are as follows: Advances in Materials Science and Engineering (1) Establish a three-dimensional model of 400 mm × 550 mm × 5000 mm (0.4m × 0.55 m × 5 m), choose a three-dimensional, solid, deformable model for the concrete and a three-dimensional, line, deformable model for the steel reinforcement, and select a model of this size to reduce the scale to restore the actual rectangular beam and to be able to facilitate the application of the load, and the consideration of the boundary conditions will be convenient for the follow-up due to the symmetry that exists in the model. When considering the boundary conditions, the balance of the model will facilitate the subsequent calculation. (2) When setting up the analysis step, the total time step is set to 7200, and the time step increment is 60, which is equivalent to a fre time of 2 h. (3) By defning the load and boundary conditions, the temperature load applied to the concrete beam is the ISO-834 standard warming curve, the front, back, and bottom surfaces of the shaft are set to be subjected to fre on three surfaces (with the more extended surface as the front surface), and the remaining three characters are set to be the insulating surfaces; in the case of fre, the thermal fuid exchanges the heat by convecting with the air where the beam is located, and the thermal convection exchange coefcient of the fre-facing surface is defned to be 30 W/(m 2 ·k), and the nonfre-facing character is defned to be 30 W/(m 2 ·k), and the nonfre-facing surface is defned to be 7200, equivalent to 2 h; the heat convection exchange coefcient of the nonfre-facing surface is 12 W/(m 2 ·k), and the integrated radiation coefcient is taken as 0.7 W/ (m 2 ·k). (4) Te unit type used for concrete is DC3D8, called an eight-node three-dimensional implicit linear thermal analysis hexahedral cell, and the division size is chosen to be 20 mm. Te unit type used for steel reinforcement is DC1D2, called a two-node onedimensional thermal analysis rod cell. Te model grid diagram is shown in Figure 2.

Grid Verifcation.
In order to explore the reasonable cell size and verify the convergence of the calculation results of diferent cell sizes, the model was divided into three cell sizes, as shown in Figure, in which the basic cell sizes of Grid 1, Grid 2, and Grid 3 are 10 mm, 20 mm, and 30 mm, respectively. To verify the computational model, the model in the literature [7] is taken as an example, and the temperature change curves under three cell sizes are shown in Figure 3. As shown in Figure 4, calculation results show that the temperature calculation error of the three cell sizes is within 5%, and the temperature change curve basically overlaps, indicating that the selection of 20 mm cell size has met the convergence requirements.

Temperature Field Results
Te factors afecting the temperature feld of the beam structure are protective layer thickness, reinforcement rate, and fre time. Diferent elements have diferent degrees of infuence on the temperature feld results, so the models L1  to L6, under the infuence of various factors, will be designed, and the L1 beam will be used as the base model and analyzed together with other models under diferent working conditions. According to ABAQUS calculation, the temperature cloud distribution of beams L1 to L3 under diferent fre periods will be obtained, and the results are shown in Figures 5-10 (the central part of the cloud is the temperature feld distribution of the span-to-center cross section of the structure, and the upper left corner is the temperature legend).
According to Figures 5 and 6, it can be concluded that when the L1 beam was subjected to fre for 60 minutes, the maximum temperature of the unit reached 892.1°C and the minimum temperature was 43.6°C; when the fre time was 120 minutes, the maximum temperature of the crew was 994.1°C and the minimum temperature was 62.2°C.
It can be seen that in the concrete beam in the ISO-834 standard heating curve, the internal temperature feld will not be uniformly presented, the temperature of diferent location units will be very diferent, and the section as a whole shows a "U"-shaped isothermal temperature feld. However, the temperature diference between the units is signifcant, but the temperature of the entire section presents warming. Although the temperature diference of each unit is substantial, the temperature of the whole passage shows a warming trend, and the warming rate of each unit is diferent. It is easy to see that the unit near the surface of the beam is hotter and warms up faster than the unit near the center, the unit near the top of the shaft warms up slower,

Prediction of Remaining Life of Concrete Beam after Fire
In the previous chapter, the fnite element software ABA-QUS is used to establish the concrete beam model, obtain the temperature distribution cloud diagrams of the concrete beam during and after the fre under diferent heating times, and bring the simulated data of the temperature feld, which are analyzed and organized to provide the theoretical and data basis for calculating the residual life prediction of the concrete beam after the fre in this chapter.
Tis chapter introduces the concept and application of carbonation depth and formula derivation, combined with the limit state equation of the beam, using the Monte-Carlo method to calculate the failure probability of concrete beams after the fre, which can be used as the basis for the calculation of the remaining life of the fnal relationship formula.

Limit State Equation for Concrete Beams.
According to the description of rebar de passivation corrosion criterion, the carbonization depth of the structural member reaches the surface of the rebar, which leads to the phenomenon that the rebar begins to rust to judge the beginning of structural durability failure, so the limit state equation of the start of corrosion of the rebar which leads to the front of structural failure is     Advances in Materials Science and Engineering where c is the protective layer thickness of the steel reinforcement in the concrete, which is a random variable; X b is the depth of damage of the concrete structural members when subjected to fre up to a certain point in time, which is a function related to the fre temperature T and the heating time t; and Xc(t) is the depth of carbonation of the concrete in the natural environment after the fre, which is also a stochastic process.

Calculation of Carbonation Depth of Concrete Reinforced
Concrete Beams after Fire. Te main types of carbonation of concrete structural members are carbonation under natural conditions and carbonation under a fre temperature feld. Te carbonation model of concrete structural members under natural conditions is mainly divided into two kinds: one is to analyze and generalize through a large number of experimental models and then derive the main infuencing factors to calculate the carbonation coefcient of structural members; the other is to derive the results through theoretical research plus derivation. Trough many calculations, scholars have reached a consensus: the carbonation depth of structural members is proportional to the square root of time.
In the literature [15], Niu et al. summarized the data in many engineering practices, obtained the relationship between the average carbonation depth of concrete structural members and the compressive strength of concrete, and gave the following calculation formula: where X c (t) is the carbonation depth of the concrete element in millimeters (mm); t is the time to determine the carbonation depth of the concrete element X c (t) in years; k is the carbonation coefcient, which is closely related to the environment; k mc is the random variable for the calculation of the mode of uncertainty; k j is the infuence coefcient of the location of the measurement point, which is 1.4 for the corner area of the element and 1.0 for the noncorner area of the element; k co 2 is the infuence coefcient of the ambient carbon dioxide concentration; k co 2 � ������ � C 0 /0.03 and C 0 are the carbon dioxide concentrations (%); k p is the infuence coefcient of the maintenance pouring, which is usually 1.2; k s is the infuence coefcient of the working stress, which is 1.0 when the structural member is under compression and 1.1 when the structural member is under tension; T 0 is the ambient temperature of the structural member, in°C; RH is the temperature of the structural member. Te unit is°C; RH is the relative humidity of the environment in which the structural member is located; and f cu,k is the standard value of concrete strength in MPa.
In order to calculate the depth of carbonation for the model of concrete structural members after fre, the above equation must be converted with the appropriate corrections because, in addition to the carbonation of the model under the natural environmental conditions without fre, it is more crucial to take into account the degree of carbonation of the concrete beam structure after experiencing a warming fre.
In this regard, we introduce a conversion factor c, which represents the conversion factor between the rapid carbonation of concrete structural members in the atmospheric environment of Fagin and the naturally occurring carbonation, and also need to introduce k ′ ca , which refers to the coefcient of high-temperature infuence on concrete structural members at high temperatures, so that we can know the formula of the model carbonation depth that can be calculated for concrete structural members after a fre, as follows: where X c (t) represents the depth of carbonation of concrete structural members in millimeters (mm); t represents the time taken from the commissioning of concrete structural members to the measured depth of carbonation X c (t) in years; c is the conversion factor between rapid carbonation and natural carbonation of concrete structural members; k ′ ca represents the coefcient of high-temperature efect of concrete structural members subjected to high temperature; and k represents the carbonation coefcient.

Carbonation and Durability Analysis of Concrete Beams.
In the previous analysis, we can see that when the depth of carbonation of the concrete structural members has touched the surface of the steel reinforcement, then the reinforcement will be a corrosion phenomenon, and then we will consider that the substructural members begin to occur carbonation durability failure, so the functional function of the durability state is as follows:

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when Z ca (t) � 0; we consider this structural element to be in the durability limit state, so when Z ca (t) < 0, the reinforcement is in the rusted state, the probability of the function at the rusted state of the reinforcement is Ten, according to the derivation of the equation , the expression of the durability reliability index of concrete structural members is as follows: where Φ − 1 indicates the inverse function.

Probabilistic Model of Protective Layer Tickness c of Concrete Structural Members.
According to the conclusions in the literature [15], it can be seen that the value of the protective layer thickness of concrete structural members obeys a normal distribution, i.e., c ∼ N(μ c , σ 2 c ); then, its probability density function is as follows: where f(c) represents the probability density function of the protective layer thickness of the concrete structural members; c represents the protective layer thickness of the concrete structural members; μ c represents the mean value of the protective layer thickness of the concrete structural members; and σ c represents the standard deviation of the protective layer thickness of the concrete structural members.

Parametric Statistics of the Burn Depth X b of Concrete Structural Elements.
Trough the conclusions of the tests in the literature [16], the burned layer in the concrete structural members contains a series of complex processes not only the high-temperature decomposition caused by the fre but also after the decomposition of the components with other substances in addition to the reaction; the burned layer will generally show a weak alkaline or neutral. Also, according to the test results, the value of the depth of the burned layer can obey a normal distribution, that is, ; therefore, its probability density function is as follows: where f(X b ) is the probability density function of the burn depth of concrete structural members after fre; X is the burn depth of concrete structural members after fre; μ X b is the mean value of the burn depth of concrete structural members after fre; and σ X b is the standard deviation of the burn depth of concrete structural members after fre.

Parametric Statistics of Carbonation Depth X c of Concrete Structural Members.
In the conclusion of the literature [15], it is stated that the carbonation depth of concrete structural members is stochastic in nature and retains a certain amount of stochastic process in it, so it can be regarded as a nonsmooth stochastic process. Ten, the one-dimensional probability density expression of the carbonation depth is as follows: where f[X c (t)] is the probability density function of the carbonation depth of concrete structural members; X c (t) is the carbonation depth of concrete structural members after the high temperature of the fre feld; t is the carbonation time; μ X e (t) is the mean value of the carbonation depth of concrete structural members; and σ X e (t) is the standard deviation of the carbonation depth of concrete structural members. Ten, the function expressions of μ X e (t) and σ X e (t) are derived by combining the formulas in Chapter 2, and this chapter is as follows: where c is the conversion factor between rapid factor and natural factor; k ′ ca is the coefcient of infuence of hightemperature factor in fre; and μ K M c and σ K M c are the uncertainty coefcients, which usually take values of 0.996 and 0.355, respectively. Similarly, the mean μ X b and standard deviation σ X b of X b can be found. 8 Advances in Materials Science and Engineering

Remaining Life of Concrete Structural Members.
According to the previous formula (11), it can be seen that the probability of failure of concrete structural components P f is a function related to the lifetime t, P f can be calculated according to the probability of failure P f and the reliability index β of the relationship between the reliability index β and the lifetime t. Tis study will be divided into the following cases: when the concrete structural members are important structures and ordinary structures, the corresponding reliability indexes β are taken as 0.5 and 0, respectively, to fnd out the remaining life of structural members under diferent conditions.

Example Analysis.
In this study, a concrete building, after experiencing a high-temperature fre in the literature [14], will be used as an example for calculation.
Te building experienced a fre for about 40 minutes, and after the on-site investigation, it was found that the temperature in the fre reached a maximum of about 750°C. Te building is a reinforced concrete shear wall with a framesupported shear wall. Te building was constructed with reinforced concrete shear walls as the main body, using a frame-supported shear wall structural system, and the design strength of the concrete was C40. Te relative humidity at the location of the building at that time was 81%, and the ambient temperature was 17.1°C.
After testing, the results of each building parameter after being subjected to fre are as follows: (1) Te mean value of the protective layer thickness c of concrete members is 27.9 mm with a standard deviation of 3.7 mm (2) Te mean value of carbonation depth for concrete members is 19.7 mm with a standard deviation of 4.5 mm (3) Te mean value of compressive strength of concrete members after fre is 36.5 MPa, the standard deviation is 3.6 MPa, and all the above parameters obey normal distribution Te Monte-Carlo method was used for the calculation with a sample size of 100,000, and the relationship between the reliability index and the remaining concrete life after fre was obtained, as shown in Figure 11.
According to Figure 11, when the structure is required to continue to serve for 15 years, the structural reliability calculated in the literature is 0.5, and the structural reliability calculated in this study is 0.6; when the structure is required to continue to serve for 35 years, the structural reliabilities calculated in the literature and in this study are both slightly higher than 0.1.
When the reliability index of the concrete structure is taken as 0.5 (components of essential buildings), the remaining life of the results of the literature is about 17 years, and it is about 18 years according to the method of this study; in contrast, the reliability index of the carbonation depth of concrete structural components is taken as 0 (details of general buildings), and the results of the literature are about 41 years. Te results of the calculations in this study are about 39 years old.
After comparison, the calculation results of this study and the literature are relatively close to the calculation results. Still, there are individual places where there are deviations, and the main reason for this phenomenon is that the method used in the literature is a little diferent from this study, so in the calculation of the same parameter, other calculation methods will be used, which leads to this study's results and the literature compared with the slightly different. However, the size of the fnal calculated data is close to the literature, and the change curve graph of the computed results also matches well with the literature results, so it can be recognized that the calculation method of the results of this study is reasonable and reliable. Figure 12, when the structure is required to remain in service for 10 years, the reliability of concrete beams with C30 strength is −0.5, which can no longer meet the service requirements; the reliability of concrete beams with C40 strength is 0.2, which can only be used as a component of general buildings in service; the reliability of concrete beams with C50 strength is 0.7, which can be used as a component of essential facilities in service.

Efect of Concrete Strength on the Results of Residual Life Prediction. As shown in
When the reliability index of the concrete structure is 0.5 (member of the critical building) when the system adopts the concrete strength of C30, the concrete structure still has about 2 years of carbonation remaining life; when the concrete strength is C40, the concrete structure still has 5 years of remaining life; when the concrete strength is C50, the concrete system still has 13 years of remaining life.
Also, the reliability index of the concrete structure for 0 (general building components) is taken; when the design uses C30 concrete strength, the remaining life of the

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concrete system is about 6 years; when the substantial power of C40 is used, the remaining life of the concrete structure is about 13 years; when the concrete strength of C50 is used, the remaining life of the concrete system is about 31 years. It can be seen that the strength grade of the material used in the concrete structural members will have an undeniable infuence on the reliability index and remaining life of the concrete after the fre, and increasing the concrete strength grade of the concrete structural members can improve the reliability of the structural members after the fre and prolong their remaining life. Figure 13, when the structure is required to remain in service for 10 years, the reliability of the concrete beam with a concrete protective layer thickness of 25 mm is −1.1, which can no longer meet the service requirements; the reliability of the concrete beam with a concrete protective layer thickness of 35 mm is 0.2, which can only be used as a general building component for service; the reliability of the concrete beam with a concrete protective layer thickness of 45 mm is 1.3, which can be used as a general building and an important building component to continue service. Te reliability of the concrete beam with a 45 mm thick substantial protection layer is 1.3, which can be used as a member of general building and important building to continue service.

Infuence of Concrete Protective Layer Tickness on Residual Life Prediction. As shown in
Te reliability index of the concrete structure takes 0.5 (important building components); if the thickness of the protective layer of concrete is 25 mm, then the remaining life of the concrete system is 0 years; at this time, the concrete structural components have not met the safety requirements and cannot be in service; if the thickness of the protective layer of concrete is 35 mm, then the remaining life of the concrete structural components is about 5 years; if the thickness of the protective layer of concrete is 45 mm, then the remaining life of the concrete structure is about 28 years.
Also, the reliability index of the concrete structure is taken as 0 (general building components); if the thickness of the protective layer of concrete is 25 mm, then the remaining life of the concrete structural components is about 2 years; if the thickness of the protective layer of concrete is 35 mm, then the remaining life of the concrete structural components is nearly 12 years; if the thickness of the protective layer of concrete is 45 mm, then the remaining life of the concrete structural components is about 43 years. If the thickness of the protective layer of concrete is 45 mm, the remaining life of the concrete structure is 43 years.
Tis comparison shows that the thickness of the protective layer of concrete signifcantly impacts the fre resistance of concrete structural members. Te more the protective layer thickness is increased, the more the reliability is, and the remaining life of the structural members after the fre will be improved.

Conclusion
In this study, the fnite element software ABAQUS is used to model the temperature feld of concrete beams under different working conditions and under the ISO-834 standard warming curve and compare them in terms of the fre time to draw relevant data and conclusions and to provide a basis for the subsequent calculations and analyses.
Tis study then proceeds to the calculation of the remaining life: frst, the concept of carbonation depth is discussed, and the Monte-Carlo method is used to calculate the probability of failure, and the formula for calculating the remaining life of a concrete beam after a fre is derived on this basis. Subsequently, the accuracy of the calculation method for residual life prediction of concrete structural members is afrmed by comparing the calculation method of this study with the results of actual cases. Finally, the infuence of the diferences in concrete strength and protective layer thickness on the remaining life prediction of concrete structural members is calculated and analyzed.
Te main research results are as follows: (1) By verifying the calculation formula of the remaining life of concrete beams obtained by derivation, the diference between the results obtained by this study's procedure and the actual results is no more than 5%, which aligns with the practical requirements.
(2) When considering the infuence of concrete strength on the reliability and remaining life of concrete beams after the fre, it can be seen that the improvement of concrete strength is pronounced. For general building components, the power of C30 can barely meet the building requirements and purposes. Still, if the consideration is the use of essential building components, it is recommended to use C40 or above or even C50-strength concrete materials. (3) From the analysis of the impact of the thickness of the protective layer of concrete on the reliability and remaining life of concrete structural components, it can be seen that the increase in the thickness of the protective layer will signifcantly improve the structural elements. When the structure needs to meet the general building components of the use requirements, it is recommended to use the protective layer thickness of 35 mm or more of the concrete structural components; its reliability and remaining life will be signifcantly improved. When the structure needs to meet the use of essential building components, it is recommended to use a protective layer thickness of 45 mm or even more concrete structural features so as to meet better the safety of the premise to achieve the purpose of use.

Data Availability
Te data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that they have no conficts of interest.