A method and system for assessing the probability of blast damage to aged reinforced concrete beams

Abstract

This invention relates to the field of structural engineering safety assessment technology, specifically to a method and system for assessing the probability of blast damage to aging reinforced concrete beams. The method includes: calculating the probability distribution of corrosion initiation time based on a chloride ion diffusion model; calculating the probability distribution of competition time based on the competition mechanism between a corrosion pit growth model and a fatigue crack propagation model; calculating the probability distribution of fatigue crack propagation time based on a fatigue crack propagation model; calculating the probability distribution of total corrosion fatigue life based on corrosion initiation time, competition time, and fatigue crack propagation time; calculating the degradation law of steel reinforcement cross-sectional area and yield strength based on a time-varying steel reinforcement performance degradation model; establishing a blast vulnerability curve based on a stochastic blast load model and a pressure-impulse curve; and assessing the evolution law of blast damage probability over time based on structural parameters at different stages of corrosion fatigue deterioration. This invention achieves a quantitative assessment of the blast resistance performance of aging reinforced concrete beams throughout their entire life cycle.

Description

Technical Field

[0001] This invention relates to the field of structural engineering safety assessment technology, specifically to a method and system for assessing the probability of blast damage to aging reinforced concrete beams. Background Technology

[0002] Reinforced concrete (RC) bridges are a critical component of modern transportation networks. Traffic loads induce cyclical effects, leading to fatigue degradation in bridge structures. Fatigue life prediction is essential for ensuring the safety of RC bridges. On the other hand, bridge structures, especially those in coastal environments or areas using de-icing salt, are also susceptible to corrosion degradation. Corrosion significantly impacts the structural integrity of RC bridges by reducing the cross-sectional area and strength of the reinforcing steel and weakening the bond strength between concrete and steel. In severe cases, corrosion can also cause concrete cracking and spalling, further reducing structural performance. During their service life, corrosion damage and fatigue damage often occur simultaneously, with corrosion exacerbating fatigue damage, resulting in severe degradation of the RC bridge's resistance and a shortened fatigue life.

[0003] Pitting corrosion is one of the main forms of steel reinforcement corrosion. Pitting corrosion causes stress concentration at the pits, significantly reducing the fatigue life of the steel reinforcement. Studies have shown that corrosion pits are often the initiation site of fatigue fracture in steel reinforcement and play a crucial role in the initiation and propagation of fatigue cracks. For the beam members of reinforced concrete (RC) bridges, brittle fracture of the tensile reinforcement is usually the primary failure mode under fatigue loading; therefore, corrosion fatigue life is typically controlled by the fracture of the tensile reinforcement. Existing research indicates that significant corrosion fatigue degradation may occur in RC beams during service, thus necessitating consideration of the impact of corrosion fatigue degradation in life-cycle performance analysis.

[0004] Some structures may be subject to terrorist attacks or accidental explosions during their service life. Explosions impose extreme dynamic loads on the structure, potentially causing severe damage to bridges or even leading to structural collapse. Existing research has extensively analyzed the damage behavior of RC beams under explosive loads using experimental and numerical methods. Based on quantitative damage levels, researchers have employed Monte Carlo simulations and machine learning frameworks to conduct reliability and vulnerability analyses to predict the probability of explosive damage. However, most existing studies primarily focus on RC beams in their intact state, which may underestimate structural damage by neglecting the effects of degradation throughout the structure's lifespan. Although a few studies have considered the impact of corrosion-induced degradation on the explosive vulnerability of RC components, there are currently no reports on the influence of corrosion-fatigue coupled degradation on the probability of explosive damage to RC beams.

[0005] Therefore, there is an urgent need for a method to assess the probability of blast damage to aged RC beams that can take into account the coupled degradation of corrosion and fatigue, so as to achieve a quantitative evaluation of the blast resistance performance of the structure throughout its entire life cycle and provide a scientific basis for the assessment of the blast resistance performance of existing RC beams and the formulation of protection strategies. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method and system for assessing the probability of blast damage to aged reinforced concrete beams. The aim is to achieve a quantitative assessment of the probability of blast damage to aged RC beams throughout their entire life cycle by organically combining a corrosion-fatigue coupled degradation model with an explosive vulnerability analysis method.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] On one hand, embodiments of the present invention provide a method for assessing the probability of blast damage to aged reinforced concrete beams, the method comprising the following steps:

[0009] S100, obtain the structural parameters, corrosion model parameters, fatigue model parameters and explosion load parameters of the aged reinforced concrete beam;

[0010] S200, Based on the corrosion model parameters and chloride ion diffusion model, calculate the probability distribution of corrosion initiation time of the aged reinforced concrete beam;

[0011] S300, based on the competition mechanism between the corrosion model parameters, the fatigue model parameters, the corrosion pit growth model and the fatigue crack propagation model, calculate the competition time probability distribution of the aging reinforced concrete beam;

[0012] S400, Based on the fatigue model parameters and fatigue crack propagation model, calculate the fatigue crack propagation time probability distribution of the aged reinforced concrete beam;

[0013] S500, based on the corrosion initiation time probability distribution, the competition time probability distribution, and the fatigue crack propagation time probability distribution, calculate the total corrosion fatigue life probability distribution of the aged reinforced concrete beam;

[0014] S600, based on the time-varying steel bar performance degradation model, calculates the degradation law of steel bar cross-sectional area and steel bar yield strength at different times according to the total corrosion fatigue life probability distribution;

[0015] S700, based on the explosive load parameters, the explosive load stochastic model, and the pressure-impulse curve, establish the explosive vulnerability curve of the aged reinforced concrete beam;

[0016] S800, based on the explosive vulnerability curve and the degradation law, evaluate the evolution of the probability of explosive damage over time in different corrosion fatigue deterioration stages of the aged reinforced concrete beam.

[0017] Optionally, in S200, calculating the probability distribution of corrosion initiation time of the aged reinforced concrete beam based on the corrosion model parameters and the chloride ion diffusion model includes:

[0018] S210, A diffusion equation for chloride ions in concrete is established based on Fick's second law. The diffusion equation characterizes the relationship between chloride ion concentration and diffusion depth and diffusion time.

[0019] S220, Based on the chloride ion concentration, chloride ion diffusion coefficient, chloride ion threshold concentration and protective layer thickness on the concrete surface in the corrosion model parameters, calculate the initial corrosion time required for the chloride ion concentration on the steel reinforcement surface to reach the chloride ion threshold concentration;

[0020] S230, Based on the probability distribution of each parameter in the corrosion model parameters, multiple sets of random samples are generated through Monte Carlo simulation, and the corrosion initial time is calculated for each set of random samples to obtain multiple sets of corrosion initial time samples.

[0021] S240, Statistical analysis is performed on the multiple sets of corrosion initiation time samples to obtain the probability distribution of corrosion initiation time.

[0022] Optionally, in S300, the calculation of the competition time probability distribution of the aging reinforced concrete beam based on the competition mechanism of the corrosion model parameters, the fatigue model parameters, the corrosion pit growth model, and the fatigue crack propagation model includes:

[0023] S310, Based on the corrosion current density and the ratio of maximum corrosion depth to uniform corrosion depth in the corrosion model parameters, the corrosion pit depth is calculated as a function of time using the corrosion pit depth model, and the corrosion pit growth rate is obtained by differentiation.

[0024] S320, Based on the stress amplitude, fatigue load frequency and initial diameter of the steel bar in the fatigue model parameters, the fatigue crack propagation rate equation is established by the stress intensity factor formula and the Paris-Erdogan law.

[0025] S330, the growth rate of the corrosion pit is equal to the growth rate of the fatigue crack, and the transition time of the corrosion pit to the fatigue crack is obtained. The difference between the transition time and the initial corrosion time is calculated as the competition time.

[0026] S340, based on the probability distribution of each parameter in the corrosion model parameters and the fatigue model parameters, multiple sets of random samples are generated through Monte Carlo simulation, and the competition time is calculated for each set of random samples to obtain multiple sets of competition time samples;

[0027] S350, Perform statistical analysis on the multiple sets of competition time samples to obtain the competition time probability distribution.

[0028] Optionally, in S400, calculating the fatigue crack propagation time probability distribution of the aging reinforced concrete beam based on the fatigue model parameters and the fatigue crack propagation model includes:

[0029] S410, the corrosion pit depth corresponding to the competition time is used as the initial crack size for fatigue crack propagation, and the critical crack size in the fatigue model parameters is used as the termination condition for fatigue crack propagation.

[0030] S420, based on the stress amplitude, fatigue load frequency, stress intensity factor threshold and material crack propagation parameters in the fatigue model parameters, perform integral calculation on the Paris-Erdogan law to calculate the fatigue crack propagation time required for the fatigue crack to propagate from the initial crack size to the critical crack size;

[0031] S430, based on the probability distribution of each parameter in the fatigue model parameters, multiple sets of random samples are generated through Monte Carlo simulation, and the fatigue crack propagation time is calculated for each set of random samples to obtain multiple sets of fatigue crack propagation time samples.

[0032] S440, Perform statistical analysis on the multiple sets of fatigue crack propagation time samples to obtain the probability distribution of fatigue crack propagation time.

[0033] Optionally, in S600, the step of calculating the degradation law of the steel bar cross-sectional area and yield strength based on the time-varying steel bar performance degradation model and the total corrosion fatigue life probability distribution includes:

[0034] S610, Based on the corrosion pit depth and initial diameter of the reinforcing bar in the corrosion model parameters, the time-varying residual cross-sectional area of ​​the reinforcing bar under corrosion fatigue is calculated through geometric relationships.

[0035] S620, Calculate the steel corrosion rate based on the time-varying remaining cross-sectional area and the cross-sectional area of ​​the steel reinforcement in the intact state;

[0036] S630, Based on the steel corrosion rate and the yield strength of the steel in the intact state, the time-varying residual yield strength of the steel is calculated using the residual yield strength formula;

[0037] S640, determine the time nodes of each degradation stage according to the total corrosion fatigue life probability distribution, extract the corresponding time-varying residual cross-sectional area and time-varying residual yield strength at the time nodes, and obtain the degradation law.

[0038] Optionally, in S700, establishing the explosion vulnerability curve based on the explosion load parameters, the explosion load stochastic model, and the pressure-impulse curve includes:

[0039] S710, based on the explosive equivalent and explosion distance in the explosion load parameters, the mean and standard deviation of the reflection peak overpressure and the mean and standard deviation of the positive phase duration are calculated respectively using the empirical formulas for reflection peak overpressure and positive phase duration.

[0040] S720, based on the mean and standard deviation of the reflected peak overpressure and the mean and standard deviation of the positive phase duration, the mean and standard deviation of the reflected impulse are determined by the impulse calculation formula;

[0041] S730, based on the concrete compressive strength, steel yield strength, reinforcement ratio and beam length in the structural parameters, calculate the reflected overpressure asymptote and reflected impulse asymptote corresponding to different damage thresholds through the pressure-impulse curve asymptote formula;

[0042] S740, establish a pressure-impulse curve based on the reflection overpressure asymptote and the reflection impulse asymptote, and construct a limit state function based on the pressure-impulse curve, the reflection peak overpressure, and the reflection impulse;

[0043] S750, based on the aforementioned limit state function, the proportion of failure samples in which the limit state function is exceeded under different explosion intensities is calculated by Monte Carlo simulation to obtain the explosion vulnerability curve.

[0044] Optionally, in S800, the step of evaluating the evolution of the probability of explosion damage over time at different corrosion fatigue deterioration stages based on the explosion vulnerability curve and the degradation law includes:

[0045] S810, Determine the degraded structural parameters corresponding to different service times according to the degradation law, wherein the degraded structural parameters include the degraded concrete compressive strength, steel yield strength and reinforcement ratio;

[0046] S820, Substitute the degraded structural parameters into the pressure-impulse curve asymptote formula to update the reflection overpressure asymptote and reflection impulse asymptote corresponding to different damage thresholds;

[0047] S830, based on the updated pressure-impulse curve and the explosive load stochastic model, re-execute the Monte Carlo simulation to obtain the explosive vulnerability curves corresponding to different service times;

[0048] S840, by comparing and analyzing the explosion vulnerability curves at different service times, the evolution law of the explosion damage probability over time is obtained.

[0049] On the other hand, embodiments of the present invention provide a system for assessing the probability of blast damage to aging reinforced concrete beams, comprising:

[0050] At least one processor;

[0051] At least one memory for storing at least one program;

[0052] When the at least one program is executed by the at least one processor, the at least one processor performs the method described above.

[0053] The embodiments of the present invention have the following beneficial effects:

[0054] The corrosion-fatigue coupled degradation model proposed in this invention innovatively introduces a competition mechanism between corrosion pits and fatigue cracks. By determining the competition time by making the growth rate of corrosion pits equal to the propagation rate of fatigue cracks, the coupling effect between corrosion degradation and fatigue degradation is quantitatively characterized, effectively solving the problem of life prediction deviation caused by considering corrosion and fatigue independently in the prior art.

[0055] The time-varying steel reinforcement performance degradation model established in this invention is based on the geometric relationship between the corrosion pit depth and the initial diameter of the steel reinforcement. It calculates the time-varying residual cross-sectional area and the time-varying residual yield strength, quantifies the performance degradation law of steel reinforcement under corrosion-fatigue action, and provides accurate structural resistance parameters for subsequent explosive vulnerability analysis.

[0056] This invention organically combines the corrosion-fatigue coupled degradation model with the explosive vulnerability analysis method. Based on the pressure-impulse curve and Monte Carlo simulation, it establishes an explosive vulnerability curve that considers different corrosion fatigue degradation stages, realizing a quantitative assessment of the probability of explosion damage throughout the entire life cycle of aged RC beams, filling a technological gap in this field.

[0057] This invention, by analyzing the evolution of explosive vulnerability curves at different service times, reveals that long-term corrosion fatigue deterioration not only increases the explosive vulnerability of the structure but also reduces the distinction between different damage levels, making the structure more prone to severe damage. This provides a scientific basis for evaluating the blast resistance performance and formulating protection strategies for existing RC bridges. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart illustrating the method for assessing the probability of blast damage to aged reinforced concrete beams in an embodiment of the present invention.

[0060] Figure 2 This is a schematic diagram illustrating the evolution process of corrosion fatigue deterioration in reinforced concrete structures in an embodiment of the present invention;

[0061] Figure 3 This is a structural detail diagram of the RC beam in the embodiment of the present invention;

[0062] Figure 4 This is a probability density function graph of the initial corrosion time in an embodiment of the present invention;

[0063] Figure 5 This is a probability density function diagram of the competition time between pits and cracks in an embodiment of the present invention;

[0064] Figure 6 This is a probability density function graph of fatigue crack propagation time in an embodiment of the present invention;

[0065] Figure 7 This is a probability density function of total corrosion fatigue life and a graph showing the percentage of average life at each stage in an embodiment of the present invention.

[0066] Figure 8 This is a graph showing the degradation pattern of steel reinforcement performance at different times in an embodiment of the present invention;

[0067] Figure 9 This is a typical explosion pressure-time history diagram in an embodiment of the present invention;

[0068] Figure 10 This is a typical pressure-impulse curve of the RC beam in an embodiment of the present invention;

[0069] Figure 11 This is a time evolution diagram of the vulnerability curves of the RC beam under three explosion damage levels under corrosion fatigue degradation in an embodiment of the present invention. Detailed Implementation

[0070] The following will provide a clear and complete description of the concept, specific structure, and technical effects of the present invention in conjunction with embodiments and accompanying drawings, so as to fully understand the purpose, solution, and effects of the present invention. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0071] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of this invention; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this invention as detailed in the appended claims.

[0072] Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this invention is for descriptive purposes only and is not intended to limit the invention.

[0073] refer to Figure 1 ,like Figure 1 The figure shows a method for assessing the probability of blast damage to aging reinforced concrete beams provided by an embodiment of the present invention. The method includes the following steps:

[0074] S100, obtain the structural parameters, corrosion model parameters, fatigue model parameters and explosion load parameters of the aged reinforced concrete beam;

[0075] S200, Based on the corrosion model parameters and chloride ion diffusion model, calculate the probability distribution of corrosion initiation time of the aged reinforced concrete beam;

[0076] S300, based on the competition mechanism between the corrosion model parameters, the fatigue model parameters, the corrosion pit growth model and the fatigue crack propagation model, calculate the competition time probability distribution of the aging reinforced concrete beam;

[0077] S400, Based on the fatigue model parameters and fatigue crack propagation model, calculate the fatigue crack propagation time probability distribution of the aged reinforced concrete beam;

[0078] S500, based on the corrosion initiation time probability distribution, the competition time probability distribution, and the fatigue crack propagation time probability distribution, calculate the total corrosion fatigue life probability distribution of the aged reinforced concrete beam;

[0079] S600, based on the time-varying steel bar performance degradation model, calculates the degradation law of steel bar cross-sectional area and steel bar yield strength at different times according to the total corrosion fatigue life probability distribution;

[0080] S700, based on the explosive load parameters, the explosive load stochastic model, and the pressure-impulse curve, establish the explosive vulnerability curve of the aged reinforced concrete beam;

[0081] S800, based on the explosive vulnerability curve and the degradation law, evaluate the evolution of the probability of explosive damage over time in different corrosion fatigue deterioration stages of the aged reinforced concrete beam.

[0082] This invention provides a method and system for assessing the probability of blast damage to aged reinforced concrete beams. By establishing a corrosion-fatigue coupled degradation model and introducing a competitive mechanism between corrosion pits and fatigue cracks, the coupling effect between corrosion degradation and fatigue degradation is quantitatively characterized. A time-varying steel reinforcement performance degradation model quantifies the performance degradation law of steel reinforcement under corrosion-fatigue conditions. By organically combining the corrosion-fatigue coupled degradation model with explosive vulnerability analysis methods, and based on pressure-impulse curves and Monte Carlo simulations, explosive vulnerability curves considering different stages of corrosion and fatigue degradation are established. This enables a quantitative assessment of the probability of blast damage to aged RC beams throughout their entire life cycle, filling the technological gap in existing technologies that lack methods for assessing the probability of blast damage to RC beams considering corrosion-fatigue coupled degradation.

[0083] The core of this embodiment lies in the organic combination of the corrosion-fatigue coupled degradation model and the explosive vulnerability analysis method. It achieves a quantitative assessment of the explosion resistance performance of aged RC beams throughout their entire lifespan through the following three stages: The first stage is the corrosion-fatigue life prediction stage, which predicts the corrosion fatigue life of the RC beam through the competition mechanism of the chloride ion diffusion model, corrosion pit growth model, and fatigue crack propagation model; the second stage is the time-varying performance degradation stage, which calculates the degradation law of the cross-sectional area and yield strength of the steel reinforcement at different times based on the time-varying steel reinforcement performance degradation model; the third stage is the explosive vulnerability assessment stage, which establishes explosive vulnerability curves for different corrosion fatigue degradation stages based on the random model of explosive load and the pressure-impulse curve, and assesses the evolution law of the explosion damage probability over time.

[0084] The evolution process of corrosion fatigue deterioration in reinforced concrete structures is as follows: Figure 2 As shown, this illustrates the entire process of the gradual degradation of structural performance over time. This process can be divided into three stages: the first stage is the initial corrosion stage, where chloride ions penetrate the concrete and trigger steel corrosion, gradually weakening the bond between the steel and concrete; the second stage is the competition stage, where fatigue cracks begin to initiate and expand, while corrosion pits continue to develop, corrosion products accumulate, and cracking of the concrete protective layer further accelerates the corrosion rate, thus enhancing the coupling effect between fatigue damage and corrosion deterioration; the final stage is the end-of-life stage, where the structure fails when the cracks expand to a critical value.

[0085] In some embodiments, S200, calculating the probability distribution of corrosion initiation time of the aged reinforced concrete beam based on the corrosion model parameters and the chloride ion diffusion model includes:

[0086] S210, A diffusion equation for chloride ions in concrete is established based on Fick's second law. The diffusion equation characterizes the relationship between chloride ion concentration and diffusion depth and diffusion time.

[0087] S220, Based on the chloride ion concentration, chloride ion diffusion coefficient, chloride ion threshold concentration and protective layer thickness on the concrete surface in the corrosion model parameters, calculate the initial corrosion time required for the chloride ion concentration on the steel reinforcement surface to reach the chloride ion threshold concentration;

[0088] S230, Based on the probability distribution of each parameter in the corrosion model parameters, multiple sets of random samples are generated through Monte Carlo simulation, and the corrosion initial time is calculated for each set of random samples to obtain multiple sets of corrosion initial time samples.

[0089] S240, Statistical analysis is performed on the multiple sets of corrosion initiation time samples to obtain the probability distribution of corrosion initiation time.

[0090] Specifically, chloride ion intrusion is one of the main factors causing steel reinforcement corrosion. It destroys the passivation film on the steel reinforcement surface, thereby triggering the corrosion process. Chloride ion diffusion follows Fick's second law, the expression of which is shown below:

[0091] (1);

[0092] In the formula, C c denoted as chloride ion concentration, i.e., the mass percentage of chloride ions in the concrete; x is the depth (cm) from the concrete surface inward along the diffusion direction; t is time (in years); D cl The chloride ion diffusion coefficient in concrete (cm² / year). When the chloride ion concentration at the surface of the reinforcing steel reaches the threshold concentration (C... th When the initial corrosion time of the reinforcing steel (T) is reached, corrosion begins. ini It can be determined by the following formula:

[0093] (2);

[0094] In the formula, c is the thickness of the protective layer (cm), C s Let T be the chloride ion concentration on the concrete surface (kg / m³), erf(·) be the error function, and T be the concentration of chloride ions on the concrete surface (kg / m³). ini C is the initial corrosion time. th This represents the chloride ion threshold concentration.

[0095] Monte Carlo simulation is used to randomize the probabilistic variables in structural parameters, corrosion model parameters, and fatigue model parameters. The initial corrosion time (T) is obtained according to formula (2). ini The probability density function (PDF) of ) is as follows Figure 4 As shown, the mean (μ) of this distribution is 6.81 years and the standard deviation (σ) is 2.36 years, indicating that under the current structural and environmental conditions, most corrosion will begin at approximately 6.81 years, with a range of variation roughly between the mean and ±2.36 years.

[0096] In some embodiments, S300, calculating the competition time probability distribution of the aging reinforced concrete beam based on the competition mechanism of the corrosion model parameters, the fatigue model parameters, the corrosion pit growth model, and the fatigue crack propagation model includes:

[0097] S310, Based on the corrosion current density and the ratio of maximum corrosion depth to uniform corrosion depth in the corrosion model parameters, the corrosion pit depth is calculated as a function of time using the corrosion pit depth model, and the corrosion pit growth rate is obtained by differentiation.

[0098] S320, Based on the stress amplitude, fatigue load frequency and initial diameter of the steel bar in the fatigue model parameters, the fatigue crack propagation rate equation is established by the stress intensity factor formula and the Paris-Erdogan law.

[0099] S330, the growth rate of the corrosion pit is equal to the growth rate of the fatigue crack, and the transition time of the corrosion pit to the fatigue crack is obtained. The difference between the transition time and the initial corrosion time is calculated as the competition time.

[0100] S340, based on the probability distribution of each parameter in the corrosion model parameters and the fatigue model parameters, multiple sets of random samples are generated through Monte Carlo simulation, and the competition time is calculated for each set of random samples to obtain multiple sets of competition time samples;

[0101] S350, Perform statistical analysis on the multiple sets of competition time samples to obtain the competition time probability distribution.

[0102] Specifically, pitting corrosion is a highly localized form of steel reinforcement corrosion that causes severe structural deterioration. Compared to uniform corrosion, which results in a uniform loss of material on the steel reinforcement surface, pitting corrosion forms localized deep pits that can significantly reduce the cross-sectional area of ​​the steel reinforcement. Based on experimental research by Andrade and Alonso, Stewart proposed a model for the pit depth at time t, expressed as follows:

[0103] (3);

[0104] In the formula, p(t) is the depth of the corrosion pit (mm), R0 is the ratio of the maximum corrosion depth to the uniform corrosion depth, and i corr (t) represents the time-varying corrosion current density (μA / cm). 2 i corr The function expression for (t) is:

[0105] (4);

[0106] In the formula, i ini (t) and i th (t) represents the corrosion current density during the initial corrosion stage and the active corrosion stage, respectively; m ini (t) and m ac (t) are the membership functions for the initial corrosion stage and the active corrosion stage, respectively. ini (t) can be determined by the exponential decay function as follows:

[0107] (5);

[0108] In the formula, ε ini This is a shape parameter with a value of 1.0. m ac (t) can be determined using a linear growth function as follows:

[0109] (6);

[0110] In the formula, m0 is the shape parameter, with a value of 0.07. ini (t) can be calculated using the following formula:

[0111] (7);

[0112] In the formula, w / c is the water-cement ratio, which can be calculated using the Bolomey formula as follows:

[0113] (8);

[0114] In the formula, f c Let be the compressive strength of the concrete (MPa). Based on formula (3), the time-dependent growth rate of the corrosion pit can be further derived as:

[0115] (9);

[0116] Steel reinforcement fracture is the primary failure mechanism in reinforced concrete (RC) structures exhibiting fatigue damage. When the maximum stress intensity factor approaches the fracture toughness of the steel reinforcement, it may trigger sudden crack propagation, leading to catastrophic structural failure. The fatigue crack propagation rate can be calculated using the Paris-Erdogan law based on linear elastic fracture mechanics.

[0117] (10);

[0118] In the formula, a is the fatigue crack size (mm), N is the number of fatigue cycles, and C is the fatigue crack size (mm). p and m are material parameters related to environmental impact, and ΔK is the stress intensity factor (MPa·m). 1 / 2 The calculation formula is as follows:

[0119] (11);

[0120] In the formula, Δσ is the stress amplitude, i.e., the difference between the maximum and minimum stress; Y is the geometric function of the notched specimen, calculated as follows:

[0121] (12);

[0122] In the formula:

[0123] (13);

[0124] (14);

[0125] (15);

[0126] In the formula, d0 is the initial diameter of the steel bar (mm), G is the geometric correction coefficient, Y1 is an auxiliary parameter related to the notch depth, and β0 is a dimensionless angular parameter characterizing the notch depth relative to the steel bar diameter.

[0127] To determine C p Regarding the values ​​of m, Salah el din and Lovegrove proposed a crack growth model suitable for long crack propagation, the expression of which is:

[0128] (16);

[0129] In the formula, ΔK th This is the threshold value for the stress intensity factor.

[0130] Figure 2 (a) shows a schematic diagram of the competition phase in the model. The solid line represents the growth rate of the corrosion pit (dp / dt). At the initial time of steel reinforcement corrosion (T... ini After this, the rate initially decreases, then accelerates due to severe concrete cracking, and eventually stabilizes at a threshold corrosion rate. The dashed line represents the fatigue crack propagation rate (da / dt), which increases over time until it catches up with and eventually surpasses the growth rate of the corrosion pit. The intersection of these two curves represents the time (t) between the corrosion pit and crack propagation. pThis refers to the moment when the crack propagation rate equals the corrosion pit growth rate. After the competition phase, i.e., T... com =t p -T ini The fatigue crack propagation rate becomes the dominant mechanism, ultimately leading to structural failure. The corresponding fatigue crack propagation failure time (T...) fcg ) can be Figure 2 The definition is shown in (a).

[0131] To quantify the competition time between fatigue crack propagation and corrosion pit growth, the corrosion pit is considered as the initial crack in the crack propagation analysis. In this model, the equivalent stress intensity factor ΔK of the corrosion pit is... p(t) The calculation is as follows:

[0132] (17);

[0133] Considering the interaction between corrosion pits and fatigue cracks, the propagation rate of fatigue cracks over time t is expressed as:

[0134] (18);

[0135] In the formula, a p The equivalent fatigue crack size corresponding to the corrosion pit is shown in mm; f represents the fatigue load frequency, defined as the effective number of damage cycles per day. In the fatigue assessment of beam members in concrete bridges, design codes such as AASHTO LRFD bridge design code and Eurocode 1 provide fatigue load models that can generate the equivalent number of damage cycles based on annual heavy traffic volume. According to the AASHTO code, the fatigue load frequency can be expressed using the average daily truck traffic volume as:

[0136] (19);

[0137] In the formula, N av λ represents the average daily traffic volume; λ is the proportion of trucks in the traffic flow, and its value depends on the road grade. In this invention, λ is taken as 0.1 for urban road bridges. q is the lane reduction factor, which is taken as 0.8.

[0138] The competition time is obtained by equalizing the fatigue crack propagation rate (Equation (18)) and the corrosion pit growth rate (Equation (9)), and its expression is as follows:

[0139] (20);

[0140] During the fatigue crack propagation stage after the competition phase ends, the transition time t will be... p The pit depth p(t) p ) is considered as the initial crack size a0 for crack propagation, i.e., a0 = p(t)p The corresponding fatigue crack propagation time can be obtained by integrating equation (16):

[0141] (twenty one);

[0142] In the formula, a c The critical crack size (mm) leading to structural failure is given by the given value, where a1 is the crack size at which the crack transitions from the intermediate crack propagation stage to the long crack propagation stage. When the stress intensity factor reaches the threshold, i.e., ΔK(a1) = ΔK... th This transition occurs at that time.

[0143] Figure 5 The PDF shows the competition time between corrosion pits and cracks, representing the time required for the growth rate of the corrosion pit depth to reach equilibrium with the equivalent fatigue crack growth rate under corrosion fatigue damage. As shown in the figure, the calculated T... com The mean is 8.26 years and the standard deviation is 2.38 years.

[0144] Figure 6 The PDF shows the fatigue crack propagation time of the RC beam under corrosion-fatigue damage. fcg The average duration is approximately 48.86 years, with a relatively large standard deviation of 28.46 years. Figure 7 The total corrosion fatigue life (T) of the RC beam was demonstrated. total The total corrosion-fatigue life is the sum of the corrosion initiation time, the competition time, and the fatigue crack propagation time, i.e., Tfatigue-fatigue-life. total =T ini +T com +T fcg . Figure 7 T is given in (a) total The PDFs have an average lifespan of 63.93 years and a standard deviation of 28.85 years. Figure 7 (b) shows the average time for each degradation stage throughout the structure's lifespan. The transformation from corrosion pits to cracks occurs at approximately 15.07 years, after which fatigue crack propagation becomes the dominant degradation mechanism. This indicates that although corrosion begins early, the majority of the corrosion-fatigue life of the RC beam is consumed during the crack propagation stage.

[0145] In some embodiments, S400, calculating the fatigue crack propagation time probability distribution of the aging reinforced concrete beam based on the fatigue model parameters and the fatigue crack propagation model includes:

[0146] S410, the corrosion pit depth corresponding to the competition time is used as the initial crack size for fatigue crack propagation, and the critical crack size in the fatigue model parameters is used as the termination condition for fatigue crack propagation.

[0147] S420, based on the stress amplitude, fatigue load frequency, stress intensity factor threshold and material crack propagation parameters in the fatigue model parameters, perform integral calculation on the Paris-Erdogan law to calculate the fatigue crack propagation time required for the fatigue crack to propagate from the initial crack size to the critical crack size;

[0148] S430, based on the probability distribution of each parameter in the fatigue model parameters, multiple sets of random samples are generated through Monte Carlo simulation, and the fatigue crack propagation time is calculated for each set of random samples to obtain multiple sets of fatigue crack propagation time samples.

[0149] S440, Perform statistical analysis on the multiple sets of fatigue crack propagation time samples to obtain the probability distribution of fatigue crack propagation time.

[0150] In some embodiments, S600, the step of calculating the degradation law of the steel bar cross-sectional area and yield strength based on the time-varying steel bar performance degradation model and the total corrosion fatigue life probability distribution includes:

[0151] S610, Based on the corrosion pit depth and initial diameter of the reinforcing bar in the corrosion model parameters, the time-varying residual cross-sectional area of ​​the reinforcing bar under corrosion fatigue is calculated through geometric relationships.

[0152] S620, Calculate the steel corrosion rate based on the time-varying remaining cross-sectional area and the cross-sectional area of ​​the steel reinforcement in the intact state;

[0153] S630, Based on the steel corrosion rate and the yield strength of the steel in the intact state, the time-varying residual yield strength of the steel is calculated using the residual yield strength formula;

[0154] S640, determine the time nodes of each degradation stage according to the total corrosion fatigue life probability distribution, extract the corresponding time-varying residual cross-sectional area and time-varying residual yield strength at the time nodes, and obtain the degradation law.

[0155] Specifically, in the corrosion fatigue model, such as Figure 2 As shown in (b), the mechanical properties of the reinforcing steel bars continuously decrease as the size of the crack or pit increases. When the crack or corrosion pit reaches the critical size a=a... c When the steel reinforcement fractures, the structure fails. This invention uses an empirical formula based on pitting corrosion to estimate the time-varying residual cross-sectional area A(t) of the steel reinforcement under corrosion-fatigue conditions. The calculation formula is as follows:

[0156] (twenty two);

[0157] In the formula:

[0158] (twenty three);

[0159] (twenty four);

[0160] (25);

[0161] (26);

[0162] (27);

[0163] Accordingly, the steel corrosion rate η is defined as:

[0164] (28);

[0165] The time-varying residual yield strength of reinforcing steel can be calculated using the following formula:

[0166] (29);

[0167] In the formula, A0 and f y0 Here, A1 and A2 represent the cross-sectional area and yield strength of the reinforcing steel in its intact state, respectively; A1 and A2 are the correction terms for the arc-shaped sector area corresponding to the pitting corrosion pit after it penetrates the steel section; θ1 and θ2 are the central angles of the steel section and the corresponding central angles of the pitting corrosion pit, respectively. p It is the half-chord length at the intersection of the pitting pit and the circular cross-section of the reinforcing bar.

[0168] Brittle fracture of reinforcing steel bars under tensile stress is the primary failure mode of reinforced concrete (RC) beams under fatigue loading. Therefore, this invention considers steel bar fracture as the dominant failure mechanism. Fatigue-induced degradation of the elastic modulus of the concrete compression zone leads to stress redistribution in the beam section, but existing studies have shown that this degradation has an impact of no more than 5% on the fatigue life prediction of corrosion-damaged RC beams. Therefore, to simplify the analysis, the influence of concrete fatigue damage on corrosion fatigue degradation is ignored in this invention, without affecting the generalizability of the results.

[0169] Figure 8 The study shows the trends of the mean and standard deviation (Mean±SD) of pit (or crack) size, steel reinforcement cross-sectional area, and yield strength over time. Figure 8 In (a), the depth of the corrosion pit increases rapidly after the corrosion starts and completes the transition from corrosion pit to crack in about 15 years. It then gradually increases during the fatigue crack propagation stage and reaches a critical average of about 8 mm at the end of the corrosion fatigue life. Figure 8 (b) and (c) illustrate the decrease in the cross-sectional area and yield strength of the reinforcing steel. The larger standard deviation during the transition phase indicates a higher degree of uncertainty in the deterioration process at this stage.

[0170] An explosion wave is generated by the explosion of explosives. It is characterized by the release of a large amount of energy in a very short time, compressing the surrounding air and forming a high-pressure shock wave front. When the shock wave front propagates in the air, it causes a rapid increase in pressure, which then gradually decays. Figure 9 This shows a typical and simplified explosion pressure-time history. In the initial stage of the explosion, the pressure rises rapidly, reaching the peak reflective pressure almost instantaneously, marking the beginning of the positive phase. During the positive phase, the pressure is above atmospheric pressure and gradually decays. The area under the positive phase curve represents the positive impulse.

[0171] A typical pressure-time history reflects the true shape of an explosion wave, including a negative phase following the positive phase, where the pressure briefly drops below atmospheric pressure before returning to stability. To simplify analysis and calculations, an idealized explosion pressure-time history is often used, which simplifies the complex waveform to a triangular waveform, retaining only the peak pressure and the duration t of the positive phase. d To improve computational efficiency.

[0172] The random fluctuations in the prediction of blast loads have a more significant impact on the structural response than changes in the beam's own performance; therefore, the uncertainty of the blast load must be fully considered in the analysis. The empirical relationship between the mean and standard deviation of the reflected peak overpressure is shown below:

[0173] (30);

[0174] (31);

[0175] (32);

[0176] In the formula, P r The unit is kPa. R is the explosion distance, in meters. W is the TNT equivalent, in kJ.

[0177] The mean and standard deviation of the duration of the corresponding positive-phase explosion load are:

[0178] (33);

[0179] (34);

[0180] In the formula, t d The duration is expressed in milliseconds; W is the weight of the TNT equivalent explosive in kilograms. Under a given proportional distance, it is assumed that the reflected peak pressure and duration are statistically independent and both follow a normal distribution, with the mean and standard deviation as shown in the formula above.

[0181] The mean and standard deviation of the reflected impulse can be determined by assuming a simplified triangular blast load time history, as shown below:

[0182] (35);

[0183] (36);

[0184] In the formula, , These are the mean and standard deviation of the reflected impulse, respectively. , These are the mean and standard deviation of the peak reflected pressure, respectively. , These are the mean and standard deviation of the duration of the positive-phase explosion load, respectively.

[0185] In some embodiments, S700, establishing the explosion vulnerability curve based on the explosion load parameters, the explosion load stochastic model, and the pressure-impulse curve includes:

[0186] S710, based on the explosive equivalent and explosion distance in the explosion load parameters, the mean and standard deviation of the reflection peak overpressure and the mean and standard deviation of the positive phase duration are calculated respectively using the empirical formulas for reflection peak overpressure and positive phase duration.

[0187] S720, based on the mean and standard deviation of the reflected peak overpressure and the mean and standard deviation of the positive phase duration, the mean and standard deviation of the reflected impulse are determined by the impulse calculation formula;

[0188] S730, based on the concrete compressive strength, steel yield strength, reinforcement ratio and beam length in the structural parameters, calculate the reflected overpressure asymptote and reflected impulse asymptote corresponding to different damage thresholds through the pressure-impulse curve asymptote formula;

[0189] S740, establish a pressure-impulse curve based on the reflection overpressure asymptote and the reflection impulse asymptote, and construct a limit state function based on the pressure-impulse curve, the reflection peak overpressure, and the reflection impulse;

[0190] S750, based on the aforementioned limit state function, the proportion of failure samples in which the limit state function is exceeded under different explosion intensities is calculated by Monte Carlo simulation to obtain the explosion vulnerability curve.

[0191] Specifically, explosive vulnerability analysis is a key method used to assess the vulnerability of structures under explosive loads. This method quantifies the probability of a structure or its components reaching a specific damage level under different explosive intensities and is widely used in reliability-based structural design, risk assessment, and protection strategy development. This analysis typically requires establishing vulnerability curves to describe the relationship between the explosive intensity index (IM) and the probability of exceeding a specific damage level. To ensure the reliability of the prediction results, the analysis must comprehensively consider factors such as material properties, structural configuration, degradation mechanisms (such as corrosion and fatigue), and uncertainties in the explosive load.

[0192] Probability of structural damage (Pr) at a certain explosion intensity dmg It can be defined as:

[0193] (37);

[0194] In the formula, X represents an n-dimensional random variable used to describe the uncertainty of the explosion load and structural resistance, x0 is the damage index corresponding to the explosion damage threshold, and G(X) is the limit state function. When G(X)≤0, it is considered that explosion damage has occurred.

[0195] In explosive vulnerability analysis, the selection of the impulse distance (IM) is crucial. Similar to earthquake vulnerability analysis, peak ground acceleration (PGA) is often used as an indicator of earthquake intensity, even though the amplitude, frequency components, and duration of the ground motion all affect the structural response. For explosive loads, the blast distance and explosive equivalent are the main influencing factors, usually normalized to a proportional distance. However, since the impulse has a non-linear relationship with these two parameters, even at the same scaling distance, different combinations of explosive amount and blast distance may produce different impulses. Therefore, a single parameter is insufficient to uniquely characterize explosive load conditions. To simplify the analysis without loss of generality, this invention uses the blast distance as the IM and fixes the explosive amount at 1000 kg.

[0196] In previous studies, Liu et al. numerically established pressure-impulse (PI) curves for RC beams corresponding to three damage thresholds (DTs) under different concrete compressive strength, steel yield strength, reinforcement ratio, and beam length. A typical example is shown below. Figure 10 As shown. The damage threshold is defined as:

[0197] (38);

[0198] In the formula, F res F represents the residual load-bearing capacity of the beam damaged by the explosion. maxThe load-bearing capacity of the undamaged beam is considered. The damage thresholds considered in this paper are DT=0.2, 0.5 and 0.8, representing mild, moderate and severe blast damage, respectively.

[0199] The PI curve can be represented as:

[0200] (39);

[0201] The reflected overpressure asymptotes and reflected impulse asymptotes (P0 and I0) corresponding to the three beam damage thresholds are as follows:

[0202] When DT=0.2:

[0203] (40);

[0204] (41);

[0205] When DT=0.5:

[0206] (42);

[0207] (43);

[0208] When DT=0.8:

[0209] (44);

[0210] (45);

[0211] In the formula, the beam length l b The unit is mm; concrete compressive strength f c and the yield strength f of the steel reinforcement y The unit is MPa; ρ is the reinforcement ratio; the unit of the reflected overpressure asymptote P0 is MPa; the unit of the reflected impulse asymptote I0 is MPa·ms.

[0212] The limit state function for explosive damage probability of RC beam based on the PI curve is defined as shown in equation (46):

[0213] (46);

[0214] In the formula:

[0215] ,and (47);

[0216] (48);

[0217] (49);

[0218] In the formula, U * P is the distance from the actual explosive load point to the origin in the PI curve graph, U is the distance from the intersection of the line connecting the explosive load point and the origin with the PI curve to the origin, and P and I are the reflected overpressure and impulse of the explosive load, respectively. I with I I These represent the reflected overpressure and impulse corresponding to the intersection of the line connecting the explosion load point and the origin with the PI curve.

[0219] Monte Carlo simulation was used to estimate explosive vulnerability. In each simulation, resistance and load variables were randomly generated based on statistical parameters, and all input variables were assumed to be statistically independent. The conditional damage probability Prdmg was calculated as the ratio of the number of failure samples exceeding the limit state to the total number of simulations. To ensure convergence, a total of 100,000 simulations were performed, consistent with the methods used in existing studies.

[0220] In some embodiments, S800, evaluating the evolution of the probability of explosion damage over time at different corrosion fatigue deterioration stages based on the explosion vulnerability curve and the degradation law includes:

[0221] S810, Determine the degraded structural parameters corresponding to different service times according to the degradation law, wherein the degraded structural parameters include the degraded concrete compressive strength, steel yield strength and reinforcement ratio;

[0222] S820, Substitute the degraded structural parameters into the pressure-impulse curve asymptote formula to update the reflection overpressure asymptote and reflection impulse asymptote corresponding to different damage thresholds;

[0223] S830, based on the updated pressure-impulse curve and the explosive load stochastic model, re-execute the Monte Carlo simulation to obtain the explosive vulnerability curves corresponding to different service times;

[0224] S840, by comparing and analyzing the explosion vulnerability curves at different service times, the evolution law of the explosion damage probability over time is obtained.

[0225] Specifically, Figure 11This paper presents the explosive vulnerability curves of reinforced concrete beams under corrosion-fatigue degradation over time, targeting three explosive damage thresholds. Under intact structural conditions, higher damage levels require significantly smaller proportional distances to achieve a higher probability of occurrence. However, as the corrosion fatigue degradation years increase, the distance between the vulnerability curves corresponding to different damage levels decreases significantly. When the corrosion fatigue age reaches 60 years, the vulnerability curves for DT=0.2, 0.5, and 0.8 tend to converge, indicating that even at relatively low explosive intensities, the beams are more susceptible to severe damage. This convergence suggests that long-term corrosion fatigue degradation not only increases the explosive vulnerability of the structure but also reduces the differentiation between different damage levels, making the structure more prone to severe damage.

[0226] In this embodiment, the structural parameters, corrosion model parameters, and fatigue model parameters of the RC beam in the example are listed in Tables 1 to 3, respectively. In actual engineering, these parameters are usually subject to uncertainty. Therefore, this invention introduces the probability distribution of these parameters in the analysis to fully consider their randomness and variability.

[0227] Table 1. Structural parameters and distribution;

[0228]

[0229] Table 2. Corrosion parameters and distribution;

[0230]

[0231] Table 3. Fatigue parameters and distribution;

[0232]

[0233] The present invention takes into account the following: Figure 3 A simply supported reinforced concrete (RC) beam exhibiting corrosion-fatigue degradation is shown as an example. The RC beam measures 200mm × 350mm × 4000mm, with a span of 3600mm. The yield strength of the reinforcing steel is 450MPa, and the compressive strength of the concrete is 40MPa. The beam is subjected to four-point fatigue loads at a spacing of 1000mm. The longitudinal reinforcement of the RC beam is affected by corrosion, while the stirrups are assumed to remain intact, consistent with the laboratory corrosion treatment method used in the experiment.

[0234] This invention also provides a system for assessing the probability of blast damage to aging reinforced concrete beams, comprising:

[0235] At least one processor;

[0236] At least one memory for storing at least one program;

[0237] When the at least one program is executed by the at least one processor, the at least one processor performs the method described above.

[0238] The content of the above method embodiments is applicable to this embodiment. The specific functions implemented in this embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments. Therefore, they will not be repeated here.

[0239] This invention also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0240] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0241] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0242] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0243] This invention also provides a computer program product, including a computer program or computer instructions, which are stored in a memory. A processor of a computer device reads the computer program or computer instructions from the memory and executes the computer program or computer instructions, causing the computer device to perform the above-described method.

[0244] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented by the embodiments of this program product are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0245] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0246] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically include computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0247] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

Claims

1. A method for assessing the probability of blast damage to aged reinforced concrete beams, characterized in that, The method includes the following steps: S100, obtain the structural parameters, corrosion model parameters, fatigue model parameters and explosion load parameters of the aged reinforced concrete beam; S200, Based on the corrosion model parameters and chloride ion diffusion model, calculate the probability distribution of corrosion initiation time of the aged reinforced concrete beam; S300, based on the competition mechanism of the corrosion model parameters, the fatigue model parameters, the corrosion pit growth model and the fatigue crack propagation model, calculate the competition time probability distribution of the aging reinforced concrete beam; S400, Based on the fatigue model parameters and fatigue crack propagation model, calculate the fatigue crack propagation time probability distribution of the aged reinforced concrete beam; S500, based on the corrosion initiation time probability distribution, the competition time probability distribution, and the fatigue crack propagation time probability distribution, calculate the total corrosion fatigue life probability distribution of the aged reinforced concrete beam; S600, based on the time-varying steel bar performance degradation model, calculates the degradation law of steel bar cross-sectional area and steel bar yield strength at different times according to the total corrosion fatigue life probability distribution; S700, based on the explosive load parameters, the explosive load stochastic model, and the pressure-impulse curve, establish the explosive vulnerability curve of the aged reinforced concrete beam; S800, based on the explosive vulnerability curve and the degradation law, evaluate the evolution of the probability of explosive damage over time in different corrosion fatigue deterioration stages of the aged reinforced concrete beam.

2. The method according to claim 1, characterized in that, In S200, the calculation of the corrosion initiation time probability distribution of the aged reinforced concrete beam based on the corrosion model parameters and chloride ion diffusion model includes: S210, A diffusion equation for chloride ions in concrete is established based on Fick's second law. The diffusion equation characterizes the relationship between chloride ion concentration and diffusion depth and diffusion time. S220, Based on the chloride ion concentration, chloride ion diffusion coefficient, chloride ion threshold concentration and protective layer thickness of the concrete surface in the corrosion model parameters, calculate the initial corrosion time required for the chloride ion concentration on the steel reinforcement surface to reach the chloride ion threshold concentration; S230, Based on the probability distribution of each parameter in the corrosion model parameters, multiple sets of random samples are generated through Monte Carlo simulation, and the corrosion initial time is calculated for each set of random samples to obtain multiple sets of corrosion initial time samples. S240, Statistical analysis is performed on the multiple sets of corrosion initiation time samples to obtain the probability distribution of corrosion initiation time.

3. The method according to claim 1, characterized in that, In S300, the calculation of the competition time probability distribution of the aging reinforced concrete beam based on the competition mechanism of the corrosion model parameters, the fatigue model parameters, the corrosion pit growth model, and the fatigue crack propagation model includes: S310, Based on the corrosion current density and the ratio of maximum corrosion depth to uniform corrosion depth in the corrosion model parameters, the corrosion pit depth is calculated as a function of time using the corrosion pit depth model, and the corrosion pit growth rate is obtained by differentiation. S320, Based on the stress amplitude, fatigue load frequency and initial diameter of the steel bar in the fatigue model parameters, the fatigue crack propagation rate equation is established by the stress intensity factor formula and the Paris-Erdogan law; S330, the growth rate of the corrosion pit is equal to the growth rate of the fatigue crack, and the transition time of the corrosion pit to the fatigue crack is obtained. The difference between the transition time and the initial corrosion time is calculated as the competition time. S340, based on the probability distribution of each parameter in the corrosion model parameters and the fatigue model parameters, multiple sets of random samples are generated through Monte Carlo simulation, and the competition time is calculated for each set of random samples to obtain multiple sets of competition time samples; S350, Perform statistical analysis on the multiple sets of competition time samples to obtain the competition time probability distribution.

4. The method according to claim 1, characterized in that, In S400, calculating the fatigue crack propagation time probability distribution of the aging reinforced concrete beam based on the fatigue model parameters and the fatigue crack propagation model includes: S410, the corrosion pit depth corresponding to the competition time is used as the initial crack size for fatigue crack propagation, and the critical crack size in the fatigue model parameters is used as the termination condition for fatigue crack propagation. S420, based on the stress amplitude, fatigue load frequency, stress intensity factor threshold and material crack propagation parameters in the fatigue model parameters, perform integral calculation on the Paris-Erdogan law to calculate the fatigue crack propagation time required for the fatigue crack to propagate from the initial crack size to the critical crack size; S430, based on the probability distribution of each parameter in the fatigue model parameters, multiple sets of random samples are generated through Monte Carlo simulation, and the fatigue crack propagation time is calculated for each set of random samples to obtain multiple sets of fatigue crack propagation time samples. S440, Perform statistical analysis on the multiple sets of fatigue crack propagation time samples to obtain the probability distribution of fatigue crack propagation time.

5. The method according to claim 1, characterized in that, In S600, the calculation of the degradation law of the cross-sectional area and yield strength of the steel bars based on the time-varying steel bar performance degradation model and the total corrosion fatigue life probability distribution includes: S610, Based on the corrosion pit depth and initial diameter of the reinforcing bar in the corrosion model parameters, the time-varying residual cross-sectional area of ​​the reinforcing bar under corrosion fatigue is calculated through geometric relationships. S620, Calculate the steel corrosion rate based on the time-varying remaining cross-sectional area and the cross-sectional area of ​​the steel reinforcement in the intact state; S630, Based on the steel corrosion rate and the yield strength of the steel in the intact state, the time-varying residual yield strength of the steel is calculated using the residual yield strength formula; S640, determine the time nodes of each degradation stage according to the total corrosion fatigue life probability distribution, extract the corresponding time-varying residual cross-sectional area and time-varying residual yield strength at the time nodes, and obtain the degradation law.

6. The method according to claim 1, characterized in that, In S700, the establishment of the explosion vulnerability curve based on the explosion load parameters, the explosion load stochastic model, and the pressure-impulse curve includes: S710, based on the explosive equivalent and explosion distance in the explosion load parameters, the mean and standard deviation of the reflection peak overpressure and the mean and standard deviation of the positive phase duration are calculated respectively using the empirical formulas for reflection peak overpressure and positive phase duration. S720, based on the mean and standard deviation of the reflected peak overpressure and the mean and standard deviation of the positive phase duration, the mean and standard deviation of the reflected impulse are determined by the impulse calculation formula; S730, based on the concrete compressive strength, steel yield strength, reinforcement ratio and beam length in the structural parameters, calculate the reflected overpressure asymptote and reflected impulse asymptote corresponding to different damage thresholds through the pressure-impulse curve asymptote formula; S740, establish a pressure-impulse curve based on the reflection overpressure asymptote and the reflection impulse asymptote, and construct a limit state function based on the pressure-impulse curve, the reflection peak overpressure, and the reflection impulse; S750, based on the aforementioned limit state function, the proportion of failure samples in which the limit state function is exceeded under different explosion intensities is calculated by Monte Carlo simulation to obtain the explosion vulnerability curve.

7. The method according to claim 1, characterized in that, In S800, the evaluation of the evolution of the probability of explosion damage over time at different corrosion fatigue deterioration stages based on the explosion vulnerability curve and the degradation law includes: S810, Determine the degraded structural parameters corresponding to different service times according to the degradation law, wherein the degraded structural parameters include the degraded concrete compressive strength, steel yield strength and reinforcement ratio; S820, Substitute the degraded structural parameters into the pressure-impulse curve asymptote formula to update the reflection overpressure asymptote and reflection impulse asymptote corresponding to different damage thresholds; S830, based on the updated pressure-impulse curve and the explosive load stochastic model, re-execute the Monte Carlo simulation to obtain the explosive vulnerability curves corresponding to different service times; S840, by comparing and analyzing the explosion vulnerability curves at different service times, the evolution law of the explosion damage probability over time is obtained.

8. A system for assessing the probability of blast damage to aging reinforced concrete beams, characterized in that, include: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor performs the method as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

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