Reliability-based method and apparatus for durability analysis of a submarine immersed tube tunnel

Abstract

This application provides a reliability-based durability analysis method and apparatus for subsea immersed tunnels. The method includes: acquiring marine environmental parameters and tunnel damage parameters of the target subsea immersed tunnel; the marine environmental parameters include seawater chloride concentration, and the tunnel damage parameters include crack length, crack width, number of cracks, and crack initiation time; establishing a target steel reinforcement surface chloride concentration calculation model for the target subsea immersed tunnel based on a pre-defined calculation model related to seawater chloride concentration, crack length, crack width, number of cracks, and crack initiation time; and calculating the durability failure probability and reliability index of the target subsea immersed tunnel based on reliability theory and the target steel reinforcement surface chloride concentration calculation model. This application can obtain comprehensive and accurate durability analysis results for subsea immersed tunnels.

Description

Technical Field

[0001] This application relates to the field of immersed tunnel inspection technology, and in particular to a reliability-based durability analysis method and apparatus for subsea immersed tunnels. Background Technology

[0002] Reinforced concrete structures in marine environments often experience premature steel corrosion due to long-term exposure to chloride ions in seawater during their service life. Therefore, in the durability design of large-scale marine engineering projects both domestically and internationally, chloride-induced steel corrosion is typically considered one of the main corrosion factors. For example, the Hong Kong-Qinghai Bridge, the Qingdao Strait Bridge, and the Great Belt Strait project in Denmark all considered chloride corrosion of steel reinforcement during the construction phase of their subsea immersed tunnel projects.

[0003] During operation, microcracks can develop in the walls of immersed tunnels under extreme loads such as uneven settlement, earthquakes, typhoons, anchoring failures, and explosions. The presence of these microcracks significantly accelerates the penetration and accumulation of chloride salts in reinforced concrete structures, reducing their load-bearing capacity and durability, and impacting their service life. Therefore, it is essential to study the durability of subsea immersed tunnels exposed to cracking conditions in the marine environment. Currently, commonly used durability analysis methods include deterministic and probabilistic methods. A representative probabilistic method is the Dura Crete reliability model from Europe. The advantage of probabilistic methods is that they consider the uncertainties of durability-influencing factors and establish a quantitative relationship between environmental factors, structural performance, and design service life.

[0004] However, due to the uncertainty of parameters and the complexity of crack characteristics when concrete cracks, existing probabilistic methods for predicting the service life of reinforced concrete structures exposed to chloride environments are usually used to predict the durability of intact concrete or only consider the influence of crack width on chloride ion diffusion rate. This results in the durability analysis conclusions obtained by existing probabilistic methods when analyzing the durability of undersea immersed tunnels within their design service life being neither comprehensive nor accurate. Summary of the Invention

[0005] This application provides a reliability-based durability analysis method and apparatus for subsea immersed tunnels, addressing the problem that existing probabilistic methods for analyzing the durability of subsea immersed tunnels within their design service life often yield incomplete and inaccurate durability analysis conclusions.

[0006] In a first aspect, embodiments of this application provide a reliability-based durability analysis method for subsea immersed tunnels, including:

[0007] The marine environmental parameters and tunnel damage parameters of the target subsea immersed tunnel are obtained. The marine environmental parameters include seawater chloride concentration, and the tunnel damage parameters include crack length, crack width, number of cracks and crack initiation time.

[0008] Based on a pre-defined calculation model of chloride ion concentration on the surface of reinforcing steel bars related to seawater chloride concentration, crack length, crack width, crack number, and crack initiation time, a calculation model of chloride ion concentration on the surface of reinforcing steel bars for the target subsea immersed tunnel is established.

[0009] Based on reliability theory and a calculation model of chloride ion concentration on the surface of the target steel reinforcement, the durability failure probability and reliability index of the target subsea immersed tunnel are calculated.

[0010] Secondly, embodiments of this application provide a reliability-based durability analysis device for subsea immersed tunnels, comprising:

[0011] The parameter acquisition module is used to acquire marine environmental parameters and tunnel damage parameters of the target subsea immersed tunnel. The marine environmental parameters include seawater chloride concentration, and the tunnel damage parameters include crack length, crack width, number of cracks, and crack initiation time.

[0012] The model building module establishes a target steel reinforcement surface chloride ion concentration calculation model based on a preset steel reinforcement surface chloride ion concentration calculation model related to seawater chloride concentration, crack length, crack width, crack number, and crack initiation time.

[0013] The analysis module is used to calculate the durability failure probability and reliability index of the target subsea immersed tunnel based on reliability theory and the chloride ion concentration calculation model on the surface of the target steel reinforcement.

[0014] This application provides a reliability-based durability analysis method and apparatus for subsea immersed tunnels. First, it acquires marine environmental parameters and tunnel damage parameters of the target subsea immersed tunnel. The marine environmental parameters include seawater chloride concentration, and the tunnel damage parameters include crack length, crack width, number of cracks, and crack initiation time. Second, based on a pre-defined calculation model for chloride ion concentration on the surface of reinforcing steel bars related to seawater chloride concentration, crack length, crack width, number of cracks, and crack initiation time, it establishes a calculation model for the chloride ion concentration on the surface of the target reinforcing steel bars for the target subsea immersed tunnel. Finally, based on reliability theory and the calculation model for chloride ion concentration on the surface of the target reinforcing steel bars, it calculates the durability failure probability and reliability index of the target subsea immersed tunnel. Compared to existing models that only consider crack width, this application establishes an analytical method that comprehensively considers the relationship between the probability of steel reinforcement corrosion initiation and crack width, length, number, and initiation time. This method can obtain comprehensive and accurate durability analysis results, effectively making up for the deficiency that most domestic and foreign probabilistic models of chloride ion-induced steel reinforcement corrosion during cracking only consider the influence of crack width. It can predict the durability failure probability of immersed tunnels when crack length, number, and initiation time change, and can provide theoretical support for the durability analysis of cracked undersea immersed tunnels during operation. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart illustrating the implementation of a reliability-based durability analysis method for subsea immersed tunnels provided in this application embodiment;

[0017] Figure 2 This is a simplified schematic diagram of a single-crack chloride diffusion model provided in an embodiment of this application;

[0018] Figure 3 This is a schematic diagram of a reliability-based durability analysis device for subsea immersed tunnels provided in an embodiment of this application. Detailed Implementation

[0019] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0020] To make the objectives, technical solutions, and advantages of this application clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.

[0021] To address the problems of existing technologies, this application provides a reliability-based durability analysis method and apparatus for subsea immersed tunnels. The reliability-based durability analysis method for subsea immersed tunnels provided in this application will be described below.

[0022] See Figure 1 The document illustrates a flowchart of the reliability-based durability analysis method for subsea immersed tunnels provided in this application, detailed below:

[0023] Step 110: Obtain marine environmental parameters and tunnel damage parameters of the target subsea immersed tunnel. Marine environmental parameters include seawater chloride concentration, and tunnel damage parameters include crack length, crack width, number of cracks, and crack initiation time.

[0024] In some embodiments, the target subsea immersed tunnel refers to any subsea immersed tunnel to be subjected to durability analysis, such as a minimally damaged subsea immersed tunnel. Before conducting the durability analysis, it is necessary to obtain its marine environmental parameters and tunnel damage parameters. The marine environmental parameters include seawater chloride concentration, i.e., the concentration of chloride ions in seawater, and the tunnel damage parameters include crack length, crack width, number of cracks, and crack initiation time.

[0025] It should be noted that for some marine environments with high sulfate concentrations, the marine environmental parameter can be the seawater sulfate concentration.

[0026] Step 120: Based on the preset calculation model of chloride ion concentration on the surface of steel bars related to seawater chloride concentration, crack length, crack width, number of cracks and crack initiation time, establish a calculation model of chloride ion concentration on the surface of steel bars for the target subsea immersed tunnel.

[0027] In some embodiments, the chloride ion concentration calculation model for the steel reinforcement surface established in this application is a model related to the seawater chloride concentration, crack length, crack width, number of cracks, and crack initiation time of the target subsea immersed tunnel. It is different from the conventional steel reinforcement surface chloride ion concentration calculation model that only considers crack width, and is the key improvement point of this application.

[0028] Specifically, for a target subsea immersed tunnel with a single crack, the pre-set calculation model for chloride ion concentration on the steel reinforcement surface is as follows:

[0029]

[0030] In the formula, C1 is the chloride ion concentration (%) on the surface of the reinforcing steel bar when there is one crack, and Cs Let represent the chloride ion concentration (%, mass of cementitious material) on the concrete surface, erf be the mathematical error function, x be the thickness of the concrete cover (mm), and D be the chloride ion diffusion coefficient (m²) in uncracking concrete. 2 / s), η is the decay exponent of the chloride ion diffusion coefficient of concrete over time, t is the design service life (year), a is the concentration correction coefficient when cracks are present, b is the equivalent protective layer thickness correction coefficient when cracks are present, c is the correction coefficient of the chloride ion diffusion coefficient for crack length and width, l is the crack length, and f is the influence factor of crack width on the chloride ion diffusion rate.

[0031] For a target subsea immersed tunnel with multiple cracks, the pre-set calculation model for chloride ion concentration on the steel reinforcement surface is as follows:

[0032]

[0033] In the formula, C i λ represents the chloride ion concentration on the surface of the reinforcing steel bar when there are i cracks, where i is the number of cracks, i ≥ 2, and λ i This is the concentration correction factor. The average value of f and the average value of l / x of multiple cracks are substituted into the pre-defined model for calculating the chloride ion concentration on the surface of steel bars with a single crack to obtain the chloride ion concentration on the surface of the steel bars.

[0034] Taking three cracks as an example, when calculating C1, we first calculate the average value of f for each of the three cracks, which can be denoted as f. 平均 And calculate the average value of l / x for each of these three cracks, which can be denoted as l / x. 平均 After that, f can be 平均 and l / x 平均 Substituting this into the aforementioned calculation model for the chloride ion concentration on the surface of a pre-defined steel reinforcement with a single crack, we get the following formula:

[0035]

[0036] In some embodiments, considering the crack initiation time of the target subsea immersed tunnel, the calculation model for the chloride ion concentration on the steel reinforcement surface is as follows:

[0037]

[0038]

[0039]

[0040] In the formula, C tTo account for the time of crack initiation, the chloride ion concentration on the steel reinforcement surface is given by: C0 is the chloride ion concentration on the steel reinforcement surface without cracks, C1 is the chloride ion concentration on the steel reinforcement surface calculated when initial micro-cracks are present, t is the design service life, t1 is the number of years since cracks began to appear, and C... s denoted as , where is the chloride ion concentration on the concrete surface, erf is the mathematical error function, x is the thickness of the concrete cover, D is the chloride ion diffusion coefficient in uncracked concrete, η is the decay exponent of the concrete chloride ion diffusion coefficient over time, a is the concentration correction coefficient when cracks are present, b is the equivalent cover thickness correction coefficient when cracks are present, c is the correction coefficient of crack length and width on the chloride ion diffusion coefficient, l is the crack length, and f1 is the influence factor of crack width on the chloride ion diffusion rate.

[0041] In this way, a suitable pre-defined calculation model for the chloride ion concentration on the surface of the reinforcing steel can be selected for different situations of the subsea immersed tunnel. After determining the pre-defined calculation model for the chloride ion concentration on the surface of the reinforcing steel, the marine environmental parameters and tunnel damage parameters of the target subsea immersed tunnel can be substituted into the determined pre-defined calculation model for the chloride ion concentration on the surface of the reinforcing steel, thereby establishing a target calculation model for the chloride ion concentration on the surface of the reinforcing steel for the target subsea immersed tunnel.

[0042] Step 130: Based on reliability theory and the calculation model of chloride ion concentration on the surface of the target steel reinforcement, calculate the durability failure probability and reliability index of the target subsea immersed tunnel.

[0043] In some embodiments, the durability failure probability and reliability index of the target subsea immersed tunnel can be calculated according to the following formula:

[0044] G=C cr -C

[0045]

[0046] In the formula, G represents the full probability durability design model for the marine chloride ion environment, and C... cr C represents the critical chloride ion concentration on the surface of the reinforcing steel bar, and C is the calculated chloride ion concentration on the surface of the reinforcing steel bar. When considering a single crack, C = C1; when considering multiple cracks, C = C2. i When considering the crack initiation time t, C = C t , P represents the number of steel bars that begin to corrode in N experiments. f β represents the probability of durability failure of the immersed tunnel, and β is the reliability index.

[0047] To facilitate understanding, the research approach of this application will be described in detail below.

[0048] See Figure 2 , Figure 2This is a simplified schematic diagram of the chloride ion diffusion model of a single crack. In this diagram, (a) is a standard segment of an immersed tunnel with a wall thickness of 150cm; (b) is a simplified reinforced concrete beam of the standard segment of the immersed tunnel with a height of 150cm, which is the wall thickness of the immersed tunnel, and a width of 24cm; (c) shows the dimensions of the cross-section and the arrangement of the reinforcing bars; and (d) is a simplified model of chloride ion diffusion under chloride ion erosion in the presence of cracks, which is a rectangle of 12cm × 75cm, where 12cm is the distance between two reinforcing bars and 75cm is half the wall thickness of the immersed tunnel.

[0049] Research has found that cracks accelerate the transport of chloride ions in concrete, with the diffusion rate of chloride ions in cracks exceeding that in the concrete matrix. Assuming the cracked concrete cover consists of intact concrete and cracks, and that each crack has its own chloride ion diffusion coefficient, the influence of cracks on the chloride ion diffusion rate is represented by the ratio f1 of the chloride ion diffusion coefficient in cracks to that in uncracked concrete. Assuming the chloride ion diffusion coefficient in cracks depends only on the crack width, the chloride ion diffusion coefficient in cracks can be expressed as:

[0050] D cr =f1D

[0051] In the above formula, D cr It is the chloride ion diffusion coefficient (m) in the crack. 2 / s), f1 is the effect factor of crack width on chloride ion diffusion rate, and D is the chloride ion diffusion coefficient (m) in uncracked concrete. 2 / s).

[0052] Based on the analytical solution of Fick's second law, an influence factor f1 on the chloride ion diffusion rate is introduced, along with the ratio of crack length to protective layer thickness l / x. In this case, the chloride ion diffusion coefficient in the crack is f1 × D. Assuming f1 ranges from 2 to 10 and l / x ranges from 0 to 1, simulation experiments are conducted to model the effect of crack length and width on the chloride ion concentration on the steel reinforcement surface. Parameter settings are shown in Table 1, and a total of 90 simulation experiments were performed using all combinations of parameters from the table.

[0053] Table 1 Simulation test parameter settings

[0054]

[0055] Based on the above simulation experiments, a crack exists on the model surface, with Cs = 5.4 and D = 3 × 10⁻¹² m. 2 / s, η=0.0614, x=80mm, t=120 years, the influence factor f1 of crack width on chloride ion diffusion rate varies between 2 and 10, and the ratio of crack length to protective layer thickness l / x varies between 0.1 and 1.

[0056] Through regression analysis, the formula for calculating the chloride ion concentration on the steel reinforcement surface under varying parameters is assumed to be represented by the following fitted formula:

[0057]

[0058] In the above formula, a, b, and c are three undetermined coefficients related to x, D, η, and t. The values ​​of a, b, and c differ under different chloride ion corrosion environments. The values ​​of the fitting parameters can be determined by designing orthogonal experiments.

[0059] Specifically, we select a, b, and c, which need to be determined in the above regression analysis, as optimization objectives, and determine the concrete protective layer thickness x, chloride ion diffusion coefficient D, the decay exponent of the concrete chloride ion diffusion coefficient over time η, and the design service life t as factors that have a significant impact on a, b, and c.

[0060] Taking data from the splash zone as an example of regression analysis, based on the four main influencing factors and using the 95% confidence interval of the parameters, the concrete cover thickness x is set to five levels: 69.4 mm, 74.7 mm, 80 mm, 85.3 mm, and 90.6 mm; the chloride ion diffusion coefficient D is set to 2 × 10⁻⁶. -12 m 2 / s, 2.4×10 -12 m 2 / s, 2.9×10 -12 m 2 / s, 3.6×10 -12 m 2 / s, 4.4×10 -12 m 2 The concrete chloride ion diffusion coefficient was measured at five levels per second (η), with decay exponents η ranging from 0.41 to 0.53. The time interval (t) was measured at five levels: 40a, 60a, 80a, 100a, and 120a. The experimental factors and levels are shown in Tables 2 and 3 below.

[0061] Table 2 Factors and levels of orthogonal experiments

[0062] factor x D η t Level 1 69.4 2 0.41 40 Level 2 74.7 2.4 0.44 60 Level 3 80 2.9 0.47 80 Level 4 85.3 3.6 0.5 100 Level 5 90.6 4.4 0.53 120

[0063] Table 3 Experimental Design Table

[0064] factor x D η t Experiment 1 69.4 2 0.41 40 Experiment 2 69.4 2.4 0.44 60 Experiment 3 69.4 2.9 0.47 80 Experiment 4 69.4 3.6 0.5 100 Experiment 5 69.4 4.4 0.53 120 Experiment 6 74.7 2 0.44 80 Experiment 7 74.7 2.4 0.47 100 Experiment 8 74.7 2.9 0.5 120 Experiment 9 74.7 3.6 0.53 40 Experiment 10 74.7 4.4 0.41 60 Experiment 11 80 2 0.47 120 Experiment 12 80 2.4 0.5 40 Experiment 13 80 2.9 0.53 60 Experiment 14 80 3.6 0.41 80 Experiment 15 80 4.4 0.44 100 Experiment 16 85.3 2 0.5 60 Experiment 17 85.3 2.4 0.53 80 Experiment 18 85.3 2.9 0.41 100 Experiment 19 85.3 3.6 0.44 120 Experiment 20 85.3 4.4 0.47 40 Experiment 21 90.6 2 0.53 100 Experiment 22 90.6 2.4 0.41 120 Experiment 23 90.6 2.9 0.44 40 Experiment 24 90.6 3.6 0.47 60 Experiment 25 90.6 4.4 0.5 80

[0065] Through 25 sets of experiments designed using an experimental design table and numerical analysis, the chloride ion concentration on the steel reinforcement surface at a certain moment was obtained when a crack existed and the crack length and width varied. Then, regression analysis was used to fit several different values ​​of a, b, and c, and plots were drawn for a, b, and c against the values ​​of chloride ions on the steel reinforcement surface. The regression curve can be obtained, thus yielding the fitting parameters.

[0066] Furthermore, using the above model, the variation of chloride ion concentration on the steel reinforcement surface when multiple cracks exist in concrete can be studied. Specifically, 2, 5, and 10 transverse cracks of different lengths and widths can be randomly generated on the left boundary of the model. The influence factor f1 of the crack width on the chloride ion diffusion rate is 1–10, and the ratio of crack length to protective layer thickness l / x is 0–0.8, all following a uniform distribution. 500 sets of simulation experiments are conducted for each type. The average values ​​of the influence factor f1 of crack width on the chloride ion diffusion rate and the ratio l / x of crack length to protective layer thickness are calculated for 2, 5, and 10 cracks respectively, and substituted into the chloride ion concentration calculation model for the steel reinforcement surface when one crack exists. The concentration values ​​from the simulation experiments are compared with the values ​​calculated by the above formula to obtain the concentration correction coefficients λ2, λ5, and λ when 2, 5, and 10 cracks exist. 10 The formula for calculating the chloride ion concentration on the surface of the reinforcing steel at this time is:

[0067]

[0068] Next, we will introduce the durability analysis. Structural reliability is an important indicator for measuring the safety, serviceability, or durability of a structure. To determine the reliability of a structure, it is necessary to determine the durability limit state and limit state equation. In this application, the beginning of corrosion (depassivation) of the reinforcing steel in the concrete is defined as the durability limit state, expressed as the chloride ion concentration on the surface of the reinforcing steel reaching the critical chloride ion concentration.

[0069] The Monte Carlo method can be used to calculate the reliability of subsea immersed tunnels and the onset time of corrosion of the inner and outer reinforcing bars of the tunnel sections. Specifically, the probability of durability failure P of the immersed tunnel can be calculated using the following formula. f and structural reliability indicators:

[0070]

[0071] This reliability index represents the probability that a structure will perform its intended function within a specified time and under specified conditions. The higher the reliability index, the lower the probability of failure and the more reliable the structure.

[0072] In this application embodiment, the effects of crack length, width, number, and initiation time on chloride ion concentration on the surface of reinforcing steel are considered, and a corresponding calculation model for chloride ion concentration on the surface of reinforcing steel is established. Compared with existing models that only consider crack width, this application establishes an analytical method that comprehensively considers the relationship between the probability of steel corrosion initiation and crack width, length, number, and initiation time. This method can obtain comprehensive and accurate durability analysis results, effectively making up for the deficiency that most domestic and foreign probability models for chloride ion-induced steel corrosion during cracking only consider the influence of crack width. It can predict the durability failure probability of immersed tunnels when crack length, number, and initiation time change, and can provide theoretical support for the durability analysis of cracked undersea immersed tunnels during operation.

[0073] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0074] The following are device embodiments of this application. For details not described in detail, please refer to the corresponding method embodiments described above.

[0075] Figure 3 A schematic diagram of the structure of the reliability-based durability analysis device for subsea immersed tunnels provided in an embodiment of the present invention is shown. For ease of explanation, only the parts relevant to the embodiments of this application are shown, and are described in detail below:

[0076] like Figure 3 As shown, the reliability-based durability analysis device for subsea immersed tunnels includes:

[0077] The parameter acquisition module 310 is used to acquire marine environmental parameters and tunnel damage parameters of the target subsea immersed tunnel. The marine environmental parameters include seawater chloride concentration, and the tunnel damage parameters include crack length, crack width, number of cracks, and crack initiation time.

[0078] The model building module 320 is used to build a target steel bar surface chloride ion concentration calculation model for the target submarine immersed tunnel based on a preset steel bar surface chloride ion concentration calculation model related to seawater chloride concentration, crack length, crack width, crack number and crack initiation time.

[0079] Analysis module 330 is used to calculate the durability failure probability and reliability index of the target subsea immersed tunnel based on reliability theory and the chloride ion concentration calculation model on the surface of the target steel reinforcement.

[0080] In some embodiments, when a single crack exists, the preset calculation model for chloride ion concentration on the steel reinforcement surface is as follows:

[0081]

[0082] In the formula, C1 is the chloride ion concentration on the surface of the reinforcing steel when a single crack exists, C s Let represent the chloride ion concentration on the concrete surface, erf be the mathematical error function, x be the thickness of the concrete cover, D be the chloride ion diffusion coefficient in uncracked concrete, η be the decay exponent of the chloride ion diffusion coefficient over time, t be the design service life, a be the concentration correction factor when cracks are present, b be the equivalent cover thickness correction factor when cracks are present, c be the correction factor for the chloride ion diffusion coefficient based on crack length and width, l be the crack length, and f be the influence factor of crack width on the chloride ion diffusion rate.

[0083] In some embodiments, when multiple cracks exist, the preset calculation model for chloride ion concentration on the steel reinforcement surface is as follows:

[0084]

[0085] In the formula, C i λ represents the chloride ion concentration on the surface of the reinforcing steel bar when there are i cracks, where i is the number of cracks, i ≥ 2, and λ i This is the concentration correction factor. The average value of f and the average value of l / x of multiple cracks are substituted into the pre-defined model for calculating the chloride ion concentration on the surface of steel bars with a single crack to obtain the chloride ion concentration on the surface of the steel bars.

[0086] In some embodiments, considering the crack initiation time, the established calculation model for chloride ion concentration on the steel reinforcement surface includes:

[0087]

[0088]

[0089]

[0090] In the formula, C t To account for the time of crack initiation, the chloride ion concentration on the surface of the reinforcing steel is given, where C0 is the chloride ion concentration on the surface of the reinforcing steel without cracks. n The chloride ion concentration on the steel reinforcement surface when initial microcracks exist, t is the design service life, t1 is the year since cracks began to appear, and C s denoted as , where is the chloride ion concentration on the concrete surface, erf is the mathematical error function, x is the thickness of the concrete cover, D is the chloride ion diffusion coefficient in uncracked concrete, η is the decay exponent of the concrete chloride ion diffusion coefficient over time, a is the concentration correction coefficient when cracks are present, b is the equivalent cover thickness correction coefficient when cracks are present, c is the correction coefficient of crack length and width on the chloride ion diffusion coefficient, l is the crack length, and f1 is the influence factor of crack width on the chloride ion diffusion rate.

[0091] In some embodiments, based on reliability theory and a calculation model of chloride ion concentration on the surface of the target reinforcing steel, the durability failure probability and reliability index of the target subsea immersed tunnel are calculated, including:

[0092] The durability failure probability and reliability index of the target subsea immersed tunnel are calculated using the following formula:

[0093] G=C cr -C

[0094]

[0095] In the formula, G represents the full probability durability design model for the marine chloride ion environment, and C... cr C represents the critical chloride ion concentration on the surface of the reinforcing steel bar, and C is the calculated chloride ion concentration on the surface of the reinforcing steel bar. When considering a single crack, C = C1; when considering multiple cracks, C = C2. i When considering the crack initiation time t, C = C t , P represents the number of steel bars that begin to corrode in N experiments. f β represents the probability of durability failure of the immersed tunnel, and β is the reliability index.

[0096] In this application embodiment, the effects of crack length, width, number, and initiation time on chloride ion concentration on the surface of reinforcing steel are considered, and a corresponding calculation model for chloride ion concentration on the surface of reinforcing steel is established. Compared with existing models that only consider crack width, this application establishes an analytical method that comprehensively considers the relationship between the probability of steel corrosion initiation and crack width, length, number, and initiation time. This method can obtain comprehensive and accurate durability analysis results, effectively making up for the deficiency that most domestic and foreign probability models for chloride ion-induced steel corrosion during cracking only consider the influence of crack width. It can predict the durability failure probability of immersed tunnels when crack length, number, and initiation time change, and can provide theoretical support for the durability analysis of cracked undersea immersed tunnels during operation.

[0097] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0098] Furthermore, the features of the embodiments shown in the accompanying drawings or the various embodiments mentioned in this specification should not be construed as independent embodiments. Rather, each feature described in one example of an embodiment can be combined with one or more other desired features from other embodiments to produce other embodiments not described in words or with reference to the accompanying drawings.

[0099] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0100] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A reliability-based durability analysis method for subsea immersed tunnels, characterized in that, include: The marine environmental parameters and tunnel damage parameters of the target subsea immersed tunnel are obtained. The marine environmental parameters include seawater chloride concentration, and the tunnel damage parameters include crack length, crack width, number of cracks, and crack initiation time. Based on a pre-defined calculation model of chloride ion concentration on the surface of reinforcing steel bars related to seawater chloride concentration, crack length, crack width, crack number, and crack initiation time, a calculation model of chloride ion concentration on the surface of reinforcing steel bars for the target subsea immersed tunnel is established. Based on reliability theory and the calculation model of chloride ion concentration on the surface of the target steel reinforcement, the durability failure probability and reliability index of the target subsea immersed tunnel are calculated. In the case of a single crack, the calculation model for the chloride ion concentration on the surface of the pre-set reinforcing steel is as follows: In the formula, C 1 represents the chloride ion concentration on the surface of the reinforcing steel bar when a single crack exists. C s The chloride ion concentration on the concrete surface. erf The mathematical error function, x The thickness of the concrete protective layer. D The chloride ion diffusion coefficient is the value of the uncracked concrete. η The decay exponent of the chloride ion diffusion coefficient of concrete over time. t For the design service life, a This is the concentration correction factor when cracks are present. b This is a correction factor for the equivalent protective layer thickness when cracks are present. c This represents the correction factor for the chloride ion diffusion coefficient based on the crack length and width. l The length of the crack. f The factor affecting the chloride ion diffusion rate is the crack width. In the presence of multiple cracks, the preset chloride ion concentration calculation model on the surface of the reinforcing steel is as follows: In the formula, C i For existence i The chloride ion concentration on the surface of the reinforcing steel bar when a crack appears. i The number of cracks, i ≥2, This is the concentration correction factor. To make multiple cracks f The average and The average value is substituted into the calculation model of chloride ion concentration on the surface of steel bar with a single crack to obtain the chloride ion concentration on the surface of steel bar. Taking into account the crack initiation time, the preset chloride ion concentration calculation model on the steel reinforcement surface includes: In the formula, C t To account for the chloride ion concentration on the surface of the reinforcing steel during crack initiation time, C 0 represents the chloride ion concentration on the surface of the reinforcing steel bar when there are no cracks. C n The chloride ion concentration on the steel reinforcement surface was calculated when initial microcracks were present. t For the design service life, t 1 represents the year in which the cracks began to appear. C s The chloride ion concentration on the concrete surface. erf The mathematical error function, x The thickness of the concrete protective layer. D The chloride ion diffusion coefficient is the value of the uncracked concrete. η The decay exponent of the chloride ion diffusion coefficient of concrete over time. a This is the concentration correction factor when cracks are present. b This is a correction factor for the equivalent protective layer thickness when cracks are present. c This represents the correction factor for the chloride ion diffusion coefficient based on the crack length and width. l The length of the crack. f This represents the effect of crack width on the chloride ion diffusion rate.

2. The reliability-based durability analysis method for subsea immersed tunnels according to claim 1, characterized in that, The reliability theory and the chloride ion concentration calculation model on the surface of the target steel reinforcement are used to calculate the durability failure probability and reliability index of the target subsea immersed tunnel, including: The durability failure probability and reliability index of the target subsea immersed tunnel are calculated according to the following formula: G = C cr - C In the formula, G A full-probability durability design model for marine chloride ion environments. C cr This represents the critical chloride ion concentration on the surface of the reinforcing steel. C To calculate the chloride ion concentration on the surface of the reinforcing steel, when considering a single crack, C = C 1. When considering multiple cracks, C = C i When considering the crack initiation time t hour, C = C t , express N The number of steel bars that began to corrode in this experiment. This represents the probability of durability failure of the immersed tunnel. This is a reliability indicator.

3. A reliability-based durability analysis device for subsea immersed tunnels, characterized in that, include: The parameter acquisition module is used to acquire marine environmental parameters and tunnel damage parameters of the target subsea immersed tunnel. The marine environmental parameters include seawater chloride concentration, and the tunnel damage parameters include crack length, crack width, number of cracks, and crack initiation time. The model building module is used to build a target steel bar surface chloride ion concentration calculation model for the target submarine immersed tunnel based on a preset steel bar surface chloride ion concentration calculation model related to seawater chloride concentration, crack length, crack width, crack number and crack initiation time. The analysis module is used to calculate the durability failure probability and reliability index of the target subsea immersed tunnel based on reliability theory and the chloride ion concentration calculation model on the surface of the target steel reinforcement. In the case of a single crack, the calculation model for the chloride ion concentration on the surface of the pre-set reinforcing steel is as follows: In the formula, C 1 represents the chloride ion concentration on the surface of the reinforcing steel. C s The chloride ion concentration on the concrete surface. erf The mathematical error function, x The thickness of the concrete protective layer. D The chloride ion diffusion coefficient is the value of the uncracked concrete. η The decay exponent of the chloride ion diffusion coefficient of concrete over time. t For the design service life, a This is the concentration correction factor when cracks are present. b This is a correction factor for the equivalent protective layer thickness when cracks are present. c This represents the correction factor for the chloride ion diffusion coefficient based on the crack length and width. l The length of the crack. f The factor affecting the chloride ion diffusion rate is the crack width. In the presence of multiple cracks, the preset chloride ion concentration calculation model on the surface of the reinforcing steel is as follows: In the formula, C i For existence i The chloride ion concentration on the surface of the reinforcing steel bar when a crack appears. i The number of cracks, i ≥2, This is the concentration correction factor. To make multiple cracks f The average and The average value is substituted into the calculation model of chloride ion concentration on the surface of steel bar with a single crack to obtain the chloride ion concentration on the surface of steel bar. Taking into account the crack initiation time, the preset chloride ion concentration calculation model on the steel reinforcement surface includes: In the formula, C t To account for the chloride ion concentration on the surface of the reinforcing steel during crack initiation time, C 0 represents the chloride ion concentration on the surface of the reinforcing steel bar when there are no cracks. C n The chloride ion concentration on the steel reinforcement surface was calculated when initial microcracks were present. t For the design service life, t 1 represents the year in which the cracks began to appear. C s The chloride ion concentration on the concrete surface. erf The mathematical error function, x The thickness of the concrete protective layer. D The chloride ion diffusion coefficient is the value of the uncracked concrete. η The decay exponent of the chloride ion diffusion coefficient of concrete over time. a This is the concentration correction factor when cracks are present. b This is a correction factor for the equivalent protective layer thickness when cracks are present. c This represents the correction factor for the chloride ion diffusion coefficient based on the crack length and width. l The length of the crack. f This represents the effect of crack width on the chloride ion diffusion rate.

4. The reliability-based durability analysis device for subsea immersed tunnels according to claim 3, characterized in that, The analysis module is also used for: The durability failure probability and reliability index of the target subsea immersed tunnel are calculated according to the following formula: G = C cr - C In the formula, G A full-probability durability design model for marine chloride ion environments. C cr This represents the critical chloride ion concentration on the surface of the reinforcing steel. C To calculate the chloride ion concentration on the surface of the reinforcing steel, when considering a single crack, C = C 1. When considering multiple cracks, C = C i When considering the crack initiation time t hour, C = C t , express N The number of steel bars that began to corrode in this experiment. This represents the probability of durability failure of the immersed tunnel. This is a reliability indicator.

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