Seismic vulnerability analysis method for underground structures

Abstract

The present invention relates to the field of computer-aided engineering analysis, and in particular to a method for analyzing the seismic vulnerability of underground structures. The content includes: calculating the seismic load through an underground structure seismic response analysis algorithm, and solving the dynamic response of the underground structure; based on the dynamic response of the underground structure, dynamically simulating the damage progression of the underground structure during an earthquake, calculating the vulnerability index, and then calculating the seismic vulnerability probability of the underground structure. It solves the problem that the traditional seismic load input model does not fully consider the time-varying frequency and nonlinear attenuation effect of seismic waves, the traditional dynamic response equation easily ignores the damping effect of groundwater fluid and soil, and the damage assessment method fails to fully consider the various dynamic responses of the underground structure under the action of an earthquake, resulting in an inaccurate assessment of the structural damage; lacks dynamic modeling of the post-earthquake recovery capacity of the underground structure, and ignores the changes of the underground structure during the entire earthquake process, resulting in the lack of long-term and comprehensiveness in the calculation of the vulnerability probability.

Description

Technical Field

[0001] The invention relates to the field of computer-aided engineering analysis, and in particular to a method for analyzing seismic vulnerability of underground structures. Background Art

[0002] With the continuous advancement of urbanization and the increasing utilization of underground space, underground structures (such as underground tunnels, underground parking lots, underground shopping malls, and subways) have occupied an important position in modern urban construction. However, since underground structures are in the underground environment for a long time, the impact of earthquakes on underground structures is particularly complex. Therefore, seismic vulnerability analysis of underground structures is an important prerequisite for ensuring the safe operation of underground structures under earthquakes.

[0003] Traditional seismic vulnerability analysis methods for underground structures are computationally simple and can provide preliminary estimation results. However, they often fail to accurately reflect the true response of underground structures under complex seismic waves because they ignore the nonlinear behavior of underground structures, the propagation effects of seismic waves, and the interaction between underground structures and soil.

[0004] With the continuous development of computer technology and numerical simulation technology, as well as the further improvement of data processing capabilities, the seismic vulnerability analysis methods of underground structures have gradually tended to be refined, multi-dimensional and comprehensive, which can better simulate the dynamic response of underground structures under complex seismic waves, accurately evaluate the damage mode and failure mechanism of underground structures under earthquakes, and provide a scientific basis for the seismic design, reinforcement and renovation, and post-disaster assessment of underground structures, and provide more solid technical support for the safety of urban underground structures.

[0005] However, the above technologies have the following technical problems: the traditional seismic load input model fails to fully consider the time-varying frequency and nonlinear attenuation effect of seismic waves, making the simulation of seismic loads inaccurate in some special scenarios, and relying on simplified sine waves or constant frequency assumptions, it cannot accurately reflect the source fluctuation frequency and attenuation characteristics, resulting in large prediction deviations of underground structure seismic response; the traditional dynamic response equation tends to ignore the damping effect of groundwater fluid and soil, but under the action of seismic loads, the damping effect of groundwater fluid and soil on underground structures cannot be ignored; the damage assessment method fails to fully consider the different contributions of various dynamic responses (such as displacement, velocity, acceleration) of underground structures under earthquakes, and does not introduce nonlinear effects, so the calculation of damage factors is often oversimplified, resulting in inaccurate assessment of structural damage, especially in the assessment of post-earthquake recovery capacity. There is a lack of dynamic modeling of the post-earthquake recovery capacity of underground structures, and the nonlinear relationship between damage and recovery is not considered, resulting in incomplete and inaccurate vulnerability prediction; it only relies on the instantaneous damage assessment of earthquakes, while ignoring the changes of underground structures during the entire earthquake process, resulting in the lack of long-term and comprehensiveness in the calculation of vulnerability probability. Summary of the invention

[0006] The present invention provides a seismic vulnerability analysis method for underground structures to solve the problems that the traditional seismic load input model fails to fully consider the time-varying frequency and nonlinear attenuation effect of seismic waves, resulting in insufficient accuracy in the simulation of seismic loads in some special scenarios. In addition, the model relies on simplified sine waves or constant frequency assumptions, which cannot accurately reflect the source fluctuation frequency and attenuation characteristics, resulting in large prediction deviations of the seismic response of underground structures. The traditional dynamic response equations tend to ignore the damping effect of groundwater fluid and soil. However, under the action of seismic loads, the damping effect of groundwater fluid and soil on underground structures cannot be ignored. The damage assessment method fails to fully consider the The different contributions of various dynamic responses (such as displacement, velocity, and acceleration) of underground structures under earthquakes are not taken into account, and nonlinear effects are not introduced, so the calculation of damage factors is often oversimplified, resulting in inaccurate assessment of structural damage, especially in the assessment of post-earthquake recovery capacity. There is a large deviation; there is a lack of dynamic modeling of the post-earthquake recovery capacity of underground structures, and the nonlinear relationship between damage and recovery is not considered, resulting in incomplete and inaccurate vulnerability prediction; it only relies on the instantaneous damage assessment of earthquakes, while ignoring the changes of underground structures during the entire earthquake process, resulting in the lack of long-term and comprehensiveness in the calculation of vulnerability probability.

[0007] The seismic vulnerability analysis method of underground structures of the present invention specifically includes the following technical solutions:

[0008] The seismic vulnerability analysis method of underground structures comprises the following steps:

[0009] S1. Calculate the seismic load and solve the dynamic response of the underground structure through the underground structure seismic response analysis algorithm; the specific implementation process of the underground structure seismic response analysis algorithm is: introduce the seismic load input model based on time-varying frequency and nonlinear attenuation to obtain the seismic load; then based on the seismic load, solve the dynamic response of the underground structure through the improved dynamic equation to obtain the displacement response, velocity response and acceleration response of the underground structure;

[0010] S2. Based on the displacement response, velocity response and acceleration response of the underground structure, the damage progress of the underground structure during the earthquake is dynamically simulated by using the underground structure damage factor calculation algorithm to calculate the damage factor;

[0011] S3, based on the damage factor, a vulnerability index is calculated by using a vulnerability index calculation algorithm;

[0012] S4. Based on the vulnerability index, the seismic vulnerability probability of the underground structure is calculated through the seismic vulnerability statistical model.

[0013] Preferably, the S1 specifically includes:

[0014] The seismic load input model based on time-varying frequency and nonlinear attenuation introduces the nonlinear correction coefficient of the earthquake source and the exponential attenuation function, and combines the sine function and the cosine function to calculate the seismic load; the calculation formula of the seismic load is:

[0015] ,

[0016] in, Indicates at time earthquake load; It indicates the initial intensity of the seismic waves generated by the earthquake source; Represents the nonlinear correction coefficient of the earthquake source; represents the cosine function; Indicates at time The dominant frequency of seismic waves; and The coefficients representing the frequency oscillation of the earthquake source are used to adjust the amplitude and period of the frequency oscillation in the earthquake load; represents the sine function; is an exponential decay function; represents the attenuation factor; Represents the power of time; Represents the regulation index.

[0017] Preferably, the S1 specifically includes:

[0018] The improved dynamic equation combines the mass, stiffness and damping coefficient of the underground structure itself, and introduces the damping coefficient of groundwater fluid and soil to simulate the response of the underground structure under earthquake action, and calculates the displacement response, velocity response and acceleration response of the underground structure.

[0019] Preferably, the S2 specifically includes:

[0020] The underground structure damage factor calculation algorithm dynamically simulates the damage progress of the underground structure during an earthquake by performing weighted calculations on the displacement response, velocity response and acceleration response of the underground structure.

[0021] Preferably, the S2 specifically includes:

[0022] In the process of implementing the calculation algorithm of underground structure damage factor, nonlinear factors are introduced to perform exponential weighting on the velocity response and displacement response of the underground structure, and the damage factor is calculated in combination with the acceleration attenuation factor.

[0023] Preferably, the S3 specifically includes:

[0024] The vulnerability index calculation algorithm is based on the damage factor, combined with the recovery factor, and introduces a coefficient for adjusting the balance between the damage factor and the recovery factor to calculate the vulnerability index.

[0025] Preferably, the S3 specifically includes:

[0026] In the process of implementing the vulnerability index calculation algorithm, based on the damage factor, a first adjustment parameter and a second adjustment parameter are introduced to calculate the recovery factor.

[0027] Preferably, the S4 specifically includes:

[0028] The earthquake vulnerability statistical model calculates the earthquake vulnerability probability of the underground structure through the normal distribution probability density function of the vulnerability index, combined with the instantaneous change of the vulnerability index and the change of the vulnerability index in the entire earthquake cycle; the calculation formula of the earthquake vulnerability probability of the underground structure is:

[0029] ,

[0030] in, represents the probability of seismic vulnerability of underground structures; Indicates the vulnerability index in the time interval Integrate all the values ​​within ; Indicates the earthquake cycle time; represents the normalization factor of the normal distribution; represents the probability density function of the normal distribution of the vulnerability index; Indicates at time Vulnerability index at ; represents the mean value of the vulnerability index; represents the standard deviation of the vulnerability index; represents the nonlinear effect of injury progression; represents the coefficient controlling the progression of damage; Represents the maximum vulnerability index.

[0031] The beneficial effects of the technical solution of the present invention are:

[0032] 1. By introducing the seismic load input model based on time-varying frequency and nonlinear attenuation, the complex characteristics of different types of seismic waves can be effectively simulated. According to the initial intensity of the seismic waves generated by the source and the nonlinear correction coefficient of the source, the amplitude and frequency fluctuation of the seismic waves can be dynamically adjusted, and the time-varying characteristics of the seismic load can be truly reflected, providing accurate and reliable input data for the subsequent response analysis of underground structures.

[0033] 2. The improved dynamic equation not only takes into account the mass, stiffness and damping effect of the underground structure itself, but also specifically incorporates the damping effect of soil and groundwater fluid. It can accurately simulate the response of underground structures under earthquakes, especially the interaction between soil and water flow during vibration transmission, further improving the authenticity and calculation accuracy of the seismic response of underground structures.

[0034] 3. Through the underground structure damage factor calculation algorithm, the displacement response, velocity response and acceleration response of the underground structure are weightedly calculated to dynamically simulate the progression of structural damage during an earthquake. The nonlinear contribution of the velocity response, displacement response and acceleration response of the underground structure to the damage and the attenuation effect of acceleration are taken into account, so that the damage factor can accurately reflect the degree of damage of the underground structure at different stages, thereby providing accurate damage assessment.

[0035] 4. The vulnerability index calculation algorithm takes into account the dynamic balance between the recovery factor and the damage factor, can measure the recovery capacity of underground structures, introduce the maximum damage factor, avoid the damage factor exceeding the physical limit, and standardize the calculation of the damage factor, thereby ensuring the rationality and accuracy of the vulnerability assessment. It is suitable for evaluating the long-term recovery potential of underground structures in earthquakes, can quantify the structural damage recovery capacity after an earthquake, and identify potential risks in advance.

[0036] 5. Based on the vulnerability index, the seismic vulnerability probability of underground structures is calculated through the seismic vulnerability statistical model, and the damage risk of underground structures in different earthquake cycles is quantified. The probability density function and exponential decay function of the normal distribution can accurately describe the nonlinear progression of underground structure damage, which can help designers identify potential risk points in advance during the design and operation stages of underground structures, and provide a scientific basis for monitoring and repair of structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 The present invention is a flowchart of the seismic vulnerability analysis method for underground structures. DETAILED DESCRIPTION

[0038] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0040] The specific scheme of the method for analyzing the seismic vulnerability of underground structures provided by the present invention is described in detail below with reference to the accompanying drawings.

[0041] Refer to the attached Figure 1 , which shows a flow chart of a method for analyzing seismic vulnerability of underground structures provided by an embodiment of the present invention, the method comprising the following steps:

[0042] S1. Calculate the seismic load and solve the dynamic response of the underground structure through the underground structure seismic response analysis algorithm; the specific implementation process of the underground structure seismic response analysis algorithm is: introduce the seismic load input model based on time-varying frequency and nonlinear attenuation to obtain the seismic load; then based on the seismic load, solve the dynamic response of the underground structure through the improved dynamic equation to obtain the displacement response, velocity response and acceleration response of the underground structure;

[0043] In order to accurately describe the dynamic response of underground structures under seismic loads, an underground structure seismic response analysis algorithm is used to calculate seismic loads and solve the dynamic response of underground structures. The specific implementation process of the underground structure seismic response analysis algorithm is as follows: an earthquake load input model based on time-varying frequency and nonlinear attenuation is introduced to simulate the complex characteristics of different seismic waves, and the dynamic response of underground structures is solved by improved dynamic equations.

[0044] The earthquake load input model based on time-varying frequency and nonlinear attenuation determines the initial amplitude of the earthquake load by the initial intensity of the earthquake wave generated by the earthquake source as the basic reference value of the earthquake load; introduces the nonlinear correction coefficient of the earthquake source to correct the changes of the earthquake wave around the epicenter or during the propagation process due to nonlinear effects; in order to further refine the simulation, introduces sine function and cosine function to simulate the periodic oscillation of the earthquake load input over time. Since the sine function and the cosine function have different starting points on the time axis, they can reflect the fluctuation characteristics of the earthquake source frequency in different vibration time periods; introduces an exponential decay function to simulate the attenuation characteristics of the earthquake load, indicating that the influence of the earthquake load gradually decreases with the passage of time, and determines the speed at which the earthquake load decays over time through the attenuation factor. The nonlinear attenuation characteristics of the earthquake load over time are adjusted by introducing an adjustment index to determine the time evolution mode of the attenuation, which affects the change curve of the earthquake load attenuation over time, so that the earthquake load can flexibly reflect the actual attenuation law of the earthquake wave;

[0045] The calculation formula for earthquake load is:

[0046] ,

[0047] in, Indicates at time The earthquake load describes the change of force on underground structures during an earthquake; It indicates the initial intensity of the seismic wave generated by the earthquake source, which is used to determine the initial amplitude of the seismic load. It is the basic reference value of the seismic load and can be set according to the specific implementation scenario. It is not limited here. The nonlinear correction coefficient of the earthquake source is used to correct the changes of earthquake waves around the epicenter or during the propagation process due to nonlinear effects. It can be set according to the specific implementation scenario and is not limited here. Represents the cosine function, which is used to simulate the periodic fluctuation characteristics of earthquake load input over time; Indicates at time The main frequency of the seismic wave is used to reflect the change of the frequency of the seismic wave over time; and The coefficient representing the frequency oscillation of the earthquake source is used to adjust the amplitude and period of the frequency oscillation in the earthquake load to simulate the periodic change of the vibration frequency of the earthquake source in different time periods to adapt to different types of earthquake waves. It can be set according to the specific implementation scenario and is not limited here. Represents the sine function, which is used together with the cosine function to simulate the periodic oscillation simulation of the earthquake load input changing with time, but it has a different phase compared to the cosine function, which means that there are different starting points on the time axis, reflecting the different stages of the source load; It is an exponential decay function, which is used to simulate the process of earthquake load decaying over time. As time goes by, the impact of earthquake load will gradually decrease; It represents the attenuation factor, which determines the speed at which the seismic load decays over time. It can be set according to the specific implementation scenario and is not limited here. The power term representing time determines the rate at which the decay process changes over time; represents the adjustment index, and , used to adjust the nonlinear attenuation characteristics of the seismic load over time, which determines the time evolution mode of the attenuation and affects the curve of the seismic load attenuation over time. It can be set according to the specific implementation scenario and is not limited here;

[0048] Based on the seismic load, the dynamic response of the underground structure is solved by the improved dynamic equation, and the displacement response, velocity response and acceleration response of the underground structure are calculated;

[0049] The improved dynamic equations take into account the damping effect of groundwater fluid and soil, especially in the vibration transmission process of underground structures, the interaction between soil and water may cause additional attenuation;

[0050] The specific formula of the improved kinetic equation is:

[0051] ,

[0052] in, Indicates the mass of the underground structure, which is used to determine the acceleration response of the underground structure. The larger the mass, the smaller the acceleration response of the underground structure, and vice versa. It can be obtained from the design documents or on-site survey reports of the underground structure; Indicates at time Acceleration response of underground structures under earthquake action; The damping coefficient of the underground structure will affect the attenuation rate of the vibration of the underground structure. The larger the value, the faster the vibration of the underground structure will attenuate. It can be estimated according to the existing empirical formula. It is a technical means well known to those skilled in the art and will not be described in detail here. It represents the damping coefficient of the soil. The damping coefficient of the soil will affect the interaction between the underground structure and the soil. The larger the value, the more the response of the underground structure will be suppressed. It can be estimated according to the existing empirical formula. It is a technical means well known to those skilled in the art and will not be described in detail here. The damping coefficient of the groundwater fluid can be estimated according to the existing empirical formula, which is a technical means well known to those skilled in the art and will not be described in detail here; Indicates at time Velocity response of underground structures under earthquake action; It indicates the stiffness of the underground structure and reflects the resistance of the underground structure to deformation. It can be obtained from the design documents or on-site survey reports of the underground structure. Indicates at time Displacement response of underground structures under earthquake action; Indicates at time The earthquake load describes the change of force on underground structures during an earthquake;

[0053] S2. Based on the displacement response, velocity response and acceleration response of the underground structure, the damage progress of the underground structure during the earthquake is dynamically simulated by using the underground structure damage factor calculation algorithm to calculate the damage factor;

[0054] In order to accurately evaluate the damage degree of underground structures under earthquakes, based on the displacement response, velocity response and acceleration response of underground structures, the damage progress of underground structures during earthquakes is dynamically simulated through the underground structure damage factor calculation algorithm, and the damage factor is calculated to help evaluate the bearing capacity and safety of underground structures in earthquakes.

[0055] The contribution of displacement response, velocity response and acceleration response of underground structures to the damage of underground structures has different weights, so a set of preset weight coefficients are used for weighted calculation; since the influence of velocity and displacement may be nonlinear in different time periods, in order to further accurately reflect the actual situation of underground structure damage, a nonlinear factor is introduced to perform exponential weighting on the velocity response and displacement response of the underground structure to capture the nonlinear effect;

[0056] The influence of acceleration on the damage of underground structures is very critical, especially in the early stage of an earthquake, when underground structures will be subjected to severe acceleration shocks. In order to take into account the special influence of acceleration on damage, an acceleration attenuation factor is introduced, so that the influence of acceleration gradually decays over time, especially in the epicenter or later stages of an earthquake, when acceleration decreases. The exponential decay function can accurately simulate the damage progression of underground structures under long-term vibration.

[0057] The damage factor is calculated as:

[0058] ,

[0059] in, Indicates at time The damage factor at the time of earthquake reflects the damage degree of underground structure under earthquake action; , and Represents the weight coefficient, which is used to adjust the relative importance of the acceleration response, velocity response and displacement response of the underground structure in the damage factor calculation. It can be set according to the specific implementation scenario and is not limited here; Indicates at time The absolute value of the acceleration response of underground structures under earthquake action; Indicates at time The absolute value of the velocity response of underground structures under earthquake action; Indicates at time The absolute value of the displacement response of underground structures under earthquake action; It is a nonlinear factor, which represents the influence index of velocity response on damage factor. It is used to control the nonlinear contribution of velocity response to damage. It can be set according to the specific implementation scenario and is not limited here. It is a nonlinear factor, which represents the influence index of displacement response on damage factor. It is used to control the nonlinear contribution of displacement response to damage. It can be set according to the specific implementation scenario and is not limited here. It represents the acceleration attenuation factor, which is used to reflect the attenuation effect of acceleration response on damage. That is, the greater the acceleration, the stronger the attenuation effect. It takes into account the time attenuation characteristics of acceleration response on underground structure damage. It represents the sensitivity coefficient of the acceleration response to the damage factor, which is used to adjust the nonlinear effect of the acceleration response on the damage factor. It can be set according to the specific implementation scenario and is not limited here.

[0060] S3, based on the damage factor, a vulnerability index is calculated by using a vulnerability index calculation algorithm;

[0061] The impact of earthquakes on underground structures is not limited to instantaneous destruction, but is also accompanied by a long recovery process. The vulnerability index calculation algorithm takes into account the damage degree of the underground structure and its post-earthquake recovery capacity, and is calculated to measure the vulnerability of underground structures in earthquakes.

[0062] The vulnerability index calculation algorithm takes into account the dynamic balance between the damage factor and the recovery factor of the underground structure, introduces a coefficient for adjusting the balance between the damage factor and the recovery factor, changes the dynamic relationship between the damage factor and the recovery factor, and reflects the sensitivity of the recovery ability of the underground structure in a damaged state; the recovery factor reflects the recovery ability of the underground structure after an earthquake. As the damage factor increases, the recovery factor decreases, reflecting that the underground structure will gradually lose its recovery ability after suffering an earthquake. The first adjustment parameter and the second adjustment parameter are introduced to control the change rate of the recovery process and adjust the influence of the damage factor on the recovery factor, respectively;

[0063] The vulnerability index calculation algorithm introduces a maximum damage factor, which reflects the maximum damage that the underground structure can withstand under the action of an earthquake, and is used to normalize the damage factor to prevent the damage factor from exceeding the actual physical limit;

[0064] The calculation formula of the vulnerability index is:

[0065] ,

[0066] in, Indicates at time The vulnerability index at 2000 km / h is used to measure the vulnerability of underground structures in earthquakes, taking into account the degree of damage to underground structures and their post-earthquake recovery capabilities; Indicates at time The damage factor at the time of earthquake reflects the damage degree of underground structure under earthquake action; It represents the coefficient used to adjust the balance between the damage factor and the recovery factor. It can change the dynamic relationship between the damage factor and the recovery factor, and reflects the sensitivity of the recovery ability of the underground structure under the damaged state. It can be set according to the specific implementation scenario and is not limited here. Indicates the maximum damage factor, which is used to reflect the maximum damage that underground structures can withstand under earthquake action, so as to normalize the damage factor and prevent it from exceeding the actual physical limit. It can be set according to the specific implementation scenario and is not limited here. It represents the recovery factor, which is used to reflect the recovery capacity of underground structures after an earthquake. As the damage factor increases, the recovery factor decreases, reflecting that the underground structure will gradually lose its recovery capacity after suffering earthquake damage. The specific calculation formula is as follows:

[0067] ,

[0068] in, represents the first adjustment parameter, which is used to control the change rate of the recovery process and can be set according to the specific implementation scenario and is not limited here; represents the second adjustment parameter, which is used to adjust the influence of the damage factor on the recovery factor, and can be set according to the specific implementation scenario, and is not limited here;

[0069] By combining the damage factor and the recovery factor, an accurate vulnerability index is calculated, which provides a reliable quantitative standard for evaluating the seismic vulnerability performance of underground structures.

[0070] S4. Based on the vulnerability index, the seismic vulnerability probability of the underground structure is calculated by using the seismic vulnerability statistical model;

[0071] The vulnerability index represents the vulnerability of underground structures and reflects the risk of damage to underground structures when an earthquake occurs. In order to further quantify the risk, a seismic vulnerability statistical model is used to describe the change in the vulnerability index and the seismic vulnerability probability of underground structures is calculated.

[0072] The seismic vulnerability statistical model not only considers the instantaneous change of the vulnerability index when calculating the probability distribution of the vulnerability index, but also integrates the change of the vulnerability index in the entire earthquake cycle, and obtains the seismic vulnerability probability of the underground structure by integrating the vulnerability index in the time period;

[0073] The earthquake vulnerability statistical model describes the probability distribution of the vulnerability index of the underground structure over time through the normal distribution probability density function of the vulnerability index, indicating that as the damage increases, the probability distribution of the vulnerability index presents a bell-shaped curve;

[0074] In order to accurately reflect the long-term damage of underground structures, the nonlinear effect of damage progression is taken into account. The exponential decay function is used to make the growth of vulnerability probability steeper as it approaches the maximum vulnerability index, reflecting the long-term impact of earthquakes on underground structures.

[0075] The calculation formula for the seismic vulnerability probability of underground structures is:

[0076] ,

[0077] in, represents the probability of seismic vulnerability of underground structures; Indicates the vulnerability index in the time interval Integrate all the values ​​in the time interval and calculate the probability distribution of the vulnerability index in the entire simulation time; Indicates the earthquake cycle time, which can be set according to the specific implementation scenario and is not limited here; The normalization factor representing the normal distribution is used to ensure that the sum of the probability distribution is 1. It is derived based on the theory of the standard normal distribution and has nothing to do with specific data. It only depends on statistical principles. It is a technical means well known to those skilled in the art and will not be described in detail here. The normal distribution probability density function of the vulnerability index describes the probability distribution of the vulnerability index of the underground structure over time, that is, as the damage increases, the probability distribution of the vulnerability index presents a bell-shaped curve; Represents the mean value of the vulnerability index, reflecting the time The average vulnerability level of underground structures; It represents the standard deviation of the vulnerability index, reflecting the degree of fluctuation of the vulnerability of underground structures; Represents the nonlinear effect of damage progression, through an exponential decay function, so that the closer to the maximum vulnerability index, the steeper the growth of vulnerability probability becomes; The coefficient for controlling the progress of damage is used to reflect the intensity of the impact of the vulnerability index on the vulnerability probability. It can be set according to the specific implementation scenario and is not limited here. Indicates the maximum vulnerability index, which is used to limit the upper limit of the vulnerability index to prevent it from increasing infinitely. It can be set according to the specific implementation scenario and is not limited here;

[0078] Through seismic vulnerability analysis of underground structures, potential risk points can be identified in advance during the design and operation stages of underground structures, and effective monitoring and repair can be carried out to ensure the long-term safety of the structures.

[0079] In summary, the seismic vulnerability analysis method of underground structures is completed.

[0080] The order of the embodiments of the invention is for description only and does not represent the advantages and disadvantages of the embodiments. The processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0081] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

[0082] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention.

Claims

1. A method for analyzing seismic vulnerability of underground structures, characterized in that: The following steps are involved: S1. Calculate the seismic load and solve the dynamic response of the underground structure through the underground structure seismic response analysis algorithm; the specific implementation process of the underground structure seismic response analysis algorithm is: introduce the seismic load input model based on time-varying frequency and nonlinear attenuation to obtain the seismic load, and the specific formula is: ， in, Indicates at time earthquake load; It indicates the initial intensity of the seismic waves generated by the earthquake source; Represents the nonlinear correction coefficient of the earthquake source; represents the cosine function; Indicates at time The dominant frequency of seismic waves; and The coefficients representing the frequency oscillation of the earthquake source are used to adjust the amplitude and period of the frequency oscillation in the earthquake load; represents the sine function; is an exponential decay function; represents the attenuation factor; Represents the power of time; represents the regulation index; Based on the seismic load, the dynamic response of the underground structure is solved by the improved dynamic equation to obtain the displacement response, velocity response and acceleration response of the underground structure. S2. Based on the displacement response, velocity response and acceleration response of the underground structure, the damage progress of the underground structure during the earthquake is dynamically simulated by using the underground structure damage factor calculation algorithm to calculate the damage factor; S3, based on the damage factor, a vulnerability index is calculated by using a vulnerability index calculation algorithm; S4. Based on the vulnerability index, the seismic vulnerability probability of the underground structure is calculated through the seismic vulnerability statistical model.

2. The seismic vulnerability analysis method for underground structures according to claim 1, characterized in that: The S1 specifically includes: The improved dynamic equation combines the mass, stiffness and damping coefficient of the underground structure itself, and introduces the damping coefficient of groundwater fluid and soil to simulate the response of the underground structure under earthquake action, and calculates the displacement response, velocity response and acceleration response of the underground structure.

3. The seismic vulnerability analysis method for underground structures according to claim 1, characterized in that: The S2 specifically includes: The underground structure damage factor calculation algorithm dynamically simulates the damage progress of the underground structure during an earthquake by performing weighted calculations on the displacement response, velocity response and acceleration response of the underground structure.

4. The seismic vulnerability analysis method for underground structures according to claim 3, characterized in that: The S2 specifically includes: In the process of implementing the calculation algorithm of underground structure damage factor, nonlinear factors are introduced to perform exponential weighting on the velocity response and displacement response of the underground structure, and the damage factor is calculated in combination with the acceleration attenuation factor.

5. The seismic vulnerability analysis method for underground structures according to claim 1, characterized in that: The S3 specifically includes: The vulnerability index calculation algorithm is based on the damage factor, combined with the recovery factor, and introduces a coefficient for adjusting the balance between the damage factor and the recovery factor to calculate the vulnerability index.

6. The seismic vulnerability analysis method for underground structures according to claim 5, characterized in that: The S3 specifically includes: In the process of implementing the vulnerability index calculation algorithm, based on the damage factor, a first adjustment parameter and a second adjustment parameter are introduced to calculate the recovery factor.

7. The seismic vulnerability analysis method for underground structures according to claim 1, characterized in that: The S4 specifically includes: The earthquake vulnerability statistical model calculates the earthquake vulnerability probability of the underground structure through the normal distribution probability density function of the vulnerability index, combined with the instantaneous change of the vulnerability index and the change of the vulnerability index in the entire earthquake cycle; the calculation formula of the earthquake vulnerability probability of the underground structure is: ， in, represents the probability of seismic vulnerability of underground structures; Indicates the vulnerability index in the time interval Integrate all the values ​​within ; Indicates the earthquake cycle time; represents the normalization factor of the normal distribution; represents the probability density function of the normal distribution of the vulnerability index; Indicates at time Vulnerability index at ; represents the mean value of the vulnerability index; represents the standard deviation of the vulnerability index; represents the nonlinear effect of injury progression; represents the coefficient controlling the progression of damage; Represents the maximum vulnerability index.

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