An evaluation method for equivalent extreme value aseismatic reliability of underground-overground integrated structure

Abstract

The application discloses a kind of underground ground integrated structure equivalent extremum aseismic reliability evaluation method, it is related to structural aseismic reliability analysis technical field;Spectral representation-random function method is used to generate seismic sample, finite element model including ground structure, underground structure, surrounding soil and soil-structure interaction relationship is established, and each floor seismic response time history is obtained;According to the aseismic performance limit value of different structure region, the normalized demand ratio is calculated, and the equivalent extremum variable of overall structure, ground structure and underground structure is respectively constructed;The marginal probability distribution of equivalent extremum variable is obtained by probability density evolution, and the time-varying aseismic reliability and failure probability of overall structure and partition structure are calculated by combining failure threshold value;Failure event controlled by multiple floors, multiple times and multiple performance limit values can be uniformly represented.

Description

Technical Field

[0001] This invention relates to the field of structural seismic reliability analysis technology, specifically to an equivalent extreme value seismic reliability assessment method for integrated underground and above-ground structures. Background Technology

[0002] As the scale of urban underground space development continues to expand, underground structures such as underground railway stations, underground commercial spaces, and underground parking garages are gradually forming integrated underground and above-ground structures that are spatially continuous, structurally connected, and share loads with above-ground buildings. Under seismic loading, these structures are simultaneously affected by the inertial effects of the above-ground structure, the constraint effects of the surrounding soil, the seismic wave propagation effects, and the force transmission effects at the connection points between the underground and above-ground structures. Their dynamic response exhibits significant spatial coupling and time-varying characteristics. Analyzing only the above-ground or underground structure independently is insufficient to accurately reflect the seismic safety status of the entire structural system.

[0003] Current structural seismic reliability assessments typically involve dynamic time-history analysis based on random ground motion samples, followed by statistical analysis of the failure probability based on whether the structural response exceeds preset performance limits. However, underground and above-ground structures differ in their stress mechanisms, deformation characteristics, and seismic performance requirements. Even when using the same response indicators such as inter-story drift angle, their corresponding performance limits are usually different. Directly comparing the responses of each floor makes it difficult to reflect the safety margins of different structural regions on a uniform scale; using a single performance limit for overall judgment may lead to incorrect identification of failure states in either above-ground or underground structures.

[0004] Furthermore, integrated underground and above-ground structures typically comprise multiple above-ground and underground floors. If any floor exceeds its corresponding performance limit at any moment during the entire seismic process, it may cause partial or overall structural failure. Therefore, its reliability assessment is essentially a system reliability problem jointly controlled by multiple floors, multiple moments, and multiple performance limits. Traditional sample counting methods are difficult to continuously describe the evolution of reliability over time with seismic action, and when the failure probability is low or the calculation model is complex, extensive dynamic time history analysis is required, resulting in high computational costs.

[0005] In view of this, the present invention provides a method for evaluating the seismic reliability of an integrated underground and above-ground structure based on equivalent extreme values. Summary of the Invention

[0006] The purpose of this invention is to provide an equivalent extreme value seismic reliability assessment method for integrated underground and above-ground structures, which addresses the problem that it is difficult to uniformly characterize the seismic response of multiple floors and times and accurately assess the time-varying seismic reliability of the overall structure and the zonal structures when different seismic performance limits are used for underground and above-ground structures.

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

[0008] This invention provides a method for evaluating the equivalent extreme value seismic reliability of integrated underground and above-ground structures, comprising the following steps:

[0009] S1. A random ground motion generation model is constructed using the spectral representation-random function method. Multiple representative points are selected in the probability space formed by finite-dimensional basic random variables. Representative probabilities are assigned to each representative point, and random ground motion acceleration time histories are generated based on each representative point to form a random ground motion probability sample set.

[0010] S2, establish an overall finite element analysis model including the above-ground structure, underground structure, foundation, surrounding soil, and the interaction between soil and structure;

[0011] S3, input the random ground motion probability sample set into the overall finite element analysis model to obtain the structural response of each floor over time under the action of each random ground motion sample;

[0012] S4. Based on the above-ground or underground structural area to which each floor belongs, determine the corresponding seismic performance limit, and process the ratio of the structural response of each floor to the corresponding seismic performance limit to obtain the normalized demand ratio of each floor.

[0013] S5, extract the maximum normalized demand ratio from the start of the earthquake to the current moment from the overall floor set, the above-ground floor set, and the underground floor set, respectively, to obtain the equivalent extreme value variables corresponding to the overall structure, the above-ground structure, and the underground structure;

[0014] S6. Using the equivalent extreme value variable as the response variable, the probability density evolution is solved to obtain the probability distribution of the equivalent extreme value variable changing with time. Based on the preset failure threshold, the time-varying seismic reliability and failure probability of the overall structure, the above-ground structure and the underground structure are calculated respectively.

[0015] As a preferred technical solution of the present invention, in step S1, the basic random variable is used to characterize one or more of the spectral characteristics, phase characteristics and intensity envelope characteristics of random ground motion; the representative points are obtained by number theory point selection, Sobol sequence, equal probability partitioning or probability complete point set method, and the representative probability corresponding to each representative point is not less than zero, and the sum of all representative probabilities is one.

[0016] As a preferred technical solution of the present invention, in step S2, the overall finite element analysis model includes above-ground structural components, underground structural components, foundations or connecting components connecting the above-ground and underground structures, soil domains surrounding the underground structure, soil boundary conditions, and contact relationships between the underground structure and the surrounding soil; the overall finite element analysis model is used to couple and calculate the inertial action of the above-ground structure, the soil constraint action of the underground structure, and the force transmission action at the connection between the above-ground and underground structures in the same model.

[0017] As a preferred technical solution of the present invention, the soil boundary conditions adopt viscoelastic boundary, free field boundary or infinite element boundary, and the underground structure and the surrounding soil establish an interaction relationship by means of contact element, interface element, spring-damped element or common node method, and the seismic motion is input from the bottom boundary of the soil domain.

[0018] As a preferred technical solution of the present invention, in step S3, the structural response includes one or more of the following: inter-story drift angle, inter-story deformation, component deformation, floor acceleration, and component internal force; when the same structural response is used as the evaluation index for the above-ground structure and the underground structure, different seismic performance limits are set for the above-ground floors and the underground floors respectively.

[0019] As a preferred technical solution of the present invention, in step S4, the normalized demand ratio is the ratio of the absolute value of the structural response of each floor to the seismic performance limit of the corresponding floor; when the normalized demand ratio is not greater than one, it is determined that the corresponding floor has not exceeded the seismic performance limit; when the normalized demand ratio is greater than one, it is determined that the corresponding floor has exceeded the seismic performance limit.

[0020] As a preferred technical solution of the present invention, in step S5, for any specified set of floors, the equivalent extreme value variable is the maximum value of the normalized demand ratio of all floors in the specified set of floors from the start of the earthquake to the current time; the specified set of floors includes the overall set of floors including above-ground floors and underground floors, the set of above-ground floors including only above-ground floors, and the set of underground floors including only underground floors.

[0021] As a preferred technical solution of the present invention, in step S6, the joint probability density evolution relationship between the equivalent extreme variable and the basic random variable is established. By integrating the joint probability density in the probability space of the basic random variable, the marginal probability density of the equivalent extreme variable is obtained. The probability that the equivalent extreme variable does not exceed the preset failure threshold is determined as the seismic reliability, and the probability that the equivalent extreme variable exceeds the preset failure threshold is determined as the failure probability.

[0022] As a preferred technical solution of the present invention, the value space of the equivalent extreme value variable is discretized by grid, and the representative probability corresponding to each representative point is taken as the probability mass and initialized at the grid position where the initial value of the corresponding equivalent extreme value variable is located. Based on the increment of the equivalent extreme value variable of each random ground motion sample between adjacent time points, the migration amount of the probability mass between adjacent grids is determined, and by refining the time step, the migration range of the probability mass within a single time step does not exceed one grid spacing.

[0023] As a preferred technical solution of the present invention, it further includes reliability verification and control floor identification: based on the representative probability of each random ground motion sample, the samples whose equivalent extreme value variables do not exceed the preset failure threshold are weighted and summed to obtain the verification reliability; the floor corresponding to the maximum normalized demand ratio of each random ground motion sample within the duration of the ground motion is determined, and the floor is taken as the control floor, and the representative probabilities corresponding to the failure samples with the same control floor are accumulated to obtain the failure contribution probability of each floor to the overall structural failure event.

[0024] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0025] This invention normalizes the seismic responses of each floor in both above-ground and underground structures to their corresponding seismic performance limits, enabling the conversion of response states under different structural regions and control standards to a unified dimensionless evaluation scale. Based on this, it extracts extreme values ​​in both the floor and time dimensions from the normalized demand ratios within the overall floor set, the above-ground floor set, and the underground floor set. This transforms failure events of complex systems controlled by multiple floors, multiple time points, and multiple performance limits into events where a single equivalent extreme variable exceeds a failure threshold, thereby reducing the complexity of failure event representation and probability calculation. Furthermore, by combining probability density evolution methods to obtain the probability distribution of equivalent extreme variables over seismic action time, it can uniformly calculate the overall reliability of the integrated above-ground and underground structures, the reliability of the above-ground structure, the reliability of the underground structure, and the corresponding failure probabilities, and identify the main control floors, improving the accuracy, continuity, and engineering applicability of seismic reliability assessment for complex coupled structures. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0027] Figure 1 This is a flowchart of the method of the present invention;

[0028] Figure 2This is a schematic diagram of an integrated above-ground and underground structure.

[0029] Figure 3 This is a schematic diagram of the overall finite element model;

[0030] Figure 4 This is a time-varying reliability curve. Detailed Implementation

[0031] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the description of this disclosure will be more complete and fully convey the concept of the exemplary embodiments to those skilled in the art. The drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted.

[0032] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more exemplary embodiments. Numerous specific details are provided in the following description to give a full understanding of exemplary embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure may be practiced with one or more specific details omitted, or methods, components, steps, etc. In other instances, well-known structures, methods, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of this disclosure.

[0033] Example 1

[0034] like Figure 1 As shown in the figure, this embodiment provides a method for evaluating the equivalent extreme value seismic reliability of an integrated underground and above-ground structure, including the following steps:

[0035] S1. A random ground motion generation model is constructed using the spectral representation-random function method. Multiple representative points are selected in the probability space formed by finite-dimensional basic random variables. Representative probabilities are assigned to each representative point, and random ground motion acceleration time histories are generated based on each representative point to form a random ground motion probability sample set.

[0036] Specifically, a spectral representation-random function method is used to generate random ground motions, and finite-dimensional basic random variables are used to characterize the uncertainty of the random ground motion process. These finite-dimensional basic random variables are expressed as follows: ;

[0037] in, Represents the vector of basic random variables of random ground motion. Let each represent a basic random variable used to describe the spectrum, phase, intensity envelope, or other random characteristics of random ground motion. The dimension of the basic random variable.

[0038] A random ground motion probability space is constructed based on the probability distribution information of each basic random variable, and N representative points are selected within the random ground motion probability space. ,in: Each representative point Configure the corresponding representative probability The represented probability satisfies:

[0039] ;

[0040] ;

[0041] The representative points can be obtained using number theory selection, Sobol sequences, equal probability partitioning, probabilistically complete point sets, or combinations thereof. Each representative point and its representative probability together constitute a probabilistically complete representative point set.

[0042] Each representative point Substituting the spectral representation-random function model, we generate random ground acceleration time histories corresponding to each representative point, and then correlate the random ground acceleration time histories with the corresponding representative probabilities. By correlating the data, a random ground motion probability sample set is formed.

[0043] In this embodiment, the number of representative points is: That is, 400 random ground motion acceleration time histories are generated, and each random ground motion acceleration time history corresponds to a representative probability. The sum of the 400 representative probabilities is 1, so that the generated random ground motion samples can collectively represent the random ground motion probability space.

[0044] S2, establish an overall finite element analysis model including the above-ground structure, underground structure, foundation, surrounding soil, and the interaction between soil and structure;

[0045] like Figure 2 As shown, this embodiment selects an integrated underground-above-ground structure as the evaluation object. The structure includes an above-ground structure and an underground structure, wherein the above-ground structure is set to 7 stories and the underground structure is set to 2 stories. The above-ground structure and the underground structure form a continuous integral load-bearing system through foundations and connecting components.

[0046] Figure 2In this diagram, the above-ground portion represents the above-ground structure, and the portion below the ground level represents the underground structure. Under seismic loading, the above-ground structure is primarily subjected to the inertial force generated by its mass, while the underground structure is simultaneously subjected to its own inertial force and the constraint of the surrounding soil. The seismic response of the above-ground structure is transmitted to the underground structure through the foundation and the above-ground-underground connection points, and the response of the underground structure and the surrounding soil, in turn, reacts on the above-ground structure. Therefore, this embodiment treats the above-ground structure, the underground structure, and their connections as a unified structural system for seismic reliability analysis, rather than establishing separate, independent models for the above-ground and underground structures.

[0047] like Figure 3 As shown, a finite element analysis model of the integrated underground and above-ground structure is established. The finite element analysis model includes the above-ground structure, the underground structure, the foundation, the surrounding soil, the soil boundary conditions, the soil-structure contact relationship, and the connection relationship between the above-ground and underground structures.

[0048] The above-ground structural components can be simulated using beam elements, column elements, shell elements, or solid elements; the side walls, top slabs, bottom slabs, central columns, and floor components of the underground structure can be simulated using beam elements, shell elements, or solid elements; the surrounding soil is simulated using solid elements. The connection between the above-ground and underground structures is set as rigid, hinged, or contact connections according to the actual connection method, while the connection between the underground structure and the surrounding soil is set as contact interfaces or shared node connections.

[0049] To simulate the impact of an infinite soil domain on seismic wave propagation, viscoelastic boundaries, free-field boundaries, or other equivalent artificial boundaries are set at the lateral boundaries of the surrounding soil model, and a seismic input boundary is set at the bottom of the soil mass. The overall finite element analysis model comprehensively considers the inertial effects of the above-ground structure, the constraint effects of the soil surrounding the underground structure, and the force transmission effects at the connection points between the above-ground and underground structures.

[0050] In this embodiment, the inter-story drift angle is used as the seismic performance evaluation index for the integrated underground and above-ground structure. Due to the different stress characteristics and seismic performance requirements of the above-ground and underground structures, different seismic performance limits for the inter-story drift angle are set for the above-ground and underground structures respectively. Specifically, the seismic performance limit for the inter-story drift angle of the above-ground structure is: ;

[0051] The seismic performance limit for inter-story drift angle of underground structures is: .

[0052] S3, input the random ground motion probability sample set into the overall finite element analysis model to obtain the structural response of each floor over time under the action of each random ground motion sample;

[0053] The 400 random ground motion probability samples generated in step S1 are input sequentially. Figure 3 The overall finite element analysis model shown is used to perform seismic response time history analysis on each random ground motion sample to obtain the random seismic response time history of each floor of the above-ground and underground structures.

[0054] In this embodiment, the duration of random ground motion is set to 30 s, and the time step for earthquake response time history analysis is set as follows:

[0055] For the q-th random seismic motion sample, the q-th Each floor at any time The structural response is denoted as: ;

[0056] in, Indicates the floor number. Indicates the random ground motion sample number. Indicates the first Each discrete time point.

[0057] In this embodiment, Specifically, the first Under the action of a random seismic motion sample, the first Each floor at any time The inter-story drift angle response. In other embodiments, the structural response may also be selected as inter-story deformation, component deformation, acceleration response, internal force response, or a combination thereof, but the corresponding seismic performance limit should correspond to the type of structural response selected.

[0058] S4. Based on the above-ground or underground structural area to which each floor belongs, determine the corresponding seismic performance limit, and process the ratio of the structural response of each floor to the corresponding seismic performance limit to obtain the normalized demand ratio of each floor.

[0059] Specifically, according to the first For each floor's structural area, corresponding seismic performance limits are configured. When the floor number corresponding to the above-ground structural floor belongs to the set of above-ground floors. At that time, there were: ;

[0060] When the floor number corresponding to the underground structure floor belongs to the set of underground floors At that time, there were: ;

[0061] The entire set of floors is denoted as And satisfy: and ;

[0062] Based on the inter-story drift response and corresponding seismic performance limits of each floor, calculate the first... Under the action of a random seismic motion sample, the first Each floor at any time Normalized demand ratio: ;

[0063] in, Indicates the first Under the action of a random seismic motion sample, the first Each floor at any time The ratio between response requirements and seismic performance capabilities.

[0064] when When, it indicates the first Each floor at any time The inter-story drift angle did not exceed the seismic performance limit corresponding to that floor; when When, it indicates the first Each floor at any time The inter-story drift angle exceeds the seismic performance limit corresponding to that floor.

[0065] By normalizing the inter-story drift angle response of different floors, the seismic safety state formed by different seismic performance limits for above-ground and underground structures is uniformly converted into a dimensionless demand-capacity relationship.

[0066] For any given set of floors Construct the first A random seismic motion sample at time [time] Equivalent extreme value variables: ;

[0067] in, This indicates the time from the start of the earthquake to the present moment. At any time between, Indicates a specified set of floors. Indicates the first A random seismic motion sample in the floor set From the initial time to the current time The maximum normalized demand ratio.

[0068] For the entire set of floors respectively Assembly on the ground floor and underground floors Construct equivalent extreme value variables for the overall structure, above-ground structure, and underground structure.

[0069] The overall structural equivalent extreme value variable is: ;

[0070] The equivalent extreme value variables of the above-ground structure are: ;

[0071] The equivalent extreme value variables of the underground structure are: ;

[0072] By using the aforementioned equivalent extreme value variables, failure events controlled by multiple floors, multiple time periods, and multiple seismic performance limits are transformed into events where a single equivalent extreme value variable exceeds a preset failure threshold.

[0073] In this embodiment, the preset failure threshold is set as follows: ;

[0074] when At that time, the judgment of the first Under the action of a random seismic motion sample, and with the floor set The corresponding structural region at time It is in a safe state;

[0075] when When this occurs, the corresponding structural region is determined to have entered a failure state.

[0076] Since the equivalent extreme value variable performs maximum value calculations on both floor level and time, any floor level exceeding its corresponding seismic performance limit at any moment during the earthquake duration can be uniformly represented as the equivalent extreme value variable exceeding 1.

[0077] S5, extract the maximum normalized demand ratio from the start of the earthquake to the current moment from the overall floor set, the above-ground floor set, and the underground floor set, respectively, to obtain the equivalent extreme value variables corresponding to the overall structure, the above-ground structure, and the underground structure;

[0078] Specifically, the equivalent extreme value variables of the overall structure, the above-ground structure, or the underground structure are used as response variables, and the basic random variables are used as the response variables. As random input variables, a joint probability density function is established for the equivalent extreme value variable and the basic random variable. And establish the generalized probability density evolution equation:

[0079] ;

[0080] in, Represents equivalent extreme value variables With basic random variables The joint probability density function, It represents the rate of change of the equivalent extreme variable over time.

[0081] The space of equivalent extremum variables is discretized by a grid, and the discrete grid is represented as follows:

[0082] ;

[0083] in: Indicates the first A grid point of equivalent extreme value variable, , Indicates the number of grid cells; Indicates the lower limit of the grid. Indicates the grid spacing.

[0084] At the initial moment, the representative probability corresponding to each representative point is... As a probabilistic quality, it is initialized at the grid position where the initial value of the corresponding equivalent extreme value variable is located.

[0085] For the For a random seismic motion sample, the increment of its equivalent extreme value variable between adjacent time points is:

[0086] ;

[0087] Determine the probabilistic mass transfer coefficient based on the equivalent extreme value variable increment:

[0088] ;

[0089] in, Indicates the first A random seismic motion sample at time [time] The corresponding probability mass transfer coefficient.

[0090] Based on the probability mass migration coefficient, the probability mass corresponding to each representative point is transferred to the equivalent extreme variable grid, thereby obtaining the evolution result of the probability density of the equivalent extreme variable over time.

[0091] To ensure the stability of the numerical solution process for probability density evolution, the time step is refined to satisfy the following: ;

[0092] In this embodiment, the target value of CFL is set to 0.80, and the number of time history sections saved is set to 151. By controlling the probabilistic mass migration coefficient to not exceed the stability limit, the numerical error caused by the probabilistic mass crossing multiple grids is reduced.

[0093] For the equivalent extreme value variables of the overall structure respectively Equivalent extreme value variables of above-ground structures Equivalent extreme value variables to underground structures Probability density evolution is performed to obtain the probability distributions of equivalent extreme variables corresponding to the overall structure, above-ground structure, and underground structure.

[0094] S6. Using the equivalent extreme value variable as the response variable, the probability density evolution is solved to obtain the probability distribution of the equivalent extreme value variable changing with time. Based on the preset failure threshold, the time-varying seismic reliability and failure probability of the overall structure, the above-ground structure and the underground structure are calculated respectively.

[0095] For the joint probability density function in the probability space of the basic random variables Integrating within the range yields the marginal probability density function of the equivalent extreme variable:

[0096] ;

[0097] According to the preset failure threshold The computational structure at time Seismic reliability:

[0098] ;

[0099] The corresponding failure probability is: ;

[0100] The time-varying seismic reliability of the overall structure is obtained by using the marginal probability density functions of the equivalent extreme value variables for the overall structure, the above-ground structure, and the underground structure, respectively. Time-varying seismic reliability of above-ground structures and the time-varying seismic reliability of underground structures And the corresponding failure probability:

[0101] ;

[0102] ;

[0103] ;

[0104] To verify the results of the probability density evolution calculation, a direct weighted statistical calculation was performed using the representative probabilities corresponding to each representative point. For the floor set... At any moment The weighted verification reliability is: ;

[0105] The corresponding weighted verification failure probability is: ;

[0106] in, This is an indicator function; it takes the value 1 if the condition within the parentheses is true, and 0 otherwise.

[0107] like Figure 4 As shown, the horizontal axis represents the duration of the seismic motion. The vertical axis represents the seismic reliability. . Figure 4 The reliability curves for the overall structure, the above-ground structure, the underground structure, and the overall structure obtained using the probability density evolution method are presented respectively.

[0108] Depend on Figure 4 It can be seen that in the initial stage of seismic action, the seismic reliability of each structural region remains at a high level. As the seismic action continues, the normalized demand ratio of some random seismic motion samples gradually increases and exceeds the failure threshold, resulting in a corresponding decrease in the seismic reliability of the overall structure, the above-ground structure, and the underground structure. After the seismic response stabilizes, the reliability curves gradually stabilize as well. The overall structural reliability curve obtained by the probability density evolution method is close to the result of the direct weighted verification of the representative probability, indicating that the probability density evolution solution can effectively reflect the time-varying seismic reliability of the integrated underground and above-ground structure under random seismic action.

[0109] Furthermore, for each random ground motion sample, the maximum normalized demand ratio for each floor during the entire duration of the ground motion is calculated:

[0110] ;

[0111] in, Indicates the duration of total seismic motion.

[0112] Determine the first Control floors corresponding to each random seismic motion sample:

[0113] ;

[0114] Failure samples where the overall structural equivalent extreme variable exceeds a preset failure threshold at the final moment are selected, and the representative probabilities corresponding to failure samples with the same control floor are summed to obtain the failure contribution probability of each floor to the overall failure event:

[0115] ;

[0116] in, Indicates the first The probability contribution of each floor to the overall structural failure event.

[0117] Through the above calculations, the time-varying reliability curves, failure probability curves, marginal probability density functions of equivalent extreme variables, cumulative distribution functions, probability density evolution results, and failure contribution probabilities of control floors can be output for the overall structure, above-ground structure, and underground structure.

[0118] This embodiment considers the coupling effect between the above-ground structure, underground structure, and surrounding soil in the same overall finite element model, and normalizes the seismic response of the above-ground and underground floors using different seismic performance limits, so that the seismic safety status of different structural areas can be compared on the same dimensionless scale. Furthermore, by performing dual extreme value calculations on the floor dimension and the time dimension, equivalent extreme value variables corresponding to the overall structure, above-ground structure, and underground structure are constructed. The complex failure events jointly controlled by multiple floors, multiple time points, and multiple performance limits are transformed into a probabilistic evolution problem of equivalent extreme value variables, thereby realizing a unified assessment of the overall reliability, zonal reliability, and failure probability of the integrated underground and above-ground structure.

[0119] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for evaluating the equivalent extreme value seismic reliability of an integrated underground and above-ground structure, characterized in that, Includes the following steps: S1. A random ground motion generation model is constructed using the spectral representation-random function method. Multiple representative points are selected in the probability space formed by finite-dimensional basic random variables. Representative probabilities are assigned to each representative point, and random ground motion acceleration time histories are generated based on each representative point to form a random ground motion probability sample set. S2, establish a finite element analysis model that includes the above-ground structure, underground structure, foundation, surrounding soil, and the interaction between soil and structure; S3, input the random ground motion probability sample set into the overall finite element analysis model to obtain the structural response of each floor over time under the action of each random ground motion sample; S4. Based on the above-ground or underground structural area to which each floor belongs, determine the corresponding seismic performance limit, and process the ratio of the structural response of each floor to the corresponding seismic performance limit to obtain the normalized demand ratio of each floor. S5, extract the maximum normalized demand ratio from the start of the earthquake to the current moment from the overall floor set, the above-ground floor set, and the underground floor set, respectively, to obtain the equivalent extreme value variables corresponding to the overall structure, the above-ground structure, and the underground structure; S6. Using the equivalent extreme value variable as the response variable, the probability density evolution is solved to obtain the probability distribution of the equivalent extreme value variable changing with time. Based on the preset failure threshold, the time-varying seismic reliability and failure probability of the overall structure, the above-ground structure and the underground structure are calculated respectively.

2. The method for evaluating the equivalent extreme value seismic reliability of integrated underground and above-ground structures according to claim 1, characterized in that, In step S1, the basic random variable is used to characterize one or more of the spectral characteristics, phase characteristics, and intensity envelope characteristics of random ground motion; the representative points are obtained by number theory point selection, Sobol sequence, equal probability partitioning, or probability complete point set, and the representative probability corresponding to each representative point is not less than zero, and the sum of all representative probabilities is one.

3. The method for evaluating the equivalent extreme value seismic reliability of integrated underground and above-ground structures according to claim 1, characterized in that, In step S2, the overall finite element analysis model includes above-ground structural components, underground structural components, foundations or connecting components connecting the above-ground and underground structures, soil domains surrounding the underground structure, soil boundary conditions, and the contact relationship between the underground structure and the surrounding soil. The overall finite element analysis model is used to couple the calculation of the inertial action of the above-ground structure, the soil constraint action of the underground structure, and the force transmission action at the connection between the above-ground and underground structures in the same model.

4. The method for evaluating the equivalent extreme value seismic reliability of integrated underground and above-ground structures according to claim 3, characterized in that, The soil boundary conditions adopt viscoelastic boundary, free field boundary or infinite element boundary. The underground structure and the surrounding soil establish an interaction relationship using contact element, interface element, spring-damped element or common node method. The seismic motion is input from the bottom boundary of the soil domain.

5. The method for evaluating the equivalent extreme value seismic reliability of integrated underground and above-ground structures according to claim 1, characterized in that, In step S3, the structural response includes one or more of the following: inter-story drift angle, inter-story deformation, component deformation, floor acceleration, and component internal force; when the same structural response is used as the evaluation index for both the above-ground and underground structures, different seismic performance limits are set for the above-ground and underground floors respectively.

6. The method for evaluating the seismic reliability of an integrated underground and above-ground structure based on equivalent extreme values ​​as described in claim 5, is characterized in that... In step S4, the normalized demand ratio is the ratio of the absolute value of the structural response of each floor to the seismic performance limit of that floor; when the normalized demand ratio is not greater than one, it is determined that the corresponding floor does not exceed the seismic performance limit, and when the normalized demand ratio is greater than one, it is determined that the corresponding floor exceeds the seismic performance limit.

7. The method for evaluating the equivalent extreme value seismic reliability of integrated underground and above-ground structures according to claim 6, characterized in that, In step S5, for any given set of floors, the equivalent extreme value variable is the maximum value of the normalized demand ratio of all floors in the given set of floors from the start of the earthquake to the current time; the given set of floors includes the overall set of floors including above-ground floors and underground floors, the set of above-ground floors including only above-ground floors, and the set of underground floors including only underground floors.

8. The method for evaluating the equivalent extreme value seismic reliability of integrated underground and above-ground structures according to claim 7, characterized in that, In step S6, the joint probability density evolution relationship between the equivalent extreme variable and the basic random variable is established. By integrating the joint probability density in the probability space of the basic random variable, the marginal probability density of the equivalent extreme variable is obtained. The probability that the equivalent extreme variable does not exceed the preset failure threshold is determined as the seismic reliability, and the probability that the equivalent extreme variable exceeds the preset failure threshold is determined as the failure probability.

9. The method for evaluating the seismic reliability of an integrated underground and above-ground structure according to claim 8, characterized in that, The value space of the equivalent extreme value variable is discretized by grid, and the representative probability corresponding to each representative point is taken as the probability mass and initialized at the grid position where the initial value of the corresponding equivalent extreme value variable is located. Based on the increment of the equivalent extreme value variable of each random ground motion sample between adjacent time points, the migration amount of the probability mass between adjacent grids is determined, and by refining the time step, the migration range of the probability mass within a single time step does not exceed one grid spacing.

10. The method for evaluating the equivalent extreme value seismic reliability of integrated underground and above-ground structures according to claim 7, characterized in that, It also includes reliability verification and control floor identification: based on the representative probability of each random ground motion sample, the samples whose equivalent extreme value variables do not exceed the preset failure threshold are weighted and summed to obtain the verification reliability; the floor corresponding to the maximum normalized demand ratio of each random ground motion sample during the ground motion duration is determined, and the floor is taken as the control floor, and the representative probabilities corresponding to the failure samples with the same control floor are accumulated to obtain the failure contribution probability of each floor to the overall structural failure event.

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