Cross-fault tunnel fault movement-seismic oscillation decoupling analysis method, device and terminal

Abstract

The invention is suitable for the technical field of seismic analysis, and provides a cross-fault tunnel fault movement-seismic oscillation decoupling analysis method and device and a terminal. The method comprises the following steps: establishing a finite element model of a cross-fault tunnel-surrounding rock; based on the dual-objective optimization function of the seismic wave, determining the separation frequency of a fault movement component and a seismic oscillation component in the current seismic wave, and obtaining fault movement component data and seismic oscillation component data from the seismic wave in the simulation area; the fault movement component data and the seismic movement component data are converted into equivalent seismic loads; and applying the equivalent seismic load to the finite element model for finite element calculation, and determining the seismic response rule of the tunnel lining under the action of the seismic motion field and the fault displacement field. According to the method, the optimal separation frequency of the seismic oscillation component and the fault movement component is determined by using the dual-objective optimization function, so that the influence of different seismic wave components on the tunnel structure is researched, and a reference basis is provided for adopting targeted anti-seismic measures for tunnel seismic resistance.

Description

Technical Field

[0001] This application relates to the field of earthquake analysis technology, specifically to a method, device, and terminal for decoupling analysis of fault displacement and ground motion in cross-fault tunnels. Background Technology

[0002] Located between the Circum-Pacific Seismic Belt and the Eurasian Seismic Belt, my country experiences frequent seismic faulting due to the compression of surrounding tectonic plates. With continuous urban economic development, the number and scale of subway tunnels and cross-sea tunnels between cities are increasing. The construction of these tunnels presents a series of challenges, some of which currently lack effective solutions. To address potential problems during tunnel construction and operation, conducting reasonable seismic response analysis of cross-fault tunnels and providing scientifically sound seismic design is a crucial issue currently facing engineering projects.

[0003] During the research process, the inventors of this application discovered that most studies on methods related to tunnel seismic resistance technology focus on the damage to tunnel structures and corresponding seismic resistance measures under the coupling action of seismic waves of different frequencies. However, in actual earthquake damage, seismic displacement is mainly concentrated in the fault motion of low-frequency earthquakes, while high-frequency ground motion mainly manifests in acceleration, which has a significant effect on tunnel structures. Studies on the impact of ground motion and fault displacement in seismic waves on tunnel seismic damage are still relatively few. Summary of the Invention

[0004] In view of this, embodiments of this application provide a method, device and terminal for decoupling analysis of fault slippage-seismic motion in cross-fault tunnels. By studying how to decouple and separate seismic motion components and fault slippage components in seismic waves and analyzing the influence of different seismic motion components on the tunnel structure, the proportion of slippage and seismic action at the tunnel structure response is determined, providing a reference for adopting targeted seismic resistance measures for tunnels.

[0005] To achieve the above objectives, this application adopts the following technical solution:

[0006] In a first aspect, embodiments of this application provide a method for decoupling analysis of fault slippage and seismic motion in cross-fault tunnels, including:

[0007] A finite element model of a cross-fault tunnel-surrounding rock is established, and a viscoelastic artificial boundary is applied to the finite element model.

[0008] The bi-objective optimization function based on seismic waves determines the separation frequency of the fault slip component and the ground motion component in the current seismic wave. The bi-objective optimization function characterizes the sum of the ratio of the 2-norm value of the acceleration time history of the fault slip component of the current seismic wave and the ratio of the 2-norm value of the displacement time history of the ground motion component of the original seismic wave.

[0009] Based on the separation frequency, fault slip component data and ground motion component data are obtained from the seismic waves in the simulated area;

[0010] Convert fault slip component data and ground motion component data into equivalent seismic loads;

[0011] The equivalent seismic load is applied to the finite element model for finite element calculation to determine the seismic response characteristics of the tunnel lining under the action of the ground motion field and the fault displacement field.

[0012] Based on the first aspect, in some embodiments, the bi-objective optimization function based on seismic waves determines the separation frequency of the fault slip component and the ground motion component in the seismic waves, including:

[0013] Filtering the seismic waves yields fault slip component data and ground motion component data;

[0014] Calculate the first ratio of the 2-norm value of the acceleration time history of the fault slip component of all stations within the sample interval to the 2-norm value of the acceleration time history of the fault slip component of the original seismic wave, and the second ratio of the 2-norm value of the displacement time history of the ground motion component to the 2-norm value of the displacement time history of the ground motion component of the original seismic wave.

[0015] Calculate the weighted sum of the first ratio and the second ratio to obtain the bi-objective optimization function;

[0016] The minimum value of the biobjective optimization function for all seismic waves in the study area is calculated to obtain the separation frequency for decoupling and separating the ground motion component data and the fault slip component data.

[0017] Based on the first aspect, in some embodiments, obtaining fault displacement component data and ground motion component data from seismic waves in the simulated region based on the separation frequency includes:

[0018] Based on the separation frequency, low-pass and high-pass filters are used to obtain fault slip field component data and ground motion field component data for the entire simulation area.

[0019] Based on the first aspect, in some embodiments, the bi-objective optimization function is:

[0020]

[0021] Among them, J(f c () represents a bi-objective optimization function, where N is the number of seismic wave samples. This represents the displacement time history of the seismic motion component in the current seismic wave. The time history represents the acceleration component of the fault displacement in the current seismic wave. The displacement time history represents the seismic motion component in the original seismic wave. The time history representing the acceleration component of the fault displacement in the original seismic wave. This indicates that the magnitude of the ground motion and fault slip component matrices of the objective function is measured using the L2 norm, where α and β are the weights of the ground motion and fault slip components, respectively.

[0022] Based on the first aspect, in some embodiments, applying the equivalent seismic load to the finite element model for finite element calculation to determine the seismic response characteristics of the tunnel lining under the action of the seismic ground motion field and the fault slip field includes:

[0023] The first equivalent nodal load value and the second equivalent nodal load value are applied to each boundary node of the finite element model, and the displacement time history response of any node on the finite element model is solved.

[0024] Based on the displacement time history response, the seismic response law of the tunnel lining under the action of the ground motion field and the fault slip field is determined.

[0025] Based on the first aspect, in some embodiments, the seismic vibration and fault faulting effects caused by the ground motion component data and fault faulting component data during the entire earthquake process are nonlinearly superimposed, and the seismic vibration and fault faulting effects are decoupled and determined: the fault faulting effect of the fault faulting component data has a greater destructive effect on the tunnel structure than the combined effect of the high ground motion data and the fault faulting component data on the tunnel structure.

[0026] Based on the first aspect, in some embodiments, establishing a finite element model of a cross-fault tunnel-surrounding rock and applying a viscoelastic artificial boundary to the finite element model includes:

[0027] Obtain fault parameters of the earthquake motion simulation area, and establish a fault rupture model based on these fault parameters;

[0028] Based on the fault rupture model, the size of the earthquake simulation area and the grid size are determined, and a terrain elevation model and an underground rock stratum velocity structure model are established.

[0029] A finite element model of a cross-fault tunnel-surrounding rock was established based on the terrain elevation model and the underground rock velocity structure model, and a viscoelastic artificial boundary was applied to the finite element model.

[0030] Based on the first aspect, in some embodiments, the step of establishing a finite element model of a cross-fault tunnel-surrounding rock based on a terrain elevation model and an underground rock stratum velocity structure model, and applying a viscoelastic artificial boundary to the finite element model, includes:

[0031] Establish a finite element model of the cross-fault tunnel and surrounding rock at the tunnel site corresponding to the simulation area, which has undulating seabed topography;

[0032] The damping coefficient and stiffness coefficient of the spring-damper are calculated based on the density, Poisson's ratio, Lamé coefficient, shear and compression wave velocities of the surrounding rock in the finite element model.

[0033] Springs and dampers are applied in three directions at each node of the finite element model boundary to form a viscoelastic artificial boundary.

[0034] Secondly, embodiments of this application provide a fault slippage-seismic motion decoupling analysis device for cross-fault tunnels, comprising:

[0035] The finite element model module is used to establish a finite element model of a cross-fault tunnel-surrounding rock and to apply viscoelastic artificial boundaries to the finite element model.

[0036] The separation frequency determination module is used to determine the separation frequency of the fault slip component and the ground motion component in the current seismic wave based on the bi-objective optimization function of the seismic wave. The bi-objective optimization function is the sum of the ratio of the 2-norm of the acceleration time history of the fault slip component of the current seismic wave and the ratio of the 2-norm of the displacement time history of the ground motion component of the original seismic wave.

[0037] A separation module is used to obtain fault displacement component data and ground motion component data from seismic waves in the simulated area based on the separation frequency.

[0038] The equivalent seismic load module is used to convert fault slip component data and ground motion component data into equivalent seismic loads.

[0039] The finite element calculation module is used to apply the equivalent seismic load to the finite element model and perform finite element calculations to determine the seismic response characteristics of the tunnel lining under the action of the ground motion field and the fault displacement field.

[0040] Thirdly, embodiments of this application provide a terminal, including a memory and a processor. The memory stores a computer program that can run on the processor. When the processor executes the computer program, it implements the cross-fault tunnel fault displacement-seismic motion decoupling analysis method as described in any of the first aspects.

[0041] The beneficial effects of the embodiments of this application compared with the prior art include:

[0042] In this embodiment, a topographic elevation model, an underground rock velocity structure model, and single or multiple fault rupture models within the earthquake motion simulation area can be encapsulated and then subjected to broadband earthquake motion simulation to obtain seismic waves at different locations and depths within the simulation area. Seismic waves at the nodes corresponding to the nodes in the earthquake motion simulation area on the boundary of the tunnel-surrounding rock finite element model can be obtained; the number and types of seismic waves are numerous. Using a filtering method, the ground motion component and fault displacement component of the seismic waves can be decoupled to obtain seismic waves containing both ground motion and fault displacement components. The fault displacement component data and ground motion component data in the seismic waves are converted into equivalent seismic loads. Applying these equivalent seismic loads to the finite element model and performing finite element calculations allows determination of the seismic response characteristics of the tunnel lining under the action of the ground motion field and fault displacement field. Under non-uniform excitation, cross-fault ground motion response analysis of the tunnel structure can yield the seismic response results of the tunnel structure subjected to high- and low-frequency earthquakes.

[0043] This application's embodiments not only allow for focused research on local areas, eliminating the need to consider far-field sources and seismic wave propagation information, but also utilize filtering methods to effectively separate seismic vibration and fault faulting. By studying the impact of two frequencies of seismic waves on the tunnel structure during ground motion, the proportions of faulting and vibration at the tunnel structure's response are determined, providing a reference for adopting targeted seismic resistance measures for tunnels. Attached Figure Description

[0044] 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.

[0045] Figure 1 This is a flowchart illustrating the fault slippage-seismic motion decoupling analysis method for cross-fault tunnels provided in this application embodiment;

[0046] Figure 2 This is a schematic diagram of the structure of the cross-fault tunnel fault slip-seismic motion decoupling analysis device provided in the embodiments of this application;

[0047] Figure 3 This is a schematic diagram of the terminal provided in the embodiments of this application. Detailed Implementation

[0048] The present application will be described more clearly below with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the function of the present application, but do not limit the present application in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present application. These all fall within the protection scope of the present application.

[0049] 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.

[0050] To address the shortcomings of existing seismic response analysis methods, which often involve the coupling effect of ground motion and fault displacement components as input, resulting in a nonlinear superposition of these components, a separate analysis of the seismic response of tunnel structures under the influence of high-frequency seismic motion and low-frequency fault displacement is lacking. Ground motion primarily affects the magnitude of seismic wave acceleration, while fault displacement is mainly reflected in the displacement time history. Since the effects of ground motion and fault displacement on the structure are nonlinear, effectively separating the response results of tunnel structures is difficult. Therefore, this application investigates the proportion of damage caused by the ground motion and fault displacement components of seismic waves in fault-crossing tunnel structures, starting with the ground motion input. This is crucial for studying seismic and fault-resistant measures at different locations in fault-crossing tunnels.

[0051] This application first obtains the simulation results of cross-fault ground motion through ground motion simulation, then establishes a dual-objective optimization model to determine the separation frequency of the ground motion and fault slip components, then uses frequency domain filtering to obtain the cross-fault ground motion and fault slip components respectively, and calculates the seismic response of the tunnel-surrounding rock finite element model under the action of ground motion and fault slip components, and finally uses the ground motion response results of the tunnel structure to explore the proportion of fault slip and ground motion in the failure of the tunnel structure.

[0052] The implementation scheme of this application will be described in detail below with reference to the accompanying drawings.

[0053] See Figure 1 The method for decoupling analysis of fault slippage and seismic motion in cross-fault tunnels provided in this application may include the following steps:

[0054] Step 101: Establish a finite element model of the cross-fault tunnel-surrounding rock and apply a viscoelastic artificial boundary to the finite element model.

[0055] In some embodiments, step 101 may include: obtaining fault parameters of the earthquake simulation area and establishing a fault rupture model based on the fault parameters; determining the size and grid size of the earthquake simulation area based on the fault rupture model, and establishing a terrain elevation model and an underground rock velocity structure model; establishing a cross-fault tunnel-surrounding rock finite element model based on the terrain elevation model and the underground rock velocity structure model, and applying a viscoelastic artificial boundary to the finite element model.

[0056] For example, when establishing a fault rupture model, the earthquake simulation area and engineering geological conditions can be preliminarily determined; based on the earthquake simulation area and the engineering geological conditions, one or more active faults in the earthquake simulation area can be selected for investigation to determine fault parameters, including the latitude and longitude coordinates of the top of the active fault section, the fault strike, dip angle, slip angle, and the length and width of the fault plane; and a fault rupture model can be established based on these fault parameters.

[0057] Specifically, the location of the tunnel (e.g., City B in Province A) can be determined based on the project background and relevant project plans. Then, geological conditions such as site survey data, seismic safety assessment reports, and nearby fault conditions can be consulted to determine if the tunnel route mainly traverses or crosses multiple different faults. Among these, fault displacement in active faults has a particularly severe impact on the tunnel structure. When conducting cross-fault seismic motion simulations, the simulation area needs to completely encompass the originating fault. The simulation area is centered on the hypocenter and extended in all directions to obtain the dimensions of the seismic motion simulation area. To ensure accurate seismic motion simulation calculations, the top of the fault model cannot be placed at the superdamped layer at the boundary of the simulation area. Generally, the thickness of the superdamped layer is assumed to be 30 grid units.

[0058] One or more active faults in City B of Province A were selected as the faults that would have the most serious impact on the tunnel route. By reviewing the literature, the geological conditions of the study area were investigated to obtain key parameters such as the latitude and longitude coordinates of the top of the active fault section, the fault strike, dip angle, slip angle, and the length and width of the fault plane.

[0059] The maximum seismic capacity of an active fault is calculated based on its length and width, according to M. W Scale relationship of the empirical formula for RA magnitude-rupture length:

[0060] M S =0.9541lg(A)+4.134(±0.31)

[0061] A=RLD×RW

[0062] Calculate the maximum seismic capacity of the fault. Where M... W The moment magnitude is M. S The magnitude is a surface wave earthquake. MW Although it is a moment magnitude earthquake, Wells et al.'s research indicates it is between 5.7 and 8.0. W Surface wave magnitude M S There is no systematic bias between them, and they are equal. Calculations revealed that the maximum seismic capacity M of the active fault is... S Approximately 6.325, which can be considered as M S = M W = 6.33.

[0063] In this embodiment, when establishing the topographic elevation model and the underground rock stratum velocity structure model, the latitude and longitude corresponding to the center point of the seismogenic fault can be determined as the center of the seismic motion simulation area; the size of the seismic motion simulation area can be determined according to the overall direction, length and burial depth of the fault rupture model; the grid size of the seismic motion simulation area can be determined according to the relationship between the effective propagation grid size of seismic waves in the seismic motion simulation area and the minimum wavelength of seismic waves; the topographic elevation model can be established according to the topographic elevation data of the seismic motion simulation area; and the underground rock stratum velocity structure model can be established according to the density, quality factor, shear and compression wave velocity of rock strata at different depths.

[0064] Specifically, the simulation area can be centered on the latitude and longitude corresponding to the center point of the seismogenic fault. Considering that the overall strike, length, and burial depth of the fault rupture model must be within the simulation area and at a certain distance from the super-damping layer, the simulation surface in the seismic motion simulation area is 18km × 30km in size and 15km in vertical depth. The latitude and longitude coordinates of the simulation starting point of the seismic motion simulation area are (36.008°N, 120.154°E). To ensure the effective propagation of seismic waves in the simulation area during broadband seismic motion simulation, the grid size is less than or equal to 1 / 8 of the minimum wavelength of the seismic wave. Δh is the grid size, λ min Since the minimum wavelength of seismic waves is 40m, the grid size for the seismic motion simulation area can be set to 40m.

[0065] The topographic elevation data for the simulated area can be obtained from the global topographic data model STRM1 with an accuracy of 30m. Establishing a velocity structure model of the subsurface rock strata requires obtaining the density, quality factor, shear and compressive wave velocities of the rock strata at different depths at various locations. The compressive and shear wave velocity data of the subsurface rock strata can be obtained using USTClitho2.0, while the density can be queried using RUST1.0. The quality factor, which describes the attenuation of seismic wave propagation, can be obtained using Q... S =V S ×50 and Q P =2×Q S Calculations show that Q S Q is the quality factor for the shear wave (S-wave). P V is the quality factor for compressed wave (P-wave).S This refers to the shear wave velocity.

[0066] In this embodiment, the step of establishing a finite element model of a cross-fault tunnel-surrounding rock based on a terrain elevation model and an underground rock stratum velocity structure model, and applying a viscoelastic artificial boundary to the finite element model, may include: establishing a finite element model of a cross-fault tunnel-surrounding rock with undulating seafloor topography at the tunnel site corresponding to the simulation area; calculating the damping coefficient and stiffness coefficient of the spring-damper based on the density, Poisson's ratio, Lamé coefficient, shear and compression wave velocities of the surrounding rock in the finite element model; and applying spring-dampers in three directions at each node of the finite element model boundary to form a viscoelastic artificial boundary.

[0067] For example, when meshing, the mesh size of the finite element model is less than or equal to 1 / 8 of the minimum wavelength of the seismic wave, the mesh size of the surrounding rock model is 40m, the rock mass around the tunnel uses the three-dimensional solid element SOLID45, the constitutive model of the surrounding rock is the Mohr-Coulomb model, and the Drucker-Prag concrete model and SHEll181 shell element are used to simulate the elastoplastic behavior of the tunnel lining under seismic action.

[0068] Specifically, a finite element model of a trans-fault tunnel and its surrounding rock with undulating seafloor topography was established at the tunnel site corresponding to the simulation area. The minimum cross-sectional size of the model was 480m × 240m, and the longitudinal length of the tunnel was 5400m. The tunnel cross-section was horseshoe-shaped with inner and outer diameters of 13.7m and 15m, respectively. To ensure the accuracy of the calculation results, the mesh size of the finite element model should not exceed 1 / 8 of the minimum wavelength of the seismic wave during mesh generation, and the mesh size of the surrounding rock model was 40m. The surrounding rock mass was modeled using the three-dimensional solid element SOLID45, the constitutive model of the surrounding rock was the Mohr-Coulomb model, and the Drucker-Prag concrete model and SHEll181 shell elements were used to simulate the elastoplastic behavior of the tunnel lining under seismic loading.

[0069] The damping and stiffness coefficients of the spring-damper are calculated based on the density, Poisson's ratio, Lamé coefficient, shear and compressive wave velocities of the surrounding rock in the finite element model. A spring-damper is applied in each of the three directions at each node of the finite element model boundary to form a viscoelastic artificial boundary. The damping and stiffness coefficients of the spring-damper are then calculated using K=α. N ×G / r b Calculate the tangential stiffness coefficient of the spring-damper using C=ρV P Calculate the tangential damping coefficient of the spring-damper using K=α T ×G / r b Calculate the normal stiffness coefficient of the spring-damper using C=ρV S Calculate the damping coefficient of the spring-damper system in the normal direction. In the formula, C represents the damping coefficient of the damper, K represents the stiffness coefficient of the damper, and V... PVs represents the compression wave velocity, and r represents the shear wave velocity. b The coordinates of the artificial boundary in the polar coordinate system are given, where G represents the shear modulus of the elastic medium, ρ represents the soil density, and α represents the... N α represents the dimensionless coefficient of the adjusted normal. T This represents the dimensionless coefficient of the adjusted tangential direction.

[0070] Step 102: Determine the separation frequency of the fault displacement component and the ground motion component in the current seismic wave based on the bi-objective optimization function of the seismic wave.

[0071] The bi-objective optimization function represents the sum of the ratio of the 2-norm of the acceleration time history of the fault fault component of the current seismic wave and the original seismic wave and the ratio of the 2-norm of the displacement time history of the ground motion component.

[0072] In some embodiments, step 102 may include: filtering the seismic waves to obtain fault slip component data and ground motion component data; calculating a first ratio of the 2-norm value of the acceleration time history of the fault slip component of all stations within the sample interval to the 2-norm value of the acceleration time history of the fault slip component of the original seismic wave, and a second ratio of the 2-norm value of the displacement time history of the ground motion component to the 2-norm value of the displacement time history of the original seismic wave; calculating a weighted sum of the first ratio and the second ratio to obtain a bi-objective optimization function; calculating the minimum value of the bi-objective optimization function for all seismic waves within the study area to obtain the separation frequency for decoupling and separating the ground motion component data and the fault slip component data.

[0073] For example, the biobjective optimization function can be:

[0074]

[0075] Among them, J(f c () represents a bi-objective optimization function, where N is the number of seismic wave samples. This represents the displacement time history of the seismic motion component in the current seismic wave. The time history represents the acceleration component of the fault displacement in the current seismic wave. The displacement time history represents the seismic motion component in the original seismic wave. The time history representing the acceleration component of the fault displacement in the original seismic wave. The L2 norm is used to measure the magnitude of the ground motion and fault slip component matrices of the objective function. α and β are the weights of the ground motion and fault slip components, respectively. Since the weights of the ground motion and fault slip components are equally important, the values ​​of α and β are usually both 1.

[0076] Near-field ground motion generally comprises two components: fault slippage and ground motion. Separating these two components from the measured records is a crucial step in studying near-fault effects, failure mechanisms, and for engineering response analysis. Fault slippage is caused by permanent crustal deformation resulting from earthquakes, manifesting as irreversible changes in the ground position near the fault region, primarily reflected in low-frequency trends in velocity time histories and permanent displacement deformation in displacement time histories. Therefore, frequency domain filtering can be used to decompose fault slippage and ground motion components; specifically, low-pass filtering extracts the low-frequency slippage component, and high-pass filtering separates the high-frequency dynamic ground motion component. Since the spectra of static displacement and dynamic ground motion are not absolutely separated at extremely low frequencies, distinguishing the separation frequencies of slippage and ground motion components is a vital step in frequency domain decomposition.

[0077] Based on the aforementioned concept of decoupling and separating ground motion and fault slippage, and considering the requirement that the acceleration time history controlled by the fault slippage component obtained after low-pass filtering of seismic waves should be as small as possible, and the displacement time history controlled by the ground motion component obtained after high-pass filtering should be as small as possible, a bi-objective optimization function is established. This function is the sum of the ratios of the 2-norm values ​​of the acceleration time histories of the fault slippage component and the original seismic wave acceleration time histories, and the ratios of the 2-norm values ​​of the displacement time histories of the ground motion component and the original seismic wave displacement time histories. When obtaining the fault slippage component and ground motion component using the frequency domain filtering method, it is necessary to determine the most suitable separation frequency between the low-frequency and high-frequency seismic waves. Therefore, by calculating the mean of the objective function for all seismic waves at different separation frequencies, the frequency corresponding to the minimum mean of the objective function is identified as the optimal separation frequency for separating the fault slippage and ground motion components.

[0078] For a single seismic wave, it is sufficient to calculate the objective function value at different separation frequencies and take the separation frequency corresponding to the minimum objective function value. For earthquake swarms with multiple seismic waves, calculate the objective function for each seismic wave and take the average value; the frequency corresponding to the minimum average value is the desired separation frequency.

[0079] By using low-pass and high-pass filters respectively to filter the input seismic waves at the tunnel site location according to the optimal separation frequency, the fault slip component and the ground motion component in the ground motion are obtained, thus achieving the decoupling and separation of fault slip and ground motion.

[0080] Specifically, 91 separation frequencies were set at intervals of 0.01 Hz within the range of 0.1 to 1 Hz. The mean value of the bi-objective optimization function for all seismic waves at each frequency was calculated, and a curve showing the change of the mean objective function value with the separation frequency was plotted. The frequency corresponding to the minimum mean objective function value was the optimal separation frequency. By calculating the minimum mean objective function value at each frequency, it was determined that the mean objective function value first decreased and then increased with increasing frequency. The frequency corresponding to the minimum value of the mean objective function value curve was 0.46 Hz, which is the optimal separation frequency for the seismic motion component and the fault slip component.

[0081] The 0.1–1 Hz range is the dividing line between low-frequency fault slip components and high-frequency ground motion components in seismic waves. Generally, components below 0.1 Hz are defined as low-frequency components, those above 1 Hz as high-frequency components, and the 0.1–1 Hz range as mid-frequency components, containing both fault slip and ground motion components. Therefore, this coarse method of using 0.1 and 1 Hz as boundaries often fails to completely separate the fault slip and ground motion components in seismic waves. Thus, it is necessary to finely divide the mid-frequency range of 0.1–1 Hz into cutoff frequencies for low-frequency and high-frequency components, and obtain the optimal cutoff frequency by establishing a bi-objective optimization model to separate low-frequency fault slip and high-frequency ground motion components as completely as possible.

[0082] Step 103: Obtain fault displacement component data and ground motion component data from the seismic waves of the simulated area based on the separation frequency.

[0083] For example, step 103 can specifically be: using a low-pass filter and a high-pass filter respectively based on the separation frequency to obtain fault slip field component data and ground motion field component data of the entire simulation area.

[0084] Step 104: Convert the fault displacement component data and ground motion component data into equivalent seismic loads.

[0085] In some embodiments, the above-mentioned conversion of fault slip component data and ground motion component data into equivalent seismic loads may include: extracting the mass matrix, stiffness matrix and damping matrix of the finite element model based on the region reduction method, and calculating the first equivalent nodal load value at the boundary of the finite element model under the fault slip component data and the second equivalent nodal load value at the boundary of the finite element model under the ground motion component data based on the mass matrix, the stiffness matrix and the damping matrix.

[0086] Specifically, it can be done through Calculate the equivalent nodal load values, where M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the finite element model, respectively, and Ω represents the local site region where the finite element model is located. + This represents another region in the system besides Ω, containing faults and earthquake sources. Ω and Ω +The interface of the region is denoted by Γ, and the subscripts b and e represent Γ and Ω respectively. + Nodes of the region; u, and These represent the time histories of displacement, velocity, and acceleration of the free field system, respectively. Represents Ω + The acceleration field of the region, Represents Ω + The velocity field of the region, Represents Ω + Displacement field of the region Represents the acceleration field in the Γ region. Represents the velocity field in the Γ region. Represents the displacement field in the Γ region. Represents the region Ω + The mass submatrices are stored in the mass matrix according to the order of nodes b and e. Represents the region Ω + The mass submatrices are stored in the mass matrix according to the order of nodes e and b. Represents the region Ω + The damping submatrix is ​​stored in the damping matrix according to the order of nodes b and e. Represents the region Ω + The damping submatrix is ​​stored in the damping matrix according to the order of nodes e and b. Represents the region Ω + The stiffness submatrix is ​​stored in the stiffness matrix in the order of nodes b and e. Represents the region Ω + The stiffness submatrix is ​​stored in the stiffness matrix in the order of nodes e and b.

[0087] Step 105: Apply the equivalent seismic load to the finite element model and perform finite element calculations to determine the seismic response characteristics of the tunnel lining under the action of the ground motion field and the fault displacement field.

[0088] In some embodiments, step 105 may include: applying the first equivalent nodal load value and the second equivalent nodal load value to each boundary node of the finite element model, solving the displacement time history response of any node on the finite element model, and determining the seismic response law of the tunnel lining under the action of the ground motion field and the fault displacement field based on the displacement time history response.

[0089] For example, the nonlinear superposition of seismic motion and fault faulting effects caused by ground motion component data and fault faulting component data throughout the entire earthquake process decouples and determines that the fault faulting effect of the fault faulting component data has a greater destructive effect on the tunnel structure than the combined effect of the high ground motion data and fault faulting component data.

[0090] Specifically, for the tunnel-surrounding rock finite element model with viscoelastic artificial boundaries, the equivalent nodal load values ​​of the seismic motion components and fault slip components calculated in step 104 can be applied to each boundary node of the finite element model, thereby solving for the displacement time history response of any node on the finite element model. Seismic motion calculations of the seismic motion components and fault slip components of the tunnel-surrounding rock finite element model reveal that, under non-uniform excitation, the response of the tunnel structure changes differently when the frequency components of the input seismic wave change. For example, when the main frequency of the input seismic wave is a seismic motion component greater than 0.46 Hz, the nodal displacement values ​​of the tunnel structure change relatively little, while the peak ground acceleration values ​​of each node are very large, reaching a maximum of 4 m / s². 2 Similarly, when the input seismic wave frequency is mainly concentrated in the range of 0.1 to 0.46 Hz, the displacement of the tunnel structure will be very large, with a maximum value of 0.4 m, while the acceleration value will be very small or even negligible.

[0091] Analysis of the stress variations in the tunnel structure revealed certain regularities in the equivalent stress, first principal stress, circumferential stress, and axial stress at the arch crown, abutment, waist, foot, and bottom of the tunnel lining. Studying the load conditions corresponding to the seismic motion and fault slip components showed that tunnel damage primarily occurred under the fault slip component, indicating that the stress variations in the tunnel structure under the combined action of earthquakes of various frequencies are not a simple linear superposition of the two load conditions. Throughout the earthquake process, the seismic motion and fault slip effects caused by the seismic waves from the seismic motion and fault slip components are nonlinearly superimposed. Decoupling revealed that, compared to the original seismic wave action, the fault slip component plays a dominant role in the damage to the tunnel structure. Therefore, it is essential to focus on low-frequency, long-period seismic motions when studying tunnel seismic resistance methods.

[0092] The aforementioned decoupling analysis method for fault slippage-seismic motion in cross-fault tunnels encapsulates the topographic elevation model, underground rock velocity structure model, and single or multiple fault rupture models within the seismic motion simulation area, then performs broadband seismic motion simulation to obtain seismic waves at different locations and depths within the simulation area. It can obtain seismic waves at the nodes corresponding to the nodes in the seismic motion simulation area at each node on the boundary of the tunnel-surrounding rock finite element model, resulting in a large number and variety of seismic waves. Using filtering methods, the seismic vibration and slippage components in the seismic waves can be decoupled, yielding seismic waves with both seismic vibration and slippage components. By using an improved domain reduction method combined with viscoelastic artificial boundaries applied at the boundaries, the seismic waves can be converted into cross-fault seismic loads and applied to each boundary node of the finite element model, achieving equivalent seismic wave input. Under non-uniform excitation, cross-fault seismic response analysis of the tunnel structure can yield seismic response results of the tunnel structure subjected to high- and low-frequency earthquakes. This application's embodiments not only allow for focused research on local areas, eliminating the need to consider far-field sources and seismic wave propagation information, but also utilize filtering methods to effectively separate seismic vibration and fault faulting. By studying the impact of two frequencies of seismic waves on the tunnel structure during ground motion, the proportions of faulting and vibration at the tunnel structure's response are determined, providing a reference for adopting targeted seismic resistance measures for tunnels.

[0093] 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.

[0094] Corresponding to the fault slip-seismic motion decoupling analysis method for cross-fault tunnels described in the above embodiments, Figure 2 The diagram shows a structural block diagram of the fault slip-seismic motion decoupling analysis device for cross-fault tunnels provided in this application embodiment. For ease of explanation, only the parts related to this application embodiment are shown.

[0095] See Figure 2 The cross-fault tunnel fault slip-seismic motion decoupling analysis device provided in this application embodiment includes a finite element model module 201, a separation frequency determination module 202, a separation module 203, an equivalent seismic load module 204, and a finite element calculation module 205.

[0096] Specifically, the finite element model module 201 is used to establish a finite element model of a cross-fault tunnel-surrounding rock and to apply a viscoelastic artificial boundary to the finite element model.

[0097] The separation frequency determination module 202 is used to determine the separation frequency of the fault slip component and the ground motion component in the current seismic wave based on the bi-objective optimization function of the seismic wave. The bi-objective optimization function is the sum of the ratio of the 2-norm value of the acceleration time history of the fault slip component of the current seismic wave and the ratio of the 2-norm value of the displacement time history of the ground motion component of the original seismic wave.

[0098] The separation module 203 is used to obtain fault displacement component data and ground motion component data from the seismic waves of the simulated area based on the separation frequency.

[0099] The equivalent seismic load module 204 is used to convert fault slip component data and ground motion component data into equivalent seismic loads.

[0100] The finite element calculation module 205 is used to apply the equivalent seismic load to the finite element model and perform finite element calculations to determine the seismic response characteristics of the tunnel lining under the action of the ground motion field and the fault displacement field.

[0101] Optionally, the separation frequency determination module 202 can be specifically used to: filter seismic waves to obtain fault slip component data and ground motion component data; calculate the first ratio of the 2-norm value of the acceleration time history of the fault slip component of all stations within the sample interval to the 2-norm value of the acceleration time history of the fault slip component of the original seismic wave, and the second ratio of the 2-norm value of the displacement time history of the ground motion component to the 2-norm value of the displacement time history of the original seismic wave; calculate the weighted sum of the first ratio and the second ratio to obtain the bi-objective optimization function; calculate the minimum value of the bi-objective optimization function of all seismic waves within the study area to obtain the separation frequency for decoupling and separating the ground motion component data and the fault slip component data.

[0102] Optionally, the separation module 203 can be specifically used to: obtain fault fault field component data and ground motion field component data of the entire simulation area using low-pass filters and high-pass filters respectively based on the separation frequency.

[0103] Optionally, the bi-objective optimization function is:

[0104]

[0105] Among them, J(f c () represents a bi-objective optimization function, where N is the number of seismic wave samples. This represents the displacement time history of the seismic motion component in the current seismic wave. The time history represents the acceleration component of the fault displacement in the current seismic wave. The displacement time history represents the seismic motion component in the original seismic wave. The time history representing the acceleration component of the fault displacement in the original seismic wave. This indicates that the magnitude of the ground motion and fault slip component matrices of the objective function is measured using the L2 norm, where α and β are the weights of the ground motion and fault slip components, respectively.

[0106] Optionally, the finite element calculation module 205 can be used to: apply the first equivalent nodal load value and the second equivalent nodal load value to each boundary node of the finite element model, solve the displacement time history response of any node on the finite element model, and determine the seismic response law of the tunnel lining under the action of the ground motion field and the fault displacement field based on the displacement time history response.

[0107] Optionally, the seismic motion and fault faulting effects caused by the ground motion component data and fault faulting component data during the entire earthquake process are nonlinearly superimposed to decouple and determine the seismic motion and fault faulting effects: the fault faulting component data has a greater destructive effect on the tunnel structure than the combined effect of the high ground motion data and fault faulting component data.

[0108] For example, the finite element model module 201 can be used to: obtain fault parameters of the earthquake simulation area, and establish a fault rupture model based on the fault parameters; determine the size and mesh size of the earthquake simulation area based on the fault rupture model, and establish a terrain elevation model and an underground rock velocity structure model; establish a cross-fault tunnel-surrounding rock finite element model based on the terrain elevation model and the underground rock velocity structure model, and apply a viscoelastic artificial boundary to the finite element model.

[0109] Optionally, the step of establishing a finite element model of a cross-fault tunnel-surrounding rock based on the terrain elevation model and the underground rock strata velocity structure model, and applying a viscoelastic artificial boundary to the finite element model, may include: establishing a finite element model of a cross-fault tunnel-surrounding rock with undulating seafloor terrain at the tunnel site corresponding to the simulation area; calculating the damping coefficient and stiffness coefficient of the spring-damper based on the density, Poisson's ratio, Lamé coefficient, shear and compression wave velocities of the surrounding rock in the finite element model; and applying spring-dampers in three directions at each node of the finite element model boundary to form a viscoelastic artificial boundary.

[0110] Figure 3 This is a schematic diagram of a terminal provided in an embodiment of the present invention. For example... Figure 3 As shown, the terminal 300 in this embodiment includes a processor 310 and a memory 320. The memory 320 stores a computer program that can run on the processor 310, such as a cross-fault tunnel fault slippage-seismic motion decoupling analysis program. When the processor 310 executes the computer program, it implements the steps in the above-described cross-fault tunnel fault slippage-seismic motion decoupling analysis method embodiment, for example... Figure 1Steps 101 to 105 are shown. Alternatively, when the processor 310 executes the computer program, it implements the functions of each module in the above-described device embodiments, for example... Figure 2 The functions of the finite element model module 201 to the finite element calculation module 205 are shown.

[0111] The terminal 300 can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The terminal may include, but is not limited to, a processor 310 and a memory 320. Those skilled in the art will understand that... Figure 3 This is merely an example of terminal 300 and does not constitute a limitation on terminal 300. It may include more or fewer components than shown, or combine certain components, or different components. For example, the terminal may also include input / output devices, network access devices, buses, etc.

[0112] The processor 310 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0113] The memory 320 can be an internal storage unit of the terminal 300, such as a hard disk or memory of the terminal 300. The memory 320 can also be an external storage device of the terminal 300, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the terminal 300. Furthermore, the memory 320 can include both internal storage units and external storage devices of the terminal 300. The memory 320 is used to store the computer program and other programs and data required by the terminal. The memory 320 can also be used to temporarily store data that has been output or will be output.

[0114] 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.

[0115] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0116] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention 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 the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for analyzing fault displacement- ground motion decoupling of a cross-fault tunnel, characterized in that, The method comprises the following steps: establishing a finite element model of a cross-fault tunnel-surrounding rock, and applying a viscoelastic artificial boundary to the finite element model; determining a separation frequency of a fault dislocation component and a seismic motion component in a current seismic wave based on a double-objective optimization function of the seismic wave, the double-objective optimization function representing a sum of a ratio of a 2-norm value of an acceleration time history of the fault dislocation component in the current seismic wave to a 2-norm value of an acceleration time history of the fault dislocation component in an original seismic wave and a ratio of a 2-norm value of a displacement time history of the seismic motion component to a 2-norm value of a displacement time history of the seismic motion component in the original seismic wave; obtaining fault dislocation component data and seismic motion component data from the seismic wave of the simulation region based on the separation frequency; converting the fault dislocation component data and the seismic motion component data into equivalent seismic loads; applying the equivalent seismic loads to the finite element model to perform finite element calculation, and determining a seismic response law of a tunnel lining under the action of a seismic motion field and a fault dislocation field.

2. The method according to claim 1, wherein, The method for determining the separation frequency of the fault dislocation component and the seismic motion component in the seismic wave based on the double-objective optimization function of the seismic wave comprises the following steps: filtering the seismic wave to obtain the fault dislocation component data and the seismic motion component data; calculating a first ratio of a 2-norm value of an acceleration time history of the fault dislocation component in a sample interval to a 2-norm value of an acceleration time history of the fault dislocation component in an original seismic wave, and a second ratio of a 2-norm value of a displacement time history of the seismic motion component to a 2-norm value of a displacement time history of the seismic motion component in the original seismic wave; calculating a weighted sum of the first ratio and the second ratio to obtain a double-objective optimization function; calculating a minimum value of the double-objective optimization function of all seismic waves in a research region to obtain a separation frequency for decoupling and separating the fault dislocation component data and the seismic motion component data.

3. The method according to claim 2, wherein, The method for obtaining the fault dislocation component data and the seismic motion component data from the seismic wave of the simulation region based on the separation frequency comprises the following steps: using a low-pass filter and a high-pass filter based on the separation frequency to obtain fault dislocation field component data and seismic motion field component data of the entire simulation region.

4. The method according to claim 2, wherein, The double-objective optimization function is as follows: where J(f c ) denotes the bi-objective optimization function, N is the number of samples of the seismic wave, denotes the displacement time history of the ground motion component in the current seismic wave, denotes the acceleration time history of the fault displacement component in the current seismic wave, denotes the displacement time history of the ground motion component in the original seismic wave, denotes the acceleration time history of the fault displacement component in the original seismic wave, denotes the L2 norm measurement on the size of the ground motion and fault displacement component matrix of the objective function, and a and β are the weights of the ground motion and fault displacement parts.

5. The method according to claim 1, wherein, The method for applying the equivalent seismic loads to the finite element model to perform finite element calculation and determining the seismic response law of the tunnel lining under the action of the seismic motion field and the fault dislocation field comprises the following steps: applying the first equivalent node load value and the second equivalent node load value to each boundary node of the finite element model to solve a displacement time history response of any node on the finite element model; determining the seismic response law of the tunnel lining under the action of the seismic motion field and the fault dislocation field according to the displacement time history response.

6. The method according to claim 5, wherein, During the entire seismic process, the seismic vibration and the fault dislocation action caused by the seismic motion component data and the fault dislocation component data are nonlinearly superimposed, and the decoupling of the seismic vibration and the fault dislocation action is determined: the damage action of the dislocation action of the fault dislocation component data on the tunnel structure is greater than the damage action of the combined action of the high seismic motion data and the fault dislocation component data on the tunnel structure.

7. The method according to claim 1, wherein, The method for establishing the finite element model of the cross-fault tunnel-surrounding rock and applying the viscoelastic artificial boundary to the finite element model comprises the following steps: obtaining fault parameters of a seismic motion simulation region, and establishing a fault rupture model based on the fault parameters; Determine the size and grid size of a seismic motion simulation region based on the fault rupture model, establish a terrain elevation model and an underground rock layer velocity structure model; Establish a cross-fault tunnel-surrounding rock finite element model according to the terrain elevation model and the underground rock layer velocity structure model, and apply a viscoelastic artificial boundary to the finite element model.

8. The method according to claim 7, wherein, The step of establishing a cross-fault tunnel-surrounding rock finite element model according to the terrain elevation model and the underground rock layer velocity structure model, and applying a viscoelastic artificial boundary to the finite element model, comprises: Establish a cross-fault tunnel-surrounding rock finite element model corresponding to the tunnel site of the simulation region with a submarine undulating terrain; Calculate the damping coefficient and stiffness coefficient of the spring-damper according to the density, Poisson's ratio, Lame coefficient, shear and compression wave velocity of the surrounding rock in the finite element model; Apply a spring-damper to each node on the boundary of the finite element model in three directions to form a viscoelastic artificial boundary.

9. A device for analyzing fault displacement- ground motion decoupling of a cross-fault tunnel, characterized by, Comprise: A finite element model module for establishing a cross-fault tunnel-surrounding rock finite element model and applying a viscoelastic artificial boundary to the finite element model; A separation frequency determination module for determining the separation frequency of the fault displacement component and the seismic motion component in the current seismic wave based on a double-objective optimization function of the seismic wave, wherein the double-objective optimization function represents the sum of the ratio of the 2-norm value of the acceleration time history of the fault displacement component in the current seismic wave to the 2-norm value of the acceleration time history of the fault displacement component in the original seismic wave and the ratio of the 2-norm value of the displacement time history of the seismic motion component to the 2-norm value of the displacement time history of the seismic motion component in the original seismic wave; A separation module for obtaining fault displacement component data and seismic motion component data from the seismic wave of the simulation region based on the separation frequency; An equivalent seismic load module for converting the fault displacement component data and the seismic motion component data into equivalent seismic loads; A finite element calculation module for applying the equivalent seismic loads to the finite element model for finite element calculation to determine the seismic response law of the tunnel lining under the action of the seismic motion field and the fault displacement field.

10. A terminal comprising a memory and a processor, said memory having stored a computer program executable on said processor, characterized in that, The processor executes the computer program to realize the steps of the cross-fault tunnel fault displacement-seismic motion decoupling analysis method according to any one of claims 1 to 8.

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