A calculation method for the seismic fortification length of a tunnel portal

Abstract

The present invention relates to the technical field of tunnel seismic resistance, and discloses a method for calculating the seismic fortification length of a tunnel portal section. The method comprises the following steps: determining the range of the tunnel portal section; collecting and analyzing the mechanical parameters of foundation beam units in the tunnel portal section to obtain statistical analysis results and random distribution functions of the mechanical parameters; establishing a finite element model of the spatial variation distribution of the tunnel portal section by using the statistical analysis results and the random distribution functions of the mechanical parameters; introducing a tunnel lateral deformation coefficient and an axial deformation coefficient, and obtaining a displacement change of the tunnel under an earthquake based on the finite element model; performing a stress-displacement analysis on the tunnel portal section to obtain a maximum bending stress change and a maximum axial stress change of the tunnel portal, and then analyzing the obtained and determined seismic fortification length of the tunnel portal section. The present invention helps to optimize the tunnel structure design and determine the seismic fortification length of the tunnel by analyzing the stress of the foundation beam unit and the displacement change under an earthquake.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel earthquake resistance, and more particularly to a method for calculating the earthquake resistance fortification length of a tunnel portal section. Background Art

[0002] Preparing the seismic resistance of a tunnel portal section is a complex and comprehensive engineering process. As the weakest link in seismic resistance, the tunnel portal section plays a crucial role in seismic design for tunnels in seismic zones. During earthquakes, this area often bears the most severe impact. Therefore, strengthening the lining structure at the tunnel portal section is a key measure to ensure the overall safety of the tunnel.

[0003] However, determining the preset length of the tunnel portal lining to optimize the structure's seismic performance is a widespread concern and urgent issue in the tunnel engineering community. Determining the preset lining length not only affects the economic efficiency of seismic design but also directly impacts safety. If the preset length is insufficient, the lining structure may not be able to effectively resist external forces during an earthquake, resulting in structural damage, affecting the tunnel's functionality and even threatening personnel safety. Conversely, if the preset length is too long, while improving seismic resistance, it also incurs additional construction and maintenance costs, resulting in unnecessary waste of resources.

[0004] Tunnels are relatively complex to design for seismic resistance due to their underground location, variable longitudinal length, and surrounding rock. Ensuring the safe and reliable operation of underground tunnels during future strong earthquakes is a pressing issue for the tunnel engineering community. Domestic and international scholars have conducted in-depth research on the seismic resistance of underground tunnel portals. These results indicate that tunnel portals are vulnerable areas to seismic damage and require reinforcement and shock absorption measures. While numerous advances have been made in the design of tunnel portal seismic pre-design, there is still no clear consensus on the pre-designed length of the portal lining. Therefore, further research is needed in this area. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the seismic fortification length of a tunnel portal section. By analyzing the stress on the foundation beam unit in the tunnel and the displacement changes under the action of an earthquake, it helps to optimize the tunnel structure design and determine the seismic fortification length of the tunnel.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for calculating the seismic fortification length of a tunnel portal section comprises the following steps:

[0008] Determine the scope of the tunnel portal section;

[0009] The mechanical parameters of the foundation beam unit in the tunnel portal section are collected and analyzed to obtain the statistical analysis results and random distribution functions of the mechanical parameters;

[0010] Under boundary conditions, a finite element model of spatial variation distribution of tunnel portal section is established by using statistical analysis results of mechanical parameters and random distribution function.

[0011] By introducing the tunnel lateral deformation coefficient and axial deformation coefficient and based on the finite element model of the spatial variation distribution of the tunnel portal section, the displacement change of the tunnel under the action of earthquake is obtained.

[0012] A stress-displacement analysis is performed on the tunnel portal section to obtain the maximum bending stress change and maximum axial stress change at the tunnel portal, and analysis is performed to determine the seismic fortification length of the tunnel portal section.

[0013] Furthermore, a statistical analysis is performed on the mechanical parameters of the foundation beam unit in the tunnel portal section to obtain the statistical analysis results of the mechanical parameters and a random distribution function; wherein the statistical analysis is performed on the mechanical parameters of the foundation beam unit in the tunnel portal section to obtain the statistical analysis results of the mechanical parameters, including:

[0014] Analyze the material properties of the foundation beam unit in the tunnel portal section, including elastic modulus, Poisson's ratio, and shear modulus;

[0015] The statistical analysis results P(E) of the elastic modulus E of the material are as follows:

[0016]

[0017] In the above formula, P(E) is the statistical analysis result of the elastic modulus of the material, σ E is the standard deviation of the elastic modulus of the material, μ E is the mean value of the elastic modulus E of the material;

[0018] The statistical analysis results of the Poisson's ratio v of the material, P(v), are as follows:

[0019]

[0020] In the above formula, P(v) is the statistical analysis result of the Poisson's ratio of the material, σ V is the standard deviation of the Poisson's ratio of the material, μ E is the mean value of the Poisson's ratio v of the material;

[0021] The statistical analysis results of the shear modulus G of the material are as follows:

[0022]

[0023] In the above formula, P(G) is the statistical analysis result of the shear modulus of the material, σ G is the standard deviation of the shear modulus of the material, μ G is the mean shear modulus of the material.

[0024] Furthermore, a statistical analysis is performed on the mechanical parameters of the foundation beam unit in the tunnel portal section to obtain a statistical analysis result and a random distribution function of the mechanical parameters; wherein the statistical analysis is performed on the mechanical parameters of the foundation beam unit to obtain a random distribution function of the mechanical parameters, specifically:

[0025]

[0026] In the above formula, Σ -1 [·] is the covariance matrix, and f(E, v, G) is the random distribution function of the elastic modulus, Poisson's ratio, and shear modulus of the material.

[0027] Furthermore, under the boundary conditions, the statistical analysis results of mechanical parameters and the random distribution function are used to establish a finite element model of the spatial variation distribution of the tunnel portal section. Specifically:

[0028] Based on the statistical analysis results of mechanical parameters, the spatial random distribution characteristics of mechanical parameters are obtained;

[0029] Using the spatial random distribution characteristics, the tunnel portal section is discretized into multiple finite element units, and each finite element unit is divided into categories to determine the number of categories of mechanical parameters;

[0030] By using random distribution function and assigning random amplitude to each finite element, a finite element model of spatial variation distribution of tunnel portal section is established.

[0031] Furthermore, the process of establishing the finite element model of the spatial variation distribution of the tunnel portal section is specifically as follows:

[0032] Assume that the geometric area of ​​the tunnel portal is Ω, which is discretized into N finite element units; each finite element unit has e = 1, 2, ..., N; the spatial area corresponding to each finite element unit is Ω e ;

[0033] Each finite element is classified into the following categories:

[0034] Assign different mechanical parameter categories C to each finite element e，j , and is represented by a random distribution function f(E, v, G), where j = 1, 2, ...; represents the number of the category of the mechanical parameter; e is the number of the finite element unit, where e = 1, 2, ...n;

[0035] F e，j (x) = Pr[f(E, v, G)∈Ce，j ]

[0036] In the above formula, F e，j (x) is the position X of each finite element, Pr[f(E, v, G)∈C e，j ] indicates that the mechanical parameters fall into the mechanical parameter category C e，j probability;

[0037] According to the random distribution function, a random amplitude is assigned to each finite element, and a finite element model of the spatial variation distribution of the tunnel portal section is established. Specifically:

[0038] For each finite element e, at the Xth position, the random amplitude of the mechanical parameter The expression is:

[0039]

[0040] In the above formula, Δf(E, v, G) is the disturbance term of the mechanical parameters generated by the random process.

[0041] Furthermore, the lateral deformation coefficient and axial deformation coefficient of the tunnel are introduced, and based on the finite element model of the spatial variation distribution of the tunnel portal section, the displacement change of the tunnel under the action of an earthquake is obtained, specifically:

[0042] According to the mechanical parameters after random amplitude, the displacement of the tunnel portal under different loads is obtained;

[0043] The stress analysis and displacement of each finite element unit are calculated, and the lateral deformation coefficient and axial deformation coefficient of the tunnel are introduced to obtain the displacement change of the tunnel under earthquake action for each finite element unit.

[0044] Furthermore, the force analysis and displacement of each finite element unit are calculated, and the lateral deformation coefficient and axial deformation coefficient of the tunnel are introduced to obtain the displacement change of the tunnel under the action of the earthquake for each finite element unit, specifically:

[0045] Assuming that the vibration caused by the earthquake is expressed as a time function f(t), the displacement change Δu of the tunnel portal section under the earthquake under each finite element unit is:

[0046] Δu(t)=(η1+η2)u(t)

[0047] In the above formula, η1 is the lateral deformation coefficient, η2 is the axial deformation coefficient, and u(t) is the displacement change of the tunnel portal section under normal circumstances.

[0048] Furthermore, a stress-displacement analysis is performed on the tunnel portal section to obtain the maximum bending stress change and the maximum axial stress change of the tunnel portal, specifically:

[0049] By performing force analysis and displacement calculation on each finite element unit, and inputting the seismic waves into the spatially variable distribution finite element model of the tunnel portal section in the form of acceleration time history, and solving it using finite element software, the maximum bending stress change and maximum axial stress change of the tunnel portal section under the action of earthquake are obtained. Then, the stiffness matrix and mass matrix of all finite element units are assembled according to the nodes to form the overall stiffness matrix and overall mass matrix.

[0050] Furthermore, force analysis and displacement calculation are performed on each finite element unit, specifically:

[0051] The calculation formula for the maximum bending stress of the tunnel portal under each finite element unit is:

[0052]

[0053] In the above formula, σ e is the maximum bending stress change of the e-th finite element, M e is the bending moment of the e-th finite element on the tunnel end face, Δu(e) is the displacement change of the tunnel portal section of the e-th finite element under earthquake action, and I is the moment of inertia of the tunnel section;

[0054] The moment of inertia I of the tunnel portal section is specifically:

[0055]

[0056] Where d is the inner diameter of the tunnel portal;

[0057] The calculation formula for the maximum axial stress in the tunnel portal section is:

[0058]

[0059] In the above formula, β e is the maximum axial stress of the tunnel portal section under the e-th finite element unit, F e is the axial force at the tunnel portal under earthquake action of the e-th finite element, A e is the area of ​​the end face at the tunnel entrance under the e-th finite element;

[0060] Get the seismic fortification length L of the tunnel seismic The expression is:

[0061]

[0062] In the above formula, L is the total length of the tunnel, and Δu is the displacement change of the tunnel portal section under the action of earthquake under all finite element units.

[0063] Furthermore, the tunnel portal section is discretized into multiple finite element units, specifically: the tunnel portal is divided into multiple finite elements, each unit is connected by nodes, and then the corresponding material properties are assigned to the tunnel lining, surrounding rock and grouting reinforcement layer, and the boundary conditions of the model are determined.

[0064] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0065] The present invention determines the seismic fortification length of the tunnel by analyzing the stress and displacement changes of the foundation beam units in the tunnel under the action of an earthquake. This can more accurately simulate the actual stress conditions of the tunnel structure and improve the reliability of the design results. The finite element model of spatial variation distribution can more accurately evaluate the response of the tunnel portal section under the action of an earthquake, thereby optimizing the seismic design and improving the safety performance of the tunnel. By analyzing the displacement and stress changes of the tunnel under the action of an earthquake, the weak links in the seismic resistance can be identified, which helps to take corresponding reinforcement measures to reduce the impact of the earthquake on the tunnel structure, thereby playing an important role in ensuring tunnel safety, reducing economic losses and improving engineering benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0067] The following is a further description of the method for calculating the seismic fortification length of the tunnel portal section of the present invention with reference to the accompanying drawings;

[0068] Figure 1 It is a flow chart of the method for calculating the seismic fortification length of a tunnel portal section provided by the present invention. DETAILED DESCRIPTION

[0069] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0070] In order to better understand the purpose, structure and function of the present invention, the present invention is further described in detail below with reference to the accompanying drawings.

[0071] like Figure 1 As shown, the present invention provides a method for calculating the seismic fortification length of a tunnel portal section, comprising the following steps:

[0072] Determine the scope of the tunnel portal section;

[0073] The mechanical parameters of the foundation beam unit in the tunnel portal section are collected and analyzed to obtain the statistical analysis results and random distribution functions of the mechanical parameters;

[0074] Under boundary conditions, a finite element model of spatial variation distribution of tunnel portal section is established by using statistical analysis results of mechanical parameters and random distribution function.

[0075] By introducing the tunnel lateral deformation coefficient and axial deformation coefficient and based on the finite element model of the spatial variation distribution of the tunnel portal section, the displacement change of the tunnel under the action of earthquake is obtained.

[0076] A stress-displacement analysis is performed on the tunnel portal section to obtain the maximum bending stress change and maximum axial stress change at the tunnel portal, and analysis is performed to determine the seismic fortification length of the tunnel portal section.

[0077] It should be noted that: by combining the calculation results of the finite element method and taking into account other factors, such as the influence of the free surface of the portal section, the properties of the surrounding rock and the cross-sectional form of the tunnel, according to the seismic fortification requirements of the tunnel, the setting of longitudinal steel bars and grouting reinforcement, the maximum seismic fortification length of the tunnel is determined. This length is the minimum length of the tunnel that can maintain structural safety under the action of an earthquake.

[0078] Performing statistical analysis on the mechanical parameters of the foundation beam unit in the tunnel portal section to obtain statistical analysis results of the mechanical parameters and a random distribution function; wherein performing statistical analysis on the mechanical parameters of the foundation beam unit in the tunnel portal section to obtain statistical analysis results of the mechanical parameters includes:

[0079] Analyze the material properties of the foundation beam unit in the tunnel portal section, including elastic modulus, Poisson's ratio, and shear modulus;

[0080] The statistical analysis results P(E) of the elastic modulus E of the material are as follows:

[0081]

[0082] In the above formula, P(E) is the statistical analysis result of the elastic modulus of the material, σ E is the standard deviation of the elastic modulus of the material, μ E is the mean value of the elastic modulus E of the material;

[0083] The statistical analysis results of the Poisson's ratio v of the material, P(v), are as follows:

[0084]

[0085] In the above formula, P(v) is the statistical analysis result of the Poisson's ratio of the material, σ V is the standard deviation of the Poisson's ratio of the material, μ Eis the mean value of the Poisson's ratio v of the material;

[0086] The statistical analysis results of the shear modulus G of the material are as follows:

[0087]

[0088] In the above formula, P(G) is the statistical analysis result of the shear modulus of the material, σ G is the standard deviation of the shear modulus of the material, μ G is the mean shear modulus of the material.

[0089] It should be noted that the size and shape of the finite element unit should be reasonably selected according to the geometric dimensions and geological conditions of the tunnel; material properties include elastic modulus, Poisson's ratio, density, tensile strength, compressive strength, etc.; the seismic wave input method can choose simple harmonic waves or actual seismic waves, and the propagation direction, frequency and amplitude of the seismic waves should be considered.

[0090] Statistical analysis is performed on the mechanical parameters of the foundation beam unit in the tunnel portal section to obtain statistical analysis results and a random distribution function of the mechanical parameters; wherein the random distribution function of the mechanical parameters obtained by statistical analysis of the mechanical parameters of the foundation beam unit is specifically:

[0091]

[0092] In the above formula, ∑ -1 [·] is the covariance matrix, and f(E, v, G) is the random distribution function of the elastic modulus, Poisson's ratio, and shear modulus of the material.

[0093] Under boundary conditions, a finite element model of the spatial variation distribution of the tunnel portal section is established using the statistical analysis results of mechanical parameters and random distribution functions. Specifically:

[0094] Based on the statistical analysis results of mechanical parameters, the spatial random distribution characteristics of mechanical parameters are obtained;

[0095] Using the spatial random distribution characteristics, the tunnel portal section is discretized into multiple finite element units, and each finite element unit is divided into categories to determine the number of categories of mechanical parameters;

[0096] By using random distribution function and assigning random amplitude to each finite element, a finite element model of spatial variation distribution of tunnel portal section is established.

[0097] The process of establishing the finite element model of the spatial variation distribution of the tunnel portal section is specifically as follows:

[0098] Assume that the geometric area of ​​the tunnel portal is Ω, which is discretized into N finite element units; each finite element unit has e = 1, 2, ..., N; the spatial area corresponding to each finite element unit is Ωe ;

[0099] Each finite element is classified into the following categories:

[0100] Assign different mechanical parameter categories C to each finite element e，j , and is represented by a random distribution function f(E,v,G), where j = 1, 2, ...; represents the number of the category of the mechanical parameter; e is the number of the finite element unit, where e = 1, 2, ...n;

[0101] F e，j (x)=Pr[f(E,ν,G)∈C e，j ]

[0102] In the above formula, F e，j (x) is the position X of each finite element, Pr[f(E,ν,G)∈C e，j ] indicates that the mechanical parameters fall into the mechanical parameter category C e，j probability;

[0103] According to the random distribution function, a random amplitude is assigned to each finite element, and a finite element model of the spatial variation distribution of the tunnel portal section is established. Specifically:

[0104] For each finite element e, at the Xth position, the random amplitude of the mechanical parameter The expression is:

[0105]

[0106] In the above formula, Δf(E,ν,G) is the perturbation term of the mechanical parameters generated by the random process.

[0107] The tunnel lateral deformation coefficient and axial deformation coefficient are introduced, and based on the finite element model of the spatial variation distribution of the tunnel portal section, the displacement change of the tunnel under the action of an earthquake is obtained, specifically:

[0108] According to the mechanical parameters after random amplitude, the displacement of the tunnel portal under different loads is obtained;

[0109] The stress analysis and displacement of each finite element unit are calculated, and the lateral deformation coefficient and axial deformation coefficient of the tunnel are introduced to obtain the displacement change of the tunnel under earthquake action for each finite element unit.

[0110] It should be noted that the maximum bending stress and maximum axial stress of the tunnel lining reflect the lateral and axial deformation characteristics of the tunnel under earthquake action. Based on these two deformation coefficients, the earthquake wave shape displacement equation is modified to more accurately describe the displacement changes of the tunnel under earthquake action.

[0111] The force analysis and displacement of each finite element unit are calculated, and the lateral deformation coefficient and axial deformation coefficient of the tunnel are introduced to obtain the displacement change of the tunnel under the action of the earthquake for each finite element unit, which is specifically:

[0112] Assuming that the vibration caused by the earthquake is expressed as a time function f(t), the displacement change Δu of the tunnel portal section under the earthquake under each finite element unit is:

[0113] Δu(t)=(η1+η2)u(t)

[0114] In the above formula, η1 is the lateral deformation coefficient, η2 is the axial deformation coefficient, and u(t) is the displacement change of the tunnel portal section under normal circumstances.

[0115] A stress-displacement analysis was performed on the tunnel portal section to obtain the maximum bending stress change and the maximum axial stress change of the tunnel portal, specifically:

[0116] By performing force analysis and displacement calculation on each finite element unit, and inputting the seismic waves into the spatially variable distribution finite element model of the tunnel portal section in the form of acceleration time history, and solving it using finite element software, the maximum bending stress change and maximum axial stress change of the tunnel portal section under the action of earthquake are obtained. Then, the stiffness matrix and mass matrix of all finite element units are assembled according to the nodes to form the overall stiffness matrix and overall mass matrix.

[0117] Perform force analysis and displacement calculation on each finite element, specifically:

[0118] The calculation formula for the maximum bending stress of the tunnel portal under each finite element unit is:

[0119]

[0120] In the above formula, σ e is the maximum bending stress change of the e-th finite element, M e is the bending moment of the e-th finite element on the tunnel end face, Δu(e) is the displacement change of the tunnel portal section of the e-th finite element under earthquake action, and I is the moment of inertia of the tunnel section;

[0121] The moment of inertia I of the tunnel portal section is specifically:

[0122]

[0123] Where d is the inner diameter of the tunnel portal;

[0124] The calculation formula for the maximum axial stress in the tunnel portal section is:

[0125]

[0126] In the above formula, β e is the maximum axial stress of the tunnel portal section under the e-th finite element unit, F e is the axial force at the tunnel portal under earthquake action of the e-th finite element, A e is the area of ​​the end face at the tunnel entrance under the e-th finite element;

[0127] Get the seismic fortification length L of the tunnel seismic The expression is:

[0128]

[0129] In the above formula, L is the total length of the tunnel, and Δu is the displacement change of the tunnel portal section under the action of earthquake under all finite element units.

[0130] The method of discretizing the tunnel portal section into multiple finite element units is as follows: the tunnel portal is divided into multiple finite elements, each of which is connected by nodes, and then the corresponding material properties are assigned to the tunnel lining, surrounding rock and grouting reinforcement layer, and the boundary conditions of the model are determined.

[0131] It should be noted that the maximum bending stress and maximum axial stress of the tunnel lining reflect the lateral and axial deformation characteristics of the tunnel under earthquake action. Based on these two deformation coefficients, the earthquake wave shape displacement equation is modified to more accurately describe the displacement changes of the tunnel under earthquake action.

[0132] It should be noted that these mechanical parameters also include the portal's free-facing surface, surrounding rock characteristics, and tunnel cross-section. Under seismic loads, the portal tunnel lining generates significant axial stress. To enhance the tunnel's seismic performance, longitudinal reinforcement is required to provide additional support and stability. Parameters such as the number, diameter, and spacing of the reinforcement should be determined based on specific design requirements to ensure that the reinforcement effectively absorbs and distributes stress during earthquakes, preventing lining damage.

[0133] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus the necessary hardware platform. Based on this understanding, the essence of the above technical solution or the portion that contributes to the existing technology can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to perform the operations or control methods described in each embodiment or certain parts of the embodiment.

[0134] Those skilled in the art will appreciate that embodiments of the present invention may be implemented in a variety of forms, including as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may also be implemented as a computer program product on a computer-usable storage medium, including computer-usable program code.

[0135] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the seismic fortification length of a tunnel portal section, characterized in that: The following steps are involved: Determine the scope of the tunnel portal section; The mechanical parameters of the foundation beam unit in the tunnel portal section are collected and analyzed to obtain statistical analysis results and random distribution functions of the mechanical parameters. The statistical analysis results of the mechanical parameters of the foundation beam unit in the tunnel portal section include: Analyze the material properties of the foundation beam unit in the tunnel portal section, including elastic modulus, Poisson's ratio, and shear modulus; The statistical analysis results P(E) of the elastic modulus E of the material are as follows: In the above formula, P(E) is the statistical analysis result of the elastic modulus of the material, σ E is the standard deviation of the elastic modulus of the material, μ E is the mean value of the elastic modulus E of the material; The statistical analysis results of the Poisson's ratio v of the material, P(v), are as follows: In the above formula, P(v) is the statistical analysis result of the Poisson's ratio of the material, σ V is the standard deviation of the Poisson's ratio of the material, μ E is the mean value of the Poisson's ratio v of the material; The statistical analysis results of the shear modulus G of the material are as follows: In the above formula, P(G) is the statistical analysis result of the shear modulus of the material, σ G is the standard deviation of the shear modulus of the material, μ G is the mean shear modulus of the material; The mechanical parameters of the foundation beam unit are statistically analyzed to obtain the random distribution function of the mechanical parameters, which is specifically: In the above formula, ∑ -1 [·] is the covariance matrix, f(E, v, G) is the random distribution function of the elastic modulus, Poisson’s ratio, and shear modulus of the material; Under boundary conditions, a finite element model of the spatial variation distribution of the tunnel portal section is established using the statistical analysis results of mechanical parameters and random distribution functions. Specifically: Based on the statistical analysis results of mechanical parameters, the spatial random distribution characteristics of mechanical parameters are obtained; Using the spatial random distribution characteristics, the tunnel portal section is discretized into multiple finite element units, and each finite element unit is divided into categories to determine the number of categories of mechanical parameters; Using random distribution function, random amplitude is assigned to each finite element to establish a finite element model of spatial variation distribution of tunnel portal section. By introducing the tunnel lateral deformation coefficient and axial deformation coefficient and based on the finite element model of the spatial variation distribution of the tunnel portal section, the displacement change of the tunnel under the action of earthquake is obtained. The process of establishing the finite element model of the spatial variation distribution of the tunnel portal section is as follows: Assume that the geometric area of ​​the tunnel portal is Ω, which is discretized into N finite element units; each finite element unit has e = 1, 2, ..., N; the spatial area corresponding to each finite element unit is Ω e ; Each finite element is classified into the following categories: Assign different mechanical parameter categories C to each finite element e，j , and is represented by a random distribution function f(E,v,G), where j = 1, 2, ...; represents the number of the category of the mechanical parameter; e is the number of the finite element unit, where e = 1, 2, ...n; F e，j (x)=Pr[f(E,v,G)∈C e，j , In the above formula, F e，j (x) is the position X of each finite element, Pr[f(E,v,G)∈C e，j ] indicates that the mechanical parameters fall into the mechanical parameter category C e，j probability; According to the random distribution function, a random amplitude is assigned to each finite element, and a finite element model of the spatial variation distribution of the tunnel portal section is established. Specifically: For each finite element e, at the Xth position, the random amplitude of the mechanical parameter The expression is: In the above formula, Δf(E, v, G) is the perturbation term of the mechanical parameters generated by the random process; A stress-displacement analysis is performed on the tunnel portal section to obtain the maximum bending stress change and maximum axial stress change at the tunnel portal, and analysis is performed to determine the seismic fortification length of the tunnel portal section.

2. The method for calculating the seismic-resistant preset length of a tunnel portal according to claim 1, characterized in that: The tunnel lateral deformation coefficient and axial deformation coefficient are introduced, and based on the finite element model of the spatial variation distribution of the tunnel portal section, the displacement change of the tunnel under the action of earthquake is obtained, specifically: According to the mechanical parameters after random amplitude, the displacement of the tunnel portal under different loads is obtained; The stress analysis and displacement of each finite element unit are calculated, and the lateral deformation coefficient and axial deformation coefficient of the tunnel are introduced to obtain the displacement change of the tunnel under earthquake action for each finite element unit.

3. The method for calculating the seismic preset length of a tunnel portal according to claim 2, characterized in that: The force analysis and displacement of each finite element unit are calculated, and the lateral deformation coefficient and axial deformation coefficient of the tunnel are introduced to obtain the displacement change of the tunnel under the action of the earthquake for each finite element unit, which is specifically: Assuming that the vibration caused by the earthquake is expressed as a time function f(t), the displacement change Δu of the tunnel portal section under the earthquake under each finite element unit is: Δu(t)=(η1+η2)u(t) In the above formula, η1 is the lateral deformation coefficient, η2 is the axial deformation coefficient, and u(t) is the displacement change of the tunnel portal section under normal circumstances.

4. The method for calculating the seismic-resistant preset length of a tunnel portal according to claim 1, characterized in that: A stress-displacement analysis was performed on the tunnel portal section to obtain the maximum bending stress change and the maximum axial stress change of the tunnel portal, specifically: By performing force analysis and displacement calculation on each finite element unit, and inputting the seismic waves into the spatially variable distribution finite element model of the tunnel portal section in the form of acceleration time history, and solving it using finite element software, the maximum bending stress change and maximum axial stress change of the tunnel portal section under the action of earthquake are obtained. Then, the stiffness matrix and mass matrix of all finite element units are assembled according to the nodes to form the overall stiffness matrix and overall mass matrix.

5. The method for calculating the seismic-resistant preset length of a tunnel portal according to claim 4, characterized in that: Perform force analysis and displacement calculation on each finite element, specifically: The calculation formula for the maximum bending stress of the tunnel portal under each finite element unit is: In the above formula, σ e is the maximum bending stress change of the e-th finite element, M e is the bending moment of the e-th finite element on the tunnel end face, Δu(e) is the displacement change of the tunnel portal section of the e-th finite element under earthquake action, and I is the moment of inertia of the tunnel section; The moment of inertia I of the tunnel portal section is specifically: Where d is the inner diameter of the tunnel portal; The calculation formula for the maximum axial stress in the tunnel portal section is: In the above formula, β e is the maximum axial stress of the tunnel portal section under the e-th finite element unit, F e is the axial force at the tunnel portal under earthquake action of the e-th finite element, A e is the area of ​​the end face at the tunnel entrance under the e-th finite element; Get the seismic fortification length L of the tunnel seismic The expression is: In the above formula, L is the total length of the tunnel, and Δu is the displacement change of the tunnel portal section under the action of earthquake under all finite element units.

6. The method for calculating the seismic-resistant preset length of a tunnel portal according to claim 1, characterized in that: The method of discretizing the tunnel portal section into multiple finite element units is as follows: the tunnel portal is divided into multiple finite elements, each of which is connected by nodes, and then the corresponding material properties are assigned to the tunnel lining, surrounding rock and grouting reinforcement layer, and the boundary conditions of the model are determined.

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