Seismic SH wave scattering analysis solving method and device, equipment and storage medium

Abstract

The invention discloses an analytical solution method and device for seismic SH wave scattering of a lining tunnel in a composite rock stratum, equipment and a storage medium. The method comprises the following steps: constructing a composite rock stratum analysis model and a lining tunnel analysis model according to a preset coordinate system; according to the composite rock stratum analysis model and the lining tunnel analysis model, a composite rock stratum SH wave field and a lining tunnel SH wave field are constructed respectively; according to the scattered wave field of each soil layer and the scattered wave field of the tunnel boundary, obtaining a series type solution of the scattered wave fields of the composite rock stratum and the lining tunnel; and finally, calculating the dynamic stress concentration coefficient of the lining tunnel in the composite rock stratum through calculation software according to the analytic solution when the seismic SH wave is propagated, so that the dynamic stress concentration coefficient of the scattered wave field of the lining tunnel can be accurately and quickly calculated, and the method can be conveniently applied to actual engineering.

Description

Technical Field

[0001] The invention relates to the field of elastic wave scattering, and in particular to an analytical solution method, device, equipment and storage medium for seismic SH wave scattering of a lining tunnel in a composite rock layer. Background Art

[0002] Earthquakes belong to endogenous dynamic geological effects. Rock vibrations are transmitted through rock particles in the form of elastic waves. The destructive consequences of earthquakes are directly or indirectly related to seismic waves. Studying seismic waves has become the basic work for studying and predicting earthquakes. Composite strata are often composed of two or more strata with different physical and mechanical parameters. The most typical combinations are "soft on top and hard on bottom" and "hard on top and soft on bottom". When the composite strata are "hard on top and soft on bottom", the lower soft soil has better stability because the upper hard soil layer supports the lower soft soil. If the composite strata are "soft on top and hard on bottom", the upper soft soil often has the problem of instability of the excavation surface during excavation. The composite strata not only bring many technical difficulties to the construction of tunnels, but also because the mechanical parameters of the composite strata are changing, the scattered wave fields of each soil layer interfere with each other, which causes great difficulties in the study of seismic waves.

[0003] When seismic waves propagate and encounter tunnel boundaries, secondary waves will be generated at the boundaries, which is also called wave scattering. At the same time, the stress at the edge of the tunnel will suddenly change, forming dynamic stress concentration. Therefore, the discussion of structural dynamic stress concentration is an important topic in elastic wave research. In actual engineering, the geological conditions are complex and changeable, and seismic motion is greatly affected by site type and propagation path. Site differences have a great impact on the propagation of seismic waves of different frequencies. Therefore, the elastic wave scattering problem of tunnels lined in composite strata is a technical problem that needs to be solved urgently.

[0004] The information disclosed in this background technology section is only intended to enhance the understanding of the overall background of the invention and should not be regarded as an acknowledgment or any form of suggestion that the information constitutes the prior art already known to a person skilled in the art. Summary of the invention

[0005] The purpose of the present invention is to provide an accurate and fast calculation method for solving the problem of the response of a lining tunnel to seismic waves.

[0006] The present invention provides an analytical solution method for seismic SH wave scattering, which is applied to a lining tunnel in a composite rock layer, comprising the steps of:

[0007] Construct composite rock formation analysis model and lining tunnel analysis model according to the preset coordinate system;

[0008] According to the composite rock formation analysis model and the lining tunnel analysis model, the composite rock formation SH wave field and the lining tunnel SH wave field are constructed respectively by using the segmentation and fitting method; wherein,

[0009] The construction of the composite rock stratum SH wave field and the lining tunnel SH wave field comprises: constructing the scattered wave field of each soil layer in the composite rock stratum and the scattered wave field of the tunnel boundary based on the wave function expansion method and the complex variable function method;

[0010] Establishing a set of equations in series form according to the scattered wave fields of the soil layers and the scattered wave fields of the tunnel boundary, and calculating analytical solutions of the set of equations by Fourier transform and truncated finite term method;

[0011] The dynamic stress concentration factor of the lining tunnel in the composite rock layer during the propagation of the earthquake SH wave is calculated by calculation software according to the analytical solution.

[0012] Preferably, in an embodiment of the present invention, the construction of the composite rock formation analysis model and the lining tunnel analysis model includes:

[0013] Dividing the composite rock formation into a plurality of sub-regions according to different physical and mechanical parameters within the composite rock formation;

[0014] Establishing a corresponding coordinate system according to each of the sub-areas;

[0015] A composite rock formation analysis model and a lining tunnel analysis model are constructed according to the coordinate system.

[0016] Preferably, in the embodiment of the present invention, the sub-areas include: a lower soil layer area, a surface soil layer area and a lining tunnel area.

[0017] Preferably, in an embodiment of the present invention, the construction of the composite rock formation SH wave field and the lining tunnel SH wave field includes:

[0018] Establishing corresponding complex planes according to each of the coordinate systems by complex variable function method;

[0019] According to the parameters in each of the complex planes, on the basis of the wave function expansion method and the complex variable function method, a large arc is set and the arc boundary is used to simulate the straight line boundary, and the coordinate translation method and the Hankel series are used to construct the scattered wave fields of the boundaries of each soil layer in the composite rock layer and the scattered wave fields of the lining tunnel boundary respectively.

[0020] Preferably, in an embodiment of the present invention, constructing the scattered wave field of each boundary in the composite rock formation includes:

[0021] displacement field and corresponding stresses of the incident wave in the underlying soil region;

[0022] The boundary of the lower soil layer region generates a displacement field and corresponding stress of scattered waves in the lower soil layer region and the surface soil layer region respectively;

[0023] The boundary of the surface soil layer region generates a displacement field of scattered waves and corresponding stress in the lower soil layer region and the surface soil layer region respectively;

[0024] The boundary of the lined tunnel area generates a displacement field of scattered waves and corresponding stress in the surface soil layer area.

[0025] Preferably, in an embodiment of the present invention, constructing the SH wave field of the lining tunnel includes:

[0026] SH waves are scattered waves at the inner and outer boundaries of the lining tunnel respectively.

[0027] Preferably, in an embodiment of the present invention, calculating the analytical solution of the system of equations includes:

[0028] The lower boundary of the surface soil layer region satisfies boundary conditions of displacement continuity and radial stress continuity;

[0029] The upper boundary of the surface soil layer region satisfies the boundary condition of radial stress freedom;

[0030] The outer wall of the lined tunnel satisfies the boundary conditions of displacement continuity and radial stress continuity;

[0031] The inner wall of the lined tunnel satisfies the boundary condition of radial stress freedom.

[0032] In another aspect of the present invention, there is also provided an analytical solution device for seismic SH wave scattering, comprising:

[0033] A model building unit, used to build a composite rock formation analysis model and a lining tunnel analysis model according to a preset coordinate system;

[0034] The SH wave field construction unit is used to construct the composite rock formation SH wave field and the lining tunnel SH wave field respectively according to the composite rock formation analysis model and the lining tunnel analysis model by using the segmentation and fitting method; wherein,

[0035] The construction of the composite rock stratum SH wave field and the lining tunnel SH wave field comprises: constructing the scattered wave field of each soil layer in the composite rock stratum and the scattered wave field of the tunnel boundary based on the wave function expansion method and the complex variable function method;

[0036] An equation group calculation unit, used for establishing an equation group in series form according to the scattered wave fields of the soil layers and the scattered wave fields of the tunnel boundary, and calculating the analytical solution of the equation group by Fourier transformation and truncated finite term method;

[0037] The dynamic stress coefficient calculation unit is used to calculate the dynamic stress coefficient of the lining tunnel in the composite rock layer when the earthquake SH wave propagates according to the analytical solution through calculation software.

[0038] On the other hand, an analytical solution device for seismic SH wave scattering is provided; the analytical solution device for seismic SH wave scattering includes a computer program stored on a medium, and the computer program includes program instructions. When the program instructions are executed by a computer, the computer executes the methods described in the above aspects and achieves the same technical effects.

[0039] In another aspect of the embodiment of the present invention, a storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, each step of the analytical solution method for seismic SH wave scattering as described in any one of the above items is implemented.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] In the present invention, firstly, a composite rock formation analysis model and a lining tunnel analysis model are constructed according to a preset coordinate system; secondly, according to the composite rock formation analysis model and the lining tunnel analysis model, a composite rock formation SH wave field and a lining tunnel SH wave field are constructed respectively, so that the scattering wave field of each soil layer in the composite rock formation and the scattering wave field of the tunnel boundary can be obtained; according to the scattering wave field of each soil layer and the scattering wave field of the tunnel boundary, a series solution of the scattering wave field of the composite rock formation and the lining tunnel is obtained; finally, according to the analytical solution, the dynamic stress concentration factor of the lining tunnel in the composite rock formation when the earthquake SH wave propagates is calculated by calculation software, and the present invention can accurately and quickly calculate the dynamic stress concentration factor of the scattering wave field of the lining tunnel, so that it is easy to be applied to actual engineering.

[0042] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention and implement it according to the contents of the specification, and to make the above and other purposes, technical features and advantages of the present invention easier to understand, one or more preferred embodiments are listed below and described in detail with the accompanying drawings as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0044] Figure 1 It is a step diagram of the analytical solution method for seismic SH wave scattering described in the present invention;

[0045] Figure 2 It is a schematic diagram of a lined tunnel in a composite rock formation under the action of an earthquake SH wave according to the present invention;

[0046] Figure 3 is a schematic diagram of constructing a composite rock formation SH wave field according to the present invention;

[0047] Figure 4 is a schematic diagram of constructing the SH wave field of the lined tunnel according to the present invention;

[0048] Figure 5 It is a schematic diagram of the calculation results of the dynamic stress coefficient calculation software of the lining tunnel in the composite rock layer under the action of the earthquake SH wave described in the present invention;

[0049] Figure 6 It is a schematic diagram of the structure of the analytical solution device for seismic SH wave scattering described in the present invention;

[0050] Figure 7 It is a schematic diagram of the structure of the analytical solution device for seismic SH wave scattering described in the present invention. DETAILED DESCRIPTION

[0051] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific implementation modes.

[0052] Unless explicitly stated otherwise, throughout the specification and claims, the term “comprise” or variations such as “include” or “comprising”, etc., will be understood to include the stated elements or components but not to exclude other elements or components.

[0053] In this document, the terms "first", "second", etc. are used to distinguish two different elements or parts, and are not used to limit a specific position or relative relationship. In other words, in some embodiments, the terms "first", "second", etc. can also be interchangeable.

[0054] Embodiment 1

[0055] In order to solve the problem of the response of lined tunnels to seismic waves, such as Figure 1 As shown, in an embodiment of the present invention, an analytical solution method for seismic SH wave scattering is provided, which is applied to a lining tunnel in a composite rock layer, and includes the steps of:

[0056] S11. constructing a composite rock formation analysis model and a lining tunnel analysis model according to a preset coordinate system;

[0057] In the embodiment of the present invention, the composite rock formation analysis model and the lining tunnel analysis model are constructed, including:

[0058] The composite rock formation is divided into multiple sub-regions according to different physical and mechanical parameters in the composite rock formation;

[0059] Establish a corresponding coordinate system according to each sub-area;

[0060] The composite rock formation analysis model and the lining tunnel analysis model are constructed according to the coordinate system.

[0061] Preferably, in an embodiment of the present invention, the composite rock formation is divided into sub-regions according to different physical and mechanical parameters of the composite rock formation, which may include: a lower soil layer region, a surface soil layer region and a lining tunnel region.

[0062] In specific application scenarios, when constructing composite rock formation analysis models and lining tunnel analysis models, such as Figure 2 As shown in the figure, the analysis of the lining tunnel in the composite rock layer under the action of earthquake SH wave is carried out. The lower soil layer area is the blue area I, the surface soil layer area is the yellow area II, and the thickness is h , the upper boundary of region II is T U Indicated by T D It indicates that the gray area III is the lined tunnel area, which is located in the surface soil layer. The distance between the center O2 and the upper boundary of the surface soil layer is h1, and the distance from the lower boundary is h2.

[0063] A vertical line can be drawn from the center O2 of the lining tunnel to the depth of the lower soil layer. A point O1 is taken on the vertical line to establish the spatial overall rectangular coordinate system X1Y1Z1. Two arcs are drawn with O1 as the center. The two arcs are tangent to the upper and lower boundaries of the surface soil layer area respectively. Then the upper boundary T of the surface soil layer area is U Become an arc Lower boundary T D Become an arc The center of the circle O2 is the local rectangular coordinate system X2Y2Z2 in space. The green plane represents the wavefront of the plane SH wave. The vibration direction of the SH wave is parallel to the Z axis, but the angle between the propagation direction and the X axis is α0. Since the problem we are studying belongs to the plane strain problem, it is simplified to the problem on the XY plane. θ1 and θ2 are the angle variables in the coordinate systems X1O1Y1 and X2O2Y2 respectively. The arc The corresponding radius is R U , arc The corresponding radius is R D , the outer diameter of the lining is b, the inner diameter is a, and the densities of the lower soil layer area, surface soil layer area and lining tunnel area in the composite rock formation analysis model are ρ1, ρ2, ρ3 respectively; the shear moduli are μ1, μ2, μ3 respectively; the shear wave velocities are c1, c2, c3 respectively; and the wave numbers of SH waves are k1, k2, k3 respectively.

[0064] S12, according to the composite rock formation analysis model and the lining tunnel analysis model, using the segmentation and fitting method to construct the composite rock formation SH wave field and the lining tunnel SH wave field respectively; wherein,

[0065] The construction of the composite rock stratum SH wave field and the lining tunnel SH wave field comprises: constructing the scattered wave field of each soil layer in the composite rock stratum and the scattered wave field of the tunnel boundary based on the wave function expansion method and the complex variable function method;

[0066] In the embodiment of the present invention, constructing the composite rock SH wave field and the lining tunnel SH wave field includes:

[0067] According to each coordinate system, the corresponding complex plane is established by the complex variable function method;

[0068] According to the parameters in each complex plane, on the basis of wave function expansion method and complex variable function method, a large circle arc is set and the arc boundary is used to simulate the straight line boundary. The coordinate translation method and Hankel series are used to construct the scattered wave fields of the boundaries of each soil layer in the composite rock layer and the scattered wave fields of the lining tunnel boundary respectively.

[0069] Furthermore, in an embodiment of the present invention, constructing the scattered wave fields of each boundary in the composite rock formation includes:

[0070] The displacement field and corresponding stress of the incident wave in the underlying soil region;

[0071] The boundary of the lower soil layer area generates the displacement field and corresponding stress of the scattered wave in the lower soil layer area and the surface soil layer area respectively;

[0072] The boundary of the surface soil layer area generates the displacement field and corresponding stress of the scattered wave in the lower soil layer area and the surface soil layer area respectively;

[0073] The boundary of the tunnel lining generates a displacement field and corresponding stress of scattered waves in the surface soil layer.

[0074] In constructing the lining tunnel SH wave field, including:

[0075] SH waves are scattered waves at the inner and outer boundaries of the lining tunnel respectively.

[0076] Specifically, the steps of constructing the composite rock SH wave field and the lining tunnel SH wave field are as follows:

[0077] S121. Introduce complex functions to describe the rectangular coordinate system. The complex plane corresponding to the rectangular coordinate system X1O1Y1 is Where z1=X1+iY1, Similarly, the complex plane corresponding to the rectangular coordinate system X2O2Y2 is Where z2=X2+iY2, The geometric parameters in the two complex planes have the following relationship:

[0078] h=h1+h2,R U =h+R D , z2=z1-i(R D +h2)

[0079] S122. According to the segmentation and matching method, firstly construct the scattering wave field of the circular hole problem in the composite rock formation;

[0080] Construct the SH wave field of composite rock formations, such as Figure 3 As shown, the incident wave, the boundaries of each soil layer and the radius are given as b The scattered wave field of the circular hole.

[0081] Incident wave W (i) The displacement field and the corresponding stress in the lower soil region can be expressed as:

[0082]

[0083] From the asymptotic property of the Hankel wave function, we know that all the scattered waves propagating outwards caused by the cylindrical surface can be written as the series solution form expanded by the first kind of Hankel function, and all the scattered waves propagating inwards can be written as the series solution form expanded by the second kind of Hankel wave function, thus constructing the form of the scattered waves in each coordinate system:

[0084] In the complex plane Inner, lower boundary The scattered wave W generated in the lower soil layer (S1) The displacement field and corresponding stress can be expressed as:

[0085]

[0086] In the complex plane Inner, lower boundary The scattered wave W generated in the surface soil layer (S2) The displacement field and corresponding stress can be expressed as:

[0087]

[0088]

[0089] Using the coordinate translation method, in the complex plane The plane can be expressed as:

[0090]

[0091] In the complex plane The scattered wave W generated by the circular hole boundary T1 (i.e. the boundary of the lining tunnel area) in the surface soil layer area (S3) The displacement field and corresponding stress can be expressed as:

[0092]

[0093] Using the coordinate translation method, in the complex plane It can be expressed as:

[0094]

[0095] In the complex plane Inside, border The scattered wave W generated in the surface soil layer (S4) The displacement field and the corresponding stress can be expressed as:

[0096]

[0097] Using the coordinate translation method, in the complex plane The plane can be expressed as:

[0098]

[0099] S123, construct SH wave field of lined tunnel;

[0100] like Figure 4 As shown, it is necessary to construct the standing wave field inside the lining:

[0101] In the complex plane In the example, the scattered wave excited by the SH wave at the outer boundary T1 of the lining tunnel is:

[0102]

[0103] The scattered waves excited by SH waves at the inner boundary T2 of the lining tunnel are:

[0104]

[0105] S13, establishing a system of equations in series form according to the scattered wave fields of the soil layers and the scattered wave fields of the tunnel boundary, and calculating analytical solutions of the system of equations by Fourier transform and truncated finite term method;

[0106] In the embodiment of the present invention, the boundary conditions are combined to form an equation, and the two ends are expanded by Fourier series according to the angular variable θ, which will result in an infinite set of equations containing infinite unknown coefficients. According to the attenuation property of the Hankel function, finite terms are taken for m and n while ensuring accuracy, and the above-mentioned set of equations in step S12 can be transformed into a finite linear set of equations, and the unknown constants are solved to obtain an analytical solution to the problem.

[0107] Preferably, the upper and lower boundaries of the surface soil layer region satisfy the following boundary conditions:

[0108] Upper displacement continuous:

[0109] Upper radial stress continuity:

[0110]

[0111] Upper radial stress free:

[0112]

[0113] The outer wall and inner wall of the lined tunnel meet the following boundary conditions:

[0114] Upper displacement continuous:

[0115] Upper radial stress continuity:

[0116] Upper radial stress free:

[0117] S14. Calculate the dynamic stress concentration factor of the lining tunnel in the composite rock layer when the earthquake SH wave propagates according to the analytical solution through calculation software.

[0118] In the embodiment of the present invention, the following function may be defined:

[0119] c * =c2 / c1, c # =c3 / c1,ρ * =ρ2 / ρ1,ρ # =ρ3 / ρ1, k * =k2 / k1, k # =k3 / k1, from k=ω / c, we know that

[0120] In order to facilitate the analysis, each medium parameter is dimensionless, and the dimensionless results are also used in the analysis of the results.

[0121] The material parameters that need to be input when using the calculation software are the density ratio and wave number ratio of rock layer I and rock layer II, and the density ratio and wave number ratio of the lining tunnel and rock layer I. The software will automatically convert the four variable relationships according to the above formula. The size parameters that need to be input are the ratio of the buried depth of the lining tunnel to the thickness of the surface rock layer, and the thickness ratio of the tunnel. By changing the parameters for calculation, the influence of the tunnel thickness on the results can be obtained.

[0122] The drawing interface can calculate the dynamic stress concentration factor of the outer wall and inner wall of the lining tunnel respectively. By adjusting different incident wave frequencies and clicking the calculation icon "Outer wall DSCF calculation" or "Inner wall DSCF calculation", a rectangular coordinate diagram of the relationship between the dynamic stress coefficient (DSCF) and the 360-degree position of the tunnel can be drawn.

[0123] Click the line color icon to switch the line to blue, red, green, and yellow. Drag the line width slider to change the line width of the image.

[0124] In order to facilitate the user to input parameters, this software presets material parameters, which is based on the common geological situation that the upper rock layer is softer than the lower rock layer. The tunnel is made of concrete, and the upper and lower limits of each parameter are set. It is a reasonable value range obtained by converting common rock and soil and structural materials. Click the default calculation to get the calculation results of the dynamic stress coefficient of the lining tunnel in the composite rock layer under the action of earthquake SH waves. The specific results are as follows Figure 5 shown.

[0125] In summary, in the embodiment of the present invention, firstly, a composite rock formation analysis model and a lining tunnel analysis model are constructed according to a preset coordinate system; secondly, according to the composite rock formation analysis model and the lining tunnel analysis model, the composite rock formation SH wave field and the lining tunnel SH wave field are respectively constructed, so that the scattering wave field of each soil layer in the composite rock formation and the scattering wave field of the tunnel boundary can be obtained; according to the scattering wave field of each soil layer and the scattering wave field of the tunnel boundary, a series solution of the scattering wave field of the composite rock formation and the lining tunnel is obtained; finally, according to the analytical solution, the dynamic stress concentration factor of the lining tunnel in the composite rock formation when the earthquake SH wave propagates is calculated by the calculation software. According to the present invention, the dynamic stress concentration factor of the scattering wave field of the lining tunnel can be accurately and quickly calculated, so that it is easy to be applied to actual engineering.

[0126] Embodiment 2

[0127] Corresponding to the method embodiment, in another aspect of the embodiment of the present invention, a device for analyzing and solving seismic SH wave scattering is also provided. Figure 6 The schematic diagram of the structure of the analytical solution device for earthquake SH wave scattering provided by the embodiment of the present invention is shown. The analytical solution device for earthquake SH wave scattering is Figure 1The device corresponding to the analytical solution method of seismic SH wave scattering described in the corresponding embodiment, that is, the device is implemented by means of a virtual device. Figure 1 The analytical solution method for earthquake SH wave scattering in the corresponding embodiment, each virtual module constituting the analytical solution device for earthquake SH wave scattering can be executed by an electronic device, such as a network device, a terminal device or a server. Specifically, the analytical solution device for earthquake SH wave scattering in the embodiment of the present invention includes:

[0128] Model building unit 01, used to build a composite rock formation analysis model and a lining tunnel analysis model according to a preset coordinate system;

[0129] In the embodiment of the present invention, the composite rock formation analysis model and the lining tunnel analysis model are constructed, including:

[0130] The composite rock formation is divided into multiple sub-regions according to different physical and mechanical parameters in the composite rock formation;

[0131] Establish a corresponding coordinate system according to each sub-area;

[0132] The composite rock formation analysis model and the lining tunnel analysis model are constructed according to the coordinate system.

[0133] Preferably, in an embodiment of the present invention, the composite rock formation is divided into sub-regions according to different physical and mechanical parameters of the composite rock formation, which may include: a lower soil layer region, a surface soil layer region and a lining tunnel region.

[0134] The SH wave field construction unit 02 is used to construct the composite rock formation SH wave field and the lining tunnel SH wave field respectively according to the composite rock formation analysis model and the lining tunnel analysis model by using the segmentation and fitting method; wherein,

[0135] The construction of the composite rock stratum SH wave field and the lining tunnel SH wave field comprises: constructing the scattered wave field of each soil layer in the composite rock stratum and the scattered wave field of the tunnel boundary based on the wave function expansion method and the complex variable function method;

[0136] In the embodiment of the present invention, constructing the composite rock SH wave field and the lining tunnel SH wave field includes:

[0137] According to each coordinate system, the corresponding complex plane is established by the complex variable function method;

[0138] According to the parameters in each complex plane, on the basis of wave function expansion method and complex variable function method, a large circle arc is set and the arc boundary is used to simulate the straight line boundary. The coordinate translation method and Hankel series are used to construct the scattered wave fields of the boundaries of each soil layer in the composite rock layer and the scattered wave fields of the lining tunnel boundary respectively.

[0139] Furthermore, in an embodiment of the present invention, constructing the scattered wave fields of each boundary in the composite rock formation includes:

[0140] The displacement field and corresponding stress of the incident wave in the underlying soil region;

[0141] The boundary of the lower soil layer area generates the displacement field and corresponding stress of the scattered wave in the lower soil layer area and the surface soil layer area respectively;

[0142] The boundary of the surface soil layer area generates the displacement field and corresponding stress of the scattered wave in the lower soil layer area and the surface soil layer area respectively;

[0143] The boundary of the tunnel lining generates a displacement field and corresponding stress of scattered waves in the surface soil layer.

[0144] In constructing the lining tunnel SH wave field, including:

[0145] SH waves are scattered waves at the inner and outer boundaries of the lining tunnel respectively.

[0146] The equation group calculation unit 03 is used to establish an equation group in the form of a series according to the scattered wave fields of the soil layers and the scattered wave fields of the tunnel boundary, and calculate the analytical solution of the equation group by Fourier transformation and truncated finite term method;

[0147] In the embodiment of the present invention, the upper and lower boundaries of the surface soil layer region satisfy the following boundary conditions:

[0148] Upper displacement continuous:

[0149] Upper radial stress continuity:

[0150]

[0151] Upper radial stress free:

[0152]

[0153] The outer wall and inner wall of the lined tunnel meet the following boundary conditions:

[0154] Upper displacement continuous:

[0155] Upper radial stress continuity:

[0156] Upper radial stress free:

[0157] The dynamic stress coefficient calculation unit 04 is used to calculate the dynamic stress coefficient of the lining tunnel in the composite rock layer when the earthquake SH wave propagates according to the analytical solution through calculation software.

[0158] In the embodiment of the present invention, the material parameters that need to be input when using the calculation software are the density ratio and wave number ratio of rock layer I and rock layer II, and the density ratio and wave number ratio of the lining tunnel and rock layer I. The software will automatically convert the four variable relationships according to the above formula. The dimensional parameters that need to be input are the ratio of the buried depth of the lining tunnel to the thickness of the surface rock layer, and the thickness ratio of the tunnel. By changing the parameters for calculation, the influence of the tunnel thickness on the analysis result can be obtained.

[0159] It should be noted that the specific implementation method and technical effect of the analytical solution device for seismic SH wave scattering in the embodiment of the present invention can be referred to Figure 1 The corresponding analytical solution method for seismic SH wave scattering will not be elaborated here.

[0160] Embodiment 3

[0161] Corresponding to the method embodiment, in the embodiment of the present invention, there is also provided an analytical solution device for earthquake SH wave scattering, such as a terminal, a server, etc. Among them, the server can be an independent physical server, or a server cluster or a distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, etc., but is not limited thereto.

[0162] An example of a hardware structure block diagram of an analytical solution device for earthquake SH wave scattering provided by an embodiment of the present invention is shown in FIG. Figure 7 As shown, it may include:

[0163] Processor 1, communication interface 2, memory 3 and communication bus 4;

[0164] The processor 1, the communication interface 2, and the memory 3 communicate with each other via the communication bus 4;

[0165] Optionally, the communication interface 2 may be an interface of a communication module, such as an interface of a GSM module;

[0166] The processor 1 may be a central processing unit CPU, or an application-specific integrated circuit ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement the embodiments of the present application.

[0167] The memory 3 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0168] The processor 1 is specifically used to execute the computer program stored in the memory 3 to perform the following steps:

[0169] S11. constructing a composite rock formation analysis model and a lining tunnel analysis model according to a preset coordinate system;

[0170] S12, according to the composite rock formation analysis model and the lining tunnel analysis model, using the segmentation and fitting method to construct the composite rock formation SH wave field and the lining tunnel SH wave field respectively; wherein,

[0171] The construction of the composite rock stratum SH wave field and the lining tunnel SH wave field comprises: constructing the scattered wave field of each soil layer in the composite rock stratum and the scattered wave field of the tunnel boundary based on the wave function expansion method and the complex variable function method;

[0172] S13, establishing a system of equations in series form according to the scattered wave fields of the soil layers and the scattered wave fields of the tunnel boundary, and calculating analytical solutions of the system of equations by Fourier transform and truncated finite term method;

[0173] S14. Calculate the dynamic stress concentration factor of the lining tunnel in the composite rock layer when the earthquake SH wave propagates according to the analytical solution through calculation software.

[0174] The above product can execute the method provided by the embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method. For technical details not fully described in this embodiment, please refer to the analytical solution method for seismic SH wave scattering provided by the embodiment of the present invention.

[0175] Embodiment 4

[0176] In an embodiment of the present invention, a storage medium is further provided, which may store a program suitable for execution by a processor, wherein the program is used to:

[0177] S11. constructing a composite rock formation analysis model and a lining tunnel analysis model according to a preset coordinate system;

[0178] S12, according to the composite rock formation analysis model and the lining tunnel analysis model, using the segmentation and fitting method to construct the composite rock formation SH wave field and the lining tunnel SH wave field respectively; wherein,

[0179] The construction of the composite rock stratum SH wave field and the lining tunnel SH wave field comprises: constructing the scattered wave field of each soil layer in the composite rock stratum and the scattered wave field of the tunnel boundary based on the wave function expansion method and the complex variable function method;

[0180] S13, establishing a system of equations in series form according to the scattered wave fields of the soil layers and the scattered wave fields of the tunnel boundary, and calculating analytical solutions of the system of equations by Fourier transform and truncated finite term method;

[0181] S14. Calculate the dynamic stress concentration factor of the lining tunnel in the composite rock layer when the earthquake SH wave propagates according to the analytical solution through calculation software.

[0182] Optionally, the detailed functions and extended functions of the program may refer to the above description.

[0183] The above product can execute the method provided by the embodiment of the present invention, and has the functional modules and beneficial effects corresponding to the execution method. For technical details not described in detail in this embodiment, please refer to the methods provided by other embodiments of the present invention.

[0184] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example 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 performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0185] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interface, device or unit, which can be electrical, mechanical or other forms.

[0186] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0187] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0188] It should be understood that in the embodiments of the present application, the various embodiments and features can be combined with each other to solve the aforementioned technical problems.

[0189] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0190] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those 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 application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An analytical solution method for seismic SH wave scattering, applied to lined tunnels in composite rock formations, characterized in that: Includes steps: Construct composite rock formation analysis model and lining tunnel analysis model according to the preset coordinate system; According to the composite rock formation analysis model and the lining tunnel analysis model, the composite rock formation SH wave field and the lining tunnel SH wave field are constructed respectively by using the segmentation and fitting method; wherein, The construction of the composite rock stratum SH wave field and the lining tunnel SH wave field comprises: constructing the scattered wave field of each soil layer in the composite rock stratum and the scattered wave field of the tunnel boundary based on the wave function expansion method and the complex variable function method; Establishing a set of equations in series form according to the scattered wave fields of the soil layers and the scattered wave fields of the tunnel boundary, and calculating analytical solutions of the set of equations by Fourier transform and truncated finite term method; The dynamic stress concentration factor of the lining tunnel in the composite rock layer during the propagation of the earthquake SH wave is calculated by calculation software according to the analytical solution.

2. The analytical solution method for earthquake SH wave scattering according to claim 1, characterized in that: The construction of the composite rock formation analysis model and the lining tunnel analysis model comprises: Dividing the composite rock formation into a plurality of sub-regions according to different physical and mechanical parameters within the composite rock formation; Establishing a corresponding coordinate system according to each of the sub-areas; A composite rock formation analysis model and a lining tunnel analysis model are constructed according to the coordinate system.

3. The analytical solution method for earthquake SH wave scattering according to claim 2, characterized in that: The sub-areas include: a lower soil layer area, a surface soil layer area and a lining tunnel area.

4. The analytical solution method for earthquake SH wave scattering according to claim 3 is characterized in that: The method of constructing the composite rock formation SH wave field and the lining tunnel SH wave field comprises: Establishing corresponding complex planes according to each of the coordinate systems by complex variable function method; According to the parameters in each of the complex planes, on the basis of the wave function expansion method and the complex variable function method, a large arc is set and the arc boundary is used to simulate the straight line boundary, and the coordinate translation method and the Hankel series are used to construct the scattered wave fields of the boundaries of each soil layer in the composite rock layer and the scattered wave fields of the lining tunnel boundary respectively.

5. The analytical solution method for earthquake SH wave scattering according to claim 4, characterized in that: Constructing the scattered wave fields of each boundary in the composite rock formation, including: displacement field and corresponding stresses of the incident wave in the underlying soil region; The boundary of the lower soil layer region generates a displacement field and corresponding stress of scattered waves in the lower soil layer region and the surface soil layer region respectively; The boundary of the surface soil layer region generates a displacement field of scattered waves and corresponding stress in the lower soil layer region and the surface soil layer region respectively; The boundary of the lined tunnel area generates a displacement field of scattered waves and corresponding stress in the surface soil layer area.

6. The analytical solution method for earthquake SH wave scattering according to claim 5, characterized in that: Constructing the SH wave field of the lining tunnel includes: SH waves are scattered waves at the inner and outer boundaries of the lining tunnel respectively.

7. The analytical solution method for earthquake SH wave scattering according to claim 1, characterized in that: Calculating an analytical solution to the system of equations includes: The lower boundary of the surface soil layer region satisfies boundary conditions of displacement continuity and radial stress continuity; The upper boundary of the surface soil layer region satisfies the boundary condition of radial stress freedom; The outer wall of the lined tunnel satisfies the boundary conditions of displacement continuity and radial stress continuity; The inner wall of the lined tunnel satisfies the boundary condition of radial stress freedom.

8. An analytical solution device for earthquake SH wave scattering, characterized in that: include: A model building unit, used to build a composite rock formation analysis model and a lining tunnel analysis model according to a preset coordinate system; The SH wave field construction unit is used to construct the composite rock formation SH wave field and the lining tunnel SH wave field respectively according to the composite rock formation analysis model and the lining tunnel analysis model by using the segmentation and fitting method; wherein, The construction of the composite rock stratum SH wave field and the lining tunnel SH wave field comprises: constructing the scattered wave field of each soil layer in the composite rock stratum and the scattered wave field of the tunnel boundary based on the wave function expansion method and the complex variable function method; An equation group calculation unit, used for establishing an equation group in series form according to the scattered wave fields of the soil layers and the scattered wave fields of the tunnel boundary, and calculating an analytical solution of the equation group by Fourier transform and truncated finite term method; The dynamic stress coefficient calculation unit is used to calculate the dynamic stress coefficient of the lining tunnel in the composite rock layer when the earthquake SH wave propagates according to the analytical solution through calculation software.

9. An analytical solution device for earthquake SH wave scattering, characterized in that: include: Memory for storing computer programs; A processor is used to call and execute the computer program to implement the steps of the analytical solution method for seismic SH wave scattering as described in any one of claims 1-7.

10. A storage medium, characterized in that: The method comprises a software program, wherein the software program is suitable for executing the steps of the analytical solution method for seismic SH wave scattering according to any one of claims 1 to 7 by a processor.

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