Method and system for calculating seismic oscillation amplification coefficient of river valley field under SV wave incidence

Abstract

The invention discloses a method and system for calculating a seismic oscillation amplification coefficient of a river valley field under SV wave incidence, and belongs to the technical field of rock-soil seismic engineering, and the method comprises the steps: building a model; analyzing an infinitesimal body; establishing a free field; establishing a scattering field; substituting boundary conditions; solving a matrix equation; and calculating an amplification coefficient. According to the method, a wave field caused by an irregular terrain of the earth surface is constructed by an interval decomposition strategy taking a terrain cuspidal point as a demarcation point, a method for calculating the seismic oscillation amplification coefficient of the river valley field under SV wave incidence is provided, and the influence of factors such as river valley geometric parameters, material parameters, the frequency and incident angle of incident waves and the like on the river valley seismic oscillation amplification coefficient is revealed; a theoretical basis is provided for aseismic design of major projects of river valleys; the calculation method is a semi-analytical method, reveals the physical nature of irregular terrains on seismic wave propagation and scattering, improves the calculation precision and efficiency, and can be used as a reference for verification of a numerical method.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of rock and earthquake engineering, and particularly relates to a method and system for calculating seismic amplification factor of valley site under SV wave incidence. BACKGROUND

[0002] In the region with many mountains and complex geological structure, when the seismic wave encounters local irregular topography such as valley during propagation, the scattering wave is generated, and the incident wave, reflected wave and scattering wave are superimposed on each other, causing the amplification, attenuation and spatial variation of the ground motion. The amplification effect of valley topography on the earthquake often aggravates the seismic disaster of the bridge, dam and other valley-crossing projects.

[0003] In order to evaluate the scattering amplification effect of valley topography on the ground motion, a method and system for calculating seismic amplification factor of valley site under SV wave incidence are provided. SUMMARY

[0004] The present application solves the technical problem of how to evaluate the scattering amplification effect of valley topography on the ground motion, and provides a method for calculating seismic amplification factor of valley site under SV wave incidence. The source point and the matching point in the method are the same set of points on the physical boundary of the model, and there is no need to set a false boundary outside the real physical boundary. By setting the source point intensity factor, the source point singularity problem of the basic solution is solved, the precision is ensured, and the calculation efficiency is improved.

[0005] The present application solves the above technical problems through the following technical scheme. The present application comprises the following steps:

[0006] S1: Model establishment

[0007] According to the topographic data, a corresponding two-dimensional V-shaped valley model is established;

[0008] S2: Micro-element analysis

[0009] A micro-element is selected in the V-shaped valley region, the stress and displacement relationship of the micro-element is analyzed, the valley displacement control equation, the stress free boundary condition of the valley surface and the horizontal ground surface are established;

[0010] S3: Free field establishment

[0011] The free field of the V-shaped valley model, i.e. the half-space free field u f is established.

[0012] S4: Scattering field establishment

[0013] An interval decomposition strategy taking the topographic sharp point as the dividing point is adopted, and the scattering field u sThat is, by arranging a set number of source points and collocation points on the boundary of the V-shaped valley model, displacement expression at the collocation points under the action of SV wave is obtained.

[0014] S5: Boundary condition substitution

[0015] The displacement and stress at the collocation points can be approximated as a linear combination of the fundamental solutions. When the collocation points coincide with the source points, the fundamental solutions will be singular. A source point intensity factor is proposed to solve the singularity problem. By substituting the displacement and stress expressions at the collocation points into the boundary conditions, corresponding matrix equations are established.

[0016] S6: Matrix equation solving

[0017] Solving the matrix equation, unknown coefficients are obtained and , and further, the scattering field and free field of the V-shaped valley model are obtained, and finally, the complete solution of the seismic wave field of the V-shaped valley model is obtained.

[0018] S7: Amplification coefficient calculation

[0019] According to the complete solution of the seismic wave field of the V-shaped valley model, the seismic ground motion amplification coefficient of the valley site under the action of SV wave is calculated.

[0020] Further, in the step S1, the V-shaped valley medium is assumed to be elastic, homogeneous and isotropic, and the material parameters are represented by mass density ρ, Poisson's ratio ν, SV wave velocity Vs, P wave velocity Vp, and Lame constants λ and μ; the incident wave of the V-shaped valley model is a column of plane harmonic SV wave with circular frequency ω, and the incident angle is θ.

[0021] Further, in the step S2, the displacement equation of the microelement is as follows:

[0022] ;

[0023] ;

[0024] Wherein, λ and μ are the Lame constants of the medium, u x and u y are the displacements in x and y directions, ρ is the mass density, t is the time, is the Laplace operator.

[0025] Further, in the step S2, the displacement of the medium in the Cartesian coordinate system is:

[0026] ;

[0027] ;

[0028] where x and y are the Cartesian coordinates in the V-shaped valley model, and ω is the circular frequency.

[0029] The displacement of the medium in the Cartesian coordinate system is substituted into the displacement equation of the micro-element to obtain the displacement control equation of the valley:

[0030] ;

[0031] ;

[0032] The stress free boundary conditions of the valley surface and the horizontal ground surface are as follows:

[0033] ;

[0034] where t f is the stress caused by the free field, t s is the stress caused by the scattering field, and x m is the collocation point in the V-shaped valley model.

[0035] Further, in the step S3, the expression of the half-space free field u f is as follows:

[0036] ;

[0037] ;

[0038] where U s is the amplitude of the incident SV wave, k is the wave number of the SV wave, , , , is the wave number of the P wave; , , ; o= ; the subscript 1 represents the x direction, the subscript 2 represents the y direction, k , , , and are parameters set for simplifying the formula expression.

[0039] Further, in the step S4, the displacement expression of the collocation point x m under the action of the SV wave is as follows:

[0040] ;

[0041] where a and b are unknown coefficients to be solved, and is the fundamental solution of displacement, and is the source point intensity factor, is the source point in the V-shaped valley model; when represents that the collocation point is located in the domain, represents that the collocation point is located on the boundary.

[0042] Further, in the step S5, the stress expression at the collocation point x m is as follows:

[0043] ;

[0044] wherein, and are the source point intensity factors, and are the fundamental solutions of stress.

[0045] Further, in the step S5, the specific processing process is as follows:

[0046] S51: the free field stress expression is obtained according to the half-space free field expression as follows:

[0047] ;

[0048] ;

[0049] wherein:

[0050] ;

[0051] ;

[0052] ;

[0053] S52: the scattered field stress expression and the free field stress expression are substituted into the ground surface stress free boundary condition formula, and the matrix equation is as follows:

[0054] ;

[0055] wherein, N represents the collocation point number of the valley surface and the horizontal ground surface;

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] .

[0062] Further, in the step S6, the matrix equation is solved to obtain unknown coefficients and , which are substituted into the expression of displacement and stress at the collocation points to obtain the scattering field of the V-shaped valley model and the free field ; the scattering field is added to the free field , and the complete wave field of the V-shaped valley model is obtained, that is:

[0063] ;

[0064] Wherein, i=1, 2 respectively correspond to x and y directions;

[0065] In the step S7, the calculation formula of the ground motion amplification factor of the valley site under the action of the SV wave is as follows:

[0066] ;

[0067] Wherein, AF is the ground motion amplification factor, i=1, 2 respectively correspond to the ground motion amplification factor of x and y directions, and i=1, 2 respectively correspond to the free field of x and y directions , and i=1, 2 respectively correspond to the scattering field of x and y directions.

[0068] The application also provides a valley site ground motion amplification factor calculation system under the incidence of the SV wave, which adopts the above calculation method to calculate the valley site ground motion amplification factor under the incidence of the SV wave, and comprises:

[0069] A model establishing module is used to establish a corresponding two-dimensional V-shaped valley model according to topographic data;

[0070] A micro-element analysis module is used to select a micro-element in the V-shaped valley region, analyze the stress and displacement relationship of the micro-element, establish a valley displacement control equation, and establish a stress free boundary condition of the valley surface and the horizontal ground surface;

[0071] A free field calculation module is used to establish the free field of the V-shaped valley model, that is, the half-space free field u f ;

[0072] A scattering field calculation module is used to adopt an interval decomposition strategy taking a topographic sharp point as a dividing point, and establish the scattering field u s ​that is, by arranging a set number of source points and matching points on the boundary of the V-shaped valley model, displacement expression of the matching points under the action of SV waves is obtained;

[0073] The matrix equation establishing module is used for putting forward the source point intensity factor for solving the singularity problem, and establishing the corresponding matrix equation by substituting the displacement and stress expressions at the matching points into the boundary conditions;

[0074] The matrix equation solving module is used for solving the matrix equation to obtain unknown coefficients and , further obtaining the scattering field and the free field of the V-shaped valley model, and finally obtaining the complete solution of the seismic wave field of the V-shaped valley model;

[0075] The amplification coefficient calculating module is used for calculating the seismic ground motion amplification coefficient of the valley site under the action of SV waves according to the complete solution of the seismic wave field of the V-shaped valley model.

[0076] Compared with the prior art, the present application has the following advantages:

[0077] (1) The interval decomposition strategy taking the terrain sharp point as the demarcation point is used to construct the wave field caused by the irregular terrain of the ground, a method for calculating the seismic ground motion amplification coefficient of the valley site under the action of SV waves is proposed, the influence of factors such as valley geometric parameters, material parameters, frequency and incidence angle of the incident wave on the valley seismic ground motion amplification coefficient is revealed, and theoretical basis is provided for the seismic design of major projects in the valley site.

[0078] (2) A method for calculating the seismic ground motion amplification coefficient of the valley site under the action of SV waves is proposed, the method is a semi-analytical method, the physical nature of the irregular terrain on the propagation and scattering of seismic waves is revealed, the calculation accuracy and efficiency are improved, and the method can also be used as a benchmark for verifying the numerical method. BRIEF DESCRIPTION OF DRAWINGS

[0079] Figure 1 is a flowchart of the method for calculating the seismic ground motion amplification coefficient of the valley site under the action of SV waves of the present application;

[0080] Figure 2 is a V-shaped valley model in the embodiment of the present application;

[0081] Figure 3 is a schematic diagram of stress of a microelement in the embodiment of the present application;

[0082] Figure 4 is a comparison diagram of the surface displacement amplitude results and the spectral element method results when the SV wave is vertically incident or obliquely incident in the second embodiment of the present application, wherein (a) is the horizontal direction (x direction) displacement amplitude result, and (b) is the vertical direction (y direction) displacement amplitude result;

[0083] Figure 5are the horizontal and vertical normalized surface displacement amplitudes (η=0.5) of the symmetric V-shaped valley with different depth-width ratios under the SV wave incidence in the third embodiment of the present application, wherein (a) is the horizontal displacement amplitude result, and (b) is the vertical displacement amplitude result;

[0084] Figure 6 is a structural schematic diagram of a valley site ground motion amplification coefficient calculation device under the SV wave incidence in the fourth embodiment of the present application. DETAILED DESCRIPTION

[0085] The embodiments of the present application are described in detail below, and the embodiments are implemented on the premise of the technical scheme of the present application, and detailed implementation manners and specific operation processes are given, but the protection scope of the present application is not limited to the following embodiments.

[0086] Embodiment one

[0087] As shown in the following table, the embodiments of the present application provide a method for calculating the ground motion amplification coefficient of a valley site under the SV wave incidence, which includes the following contents: Figures 1-6

[0088] Step 1: According to the terrain data, a corresponding two-dimensional V-shaped valley model is established;

[0089] Step 2: A microelement is selected in the V-shaped valley region, the stress and displacement relationship of the microelement is analyzed, and the valley displacement control equation and the stress free boundary condition of the valley surface and the horizontal ground surface are established;

[0090] Step 3: The free field of the V-shaped valley model, i.e., the half-space free field u f is established;

[0091] Step 4: The scattering field u s caused by the V-shaped valley model is established by the singular boundary method, and the expression of the V-shaped valley scattering field under the SV wave action is obtained by arranging a certain number of source points and matching points on the model boundary;

[0092] Step 5: The displacement and stress of the model matching point can be approximately linearly combined with the basic solution, and when the matching point coincides with the source point, the basic solution will be singular, therefore, the source point intensity factor solving the singularity problem is proposed. The expression of the displacement and stress of the matching point is substituted into the boundary condition, and the problem is solved;

[0093] Step 6: The matrix equation is solved to obtain the unknown coefficients and , and the displacement field and stress field of the valley model are further obtained, and finally the theoretical solution of the model is obtained;

[0094] Step 7: According to the above results, the convergence test and correctness verification of the ground surface displacement amplitude are performed; ​

[0095] Step 8: According to the above steps, the parameter analysis of the seismic amplification effect of the valley site under the action of SV wave is carried out, wherein the seismic amplification coefficient refers to the amplification coefficient of the displacement amplitude of the valley surface relative to the displacement amplitude of the horizontal ground surface;

[0096] Step 9: According to the above results, the corresponding seismic design is carried out for the valley site.

[0097] As more specifically, in step 1, according to the terrain data, a corresponding two-dimensional V-shaped valley model is established.

[0098] As shown in Figure 2 , the left half width of the V-shaped valley is denoted as b1, the right half width is denoted as b2, and the depth is denoted as d. If the valley is a symmetric V-shaped valley with symmetrical left and right banks, the half widths of the left and right sides are denoted as b (i.e. b1=b2=b).

[0099] It should be noted that in this embodiment, the scattering field is the scattering displacement field, and the free field is the flat free field.

[0100] In this embodiment, the valley medium is assumed to be elastic, homogeneous and isotropic, and the material parameters are represented by density ρ, Poisson's ratio ν, SV wave velocity Vs, P wave velocity Vp, and Lame constants λ and μ. The incident wave of the valley model is a column of plane harmonic SV wave with circular frequency ω, and the incident angle is θ.

[0101] As more specifically, in step 2, a micro-element body is selected in the valley area, and its force diagram is shown in Figure 3 .

[0102] Among them, the displacement equation of the micro-element body is:

[0103] (S1)

[0104] (S2)

[0105] Among them, λ and μ are the Lame constants of the medium, u x and u y are the displacements in x and y directions, ρ is the mass density, t is the time, is the Laplace operator.

[0106] As more specifically, in step 2, the displacement of the medium in the Cartesian coordinate system is:

[0107] (S3)

[0108] (S4)

[0109] Among them, x and y are the Cartesian coordinates in the model, and ω is the circular frequency.

[0110] Substituting equation (S3) and equation (S4) into equation (S1) and equation (S2) respectively, displacement control equations in frequency domain can be obtained as follows:

[0111] (S4.1)

[0112] (S4.2)

[0113] As more specifically, in step 2, in addition to satisfying the displacement control equations mentioned above, the displacement field and the stress field also need to satisfy the stress free boundary conditions of the valley surface and the horizontal ground surface:

[0114] (S5)

[0115] where t f is the stress caused by the free field, t s is the stress caused by the scattering field, and x m is the collocation point in the V-shaped valley model.

[0116] As more specifically, in step 3, the free field of the model is constructed.

[0117] The free field equation of the V-shaped valley model for scattering of plane SV waves is:

[0118] (S6)

[0119] (S7)

[0120] where U s is the amplitude of the incident SV wave, is the wave number of the SV wave, , , , is the wave number of the P wave. In addition, , , . The subscript 1 represents the x direction, the subscript 2 represents the y direction, k , , , and are parameters set for the expression of the simplified formula and have no actual physical meaning.

[0121] As more specifically, in step 4, by using the interval decomposition strategy with the terrain sharp point as the demarcation point, the singular boundary method is used to establish the scattering field u s caused by the V-shaped valley model.

[0122] The displacement expression of the collocation point x m under the action of SV wave is given by arranging a certain number of source points and collocation points on the boundary of the model (the expression of the scattered field is the displacement expression above):

[0123] (S8)

[0124] where, and are unknown coefficients to be solved, and are basic solutions of displacement, and are source point intensity factors. The subscript 1 represents the x direction, and the subscript 2 represents the y direction, is a source point in a two-dimensional V-shaped valley model. The formula is divided into two parts, when indicates that the collocation point is located in the domain, indicates that the collocation point is located on the boundary.

[0125] The expressions of the source point intensity factors and are as follows:

[0126] (S9)

[0127] where, L m represents half of the distance between the source point y n-1 and y n+1 , τ1 and τ2 are the components of the unit tangent vector in the x and y directions, respectively, and the expression of ξ is:

[0128] (S10)

[0129] where, is a parameter set for simplifying the expression of the formula, which has no actual physical meaning.

[0130] The expressions of the basic solutions of displacement and are as follows:

[0131] , (S11)

[0132] where,

[0133]

[0134] , is the Kronecker delta function, , K0 and K1 are the modified Bessel functions of the second kind of order 0 and 1, respectively, and r represents the collocation point xm The Euclidean distance between source point y n A and B are parameters set for the expression of simplified formula, without actual physical meaning.

[0135] It should be noted that the complete wave field of V-shaped valley is composed of the superposition of the scattering field and the free field on the flat ground:

[0136] (S12)

[0137] Where i = 1, 2 corresponds to the x and y directions.

[0138] As more specifically, in step 5, the displacement and stress at the model point x m may be approximated as a linear combination of the fundamental solutions.

[0139] In this embodiment, when the model point x m coincides with the source point y m , the fundamental solution will be singular.

[0140] In this embodiment, , , and are the source point intensity factors proposed to solve the singularity problem.

[0141] In this embodiment, the stress expression at the model point x m is:

[0142] (S13)

[0143] Where, and are the source point intensity factors, and are the fundamental solutions of stress.

[0144] The expressions of the source point intensity factors and are:

[0145] (S14)

[0146] The expressions of the fundamental solutions of stress and are:

[0147] (S15)

[0148] Where A' and B' represent the derivatives of A and B with respect to r, n1 and n2 represent the components of the unit outer normal vector in the x and y directions, respectively.

[0149] As more specifically, in step 5, the unknown coefficients in the scattered wavefield and can be obtained by the boundary condition equation (S5).

[0150] In equation (S5), the stress induced by the scattered field has been given by equation (S13).

[0151] The free-field stress expression is obtained by displacement expressions (S6) and (S7) as

[0152] (S16)

[0153] (S17)

[0154] where:

[0155] (S18)

[0156] (S19)

[0157] (S20)

[0158] As more specifically, in step 6, and Substituting into the surface stress free boundary condition equation (S5), the following matrix equation can be obtained:

[0159] (S21)

[0160] where N represents the number of collocation points on the valley surface and the horizontal surface;

[0161] (S22)

[0162] (S23)

[0163] (S24)

[0164] (S25)

[0165] (S26)

[0166] (S27)

[0167] As more specifically, solving the matrix equation (S21), the unknown coefficients and The scattering displacement field and stress field of the valley model can be obtained by substituting the above-mentioned results into formula (S8) and (S13).

[0168] As a more specific example, in step 6, the scattering displacement field and stress field are substituted into formula (S12) to obtain the complete solution of the seismic wave field in the valley region.

[0169] As a more specific example, in step 7, the ground motion amplification factor refers to the amplification factor of the displacement amplitude of the valley surface relative to the displacement amplitude of the horizontal ground surface. The calculation formula of the ground motion amplification factor of the valley site under the action of SV wave is as follows:

[0170] ;

[0171] Wherein, AF is the ground motion amplification factor, i=1, 2 respectively corresponds to the ground motion amplification factor of x and y direction, i=1, 2 respectively corresponds to the free field of x and y direction respectively corresponds to the free field of x and y direction respectively corresponds to the scattering field of x and y direction.

[0172] In this embodiment, after step 8 is completed, the influence of the depth-width ratio of the symmetrical V-shaped valley, the asymmetry of the two sides of the V-shaped valley, the dimensionless frequency of the incident SV wave and the incident direction on the ground motion amplification factor of the V-shaped valley site is mainly analyzed.

[0173] In the above-mentioned embodiment, according to the calculation results of the ground motion amplification factor of the V-shaped valley site, the amplification and attenuation effects of different regions of the valley site on the scattering of SV wave are judged.

[0174] The ground motion amplification factor AF refers to the amplification factor of the displacement amplitude of the valley surface relative to the displacement amplitude of the horizontal ground surface. When AF>1, it is considered that compared with the flat site, the valley site has ground motion amplification effect on SV wave; when AF<1, it is considered that the valley site attenuates SV wave. y Similarly.

[0175] It should be noted that the geometric parameters and material parameters of the V-shaped valley can be obtained according to the topographic and geological data, and the incident wave angle and dimensionless frequency can be obtained according to the seismic monitoring data. The relevant anti-seismic measures are taken in time for the significant region of the V-shaped valley scattering amplification effect.

[0176] Example Two

[0177] This embodiment provides a specific implementation case 1: the complete expression of the seismic wave field in the V-shaped valley region can be obtained by steps 1-6 in embodiment 1.

[0178] As a more specific example, in step 7: Figure 2The physical model is a symmetric V-shaped valley, and the calculation parameters are set as follows: the half-width of the valley b = 100 m, the depth d = 100 m, the density of the medium p = 2000 kg / m 3 , the shear modulus m = 100 MPa, the Poisson's ratio v = 0.25, and the wavelength of the incident SV wave l = 100 m. s

[0179] For the analysis of the calculation results below, the dimensionless frequency is defined as follows:

[0180] (S28)

[0181] In this embodiment, the valley is symmetric V-shaped, and b in the above formula is the half-width of the valley.

[0182] As a more specific example, in step 7, in order to ensure the convergence of the calculation results, the number of boundary points or the range of the horizontal surface boundary is increased, and the convergence of the normalized displacement amplitude of the horizontal and vertical standard surfaces of the V-shaped valley is analyzed.

[0183] As a more specific example, the dimensionless calculation parameters of the symmetric V-shaped valley model are as follows: d / b = 1, p = 1, V s = 1, and v = 0.25. The dimensionless frequency of the incident SV wave is 4, and the incident angle is 0°.

[0184] As a more specific example, the number of boundary points is increased, the length of the horizontal surface on the left and right sides of the valley is L = 10b, and the number of points N c on the surface of the V-shaped valley is 100, 140, 180, and 220, and the number of points N g on the single horizontal surface is 250, 350, 450, and 550, respectively. The convergence test results are shown in Table 1.

[0185] Table 1 Convergence test of normalized displacement amplitude (increasing the number of boundary points)

[0186]

[0187] Further, the range of the horizontal surface boundary is increased, the number of points N c on the surface of the V-shaped valley is 180, and L = 10b, L = 12b, and L = 14b correspond to N g of 450, 540, and 630, respectively. The convergence test results are shown in Table 2.

[0188] Table 2 Convergence test of normalized displacement amplitude (increasing the range of the horizontal surface boundary)

[0189]

[0190] ​Further, by verifying the increase of the number of boundary points and the increase of the horizontal ground surface boundary intercept range, the relative error of the displacement amplitude of most boundary points on the ground surface remains at 10 -3 The horizontal direction shows that the calculation method of the seismic amplification factor of the valley site under the SV wave proposed by the application has good numerical stability.

[0191] It should be noted that, as Figure 4 shown, in step 7, the calculation method proposed by the application is verified by comparing with the spectral element method calculation result.

[0192] Example three

[0193] This embodiment provides a specific implementation case 2: the material parameters of the valley medium are: ρ = 1, V s = 1, ν = 0.25. The dimensionless frequency of the incident SV wave is η = 0.5.

[0194] As a more specific, the depth-width ratio of the symmetric V-shaped valley is changed d / b = 0.5, d / b = 1.0, d / b = 1.5, d / b = 2.0, and the incident angle θ is 0°. The normalized ground surface displacement amplitude in the horizontal direction and the vertical direction of the symmetric V-shaped valley with different depth-width ratios is analyzed.

[0195] As a more specific, under this embodiment, the normalized ground surface displacement amplitude in the horizontal direction and the vertical direction of the symmetric V-shaped valley with different depth-width ratios is as Figure 5 shown.

[0196] In this embodiment, as Figure 5 shown, with the increase of the depth-width ratio of the V-shaped valley, the maximum value of the horizontal and vertical ground surface displacement amplitude tends to increase.

[0197] As a more specific, the frequency of the horizontal and vertical displacement amplitude fluctuation in the V-shaped valley region (-1 ≤ x / b ≤ 1) will significantly increase with the increase of the valley depth-width ratio.

[0198] As a more specific, according to the horizontal and vertical ground surface displacement amplitude at each point, the corresponding seismic amplification factor can be obtained:

[0199] (S29)

[0200] wherein, is the seismic amplification factor, i = 1, 2 respectively corresponds to the seismic amplification factor in the x and y directions, i = 1, 2 when respectively corresponds to the free field in the x and y directions, i = 1, 2 when respectively corresponds to the scattering field in the x and y directions.

[0201] The above phenomenon means that the topographic amplification effect of the valley with large depth-width ratio is more significant, which needs to be focused on.

[0202] Further, as shown in Figure 2 , the seismic wave is incident from the lower left corner, i.e. the left side of the valley is the windward side, and the right side of the valley is the leeward side.

[0203] Further, as shown in Figure 5 , the displacement amplitude of the windward side of the valley is often larger than that of the leeward side, and the fluctuation of the displacement amplitude of the windward side is more frequent.

[0204] Example Four

[0205] The device for calculating the ground motion amplification factor of the valley site under SV wave incidence in this embodiment comprises a computer input end, a computer processing end, a computer output end and a computer storage end, which are connected to each other.

[0206] The computer input end includes but is not limited to the geometric parameters and material parameters of the V-shaped valley, the input of the type, angle and dimensionless frequency of the seismic wave, and is used for the calculation of the ground motion amplification factor of the valley site.

[0207] The computer processing end is built-in with a variety of algorithms, including differential equation solving, stress and displacement control equation solving, wave field solving, boundary condition checking, precision control, etc., which are used for the calculation of the ground motion amplification factor of the valley site.

[0208] Whether the calculation result of the valley surface displacement amplitude meets the convergence and accuracy requirements is considered, if the relative error of the surface displacement amplitude of all boundary points remains at 10 -3 horizontal, it is considered to meet the convergence and accuracy requirements, and the next output end is entered, otherwise the computer processing end is adjusted and re-input.

[0209] The computer storage end is used for storing the computer program and the computer output result, the computer program includes program instructions, and the computer program is executed by one or more processors to realize the above-mentioned method for calculating the ground motion amplification factor of the valley site under SV wave incidence.

[0210] Although the embodiments of the present application have been shown and described above, it should be understood that the above-mentioned embodiments are exemplary and cannot be understood as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-mentioned embodiments within the scope of the present application.

Claims

1. A method for calculating a valley site ground motion amplification factor under SV wave incidence, characterized by, It comprises the following steps: S1: model establishment According to the topographic data, a corresponding two-dimensional V-shaped valley model is established; S2: micro-element analysis A micro-element is selected in the V-shaped valley region, the stress and displacement relationship of the micro-element is analyzed, the valley displacement control equation, the valley surface and the horizontal ground stress free boundary condition are established; S3: free field establishment Establishing the free field of V-shaped valley model, i.e. half-space free field u f ; S4: scattering field establishment The interval decomposition strategy with the terrain cusp as the demarcation point is adopted to establish the scattering field u caused by the V-shaped valley model by singular boundary method s That is, the displacement expression at the collocation point under the action of SV wave is obtained by arranging a certain number of source points and collocation points on the boundary of the V-shaped valley model. S5: boundary condition substitution The displacement and stress at the matching point can be approximately linear combination of the basic solution. When the matching point coincides with the source point, the basic solution will be singular. The source point intensity factor is proposed to solve the singularity problem. By substituting the expressions of displacement and stress at the matching point into the boundary condition, the corresponding matrix equation is established; S6: matrix equation solving Solving the matrix equation, the unknown coefficients are obtained and , and the scattering field and free field of the V-shaped valley model are further obtained, and finally the complete solution of the seismic wave field of the V-shaped valley model is obtained; S7: amplification coefficient calculation According to the complete solution of the seismic wave field of the V-shaped valley model, the valley site seismic amplification coefficient under the action of SV wave is calculated. 2.The method according to claim 1, wherein, In the step S1, the V-shaped valley medium is assumed to be elastic, homogeneous and isotropic, and the material parameters are represented by mass density ρ, Poisson's ratio ν, SV wave velocity Vs, P wave velocity Vp, and Lame constants λ and μ; the incident wave of the V-shaped valley model is a column of plane harmonic SV wave with circular frequency ω, and the incident angle is θ. 3.The method of claim 1, wherein, In the step S2, the displacement equation of the micro-element is as follows: ； ； where λ and μ are the Lame constants of the medium, u x and u y are the displacements in the x and y directions, respectively, p is the mass density, t is time, is the Laplacian operator. 4.The method of claim 3, wherein, In the step S2, the displacement of the medium in the Cartesian coordinate system is: ； ； Wherein, x and y are the Cartesian coordinates in the V-shaped valley model, and ω is the circular frequency; The displacement of the medium in the Cartesian coordinate system is substituted into the displacement equation of the micro-element to obtain the valley displacement control equation: ； ； The valley surface and the horizontal ground stress free boundary condition are as follows: ； where t f is the stress due to the free field, t s is the stress due to the scattered field, x m is the collocation point in the V-shaped valley model. 5.The method of claim 4, wherein, In said step S3, the half-space free field u f is expressed as follows: ； ； where U s is the amplitude of the incident SV wave, is the wave number of the SV wave, , , , is the wave number of the P wave; , , ; o= ; the 1 in the subscript indicates the x direction, and the 2 in the subscript indicates the y direction, k、 , , , and are parameters set for the purpose of simplifying the formula expression. 6.The method of claim 5, wherein, In the step S4, the displacement expression of the point x m under the SV wave action is as follows: ； where and are unknown coefficients to be determined, and are the basic solutions of displacement, and are the source intensity factors, is the source in the V-shaped valley model; when denotes that the collocation point is located in the domain, denotes that the collocation point is located on the boundary. 7.The method of claim 6, wherein, In the step S5, the stress expression at the point x m is as follows: ； wherein, and are source point intensity factors, and are the elementary solutions for stress. 8.The method of claim 7, wherein, In the step S5, the specific processing process is as follows: S51: the free field stress expression is obtained according to the free field expression of half space as follows: ； ； Wherein: ； ； ； S52: the scattering field stress expression and the free field stress expression are substituted into the ground stress free boundary condition formula to obtain the matrix equation as follows: ； Wherein, N represents the number of matching points of the valley surface and the horizontal ground; ； ； ； ； ； 。 9.The method of claim 1, wherein, In the step S6, the matrix equation is solved to obtain the unknown coefficients and After that, the expressions of displacement and stress at the collocation points are obtained by substituting the unknown coefficients into the expressions of displacement and stress at the collocation points, and the scattering field of the V-shaped valley model is obtained and the free field ; the complete wave field of the V-shaped valley model is obtained by adding the scattering field and the free field , that is: ； Wherein, i=1,2 respectively correspond to x and y directions; In the step S7, the calculation formula of the valley site seismic amplification coefficient under the action of SV wave is as follows: ； Wherein, AF is the ground motion amplification factor, i = 1, 2 respectively corresponding to the x and y direction ground motion amplification factor, i = 1, 2 when Corresponding to the x and y direction free field, i = 1, 2 when Corresponding to the x and y direction scattering field.

10. A system for calculating a valley site amplification factor of seismic motion under SV wave incidence, characterized by, The calculation method of any one of claims 1-9 is used to calculate the valley site seismic amplification coefficient under the action of SV wave, comprising: A model establishment module is configured to establish a corresponding two-dimensional V-shaped valley model according to topographic data; A micro-element analysis module is configured to select a micro-element in the V-shaped valley region, analyze the stress and displacement relationship of the micro-element, and establish a valley displacement control equation, a valley surface and a horizontal ground stress free boundary condition; a free field calculation module for establishing a free field of the V-shaped valley model, i.e. a half-space free field u f ; The scattering field calculation module is used for adopting an interval decomposition strategy with a terrain cusp as a demarcation point, establishing a V-shaped valley model caused scattering field u by a singular boundary method s That is, by arranging a set number of source points and matching points on the boundary of the V-shaped valley model, a displacement expression of the matching points in the V-shaped valley under the action of SV waves is obtained. A matrix equation establishment module is configured to propose a source point intensity factor to solve the singularity problem, and establish a corresponding matrix equation by substituting the expressions of displacement and stress at the matching point into the boundary condition; A matrix equation solving module is configured to solve a matrix equation to obtain unknown coefficients and , and further obtain a scattering field and a free field of the V-shaped valley model, and finally obtain a complete solution of the seismic wave field of the V-shaped valley model; An amplification coefficient calculation module is configured to calculate the valley site seismic amplification coefficient under the action of SV wave according to the complete solution of the seismic wave field of the V-shaped valley model.

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