Seismic wave slope terrain amplification effect analysis method and device and electronic equipment

Abstract

The invention provides a seismic wave side slope terrain amplification effect analysis method and device and electronic equipment, and the method comprises the steps: building a side slope analysis model, and setting a plurality of coordinate systems and the relation between the coordinate systems based on the side slope analysis model; a virtual boundary is introduced into the slope analysis model, sub-region division is carried out on the slope analysis model, and a free field displacement equation is determined; determining a wave function series solution meeting the sub-region stress boundary condition and the displacement boundary condition of the slope analysis model; and determining an optimal truncation item number according to each parameter of the slope analysis model and the incidence condition of the seismic wave. According to the method, the effectiveness and reliability of the seismic wave numerical algorithm can be tested and evaluated, the method has certain advantages in research of high-frequency problems, and the problem that an existing canyon terrain research method is poor in applicability is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of geological disaster prevention and control, and particularly to a method, device and electronic device for analyzing the amplification effect of seismic waves on slope terrain. Background Art

[0002] The surface terrain is considered to be one of the most important factors affecting the surface motion induced by earthquakes. For the propagation of seismic motion caused by terrain changes and the possible amplification effect, it has always attracted the attention and research of many scholars, and a series of practical research results have been obtained.

[0003] Since the 1970s, some scholars have established simplified models to describe the cross-section of real canyons. The symmetric V-shaped canyon model is the most basic and common simplified model. Many scholars have proposed different numerical simulation methods to study the scattering effect of SH waves induced by terrain. The Aki-Larner method proposed by Bouchon (1973), the asymptotic coefficient matching method proposed by Sabina and Willis (1975), the integral equation method proposed by Sills (1978), Sanchez-Sesma and Rosenblueth (1979), the hybrid finite element-analytical method proposed by Shah et al (1982), the hybrid finite-infinite element method proposed by Zhang and Zhao (1988), the complex variable function method proposed by Liu and Han (1991), and the boundary element method proposed by Hirai (1988), Takemiya and Fujiwara (1994) have all been widely used in the simulation of surface motion under earthquake action. For some simple geometric terrains, Paolucci (2002) proposed the method of separation of variables (MSV) to obtain strict analytical solutions. However, the above methods generally have problems such as difficult calculation, high computational resource requirements, and limited applicability. In particular, they are not applicable to the calculation and analysis of asymmetric terrains, and it is difficult to effectively obtain the general law of the amplification effect of seismic waves on slope terrain.

[0004] For the problem of poor applicability of existing canyon terrain research methods, no effective solution has been proposed yet. Summary of the Invention

[0005] The present invention provides a method, device and electronic device for analyzing the amplification effect of seismic waves on slope terrain, so as to solve the defect of poor applicability of existing canyon terrain research methods.

[0006] In a first aspect, the present invention provides a method for analyzing the amplification effect of seismic waves on slope terrain, including: Establishing a slope analytical model, and setting a plurality of coordinate systems and the relationships between the coordinate systems based on the slope analytical model; Introduce a virtual boundary into the slope analysis model, divide the slope analysis model into sub-regions, and determine the free-field displacement equation; Determine the wave function series solution that satisfies the sub-region stress boundary conditions and displacement boundary conditions of the slope analysis model; Determine the optimal truncation term number according to the various parameters of the slope analysis model and the incident situation of the seismic wave; Obtain several variables, perform parameter analysis on the slope analysis model, and determine the influence of each target parameter on the change of the local terrain displacement value and the displacement amplification factor of the slope.

[0007] According to an analysis method for the seismic wave slope terrain amplification effect provided by the present invention, set several coordinate systems and the relationships between the coordinate systems based on the slope analysis model, including: Based on the slope analysis model, set a global rectangular coordinate system, a polar coordinate system, and a local rectangular coordinate system; Determine the relationship between the global rectangular coordinate system and the local rectangular coordinate system.

[0008] According to an analysis method for the seismic wave slope terrain amplification effect provided by the present invention, introduce a virtual boundary into the slope analysis model, divide the slope analysis model into sub-regions, and determine the free-field displacement equation, including: Introduce a virtual boundary into the slope analysis model, and divide the slope analysis model into two sub-regions: an inner domain wave field and an outer domain wave field; Determine the stress boundary conditions of the slope analysis model, and generate a free-field displacement equation according to the slope analysis model.

[0009] According to an analysis method for the seismic wave slope terrain amplification effect provided by the present invention, determine the wave function series solution that satisfies the sub-region stress boundary conditions and displacement boundary conditions of the slope analysis model, including: Solve the motion equation in the sub-region of the slope analysis model to determine the corresponding wave field; Match the stress continuity condition and the displacement continuity condition at the virtual boundary of the sub-region of the slope analysis model to solve the unknown coefficients in the displacement field function of the sub-region of the slope model.

[0010] According to an analysis method for the seismic wave slope terrain amplification effect provided by the present invention, determine the optimal truncation term number according to the various parameters of the slope analysis model and the incident situation of the seismic wave, including: According to the various parameters of the slope analysis model and the incident situation of the seismic wave, select several special points and determine the displacement values of the special points; Select a number of displacement monitoring points and calculate the relative errors between the displacement monitoring points when different truncation terms are used. Determine the optimal number of truncation terms based on the calculation results of the relative errors.

[0011] According to an analysis method for the seismic wave slope terrain amplification effect provided by the present invention, determine the influence of each target parameter on the change of the slope local terrain displacement value, including: Adopt the dimensionless frequency representation method to normalize the displacement value of the incident wave. Select different slope angles and analyze the change of the slope local terrain displacement value.

[0012] According to an analysis method for the seismic wave slope terrain amplification effect provided by the present invention, the dimensionless frequency is determined by the ratio of the maximum width of the canyon to the incident wavelength.

[0013] According to an analysis method for the seismic wave slope terrain amplification effect provided by the present invention, determine the influence of each target parameter on the slope local terrain displacement amplification factor, including: Based on the terrain amplification effect, select different slope angles and analyze the change trend of the slope surface displacement amplification factor.

[0014] In a second aspect, the present invention also provides an analysis device for the seismic wave slope terrain amplification effect, including: A construction module for establishing a slope analytical model and setting a number of coordinate systems and the relationships between the coordinate systems based on the slope analytical model. A division module for introducing a virtual boundary into the slope analytical model, dividing the slope analytical model into sub-regions, and determining the free-field displacement equation. A determination module for determining the wave function series solution that satisfies the sub-region stress boundary conditions and displacement boundary conditions of the slope analytical model. A processing module for determining the optimal number of truncation terms according to the parameters of the slope analytical model and the incident situation of the seismic wave. An analysis module for obtaining a number of variables, performing parameter analysis on the slope analytical model, and determining the influence of each target parameter on the change of the slope local terrain displacement value and the displacement amplification factor.

[0015] In a third aspect, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the method described in the first aspect above is implemented.

[0016] Fourthly, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the method described in the first aspect above is implemented.

[0017] Fifthly, the present invention also provides a computer program product, including a computer program, and when the computer program is executed by a processor, the method described in the first aspect above is implemented.

[0018] Compared with the prior art, the present invention has the following beneficial effects: The method for analyzing the seismic wave slope terrain amplification effect provided by the present invention adopts the methods of domain decomposition and domain matching, decomposes the overall research area into different sub-regions, and respectively constructs the series solution of the wave function that conforms to the stress and displacement boundary conditions of the sub-regions under the excitation of plane SH waves. And the Graf addition theorem of the fractional-order Bessel function suitable for the slope analytical model is introduced to realize the wave function coordinate transformation from the local coordinate system to the global coordinate system. By using the stress continuity condition and displacement continuity condition on the virtual boundary, the undetermined coefficients in the wave field displacement function of the sub-region are solved, and the corresponding wave field displacement function solution of the sub-region is obtained. Through the above process, a strict analytical solution is obtained, which helps to test and evaluate the effectiveness and reliability of the seismic wave numerical algorithm, and has certain advantages in the research of high-frequency problems, and solves the problem of poor applicability of the existing canyon terrain research methods. Description of the Drawings

[0019] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the implementation examples or the description of the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to these drawings.

[0020] Figure 1 is the flowchart of the method for analyzing the seismic wave slope terrain amplification effect provided by the present invention; Figure 2 is the schematic diagram of the set of slope analytical models in the embodiment of the present invention; Figure 3 is the distribution diagram of the displacement monitoring points in the embodiment of the present invention; Figure 4 is the displacement change diagram of each reference point under different slope angle conditions in the embodiment of the present invention; Figure 5 is the change diagram of the displacement PDA of the reference point on the slope surface with the slope angle in the embodiment of the present invention; Figure 6 is the structural block diagram of the device for analyzing the seismic wave slope terrain amplification effect provided by the present invention; Figure 7 It is a schematic structural diagram of the electronic device provided by the present invention. Detailed implementation manners

[0021] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts shall fall within the protection scope of the present invention.

[0022] The present invention provides a method for analyzing the amplification effect of seismic waves on slope topography. Figure 1 It is a flowchart of the method for analyzing the amplification effect of seismic waves on slope topography provided by the present invention. As Figure 1 shown, the method includes the following steps: Step S101: Establish a slope analytical model, and set a plurality of coordinate systems and the relationships between the coordinate systems based on the slope analytical model; Step S102: Introduce a virtual boundary into the slope analytical model, divide the slope analytical model into sub-regions, and determine the free-field displacement equation; Step S103: Determine the series solution of the wave function that satisfies the sub-region stress boundary conditions and displacement boundary conditions of the slope analytical model; Step S104: Determine the optimal truncation number according to the parameters of the slope analytical model and the incident situation of the seismic wave; Step S105: Obtain a plurality of variables, perform parameter analysis on the slope analytical model, and determine the influence of each target parameter on the change of the local terrain displacement value of the slope and the displacement amplification coefficient.

[0023] In this method, first, a slope analytical model is constructed, and a plurality of coordinate systems participating in the analysis of the amplification effect of slope topography and the relationships between the coordinate systems are determined. Then, a virtual boundary is introduced, and the slope analytical model is divided into sub-regions to achieve regional decomposition. Then, a series solution of the wave function that conforms to the sub-region stress boundary conditions and displacement boundary conditions under the excitation of plane SH waves is constructed. Then, according to the parameters of the slope analytical model and the incident situation of the seismic wave, a convergence test is performed to determine the optimal truncation number. Finally, based on the slope analytical model, different variables are selected for parameter analysis to explore the influence of these parameters on the change of the local terrain displacement value of the slope and the displacement amplification coefficient (PDA).

[0024] In the above process, the methods of region decomposition and region matching are adopted. The overall research region is decomposed into different sub-regions, and the series solutions of wave functions that meet the stress and displacement boundary conditions of the sub-regions are constructed respectively under the excitation of plane SH waves. And the Graf addition theorem of the fractional-order Bessel function suitable for the slope analytical model is introduced to realize the coordinate transformation of the wave function from the local coordinate system to the global coordinate system. By using the stress continuity condition and displacement continuity condition on the virtual boundary, the undetermined coefficients in the wave field displacement function of the sub-region are solved, and the wave field displacement function solutions of the corresponding sub-regions are obtained. Through the above process, a strict analytical solution is obtained, which helps to test and evaluate the effectiveness and reliability of seismic wave numerical algorithms, and has certain advantages in the research of high-frequency problems, solving the problem of poor applicability of existing canyon terrain research methods.

[0025] In some of these embodiments, in step S101, a plurality of coordinate systems and the relationships between the coordinate systems are set based on the slope analytical model, including: based on the slope analytical model, a global rectangular coordinate system, a polar coordinate system, and a local rectangular coordinate system are set; the relationship between the global rectangular coordinate system and the local rectangular coordinate system is determined.

[0026] Specifically, assume that the incident wave is a line-source cylindrical SH wave, select a homogeneous, isotropic, linearly elastic semi-infinite medium, measure the parameters of the incident wave and the slope model in advance, and initially establish a slope analytical model. Based on the slope analytical model, set the origin and the directions of each coordinate axis of the original global rectangular coordinate system, polar coordinate system, local rectangular coordinate system, and polar coordinate system, and determine the relationship between the global rectangular coordinate system and the local rectangular coordinate system.

[0027] Exemplarily, assume that the angular frequency of the incident wave is , and the angle with the y-axis is . The half-width of the slope analytical model is a , the depth is d , the shear modulus is , and the shear wave velocity is . As shown in Figure 2 , Figure 2 is a schematic diagram of the set of slope analytical models in the embodiments of the present invention. The origins of the global rectangular coordinate system and the polar coordinate system are both set at the center of the top of the model. The origins of the local rectangular coordinate system and the polar coordinate system are set at the tip of the bottom of the slope, and the directions of each coordinate axis are as shown in the figure. The relationship between the global rectangular coordinate system and the local rectangular coordinate system is represented by , and is calculated from the geometric dimensions of the slope model.

[0028] In some of these embodiments, in step S102, a virtual boundary is introduced into the slope analysis model, the slope analysis model is divided into sub-regions, and the free-field displacement equation is determined, including: introducing a virtual boundary into the slope analysis model, dividing the slope analysis model into two sub-regions, namely the inner domain wave field and the outer domain wave field; determining the stress boundary conditions of the slope analysis model, and generating the free-field displacement equation according to the slope analysis model.

[0029] As Figure 2 shown, a semi-circular virtual boundary is introduced into the slope analysis model , and the model is divided into Region 1 and Region 2. In these two regions, the steady-state out-of-plane vibration needs to satisfy the Helmholtz equation:

[0030] Where represents the two-dimensional Laplace operator, represents the total displacement field of the region, and the subscripts represent Region 1 and Region 2 respectively, represents the wave number, where represents the angular frequency, represents the shear wave velocity. The stress boundary conditions of the horizontal ground surface and the canyon surface of the slope analysis model are determined by the following formulas:

[0031] Where represents the circumferential shear stress on the horizontal ground surface in Model Region 1, represents the circumferential shear stress on the horizontal ground surface in Model Region 2, represents the radial shear stress in Model Region 1, represents the shear modulus, represents the displacement field of Region 1, represents the displacement field of Region 2, r represents the polar radius of the original global polar coordinate system, represents the polar angle of the original global polar coordinate system, represents the polar radius of the local polar coordinate system, represents the polar angle of the local polar coordinate system, a represents the half-width of the slope analysis model. For a half-plane medium without any surface irregularities, the free-field displacement can be expressed as the sum of the incident wave and its reflected wave on the horizontal ground surface, that is:

[0032] Where represents the free-field displacement, i represents the imaginary unit, represents the wave number, and r represents the radius. The above formula is expanded by Jacobi-Anger, that is:

[0033] Among them, represents the Neumann factor. When n = 0, ; when n is 1, ; represents the Bessel function of the first kind of order n.

[0034] In some of these embodiments, in step S103, determining the wave function series solution that satisfies the sub-region stress boundary condition and displacement boundary condition of the slope analytical model includes: solving the motion equation in the sub-region of the slope analytical model to determine the corresponding wave field; applying the stress continuity condition and displacement continuity condition at the virtual boundary of the sub-region of the slope analytical model for matching, and solving the unknown coefficients in the displacement field function of the sub-region of the slope model.

[0035] Exemplarily, for the displacement boundary condition of region 1 (outer domain wave field), its total scattered wave field can be divided into two parts: and , that is . represents the scattered wave field without considering region 2, and it satisfies the following conditions:

[0036] where represents the Hankel function of the second kind of order n, and represent the derivative functions of the corresponding functions. The second part of the scattered wave field in region 1 represents the scattered wave field due to the presence of region 2, and it can be expressed as:

[0037] where the coefficient , is the unknown coefficient to be solved. The total displacement function of region 1 can be expressed as the sum of the free wave field displacement function without considering the scattered wave field and the wave field displacement function considering the influence of the scattered wave field:

[0038] where represents the free wave field displacement function without considering the scattered wave field, represents the wave field displacement function considering the influence of the scattered wave field.

[0039] For the displacement boundary condition of region 2 (inner domain wave field), the displacement field function is as follows:

[0040] where , , complex coefficients are the unknown coefficients to be determined, The value of is the slope angle plus 90°. If the displacement function in Region 2 is to be expressed in the global coordinate system , according to the Graf addition rule, the transformed displacement formula for Region 2 is as follows:

[0041] where m and n are integers. Combining the above formulas, we get:

[0042] where, .

[0043] For the virtual boundary at the junction of the open Region 1 and the closed Region 2 , the stress continuity condition and the displacement continuity condition need to be satisfied, that is:

[0044] where, represents the radial shear stress in Model Region 2. From the stress continuity condition, we get:

[0045] where, and are both unknown coefficients to be solved, , , . Through transformation, arrangement, and simplification, we get:

[0046] where: , , ; where: ; .

[0047] From the displacement continuity condition, we get:

[0048]

[0049] where: ; ; ; ; ; ; ; .

[0050] In the area Combining the above formulas, we can get:

[0051]

[0052] Furthermore, substituting into the above formula, we can get:

[0053]

[0054] From the above formula, after selecting the appropriate number of terms, the unknown coefficients can be solved by the standard matrix method For numerical calculations, it is very necessary to truncate the infinite series to finite terms. In the above formula, the summation index n and the weight index q are truncated to 2N-1 and N-1 terms respectively. The truncation term of the infinite series depends only on the required calculation accuracy. Once the unknown coefficients are obtained , then the unknown coefficients can be solved and .

[0055] In some of the embodiments, step S104, determining the optimal number of truncation items according to the various parameters of the slope analytical model and the incident conditions of the seismic waves, includes: selecting a number of special points according to the various parameters of the slope analytical model and the incident conditions of the seismic waves, and determining the displacement values ​​of the special points; selecting a number of displacement monitoring points, and calculating the relative errors between the displacement monitoring points when different numbers of truncation items are used; and determining the optimal number of truncation items according to the calculation results of the relative errors.

[0056] Exemplarily, n special points are selected according to various parameters of the model and the incident conditions of the seismic wave, and their displacement values ​​are calculated and outputted, and m equally spaced displacement monitoring points are selected, and the relative errors between these points are calculated, and the maximum value is taken, and different N and M values ​​are selected for multiple calculations, and the most appropriate N and M values ​​are obtained by comparing the results; Reasonable N and M values ​​can reduce the relative error of the calculation process and make the analysis results more accurate. as follows:

[0057] Among them, represents the relative error, and respectively represent the displacement amplitudes of two adjacent calculation points. In this embodiment, taking , 's slope analysis model as an example, only considering the case of horizontal incidence of seismic waves ( ), 4 special points are selected, and their displacement values are calculated and output. The four special points are respectively , , , . In this embodiment, 600 equally spaced displacement monitoring points are selected, and their values range from to , and the interval between each monitoring point is . The relative errors between 600 equally spaced displacement monitoring points are calculated, and the maximum value of all relative errors is taken. The convergence test results are shown in Tables 1 and 2: Table 1 Displacement values and relative errors of key monitoring points under different truncation terms N

[0058] Table 2 Displacement values and relative errors of key monitoring points under different truncation terms M

[0059] According to the results of Tables 1 and 2, considering the comprehensive calculation accuracy and calculation efficiency, when , for , 's geometric model, it is most appropriate to select the truncation term numbers N and M as 12.

[0060] Based on the above embodiment, in step S105, to determine the influence of each target parameter on the change of the displacement value of the slope local terrain, including: using the dimensionless frequency representation method to normalize the displacement value of the incident wave; selecting different slope angles and analyzing the change of the displacement value of the slope local terrain. Among them, the dimensionless frequency is determined by the ratio of the maximum width of the canyon to the incident wavelength.

[0061] As Figure 2 shown, to minimize the influence of the right circular arc slope part on the calculation of the left slope model as much as possible, the corresponding geometric dimension conditions need to be satisfied:

[0062] Among them, d represents the depth, L1 represents the horizontal distance from the slope top to the slope angle, and L2 represents the horizontal distance from the slope bottom to the slope angle of the right circular arc slope. Before changing each variable, the geometric dimension conditions are judged, and appropriate model sizes are selected for analysis to minimize the influence of the right circular arc part model on the calculation results of the slope model as much as possible. For the convenience of extracting corresponding observation points for subsequent analysis, a geometric diagram as shown in Figure 3 is drawn, Figure 3 which is the distribution diagram of displacement monitoring points in the embodiment of the present invention. Representative observation points are selected, namely the slope bottom reference point 1, the slope middle reference point 2, and the slope top reference point 3.

[0063] In this embodiment, the slope angle is selected as an example to explore the influence of the change of the slope angle on the change of the local terrain displacement value of the slope and the PDA.

[0064] The dimensionless frequency representation method is adopted to normalize the displacement amplitude of the incident wave for easy analysis. The dimensionless frequency is defined as the ratio of the maximum width of the canyon to the incident wavelength, that is:

[0065] Among them, represents the incident wave wavelength. The geometric dimensions are selected as , and it can be obtained through inspection that the geometric dimensions at this time meet the analysis requirements. The dimensionless frequency is selected as , and the wavelength is 4a. Keeping the slope height unchanged, the incident angle of the seismic wave is set to 90°, that is, horizontally incident, and the slope angle is changed, which are 30°, 35°, 40°, 45°, 50°, 55°, and 60° respectively. The geometric dimensions of the model under different slope angles are inspected respectively, and all meet the conditions of not considering the influence of the right circular arc part. The program is called to calculate them respectively. The monitoring points are selected in the left half of the slope area, and the monitoring area is [-12a, 0], that is, 3 times the wavelength. 100 monitoring points are taken for each segment, with an interval of 0.01a. For each working condition with different slope angles, appropriate truncation term coefficients N and M are selected through convergence tests. The calculation results of the slope surface displacement under different slope angle working conditions are as shown in Figure 4 , Figure 4 which is the displacement change diagram of each reference point under different slope angle working conditions in the embodiment of the present invention.

[0066] It can be easily known from Figure 4 that: under the working conditions where the slope angles are 30°, 35°, 40°, 45°, 50°, 55°, and 60° respectively, for the slope bottom reference point 1 (that is, ), the slope middle reference point 2 (that is, ), and the slope top reference point 3 (that is, For , its displacement value shows a trend of first increasing and then decreasing with the increase of the slope angle.

[0067] Correspondingly, to determine the influence of each target parameter on the displacement amplification factor of the local terrain of the slope, it includes: based on the terrain amplification effect, different slope angles are selected, and the change trend of the displacement amplification factor on the slope surface is analyzed.

[0068] Specifically, the terrain amplification effect can be expressed as the displacement amplitude at any terrain divided by the amplitude of the half-space free field without terrain:

[0069] Among them, PDA j represents the amplitude of the free field, represents the displacement amplitude at any terrain; represents the displacement amplitude of the half-space free field without terrain.

[0070] The analysis steps are basically the same as those for the displacement value of the slope. The difference is that the monitoring area is selected from the top of the slope to the bottom of the slope (extended appropriately to the left of the top of the slope and to the right of the bottom of the slope). According to Figure 3 , the coordinates of the top of the slope are , the coordinates of the bottom of the slope are , that is, the monitoring area is selected as . The calculation results of the displacement amplification factor on the slope surface under different slope angle conditions are as shown in Figure 5 , Figure 5 is the variation diagram of the displacement PDA of the reference point on the slope surface with the slope angle in the embodiment of the present invention.

[0071] It can be seen from Figure 5 that with the increase of the slope angle, for the reference point 1 at the bottom of the slope, the reference point 2 in the middle of the slope, and the reference point 3 at the top of the slope, the displacement amplification factor all shows a trend of first increasing and then decreasing, and the maximum value of the displacement amplification factor PDA does not necessarily always appear at the top of the slope (reference point 3 at the top of the slope).

[0072] In summary, by using a similar method, the influence of other parameters (such as slope height, dimensionless frequency, seismic wave incident angle, etc.) on the change of the local terrain displacement value of the slope and the displacement amplification factor (PDA) can be analyzed based on the slope analytical model.

[0073] The present invention also provides an analysis device for the seismic wave slope terrain amplification effect. The analysis device for the seismic wave slope terrain amplification effect provided by the present invention will be described below. The analysis device for the seismic wave slope terrain amplification effect described below can be correspondingly referred to the analysis method for the seismic wave slope terrain amplification effect described above. Figure 6 is the structural block diagram of the analysis device for the seismic wave slope terrain amplification effect provided by the present invention. As shown in Figure 6 , the device includes: A construction module 601 for establishing a slope analysis model and setting a number of coordinate systems and the relationships between the coordinate systems based on the slope analysis model; A partitioning module 602 for introducing a virtual boundary into the slope analysis model, partitioning the slope analysis model into sub-regions, and determining the free-field displacement equation; A determination module 603 for determining the series solution of wave functions that satisfy the sub-region stress boundary conditions and displacement boundary conditions of the slope analysis model; A processing module 604 for determining the optimal number of truncation terms according to the parameters of the slope analysis model and the incident situation of seismic waves; An analysis module 605 for obtaining a number of variables, performing parameter analysis on the slope analysis model, and determining the influence of each target parameter on the change of the local terrain displacement value of the slope and the displacement amplification factor.

[0074] When this device is in use, first, the construction module 601 constructs a slope analysis model and determines a number of coordinate systems involved in the slope terrain amplification effect analysis and the relationships between the coordinate systems. Then, the partitioning module 602 introduces a virtual boundary and partitions the slope analysis model into sub-regions to achieve regional decomposition. The determination module 603 then constructs the series solution of wave functions that meet the sub-region stress boundary conditions and displacement boundary conditions under the excitation of plane SH waves. Then, the processing module 604 performs a convergence test according to the parameters of the slope analysis model and the incident situation of seismic waves to determine the optimal number of truncation terms. Finally, the analysis module 605 selects different variables based on the slope analysis model for parameter analysis to explore the influence of these parameters on the change of the local terrain displacement value of the slope and the displacement amplification factor (PDA).

[0075] In the above process, the methods of regional decomposition and regional matching are adopted. The overall research area is decomposed into different sub-regions, and the series solutions of wave functions that meet the sub-region stress and displacement boundary conditions are constructed respectively under the excitation of plane SH waves. And the Graf addition criterion of the fractional-order Bessel function suitable for the slope analysis model is introduced to realize the wave function coordinate transformation from the local coordinate system to the global coordinate system. Using the stress continuity condition and displacement continuity condition on the virtual boundary, the undetermined coefficients in the sub-region wave field displacement function are solved, and the corresponding sub-region wave field displacement function solution is obtained. Through the above process, a strict analytical solution is obtained, which helps to test and evaluate the effectiveness and reliability of seismic wave numerical algorithms, and has certain advantages in the research of high-frequency problems, solving the problem of poor applicability of existing canyon terrain research methods.

[0076] Figure 7 An example of the physical structure diagram of an electronic device is shown in Figure 7As shown in the figure, the electronic device may include: a processor 701, a communications interface 702, a memory 703, and a communication bus 704. Among them, the processor 701, the communications interface 702, and the memory 703 communicate with each other through the communication bus 704. The processor 701 may call the logical instructions in the memory 703 to execute the seismic wave slope terrain amplification effect analysis method, and this method includes: Establish a slope analysis model, and set a number of coordinate systems and the relationships between the coordinate systems based on the slope analysis model; Introduce a virtual boundary into the slope analysis model, divide the slope analysis model into sub-regions, and determine the free-field displacement equation; Determine the wave function series solution that satisfies the sub-region stress boundary conditions and displacement boundary conditions of the slope analysis model; According to the parameters of the slope analysis model and the incident situation of the seismic wave, determine the optimal truncation term number; Obtain a number of variables, perform parameter analysis on the slope analysis model, and determine the influence of each target parameter on the change of the slope local terrain displacement value and the displacement amplification factor.

[0077] In addition, when the logical instructions in the above-mentioned memory 703 are implemented in the form of software function units and sold or used as an independent product, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to enable a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. And the aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0078] On the other hand, the present invention also provides a computer program product. The computer program product includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the seismic wave slope terrain amplification effect analysis method provided by the above-mentioned various methods, and this method includes: Establish a slope analysis model, and set a number of coordinate systems and the relationships between the coordinate systems based on the slope analysis model; Introduce a virtual boundary into the slope analytical model, divide the slope analytical model into sub-regions, and determine the free-field displacement equation; Determine the wave function series solution that satisfies the sub-region stress boundary conditions and displacement boundary conditions of the slope analytical model; Determine the optimal truncation number according to the parameters of the slope analytical model and the incident situation of the seismic wave; Obtain several variables, conduct parameter analysis on the slope analytical model, and determine the influence of each target parameter on the change of the local terrain displacement value and the displacement amplification factor of the slope.

[0079] On the other hand, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the seismic wave slope terrain amplification effect analysis method provided by the above-mentioned various methods. The method includes: Establish a slope analytical model, and set several coordinate systems and the relationships between the coordinate systems based on the slope analytical model; Introduce a virtual boundary into the slope analytical model, divide the slope analytical model into sub-regions, and determine the free-field displacement equation; Determine the wave function series solution that satisfies the sub-region stress boundary conditions and displacement boundary conditions of the slope analytical model; Determine the optimal truncation number according to the parameters of the slope analytical model and the incident situation of the seismic wave; Obtain several variables, conduct parameter analysis on the slope analytical model, and determine the influence of each target parameter on the change of the local terrain displacement value and the displacement amplification factor of the slope.

[0080] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated. The components shown as units may or may not be physical units, that is, they may be located in one place, or they may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative labor.

[0081] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing the seismic wave slope terrain amplification effect, characterized in that: include: Establishing a slope analytical model, and setting a number of coordinate systems and the relationship between the coordinate systems based on the slope analytical model; Introducing a virtual boundary into the slope analytical model, dividing the slope analytical model into sub-regions, and determining a free field displacement equation; Determining a wave function series solution that satisfies the sub-region stress boundary condition and the displacement boundary condition of the slope analytical model; Determining the optimal number of truncation items according to various parameters of the slope analytical model and the incident conditions of seismic waves; A number of variables are obtained, and parameter analysis is performed on the slope analytical model to determine the influence of various target parameters on the change of local terrain displacement value and displacement amplification factor of the slope.

2. The method for analyzing the seismic wave slope terrain amplification effect according to claim 1, characterized in that: Based on the slope analytical model, several coordinate systems and the relationship between the coordinate systems are set, including: Based on the slope analytical model, a global rectangular coordinate system, a polar coordinate system, and a local rectangular coordinate system are set; A relationship between the global rectangular coordinate system and the local rectangular coordinate system is determined.

3. The method for analyzing the seismic wave slope terrain amplification effect according to claim 1, characterized in that: A virtual boundary is introduced into the slope analytical model, the slope analytical model is divided into sub-regions, and a free field displacement equation is determined, including: A virtual boundary is introduced into the slope analytical model to divide the slope analytical model into two sub-areas: an inner domain wave field and an outer domain wave field; The stress boundary conditions of the slope analytical model are determined, and a free field displacement equation is generated based on the slope analytical model.

4. The method for analyzing the seismic wave slope terrain amplification effect according to claim 1, characterized in that: Determining a wave function series solution that satisfies the sub-region stress boundary condition and the displacement boundary condition of the slope analytical model includes: Solving the equation of motion in a sub-region of the slope analytical model to determine a corresponding wave field; Stress continuity conditions and displacement continuity conditions are matched at virtual boundaries of the sub-region of the slope analytical model to solve unknown coefficients in the displacement field function of the sub-region of the slope model.

5. The method for analyzing the seismic wave slope terrain amplification effect according to claim 1, characterized in that: According to the various parameters of the slope analytical model and the incident conditions of the seismic wave, the optimal number of truncation items is determined, including: According to various parameters of the slope analytical model and the incident conditions of the seismic wave, several special points are selected, and the displacement values ​​of the special points are determined; Selecting a number of displacement monitoring points and calculating relative errors between the displacement monitoring points when different numbers of truncation terms are used; According to the calculation results of relative error, the optimal number of truncation items is determined.

6. The method for analyzing the seismic wave slope terrain amplification effect according to claim 1, characterized in that: Determine the impact of each target parameter on the change of local terrain displacement value of the slope, including: The displacement value of the incident wave is normalized using the dimensionless frequency representation method; Select different slope angles to analyze the changes in the local terrain displacement values ​​of the slope.

7. The method for analyzing the seismic wave slope terrain amplification effect according to claim 6, characterized in that: The dimensionless frequency is determined by the ratio of the maximum width of the canyon to the incident wavelength.

8. The method for analyzing the seismic wave slope terrain amplification effect according to claim 1, characterized in that: Determine the impact of various target parameters on the local terrain displacement amplification factor of the slope, including: Based on the terrain amplification effect, different slope angles are selected to analyze the changing trend of the slope surface displacement amplification coefficient.

9. A seismic wave slope terrain amplification effect analysis device, characterized in that: include: A construction module is used to establish a slope analytical model and set a number of coordinate systems and the relationship between the coordinate systems based on the slope analytical model; A partitioning module, used for introducing a virtual boundary into the slope analytical model, performing sub-region partitioning on the slope analytical model, and determining a free field displacement equation; A determination module, used to determine a wave function series solution that satisfies the sub-region stress boundary condition and the displacement boundary condition of the slope analytical model; A processing module, used for determining the optimal number of truncation items according to various parameters of the slope analytical model and the incident conditions of seismic waves; The analytical module is used to obtain a number of variables, perform parameter analysis on the slope analytical model, and determine the influence of various target parameters on the change of local terrain displacement value and displacement magnification coefficient of the slope.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for analyzing the seismic wave slope terrain amplification effect as described in any one of claims 1 to 8 is implemented.

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